Datasets:

tomekkorbak

/

pii-pile-chunk3-0-50000

like 0

[ "A review of evidence-based approaches for reduction of alcohol consumption in Native women who are pregnant or of reproductive age.", "\nFetal alcohol spectrum disorders (FASDs) are the leading preventable cause of developmental disabilities in the United States and likely throughout the world. ", "FASDs can be prevented by avoiding alcohol use during pregnancy; however, efforts to prevent risky alcohol consumption in women of childbearing potential have not been universally successful. ", "Data suggest that successful interventions may require tailoring methods to meet the needs of specific populations and cultures. ", "Key findings of interventions previously tested among American Indian and Alaskan Native (AI/AN) women who are or may become pregnant, data gaps, and promising ongoing interventions are reviewed. ", "A systematic review of the current literature on empirically based interventions among AI/AN women was conducted. ", "Selected alternative approaches currently being tested in AI/AN settings are also described. ", "Similar to findings among other populations of women in the United States, a number of interventions have been implemented; however, only a small number have measured results. ", "Approaches have included standard interventions involving hospitalization, inpatient, or outpatient care; wellness education; traditional approaches; and case management for high-risk women. ", "An ongoing Screening, Brief Intervention, and Referral to Treatment (SBIRT) protocol comparing the effectiveness of a web-based culturally adapted tool, or a peer health educator model to standard clinical practice is described. ", "Translation of successful interventions from other settings to AI/AN populations holds promise. ", "FASDs represent a significant health issue with high personal and societal costs. ", "Improvement of interventions to prevent prenatal alcohol consumption in specific populations, including AI/AN women, is a critical public health need." ]

{ "pile_set_name": "PubMed Abstracts" }

[ 0, 0.00625, 0.005208333333333333, 0, 0.01020408163265306, 0.008771929824561403, 0.010752688172043012, 0, 0, 0, 0.010416666666666666, 0.012195121951219513, 0.006666666666666667 ]

[ "Donald Trump once dismissed it as a “hoax” created by the Chinese to destroy American jobs, but on a freezing Thursday night in the eastern US the president found himself pining for some of that “good old global warming”.", "\n\nOn holiday in Florida on Thursday, Trump wondered if global warming might not be such a problem after all.", "\n\nTrump drops climate change from US national security strategy Read more\n\nAs severe cold and record amounts of snow swept across the US east coast, Trump wrote on Twitter that his people “could use a little bit of that good old Global Warming that our Country, but not other countries, was going to pay TRILLIONS OF DOLLARS to protect against”.", "\n\n“Bundle up!” ", "he added.", "\n\nThe president was reheating two favourite tropes: the conflation of weather with climate to pour scepticism on global warming, and the supposed cost to the American taxpayer of the Paris climate accord, from which he has confirmed the US will withdraw.", "\n\nClimate scientists, however, have long warned against using individual weather events to ponder the existence or otherwise of global warming. ", "Weather, they point out, refers to atmospheric conditions during a short period; climate relates to longer-term weather patterns.", "\n\nOn Friday, Anthony Leiserowitz, director of Yale University’s project on climate change communication, said Trump’s tweet was “scientifically ridiculous and demonstrably false”.", "\n\n“There is a fundamental difference in scale between what weather is and what climate is,” he said. “", "What’s going on in one small corner of the world at a given moment does not reflect what’s going on with the planet.”", "\n\nThe extreme cold snap in the eastern US is a rare example of a place experiencing below-average winter temperatures, he said, a point that was neatly illustrated by a map tweeted out by the Weather Channel on Friday.", "\n\nThe Weather Channel (@weatherchannel) 1) There is a difference between #weather and #climate.", "\n\n2) Short-term #cold snaps will continue to occur in a warming climate.", "\n\n3) 2017 will likely be a top three warmest year on record for the globe.", "\n\n(Graphic: Univ. ", "of Maine - Climate Change Institute) https://t.co/kzuugeXi80 pic.twitter.com/gueOsp4yvu\n\nElsewhere, Matthew England, a climate scientist from the University of New South Wales, called Trump’s comment “an ignorant misconception of the way the earth’s climate works”.", "\n\n“Nobody ever said winter would go away under global warming, but winter has become much milder and the record cold days are being far outnumbered by record warm days and heat extremes,” he said. “", "Climate change is not overturned by a few unusually cold days in the US.”", "\n\nDavid Karoly, a climate scientist from the University of Melbourne, put it even more bluntly: “It’s winter in the US. ", "Cold temperatures are common in winter.”", "\n\nClimate modelling showed cold snaps like the one in the US were actually becoming less common as a result of global warming, Karoly said, adding that rapid attribution analysis means scientists are now able to look more closely at “classes of events”.", "\n\nThat type of modelling for the north-east of the US, he said, showed that although there was a great deal of year-to-year variability, the average coldest temperature in December in the region has increased in the past 50 years.", "\n\nIn any case, the US is already getting that “good old global warming”. ", "2017 is set to be the third-warmest on record, prompting among other things a climate-fuelled hurricane season in the country’s south.", "\n\nExperts also know climate change is linked to a dangerous pattern of major weather events. ", "According to the National Oceanic and Atmospheric Administration (NOAA), the US is on track to match or exceed the previous record year for extreme weather and climate events costing more than $1bn, including wildfires, hurricanes and flooding.", "\n\nThere had been 15 such events by the end of September, compared with 15 for the whole of 2016 and 16 in the record year of 2011.", "\n\nAdam Smith, a climatologist at NOAA, said: “Climate change is playing a role, amplifying the frequency and intensity of some types of extreme weather that lead to billion-dollar disasters.”", "\n\nWith Hurricane Harvey devastating Texas and extraordinary wildfires in California, Smith said 2017 was expected to “shatter” the record for the US’s costliest year in terms of weather events. ", "That was 2005, with losses of $215bn from disasters including Hurricane Katrina.", "\n\nTrump’s tweet also revisited his claim that the Paris climate accord would have cost the US “trillions” of dollars. ", "At a rally in Pennsylvania in April to mark his 100th day in office, Trump said “full compliance with the agreement could ultimately shrink America’s GDP by $2.5tn over a 10-year period”.", "\n\nThe politically non-aligned website Factcheck.org asked the White House for a source for that remark, and was pointed to a 2016 study by the conservative Heritage Foundation which found the Paris agreement “will result in over $2.5tn in lost GDP by 2035”.", "\n\nWhile that is an 18-year period, not 10, Factcheck.org found the accuracy of Heritage’s statements depended on which numbers were used. ", "The Heritage study used a carbon tax rate of $36, increasing 3% each year from 2015 to 2035. ", "Other analyses have found the US would have needed only a carbon tax of $21.22 starting in 2017 to meet its Paris target by 2025.", "\n\nLeiserowitz, meanwhile, criticised the president’s use of social media. “", "It’s meant to be red meat for his base,” he said. “", "They’re the ones most likely to be dismissive of climate change and the most likely to vote in the 2018 Republican primaries – so it’s a warning shot for the GOP members in Congress.”", "\n\nThe global warming tweet, he said, was another attempt by Trump to distract from special counsel Robert Mueller’s Russia investigation.", "\n\nHe added that the idea a cold snap disproves global warming is a “zombie argument”, because though “it’s killed over and over by the science” it “keeps coming back for more brains”.", "\n\nTrump’s tweet was “troll-like”, the scientist said, showing the president “delighting in sparking outrage among [his] opponents”." ]

{ "pile_set_name": "OpenWebText2" }

[ 0.004524886877828055, 0.009259259259259259, 0.005797101449275362, 0, 0, 0, 0, 0, 0.01675977653631285, 0, 0, 0.0045871559633027525, 0.010526315789473684, 0, 0, 0, 0.01509433962264151, 0, 0, 0.016666666666666666, 0, 0.003952569169960474, 0, 0, 0, 0, 0.00819672131147541, 0, 0.010471204188481676, 0.005154639175257732, 0, 0, 0.0053475935828877, 0.011673151750972763, 0.014492753623188406, 0.010752688172043012, 0, 0.013333333333333334, 0, 0.01092896174863388, 0.0072992700729927005, 0, 0 ]

[ "Obscure gastrointestinal bleeding and Turner syndrome.", "\nGastrointestinal bleeding in individuals with Turner syndrome is relatively rare and there have been only a handful of reported cases in the literature. ", "Here, we present two patients with Turner syndrome who were evaluated for obscure gastrointestinal bleeding. ", "Our first patient presented with iron deficiency anemia and the work-up for a possible gastrointestinal bleed was pertinent only for polyps and a non-bleeding vein in the colon seen on colonoscopy. ", "Our second patient had a history of unexplained recurrent melena and iron deficiency anemia, with previously normal esophagogastroduodenoscopies, colonoscopies and a Meckel's diverticulum scan. ", "Both patients were subsequently diagnosed with gastrointestinal vascular malformations via capsule endoscopy." ]

{ "pile_set_name": "PubMed Abstracts" }

[ 0.018518518518518517, 0.006493506493506494, 0.009174311926605505, 0, 0.005154639175257732, 0 ]

[ "Using pulse field gradient NMR diffusion measurements to define molecular size distributions in glycan preparations.", "\nGlycans comprise perhaps the largest biomass in nature, and more and more glycans are used in a number of applications, including those as pharmaceutical agents in the clinic. ", "However, defining glycan molecular weight distributions during and after their preparation is not always straightforward. ", "Here, we use pulse field gradient (PFG) (1)H NMR self-diffusion measurements to assess molecular weight distributions in various glycan preparations. ", "Initially, we derived diffusion coefficients, D, on a series of dextrans with reported weight-average molecular weights from about 5 kDa to 150 kDa. ", "For each dextran sample, we analyzed 15 diffusion decay curves, one from each of the 15 major (1)H resonance envelopes, to provide diffusion coefficients. ", "By measuring D as a function of dextran concentration, we determined D at infinite dilution, D(inf), which allowed estimation of the hydrodynamic radius, R(h), using the Stokes-Einstein relationship. ", "A plot of log D(inf) versus log R(h) was linear and provided a standard calibration curve from which R(h) is estimated for other glycans. ", "We then applied this methodology to investigate two other glycans, an alpha-(1-->2)-L-rhamnosyl-alpha-(1-->4)-D-galacturonosyl with quasi-randomly distributed, mostly terminal beta(1-->4)-linked galactose side-chains (GRG) and an alpha(1-->6)-D-galacto-beta(1-->4)-D-mannan (Davanat), which is presently being tested against cancer in the clinic. ", "Using the dextran-derived calibration curve, we find that average R(h) values for GRG and Davanat are 76+/-6 x 10(-10) m and 56+/-3 x 10(-10) m, with GRG being more polydispersed than Davanat. ", "Results from this study will be useful to investigators requiring knowledge of polysaccharide dispersity, needing to study polysaccharides under various solution conditions, or wanting to follow degradation of polysaccharides during production." ]

{ "pile_set_name": "PubMed Abstracts" }

[ 0, 0, 0, 0.013333333333333334, 0, 0, 0, 0, 0.008645533141210375, 0.02072538860103627, 0 ]

[ "Q:\n\nGridView item position\n\nI have GridView:\n<?", "xml version=\"1.0\" encoding=\"utf-8\"?", ">\n<LinearLayout\n xmlns:android=\"http://schemas.android.com/apk/res/android\"\n android:layout_width=\"match_parent\"\n android:layout_height=\"match_parent\"\n android:id=\"@+id/frag_books_grid_view_layout\"\n android:orientation=\"vertical\">\n <GridView\n android:cacheColorHint=\"@color/bg_default\"\n android:listSelector=\"@drawable/list_selector_background\"\n android:id=\"@+id/frag_books_grid_view\"\n android:layout_width=\"fill_parent\"\n android:layout_height=\"wrap_content\"\n android:columnWidth=\"120px\"\n android:gravity=\"center\"\n android:horizontalSpacing=\"15dp\"\n android:scrollbars=\"none\"\n android:stretchMode=\"columnWidth\"\n />\n</LinearLayout>\n\nAnd single item (placed in cell of this grid):\n<ListView\n xmlns:android=\"http://schemas.android.com/apk/res/android\"\n android:cacheColorHint=\"@color/bg_default\"\n android:scrollbars=\"none\"\n android:listSelector=\"@drawable/list_selector_background\"\n android:layout_gravity=\"center_vertical|left\"\n android:gravity=\"center_vertical|left\"\n android:padding=\"15dp\"\n android:id=\"@+id/frag_book_list_view\"\n android:layout_width=\"match_parent\"\n android:layout_height=\"match_parent\"\n android:verticalSpacing=\"5dp\"/>\n\nHow it looks: http://i.imgur.com/rhZiu.png\nEverything is fine with blue selection, but the contents of the cell is not centered inside of it. ", "\nThis picture explains what I want: http://i.imgur.com/OumWu.png\n\nA:\n\nBesides it's not recommended to have nested scrollable components, you have the dimensions of list view set to match_parent. ", "So it's not possible to center, since it's already occupying all available space.", "\nIf you want to center, you first have make the listView smaller (setting fixed size). ", "And then use gravity=\"center\" on the container. ", "You also can apply a uniform padding to the container, this will also make the listView look centered.", "\n\n" ]

{ "pile_set_name": "StackExchange" }

[ 0.02127659574468085, 0.02857142857142857, 0.0061643835616438354, 0.005128205128205128, 0, 0, 0, 0, 0 ]

[ "GetTheReferral App: Easy Referrals\n\nGetTheReferralMaking Referral Programs Go Viral and Mobile\n\nGetTheReferral is a company founded on the principle that referrals are the best way to get leads and turn them into sales. ", "They contacted LeewayHertz to develop a mobile app that would integrate into their content management and customer relationship management systems, which resulted in this successful app – now vital to their organization’s business strategy.", "\n\nThe app has a personalized dashboard where customers can keep track of their conversion rate, referral performance, incentive programs, and more. ", "Users can create, submit, and track referrals from the app and monitor rewards and affiliate growth from a web-based CMS. ", "Additionally, the app delivers notifications and updates via a fully automated system." ]

{ "pile_set_name": "Pile-CC" }

[ 0.00909090909090909, 0.004166666666666667, 0, 0.00819672131147541, 0 ]

[ "http://messages.yahoo.com/bbs?.mm=FN&action=m&board=7081781&tid=ene&sid=708178\n1&mid=11711" ]

{ "pile_set_name": "Enron Emails" }

[ 0.011111111111111112 ]

[ "Q:\n\nAngular Reactive Form Array, Change detection overriding form\n\nIve used the following question as a basis for my form design for a FormArray. ", " The jist of what im trying to do is keep a form up to date with changes elsewhere on the page, but toggle a boolean/checkbox in this form. (", "Users have a list of cards they select, this form shows a list of this selection) \nUnfortunately, it seems that ngOnChanges is constantly updating the form, and my changes are being overwritten. ", "In my constructor I detect value changes, with an intent to emit those changes. ", "However, \nthis.contextSummaryForm.dirty\n\nis always false. ", " A breakpoint on rebuildForm() demonstrates that the method is invoked multiple times a second - thus changing contextItem.isEditEnable to false is completely overwritten. ", "I can read my logic and see why that is happening sort of - but I seriously don't understand what I'm supposed to do to allow updates to contextList from its parent component AND allow users to update the form here.", "\nConstructor, and change detection\n@Input()\ncontextList: ContextItem[];\n\n@Output()\ncontextListChange = new EventEmitter<any>();\n\nvalueChangeSubscription = new Subscription;\ncontextSummaryForm: FormGroup;\nisLoaded: boolean = false;\n\nconstructor(protected fb: FormBuilder) {\n this.createForm();\n\n this.valueChangeSubscription.add(\n this.contextSummaryForm.valueChanges\n .debounceTime(environment.debounceTime)\n .subscribe((values) => {\n if (this.isLoaded && this.contextSummaryForm.valid && this.contextSummaryForm.dirty) {\n\n this.contextSummaryForm.value.plans.forEach(x => {\n var item = this.contextList.find(y => y.plan.id === x.id);\n item.isEditEnabled = x.isEditEnabled;\n });\n\n this.contextListChange.emit(this.contextList);\n this.contextSummaryForm.markAsPristine();\n }\n }));\n }\n\nForm Creation:\ncreateForm(): void {\n this.contextSummaryForm = this.fb.group({\n plans: this.fb.array([this.initArrayRows()])\n });\n}\n\ninitArrayRows(): FormGroup {\n return this.fb.group({\n id: [''],\n name: [''],\n isEditEnabled: [''],\n});\n}\n\nOnChanges\n ngOnChanges(changes: SimpleChanges) {\nfor (let propName in changes) {\n if (propName === 'contextList') {\n if (this.contextList) {\n this.rebuildForm();\n this.isLoaded = true;\n }\n }\n}\n}\n\nrebuildForm() {\n this.contextSummaryForm.reset({\n });\n //this.fillInPlans();\n this.setPlans(this.contextList);\n}\n\n setPlans(items: ContextItem[]) {\n let control = this.fb.array([]);\n items.forEach(x => {\n control.push(this.fb.group({\n id: x.plan.id,\n name: x.plan.", "Name,\n isEditEnabled: x.isEditEnabled,\n }));\n });\n this.contextSummaryForm.setControl('plans', control);\n }\n\nJust to summarize: i need a way to use formarrays built from an input binding that keeps up with changes without rapidly overwriting the form.", "\n\nA:\n\nAccording to angular's documentation\n\nOnChanges: A lifecycle hook that is called when any data-bound property of a directive changes\n\nHaving said that, it's not the change detection nor the onChanges hook that overrides the form. ", "As the best practice, we should build the form only once and use the FormArray's methods to interfere with the Array \nInstead of rebuilding the form, you can utilize the FormArray methods and push items directly on the array. ", "I assume that the problem you are facing is that you are rebuilding the form, no matter the data are. ", "\nWhat I mean is: Think that you have two components. ", "Child and Parent. ", "The child is responsible to manipulate the data (add, remove), and the parent is responsible to display on a form those data. ", "Although it seems to be trivial to do so, you have to filter out any items that have already been processed by Child component.", "\nIn your implementation, try to not to rebuild the form on the onChanges but rather push items on the array.", "\nWhich items should you push to array? (", "filter out any items that have already been processed)\nconst contextItemsToInsert = \n this.contextList.filter((it: any) => !", "this.plans.value.map(pl => pl.id).includes(it.id));\n\nThis is an approach that could solve your problem\nngOnChanges(changes: SimpleChanges) {\n for (let propName in changes) {\n if (propName === 'contextList') {\n\n const contextItemsToInsert = \n this.contextList.filter((it: any) => !", "this.plans.value.map(pl => pl.id).includes(it.id));\n\n contextItemsToInsert.forEach((x: any) => {\n\n this.plans.push(this.fb.group({\n id: x.id,\n name: x.name,\n isEditEnabled: x.isEditEnabled,\n }))\n })\n\n // similar approach for deleted items\n }\n }\n }\n\n ngOnInit() {\n this.createForm();\n }\n\n createForm(): void {\n this.contextSummaryForm = this.fb.group({\n plans: this.fb.array([this.initArrayRows()])\n });\n }\n\n initArrayRows(): FormGroup {\n return this.fb.group({\n id: [''],\n name: [''],\n isEditEnabled: ['']\n });\n }\n\nHere you can find a working example https://stackblitz.com/edit/stackoverflow-53836673\nIt's not a fully working example, but it helps get the point of the issue.", "\nI hope I understood correctly what the problem you are facing is\n\n" ]

{ "pile_set_name": "StackExchange" }

[ 0.006802721088435374, 0, 0, 0, 0, 0, 0, 0.008933889219773675, 0, 0, 0.008849557522123894, 0, 0, 0, 0, 0, 0, 0, 0, 0.003289473684210526, 0.0059665871121718375, 0 ]

[ "Reinaldo Flores, an unemployed transit worker in his 50s, walks through the streets of Cerro, one of Havana’s poorest neighborhoods. ", "The street is flanked by once-grand buildings in faded shades of blue, green, and orange.", "\n\nIn some ways, it’s a typical day for Mr. Flores: he’s looking for work. ", "But for him and tens of thousands of others across Cuba, today is also dramatically different.", "\n\nIt’s the first day in his life his president’s named something other than Castro.", "\n\nCuba’s National Assembly, a group of more than 600 handpicked politicians who run unopposed, nominated the island’s next president this week. ", "Vice President Miguel Díaz-Canel, the only candidate put forth, will be Cuba’s first leader in nearly 60 years who wasn’t part of the revolution that overthrew US-backed dictator Fulgencio Batista and installed a Communist government on the island. ", "Mr. Díaz-Canel is also the first leader in nearly 70 years who isn’t part of the armed forces.", "\n\nThe changing of the guard – after decades of leadership by Fidel Castro and 12 years under his brother Raúl – is significant. ", "But, observers say, it’s largely symbolic. ", "In a centralized system that works on a “one state, one party” principle of entrenched revolutionary values, the rise of a new head of state without direct ties to the Castros’ uprising is more likely to lay the groundwork for future change than create big waves in the short term.", "\n\nCuba’s economy is struggling. ", "Vital benefactors like Venezuela are distracted by their own crises, there’s little foreign investment, infrastructure is crumbling, and the dual currency system is increasingly burdensome. ", "These are issues observers say need to be tackled head on. ", "Although Cuba’s “old guard” is nominally clearing the way for a new generation of leadership on the island, Raúl Castro is still top dog in Cuba’s Communist Party and armed forces, unlikely to give Díaz-Canel much wiggle room to create significant changes anytime soon.", "\n\n“If the situation Cubans are living doesn’t improve, the political changes will be in vain,” Mr. Flores says of the historic transition of power.", "\n\nWhile many in the United States view a non-Castro Cuban president as a chance to shed some of the historic baggage that’s held back relations between the two nations, in Cuba there’s less optimism. ", "Most are wondering what they can expect – or if they should expect anything at all.", "\n\n“The change in government doesn’t leave us with a lot of hope, but it does leave us with a big question: What is going to happen to Cuba?” ", "says Boris González Arena, a journalist for the local news site Diario de Cuba.", "\n\nIrene Perez/Cubadebate/Reuters Cuba's former President Raul Castro (center-left) and former First Vice-President Miguel Diaz-Canel (center-right) arrive for a session of the National Assembly in Havana, Cuba, on April 18, 2018. ", "Mr. Diaz-Canel was sworn in to replace Mr. Castro as president on Thursday.", "\n\n‘Like-minded’ leader?", "\n\nCuba has changed significantly under Raúl Castro’s two presidential terms. ", "He did what for many was the unthinkable: warming ties with the United States, allowing private micro-businesses and entrepreneurship to blossom, and doing away with exit visas required for Cubans to leave the island. ", "But he was still a Castro, lending him a certain cachet, and many question whether Díaz-Canel will have the same support for policies that push against the grain of the revolutionary project.", "\n\nCuba’s economy is weak, with many outside economists pointing to 2016 as a full-blown recession. ", "Sugar harvests were devastated by hurricane Irma, and US tourism dollars that prop up the self-employed are flagging. ", "The dual currency is creating imbalances in human capital, with those working in the tourism sector earning significantly more than highly-trained doctors or engineers.", "\n\nThe first task for Díaz-Canel will be getting the economy back on track, but just how radically he can approach the problems is at question – if he has a different approach in mind, to begin with.", "\n\n“We have to consider that more likely than not [Díaz-Canel] was chosen as the next leader because he’s like-minded” with the Castro generation, says Gustavo Flores-Macías, an associate professor at Cornell University who specializes in Latin American politics. ", "In a video leaked last year, Díaz-Canel is seen lambasting the US and emphasizing the same hardline ideology as his Castro predecessors, accusing dissidents and independent media of subverting the state.", "\n\nOn Thursday, Castro said he expected the new leader to serve two five-year terms as president and take over for him as head of the Communist Party when Castro steps down in 2021 – the date many here view as the more realistic gateway to change by a new generation of leaders.", "\n\nCuban blogger Regina Coyula, who was born just before Castro’s 1959 rise to power, hasn’t written anything about the presidential transition on her widely read blog, “La Mala Letra” (“Bad Handwriting”). ", "For her, this week is less significant than the long game.", "\n\n“Whatever the new president does will be overseen by the Communist Party,” she says. ", "As head of the party and the armed forces, Castro is still in control of some of the most economically important sectors, like tourism, placing yet another limit on Díaz-Canel’s power.", "\n\n“There’s always the chance that [Díaz-Canel] has hidden his true perspective and he will surprise all of us,” says Ms. Coyula, acknowledging that it’s not something she’s holding her breath for. “", "In any case, it’s up to him now to bring fresh air into our economy.”", "\n\nDespite the desire for economic change, not all Cubans on the island want to see a complete overhaul of the Castro’s revolutionary agenda.", "\n\n“We want things to change, but we also want the things that make Cuba what it is to remain,” says Aliot Castro, a teenager. ", "He tics off security, public health, and free education as elements that are worth maintaining by any future president. ", "His friend Alejandro Lázaro agrees about continuity, but “we want a future with more possibilities for youth, a new way of thinking from the government,” he says.", "\n\nResidents proudly boast to visitors that violent crime is essentially zero on the island (The US Embassy, however, says nonviolent crimes against tourists are common, like pickpocketing). ", "When the Cuban revolution launched, roughly one-quarter of Cubans could not read. ", "Today, the education system serves as a model for nations around the region, and literacy is almost universal. ", "Medical professionals are essentially exported and traded for needed resources, like oil, with nations from Venezuela to Brazil.", "\n\n“Cuba’s human capital, and its deep investment in human capital for decades, is crucial for the island. ", "It’s something most anyone on the left or right can agree on,” says Mr. Flores-Macias.", "\n\nToday’s transition of power takes place on the anniversary of the failed US-backed Bay of Pigs operation against Castro, and coincides with new bumps in the US-Cuba relationship. ", "President Trump last year announced some rollbacks to Obama’s historic diplomatic rapprochement with Cuba, and more than half of US diplomats have been ordered off the island following mysterious hearing loss and what were initially described as suspected “sonic attacks.”", "\n\nDuring the conclusion of the two-day National Assembly session today, where Raúl Castro stepped down, Díaz-Canel promised to defend the regime created by his predecessors.", "\n\n“The revolution continues,” he said.", "\n\nGet the Monitor Stories you care about delivered to your inbox. ", "By signing up, you agree to our Privacy Policy\n\nThe Castros’ armed revolution and rise to power via force has little “to do with the changes taking place now,” says Dimas Castellanos, a former university history professor here who researches race on the island. ", "Raul’s generation of guerrilla fighters are giving up their posts, if not all of their power, he says.", "\n\n“But even if [Díaz-Canel] doesn’t want to, the new president must make changes. ", "The warehouses are empty. ", "The only thing that can’t happen now is that nothing changes.”" ]

{ "pile_set_name": "OpenWebText2" }

[ 0.007518796992481203, 0, 0.013513513513513514, 0, 0.012048192771084338, 0.006944444444444444, 0.008032128514056224, 0.010638297872340425, 0.015625, 0, 0.0035587188612099642, 0, 0, 0, 0.011152416356877323, 0.006802721088435374, 0, 0.012048192771084338, 0, 0.02531645569620253, 0.017391304347826087, 0.02666666666666667, 0, 0.012987012987012988, 0, 0.010471204188481676, 0, 0.00847457627118644, 0, 0.005050505050505051, 0.015209125475285171, 0.009852216748768473, 0.010830324909747292, 0.00975609756097561, 0, 0.011494252873563218, 0.010869565217391304, 0.005050505050505051, 0, 0.007142857142857143, 0.007936507936507936, 0, 0.006172839506172839, 0.005263157894736842, 0, 0, 0, 0, 0.011627906976744186, 0.0055248618784530384, 0.007352941176470588, 0.017341040462427744, 0, 0, 0.003816793893129771, 0, 0.012195121951219513, 0, 0 ]

[ "Here at Goodreads, we spend a lot of time looking forward to the big books on the horizon. ", "However, with the year halfway done, we decided to take a look backward. ", "Which 2018 books have your fellow readers loved the most? ", "We've got the answer.", "To find the cream of the publishing crop published from January to June of this year, we focused on the books that have been added the most to Goodreads members' shelves . ", "But we didn't just want what's—we wanted the best. ", "So we narrowed down our list to include only books with at least a four-star average rating.", "In other words, brace yourselves for some epic book browsing. ", "Don't forget to add the top-rated titles that catch your eye to your Want to Read shelf." ]

{ "pile_set_name": "OpenWebText2" }

[ 0.01098901098901099, 0, 0, 0, 0.005813953488372093, 0, 0, 0, 0 ]

[ "Q:\n\nTraversing a hash in order\n\nI would like to traverse the HASH but one by one. ", "Not in Random ways. ", "Any idea. ", "For example i have hash file something like this...\nour %HASH = (\n'rajesh:1700' => Bangalore,\n'rajesh:1730' => Delhi,\n'rajesh:1770' => Ranchi,\n'rajesh:1780' => Mumbai,\n'rajesh:1800' => MYCITY,\n'rajesh:1810' => XCF,\n);\n\nand it should print in same fashion. ", "I tried with following but failed. ", "Any ideas?", "\nwhile ( my $gPort = each %HASH)\n{\n print \"$gPort\\n\";\n}\n\nfor my $gPort ( keys %HASH )\n{\n print \"$gPort\\n\";\n}\n\nA:\n\nGiven the keys in your question, a simple change to the sort comparator will give your desired output.", "\nfor my $gPort (sort keys %HASH) {\n print \"$gPort => $HASH{$gPort}\\n\";\n}\n\nNote: the code above assumes all numbers in keys will occur at the same position and have the same length. ", "For instance, a rajesh:001775 key will come out first rather than between 1770 and 1780.", "\n\n" ]

{ "pile_set_name": "StackExchange" }

[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]

[ "var baseIteratee = require('./_baseIteratee'),\n baseSortedUniq = require('./_baseSortedUniq');\n\n/**\n * This method is like `_.uniqBy` except that it's designed and optimized\n * for sorted arrays.", "\n *\n * @static\n * @memberOf _\n * @since 4.0.0\n * @category Array\n * @param {Array} array The array to inspect.", "\n * @param {Function} [iteratee] The iteratee invoked per element.", "\n * @returns {Array} Returns the new duplicate free array.", "\n * @example\n *\n * _.sortedUniqBy([1.1, 1.2, 2.3, 2.4], Math.floor);\n * // => [1.1, 2.3]\n */\nfunction sortedUniqBy(array, iteratee) {\n return (array && array.length)\n ? ", "baseSortedUniq(array, baseIteratee(iteratee))\n : [];\n}\n\nmodule.exports = sortedUniqBy;\n" ]

{ "pile_set_name": "Github" }

[ 0.005050505050505051, 0.045454545454545456, 0.015151515151515152, 0.017241379310344827, 0.005780346820809248, 0.03333333333333333 ]

[ "Hi, I’m Emily Graslie, and welcome to season\ntwo of Crash Course Big History.", "\nIn the first 10 episodes of Big History, we\nfollowed the history of the Universe from\nthe Big Bang into the Deep Future.", "\nThe theme of this season is “Why Does This\nMatter?”", "\nAs fascinating as the tale of 13.8 billion\nyears is – from the vast cosmos to ancient\nlife on Earth – one has to wonder why learning\nabout this history is relevant to our own\nfleeting lives in this world.", "\nYou don’t exactly need to know about the\nBig Bang to fill out your tax returns.", "\nBut the reason we learn big history is the\nsame reason we learn any history at all.", "\nHistory matures us, seasons our attitudes,\nand enriches our perspectives.", "\nIf we read enough human history, going back\nthousands of years, we live a thousand lives.", "\nIf we don’t read history, we live only one.", "\nLet’s take that thought one step further.", "\nNever mind the past 5,000 years of written\nhistory, or even the past 250,000 years that\nhuman beings have existed on the planet.", "\nBy traversing the crash and thunder of the\ncosmos, to the tooth and claw of the evolutionary\nepic, we are transported across billions of\nyears.", "\nIn a world that has learned so much about\nthe cosmos, and a humanity that grows ever\nmore closely interwoven in the 21st century,\nit pays to know the history of the Universe\nand our planet as well as we know, say, the\npast 200 years of our national histories.", "\nLearn about Big History, and hopefully the\nworld around you will appear as one long continuum\nto which you belong, indivisible and unbroken\nsince the Big Bang, with an underlying pattern\nthat unites it all.", "\nHuman to human, and humanity to the Universe.", "\nIt is a great leap forward into a wider world.", "\nINTRO\nIn the Big Bang episode of Crash Course Big\nHistory, we learned about how our view of\nthe Universe evolved in the early 20th century,\nleading into how our view of the Universe\ncontinues to evolve with every fascinating\ntheory and new discovery.", "\nOne such theory is cosmic inflation, a theory\nabout what happened a split second after the\nBig Bang.", "\nIt was originally devised in the 1980s by\nAlan Guth, to explain why the early Universe\nwas so smooth and stable.", "\nAt approximately 10 to the power of negative\n35 to negative 32 seconds, the Universe expanded\nrapidly from being about the size of a quantum\nparticle, to the size of a grapefruit.", "\nThis is stupendously fast.", "\nEven though the Universe is expanding fast\ntoday, it’s still way slower than it was.", "\nIf a grapefruit-sized universe expanded at\nthe same speed as during cosmic inflation,\nin another split second, it would be the size\nof our current Universe, about 93 billion\nlight years across.", "\nIf the early Universe had expanded at its\nslower, present day rate, gravity would have\nbeen too strong and sucked more clumps of\nmatter and energy together, and the Universe\nwould not be as evenly distributed.", "\nThere would be huge inequalities, enormous\nheavy chunks of energy that are billions of\nlight years across.", "\nBut the Universe expanded so fast during cosmic\ninflation that it was smoothed out, with no\nhuge chunks of matter and energy anywhere.", "\nInstead we see a largely homogenous Universe\nwith just a smattering of tiny unequal wrinkles\nthat created stars.", "\nAnd that’s another reason why cosmic inflation\nwas so important.", "\nWhen the Universe was still very, very small,\nat the quantum scale, tiny fluctuations were\npopping in and out of existence.", "\nThese tiny blips of energy usually don’t\naffect the physics of the larger world.", "\nBut, during inflation, they were suddenly\nclear when the Universe became big, causing\nslight inequalities in matter and energy.", "\nThese wrinkles created all the complexity\nthat was to follow.", "\nWithout these unequal distributions of energy,\nthere wouldn’t have been enough energy for\nstars to burn, for supernovae to explode,\nfor planets to form, for life to exist, and\nfor us to be here.", "\nWe are the children of those tiny wrinkles,\nand the events that happened during cosmic\ninflation were the bedrock of the next 13.8\nbillion years.", "\nKnow this part of the story, and you know\nwhere you came from, in the most extreme sense\nof the phrase.", "\nA second theory holds that cosmic inflation\nmay imply something curious about our Universe\nthat has become known as the eternal inflation\nhypothesis, originally developed by Paul Steinhardt.", "\nLet’s go to the Thought Bubble.", "\nAccording to eternal inflation,\nthe cosmic inflation that happened in a tiny,\ntiny sliver of a second may still be going\non, for billions and billions of years, elsewhere\nin the Universe.", "\nOur cosmic bubble, which is 93 billion light\nyears across, is no longer in a state of eternal\ninflation.", "\nThe Universe continues to expand, and even\naccelerate in that expansion, but not quite\nat the breakneck speed of inflation.", "\nThe eternal inflation hypothesis implies that,\nwithin the sea of eternal inflation, new bubbles\nare popping up all the time.", "\nOther universes in a multiverse!", "\nOur fundamental laws of physics formed during\ninflation.", "\nIt is highly conceivable that other sets of\nfundamental laws would govern these other\nuniverses, and these laws and rules would\nbe completely foreign to our own.", "\nAnd there is a staggering number of possible\nsets of physical laws, about 10 to the power\nof 500.", "\nThat’s a 1 with 500 zeros.", "\nAnd that’s not the number of other universes\nin a multiverse, but the possible set of rules\non which an almost infinite number of universes\ncould operate.", "\nEven when the cosmic bubbles that come into\nexistence in that vast inflationary sea operate\non the same rules, they can have completely\ndifferent outcomes.", "\nIt’s possible the outcomes are similar,\nbut slightly different to ours.", "\n1.", "\nA universe out there may exist where you watch\nthis video approximately 30 seconds later.", "\n2.", "\nOr a universe out there may exist where I\nwas never born.", "\n3.", "\nA universe may exist where everything is made\nout of diamonds or pizza or something completely\ndifferent from atoms.", "\n4.", "\nAnd many universes would exist without any\nstars or forms of complexity at all.", "\nDead universes, where… everything is dead.", "\nThanks Thought Bubble.", "\nSo, from here, physicists have postulated\nthat the behaviour of Universes may operate\nunder some form of “natural selection”\nlike species do in nature - but for the cosmos.", "\nBy some variable or another, some universes\nmake it into existence, and some do not.", "\nOr, more mind-bogglingly, that certain universes\ngive rise to forms of extremely complex, intelligent,\nand powerful life that over time gain the\nability to create and shape new universes,\nin a form of cosmic artificial selection.", "\nSort of like how we breed different kinds\nof dogs or pigeons.", "\nAll of this is truly “out there” but that’s\nhow our view of the Universe continues to\nevolve.", "\nThe Big Bang theory might have seemed preposterous\nto most scientists 150 years ago.", "\nGive us another 1000 years of scientific advancement,\nand who knows what our picture of the Universe\nmay look like.", "\nAs it is, eternal inflation implies that our\ncosmic bubble, already a massive 93 billion\nlight years across, may actually be a very\ntiny bubble indeed, in a giant cosmic ocean\nknown as the multiverse that is just teeming\nwith other bubbles.", "\nAs furiously as scientists are working at\nunravelling the beginnings of our Universe,\nit has remained a very curious question about\nhow the Universe will “end” -- whatever\nend means when you’re talking about something\ninfinite.", "\nFor a long time, the most intuitive and prevailing\ntheory was the Big Bounce.", "\nThat is, the expansion of the Universe continues\nto be slowed down by the force of gravity.", "\nEventually, many billions upon billions of\nyears from now, the Universe begins to contract.", "\nGravity sucks everything, all matter, all\nenergy, back into the singularity from which\nit sprang.", "\nThe immense pressure that forms that singularity\nforces everything out again in yet another\nBig Bang.", "\nAnd the whole cycle begins anew.", "\nExpanding, contracting, over and over and\nover.", "\nHence the name: Big Bounce.", "\nAnd it makes logical sense, right?", "\nAfter all, what goes up, must come down.", "\nAnd there is another appeal to the theory.", "\nThat of birth, death, and rebirth.", "\nA circle of life, not just for nature and\nthe characters of the Lion King, but one for\nthe entire Universe.", "\nThis is by far the most cheerful and pleasing\nscenario for the end of the Universe.", "\nAnd, alas, now the least likely one.", "\nThe Big Bounce presumes that eventually the\nexpansion of the Universe will slow down.", "\nBut, we now know it’s not slowing down.", "\nIt’s accelerating.", "\nThere are many hypotheses about why, one of\nthe most prominent being the influence of\nthe mysterious force of dark energy.", "\nSo, there are two more likely scenarios.", "\nThe first is the Big Rip.", "\nIf the expansion of the Universe continues\nto accelerate at an insanely fast rate, then\nthe distances between things would become\nvirtually infinite.", "\nThis means the forces that hold the Universe\ntogether would be destroyed.", "\nThe gravity that holds the stars in the galaxy\ntogether would be too weak and the Milky Way\nwould fly apart.", "\nThe planets would be ripped away from the\nSun.", "\nEventually the strong and weak nuclear forces\nthat hold together atoms would be shorn apart\nas well.", "\nThe scariest part of this scenario is how\nsoon it could happen.", "\nEven within 10 or 20 billion years, which\nimplies the Universe is roughly middle-aged.", "\nThe final scenario, and currently the most\nlikely, is one that we covered in episode\n10 of season one of Crash Course Big History:\nHeat Death or the Big Freeze.", "\nIn this scenario, the Universe continues to\nexpand for trillions upon trillions of years\ntill all forms of complexity exhaust themselves\nand break down.", "\nStars flicker out, matter dissolves back into\nenergy, and the Universe becomes an evenly\ndistributed weak ball of energy.", "\nThe inequalities in energy created during\ninflation finally disappear.", "\nWhile not the most cheerful end to our story,\nit is decidedly less violent than the Big\nRip.", "\nAnd it gives complexity in the Universe a\ngreat deal more time to exist - on the scale\nof trillions of years.", "\nTime and more research will tell whether the\nBig Rip or the Big Freeze is more likely.", "\nKeep your eye on the experts as they continue\nto update you on the Universe’s most terrifying\nweather forecast.", "\nCloudy with a chance of absolute zero, or\nwindy with a possibility of a vicious atom\nshredding later in the afternoon?", "\nFinally, a last theory asks if the Universe\nis even real, or is it a simulation that our\nminds are inhabiting?", "\nThis is actually the subject of some very\ninteresting speculations by scientists and\nphilosophers, like Nick Bostrom.", "\nJust think about how far video games have\ncome since the 1980s.", "\nExtend that rate of progress another 500 years.", "\nA simulated Universe isn’t so fanciful on\nthat scale.", "\nAccording to Bostrom, one of the following\nstatements must be true:\n* Either such total simulations are impossible\nto create.", "\n* Or, it is possible to create them but such\nan advanced society would put that computational\npower to better use.", "\n* Or, they are possible to create, advanced\nsocieties do create them, and as a result\nthere is a high likelihood we are currently\nliving in a simulation rather than a base\nreality.", "\nWhy?", "\nBecause, as Elon Musk puts it, given the rapid\nrate of technological advancements in virtual\nreality, if we are one day going to create\nthose simulations anyway, the odds of us existing\nin the base reality that produces them really\nlow.", "\nBut does a simulation reflect the outside\nUniverse that created it?", "\nOr is the simulation a made-up, sort of fantasy\nreality?", "\nIf it is the latter it would explain why physical\nlaws only make sense to a certain point and\nwhy, when we get down to the scale of quantum\nphysics, things seem so much more unpredictable.", "\nIn a way, the pixels “blur” when we look\nthat closely at the screen.", "\nHowever this may just be a convenient explanation\nto otherwise much more puzzling questions\nabout quantum physics.", "\nIt is, perhaps, a bit too convenient.", "\nBut intriguing all the same.", "\nIn the 21st century, science has advanced\nby leaps and bounds.", "\nHumanity meanwhile is becoming more interdependent\nand in need of a common story.", "\nOur evolving view of the Universe continues\nto form the bedrock of that story, and as\nthat view changes, so too will the view of\nourselves as a part of the grand unfolding\ntale of 13.8 billion years.", "\nThanks for watching, see you next time.", "\n" ]

{ "pile_set_name": "YoutubeSubtitles" }

[ 0.025974025974025976, 0.024793388429752067, 0, 0, 0, 0.011904761904761904, 0, 0, 0, 0, 0, 0, 0, 0.004830917874396135, 0.021739130434782608, 0, 0.00398406374501992, 0, 0.008849557522123894, 0.011111111111111112, 0, 0.011764705882352941, 0.005154639175257732, 0.004761904761904762, 0, 0, 0.008849557522123894, 0, 0.008064516129032258, 0, 0, 0, 0, 0, 0, 0.005235602094240838, 0, 0.005319148936170213, 0, 0.008064516129032258, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.0125, 0, 0, 0.005780346820809248, 0, 0, 0, 0.010638297872340425, 0, 0, 0, 0.008771929824561403, 0.01282051282051282, 0.010869565217391304, 0.010869565217391304, 0, 0, 0, 0, 0.03571428571428571, 0, 0, 0, 0, 0.009259259259259259, 0, 0, 0.011627906976744186, 0, 0, 0, 0, 0.038461538461538464, 0.006666666666666667, 0, 0, 0, 0, 0, 0.011494252873563218, 0.006211180124223602, 0.006535947712418301, 0, 0, 0, 0.00909090909090909, 0, 0, 0, 0, 0.00847457627118644, 0, 0, 0.018518518518518517, 0.007936507936507936, 0, 0, 0, 0, 0, 0, 0.005291005291005291, 0, 0.008695652173913044, 0, 0, 0, 0, 0.005, 0, 0 ]

[ "Fordism\n\nFordism is the basis of modern economic and social systems in industrialized, standardized mass production and mass consumption. ", "The concept is named for Henry Ford. ", "It is used in social, economic, and management theory about production, working conditions, consumption, and related phenomena, especially regarding the 20th century.", "\n\nOverview\n\nFordism is \"the eponymous manufacturing system designed to spew out standardized, low-cost goods and afford its workers decent enough wages to buy them.\" ", "It has also been described as \"a model of economic expansion and technological progress based on mass production: the manufacture of standardized products in huge volumes using special purpose machinery and unskilled labor.\" ", "Although Fordism was a method used to improve productivity in the automotive industry, the principle could be applied to any kind of manufacturing process. ", "Major success stemmed from three major principles:\n\n The standardization of the product (nothing is handmade, but everything is made through machines and molds by unskilled workers)\n The employment of assembly lines, which use special-purpose tools and/or equipment to allow unskilled workers to contribute to the finished product\n Workers are paid higher \"living\" wages so that they can afford to purchase the products they make\n\nThe principles, coupled with a technological revolution during Henry Ford's time, allowed for his revolutionary form of labor to flourish. ", "His assembly line was revolutionary though not original as it had previously been used at slaughterhouses. ", "His most original contribution to the modern world was breaking down complex tasks into simpler ones, with the help of specialised tools. ", "Simpler tasks created interchangeable parts that could be used the same every time. ", "That allowed for a very adaptable flexibility, creating an assembly line that could change its constituent components to meet the needs of the product being assembled. ", "In reality, the assembly line had already been around before Ford although not in quite the same effectiveness as he would create. ", "His real accomplishment was recognizing the potential by breaking it all down into its components, only to build it back up again in a more effective and productive combination, thereby producing an optimum method for the real world.", "\n\nThe major advantages of such a change was that it cut down on the manpower necessary for the factory to operate, and it deskilled the labour itself, cutting down on costs of production. ", "There are four levels of Fordism, as described by Bob Jessop.", "\n\nBackground\n\nThe Ford Motor Company was one of several hundred small automobile manufacturers that emerged between 1890 and 1910. ", "After five years of producing automobiles, Ford introduced the Model T, which was simple and light but sturdy enough to drive on the country's primitive roads. ", "The mass production of this automobile lowered its unit price, making it affordable for the average consumer. ", "Furthermore, Ford substantially increased his workers' wages to combat rampant absenteeism and employee turnover, which approached 400% annually, which had the byproduct of giving them the means to become customers. ", "That led to massive consumption. ", "In fact, the Model T surpassed all expectations because it attained a peak of 60% of the automobile output within the United States.", "\n\nThe production system that Ford exemplified involved synchronization, precision, and specialization within a company.", "\n\nFord and his senior managers did not use the word \"Fordism\" themselves to describe their motivations or worldview, which they did not consider an \"ism\". ", "However, many contemporaries framed their worldview as one and applied the name Fordism to it.", "\n\nHistory\nThe term gained prominence when it was used by Antonio Gramsci in 1934 in his essay \"Americanism and Fordism\" in his Prison Notebooks. ", "Since then, it has been used by a number of writers on economics and society, mainly but not exclusively in the Marxist tradition.", "\n\nAccording to historian Charles S. Maier, Fordism proper was preceded in Europe by Taylorism, a technique of labor discipline and workplace organization, based upon supposedly-scientific studies of human efficiency and incentive systems. ", "It attracted European intellectuals, especially in Germany and Italy, from the fin de siècle to World War I.\n\nAfter 1918, however, the goal of Taylorist labor efficiency thought in Europe moved to \"Fordism,\" the reorganization of the entire productive process by the moving assembly line, standardization, and the mass market. ", "The grand appeal of Fordism in Europe was that it promised to sweep away all the archaic residues of precapitalist society, by subordinating the economy, society, and even the human personality to the strict criteria of technical rationality. ", "The Great Depression blurred the utopian vision of American technocracy, but World War II and its aftermath revived the ideal.", "\n\nThe principles of Taylorism were quickly picked up by Vladimir Lenin and applied to the industrialization of the Soviet Union.", "\n\nLater, under the inspiration of Gramsci, Marxists picked up the Fordism concept in the 1930s and developed Post-Fordism in the 1970s. ", "Antonio and Bonanno (2000) trace the development of Fordism and subsequent economic stages, from globalization to neoliberal globalization, during the 20th century, and emphasized the United States role in globalization. \"", "Fordism,\" for Gramsci, meant routine, intensified labor to promote production. ", "Antonio and Bonanno argue that Fordism peaked in the post-World War II decades of American dominance and mass consumerism but collapsed from political and cultural attacks on the people in the 1970s.", "\n\nAdvances in technology and the end of the Cold War ushered in a new \"neoliberal\" phase of globalization in the 1990s. ", "Antonio and Bonanno further suggest that negative elements of Fordism, such as economic inequality, remained, allowing related cultural and environmental troubles, which inhibited America's pursuit of democracy to surface.", "\n\nHistorian Thomas Hughes has detailed how the Soviet Union, in the 1920s and the 1930s, enthusiastically embraced Fordism and Taylorism by importing American experts in both fields as well as American engineering firms to build parts of its new industrial infrastructure. ", "The concepts of the Five-Year Plan and the centrally-planned economy can be traced directly to the influence of Taylorism on Soviet thinking. ", "Hughes quotes Joseph Stalin:\n\nHughes describes how, as the Soviet Union developed and grew in power, both the Soviets and the Americans chose to ignore or deny the contribution of American ideas and expertise. ", "The Soviets did so because they wished to portray themselves as creators of their own destiny and not indebted to their rivals, while the Americans did so because they did not wish to acknowledge, during the Cold War, their part in creating a powerful rival.", "\n\nRegulation theory\n\nFordism is a key concept in the theories of the Regulation school, often in contrast to post-Fordism, and the term is also used in Western Marxist thought.", "\n\nIn Regulation theory, it is a \"regime of accumulation\" or a macroeconomic pattern of growth, developed in the US and diffused in various forms to Western Europe after 1945. ", "It consisted of domestic mass production with a range of institutions and policies supporting mass consumption, including stabilizing economic policies and Keynesian demand management that generated national demand and social stability; it also included a class compromise or social contract entailing family-supporting wages, job stability and internal labor markets leading broadly shared prosperity: rising incomes were linked to national productivity from the late 1940s to the early 1970s. ", "At the level of the labor process Fordism is Taylorist and as a national mode of regulation Fordism is Keynesianism.", "\n\nThe social-scientific concept of \"Fordism\" was introduced by the French regulation school, sometimes known as regulation theory, which is a Marxist-influenced strand of political economy. ", "According to the regulation school, capitalist production paradigms are born from the crisis of the previous paradigm; a newborn paradigm is also bound to fall into crisis sooner or later. ", "The crisis of Fordism became apparent to Marxists in late 1960s.", "\n\nMarxist regulation theory talks of Regimes of Capital Accumulation (ROA) and Modes of Regulation (MOR). ", "ROAs are periods of relatively settled economic growth and profit across a nation or global region. ", "Such regimes eventually become exhausted, falling into crisis, and are torn down as capitalism seeks to remake itself and return to a period of profit. ", "Such periods of capital accumulation are \"underpinned,\" or stabilised, by MOR. ", "A plethora of laws, institutions, social mores, customs and hegemonies both national and international work together to create the environment for long-run capitalist profit.", "\n\nFordism is a tag used to characterise the post-1945 long boom experienced by western nations. ", "It is typified by a cycle of mass production and mass consumption, the production of standardized (most often) consumer items to be sold in (typically) protected domestic markets, and the use of Keynesian economic policies. ", "While the standard pattern is postwar America, national variations of this standard norm are well known. ", "Regulation theory talks of National Modes of Growth to denote different varieties of Fordism across western economies.", "\n\nFordism as an ROA broke down, dependent on national experiences, somewhere between the late 1960s and the mid-1970s. ", "Western economies experienced slow or nil economic growth, rising inflation and growing unemployment, much of this as a result of the 1973 oil shock.", "\n\nPost-Fordism\n\nThe period after Fordism has been termed Post-Fordist and Neo-Fordist. ", "The former implies that global capitalism has made a clean break from Fordism, including overcoming its inconsistencies, but the latter implies that elements of the Fordist ROA continued to exist. ", "The Regulation School preferred the term After-Fordism (or the French Après-Fordisme) to denote that what comes after Fordism was or is not clear.", "\n\nIn Post-Fordist economies:\n New information technologies are important.", "\n Products are marketed to niche markets rather than in mass consumption patterns based on social class.", "\n Service industries predominate over manufacturing.", "\n The workforce is feminized.", "\n Financial markets are globalized.", "\n\nCultural references\nThe mass-produced robots in Karel Čapek's play R.U.R. have been described as representing \"the traumatic transformation of modern society by the First World War and the Fordist assembly line.\"", "\n\nA religion based on the worship of Henry Ford is a central feature of the technocracy in Aldous Huxley's Brave New World, where the principles of mass production are applied to the generation of people as well as to industry.", "\n\nSee also\n Post-Fordism\n\n Division of labour\n Cognitive-cultural economy\n Modern Times (film)\n\nReferences\n\nBibliography\n Antonio, Robert J. and Bonanno, Alessandro. \"", "A New Global Capitalism? ", "From 'Americanism and Fordism' to 'Americanization-globalization.'\" ", "American Studies 2000 41(2–3): 33–77. .", "\n Banta, Martha. ", "Taylored Lives: Narrative Production in the Age of Taylor, Veblen, and Ford. ", "U. of Chicago Press, 1993. ", "431 pp.", "\n \n Baca, George. \"", "Legends of Fordism.\" ", "Social Analysis Fall 2004: 171–180.", "\n Doray, Bernard (1988). ", "From Taylorism to Fordism: A Rational Madness.", "\n Holden, Len. \"", "Fording the Atlantic: Ford and Fordism in Europe\" in Business History Volume 47, #1 January 2005 pp.", " 122–127.", "\n \n Hughes, Thomas P. (2004). ", "American Genesis: A Century of Invention and Technological Enthusiasm 1870–1970. ", "2nd ed. ", "The University of Chicago Press. ", "\n Jenson, Jane. \"'", "Different' but Not 'Exceptional': Canada's Permeable Fordism,\" Canadian Review of Sociology and Anthropology, Vol. ", "26, 1989\n Koch, Max. (", "2006). ", "Roads to Post-Fordism: Labour Markets and Social Structures in Europe\n Ling, Peter J. America and the Automobile: Technology, Reform, and Social Change chapter on \"Fordism and the Architecture of Production\"\n Maier, Charles S. \"Between Taylorism and Technocracy: European Ideologies and the Vision of Industrial Productivity.\" ", "Journal of Contemporary History (1970) 5(2): 27–61. ", " Fulltext online at Jstor\n Mary Nolan; Visions of Modernity: American Business and the Modernization of Germany Oxford University Press, 1994 online\n Mead, Walter Russell. \"", "The Decline of Fordism and the Challenge to American Power.\" ", "New Perspectives Quarterly; Summer 2004: 53–61.", "\n Meyer, Stephen. (", "1981) \"The Five Dollar Day: Labor Management and Social Control in the Ford Motor Company, 1908–1921\" State University of New York Press\n Spode, Hasso: \"Fordism, Mass Tourism and the Third Reich.\" ", "Journal of Social History 38(2004): 127–155.", "\n Pietrykowski, Bruce. \"", "Fordism at Ford: Spatial Decentralization and Labor Segmentation at the Ford Motor Company, 1920–1950,\" Economic Geography, Vol. ", "71, (1995) 383–401 online\n Roediger, David, ed. \"", "Americanism and Fordism - American Style: Kate Richards O'hare's 'Has Henry Ford Made Good?'\" ", "Labor History 1988 29(2): 241–252. ", "Socialist praise for Ford in 1916.", "\n Settis, Bruno. (", "2016) \"Fordismi. ", "Storia politica della produzione di massa\", Mulino Bologna\n Shiomi, Haruhito and Wada, Kazuo. (", "1995). ", "Fordism Transformed: The Development of Production Methods in the Automobile Industry Oxford University Press.", "\n Tolliday, Steven and Zeitlin, Jonathan eds. (", "1987) The Automobile Industry and Its Workers: Between Fordism and Flexibility Comparative analysis of developments in Europe, Asia, and the United States from the late 19th century to the mid-1980s.", "\n Watts, Steven. (", "2005). ", "The People's Tycoon: Henry Ford and the American Century.", "\n Williams, Karel, Colin Haslam and John Williams, \"Ford versus 'Fordism': The Beginning of Mass Production?\" ", "Work, Employment & Society, Vol. ", "6, No. ", "4, 517–555 (1992). ", "Stress on Ford's flexibility and commitment to continuous improvements.", "\n Gielen, Pascal. (", "2009). ", "The Murmuring of the Artistic Multitude. ", "Global Art, Memory and Post-Fordism. ", "Valiz: Amsterdam.", "\n\nCategory:Production economics\nCategory:Manufacturing\nCategory:Social theories\nCategory:Modern economic history\nCategory:Henry Ford\nCategory:History of science and technology in the United States\nCategory:Economic history of the United States\nCategory:Modernity\nCategory:Modes of production" ]

{ "pile_set_name": "Wikipedia (en)" }

[ 0, 0.02702702702702703, 0, 0, 0, 0, 0.0017543859649122807, 0.009345794392523364, 0, 0, 0, 0.007633587786259542, 0, 0, 0.01639344262295082, 0.007633587786259542, 0.00625, 0, 0.004629629629629629, 0, 0, 0.008403361344537815, 0.0064516129032258064, 0, 0.006896551724137931, 0, 0.0041841004184100415, 0, 0, 0, 0.0078125, 0.022058823529411766, 0.009009009009009009, 0.012658227848101266, 0.010050251256281407, 0, 0.009009009009009009, 0.003663003663003663, 0, 0.014285714285714285, 0, 0, 0, 0, 0.017241379310344827, 0, 0, 0, 0.018867924528301886, 0, 0, 0.012658227848101266, 0, 0, 0, 0, 0.00847457627118644, 0, 0, 0.011494252873563218, 0, 0.00684931506849315, 0.0136986301369863, 0, 0, 0, 0, 0.009345794392523364, 0.00881057268722467, 0.011976047904191617, 0, 0, 0.02564102564102564, 0.058823529411764705, 0.012987012987012988, 0.037037037037037035, 0, 0.05263157894736842, 0, 0, 0.04, 0, 0.0625, 0.01, 0, 0.03333333333333333, 0.012345679012345678, 0, 0.030303030303030304, 0.05263157894736842, 0.008695652173913044, 0.08695652173913043, 0, 0.01834862385321101, 0.019230769230769232, 0.028901734104046242, 0.03278688524590164, 0, 0, 0.02030456852791878, 0.022727272727272728, 0, 0.023255813953488372, 0, 0.010638297872340425, 0, 0.058823529411764705, 0.05555555555555555, 0.058823529411764705, 0.020833333333333332, 0, 0.01818181818181818, 0.0425531914893617, 0.005025125628140704, 0.05555555555555555, 0, 0.05263157894736842, 0.03636363636363636, 0, 0, 0, 0.014084507042253521, 0, 0, 0, 0, 0, 0.003436426116838488 ]

[ "454 F.2d 229\nRhoda GERSHMAN, Appellant,v.Robert H. FINCH, Secretary of Health, Education and Welfare, Appellee.", "\nNo. ", "71-1052.", "\nUnited States Court of Appeals,Fourth Circuit.", "\nArgued Oct. 7, 1971.Decided Dec. 15, 1971.", "\n\nSamuel Shepard Jones, Jr., Washington, D. C. (Court-assigned counsel), Hogan & Hartson, Washington, D. C., for appellant.", "\nJean G. Rogers, Asst. ", "U. S. Atty. ", " (George Beall, U. S. Atty., ", "on brief), for appellee.", "\nBefore WINTER and BUTZNER, Circuit Judges, and DUPREE, District Judge.", "\nWINTER, Circuit Judge:\n\n\n1\nPlaintiff, Rhoda Gershman, sought review of the Secretary's denial of her claim for mother's insurance benefits as the divorced former wife of a deceased wage earner. ", " Her companion claim for benefits for her children was allowed. ", " The Secretary concluded that plaintiff was not receiving at least one-half of her support from her deceased husband at the time of his death; and the district court, concluding that there was substantial evidence to support this finding, affirmed the Secretary's determination. ", " We disagree and reverse, remanding the case for entry of an appropriate order.", "\n\n\n2\n* Plaintiff and Benjamin Gershman were married in Philadelphia, Pennsylvania, in 1941. ", " Two children were born of the marriage: Michael, born in 1945, and Lois, born in 1949. ", " In December, 1950, plaintiff and her husband separated and, in 1951, divorce proceedings were instituted in the Court of Common Pleas, Philadelphia, Pennsylvania, and resulted in the entry of a decree. ", " In December, 1951, the parties entered into a written separation agreement and, in April, 1952, a final decree of divorce was granted. ", " Following the separation and subsequent divorce, the children remained in the care and custody of plaintiff until Michael was of an age to establish his own residence and Lois reached eighteen and married. ", " To date, plaintiff has not remarried. ", " Mr. Gershman, an insured wage earner, died in January, 1960.", "\n\n\n3\nUnder Pennsylvania law alimony pendente lite is allowable in all cases, Commonwealth v. Scholl, 156 Pa. Super. ", "136, 39 A.2d 719 (1944); but, upon the grant or refusal of a divorce a vinculo matrimonii, alimony must cease, except in the case of a wife who is insane. ", " See, Hooks v. Hooks, 123 Pa. Super. ", "507, 187 A. 245 (1936); 23 Purdon's Pa. Stat.", "Ann. ", "Secs. ", "46, 47 (1955). ", " See also, Commissioner of Internal Revenue v. Mesta, 123 F.2d 986 (3 Cir. ", "1941), cert. ", "den., ", "316 U.S. 695, 62 S.Ct. ", "1290, 86 L.Ed. ", "1765 (1942). ", " The separation agreement between the parties provided that Mr. Gershman would pay $50.00 per week for the support and maintenance of plaintiff and their two children until a final decree of divorce was granted. ", " Thereafter, he was to continue to pay $50.00 each week, but the agreement provided that this money was to be paid to plaintiff \"as beneficiary for the two minor children . . . ", "until the said minor children reached the age of eighteen or have fully completed their education.\" ", " After cessation of the children's support, plaintiff was to receive $10.00 per week provided she did not remarry.1\n\n\n4\nAfter the divorce was granted, Mr. Gershman made payments in accordance with the agreement, although frequently plaintiff was required to resort to the courts to obtain them. ", " These payments were the sole means of support for plaintiff and her children. ", " She had no other income and she was not employed.2 The payments thus provided food, housing and other necessities for plaintiff and her two children. ", " On a number of occasions plaintiff resorted to the district attorney's office in Philadelphia in an effort to obtain more money. ", " At one point the weekly payments were increased by court order to $53.00 per week, although they were later cut back to $50.00, as provided in the agreement. ", " Plaintiff was required to account to the district attorney's office as to how she spent the money and she showed that the $50.00 weekly payments were used for her own support, as well as that of her children. ", " There was also evidence that the attorneys who prepared the separation agreement and the court granting the divorce were all aware that plaintiff would and did apply the payments to her as \"beneficiary\"3 for the children for her own support, as well as that of the children, and there was no suggestion that this would be improper.", "\n\n\n5\nFollowing the death of her husband, plaintiff sought mother's and child's insurance benefits from the Social Security Administration. ", " Although her application for the children was granted, the application for herself was denied on the ground that she did not show that she had received support from her husband pursuant to agreement or court order, as the statute then required.4 Judicial review was not sought.", "\n\n\n6\nAfter the 1965 amendments, plaintiff filed another application, seeking benefits for herself. ", " The application was filed March 30, 1966, and sought retroactive benefits for the twelve months preceding (42 U.S.C.A. Sec. ", "402(j) (1), as well as future benefits.5\n\n\n7\nThe second application went to hearing and, notwithstanding the uncontradicted testimony of plaintiff that she was supporting herself from the payments made to her as \"beneficiary\" for her children, corroborated by the evidence of the attorneys with knowledge of her personal situation and an assistant district attorney of Philadelphia, the claim was denied on the ground that \"[t]he wording of the agreement, and of the court order in effect at the time of the death of the wage earner, provided only for the support of the children, and did not provide support or maintenance of claimant. ", " The $50.00 contributions clearly were specified for the support of the children.\" ", " In deciding that there was substantial evidence to support the Secretary's determination, the district court apparently concluded that the recitals in the support agreement and the decree granting the divorce constituted substantial evidence to support the Secretary's determination.6\n\nII\n\n8\nThe decision in this case turns upon the 1965 amendments to 42 U.S.C.A. Sec. ", "402(g) (1) (F) (i) insofar as eligibility is dependent upon support from the deceased wage earner. ", " That portion of the statute, as amended, requires the claimant to show\n\n\n9\n(I) she was receiving at least one-half of her support, as determined in accordance with regulations prescribed by the Secretary, from such individual, or\n\n\n10\n(II) she was receiving substantial contributions from such individual (pursuant to a written agreement), or\n\n\n11\n(III) there was a court order for substantial contributions to her support from such individual. ", " (emphasis supplied)7\n\n\n12\nWhen compared with the statute as it existed prior to the amendment, the amended statute eliminates the requirement that at least one-half of the claimant's support be received \"pursuant to agreement or court order.\" ", " The legislative history of the amendment does not illuminate the amendment, although illumination would seen unnecessary in the light of the obvious inference to be drawn from the elimination of the quoted language. ", " Indeed, the Secretary's regulation, 20 C.F.R. Sec. ", "404.350(a) states that prior to the 1965 amendments, a claimant was required to show that one-half of her support was received pursuant to agreement or court order, but that proof of such technical niceties is not required for the period after the 1965 amendments.", "\n\n\n13\nGiven the indisputable proposition that since the 1965 amendments a claimant is not required to show that at least one-half of her support was received \"pursuant to agreement or court order,\" we view the test of whether she received one-half of her support from the deceased wage earner as a pure question of fact. ", " And in the instant case we view the record as showing, equally indisputable, that plaintiff did receive at least one-half of her support from her deceased husband. ", " Of course, the agreement specified that the moneys she received were received as \"beneficiary\" for her minor children and that after the deceased wage earner's obligation to support them terminated, she would receive only $10.00 per week from him for herself. ", " We recognize that the agreement does constitute some evidence of the nature of the $50.00 weekly payments, but the explanation that these payments, irrespective of how they were formally designated, were intended to be applied and were applied as the sole means of support for her, as well as her children, is not controverted. ", " We infer that the deceased wage earner, and his attorneys, termed the payments as solely child support not only to meet Pennsylvania's prohibition against payment of alimony to a sane, divorced wife, but also to preserve for him the full dependency deduction for federal income tax purposes for his children whom he was supporting.", "\n\n\n14\nWe conclude that there was not substantial evidence for the Secretary's determination; and, since the uncontroverted, corroborated evidence that the purported payments for support of the children were plaintiff's sole means of support, there is no further factual determination to be made by the Secretary. ", " We are thus warranted in directing that plaintiff's claim for herself be allowed.", "\n\n\n15\nSchroeder v. Hobby, 222 F.2d 713 (10 Cir. ", "1955), relied upon by the Secretary, does not require a contrary result. ", " In Schroeder the wage earner conveyed certain rental property to the claimant as part of a property settlement incident to divorce, and there it was found that the parties intended that the rent generated by the property was intended to be the husband's exclusive provision for his former wife's support. ", " The husband also paid $100.00 per month for the support of his children, and there was evidence that the divorced wife diverted the child support payments, in whole or in part, to maintain the rental property. ", " Nevertheless, it was held the surviving divorced wife was not entitled to benefits, because the death of the wage earner did not cause any impact upon the divorced wife's economic condition and her diversion of child support payments made no difference, since it had been intended that she was to be supported from the rentals and not from the payments made for the children. ", " Moreover, Schroeder was a pre-1965 Social Security amendments case, and that there was no reason for the court not to adhere strictly to the designations contained in the property settlement and divorce decree. ", " By contrast, the record in this case establishes that plaintiff suffered a complete loss of economic support when Mr. Gershman died.", "\n\n\n16\nSimilarly, we think Adair v. Finch, 421 F.2d 652 (10 Cir. ", "1970), inapposite. ", " It, too, concerned a property settlement incident to divorce, undisturbed by the former husband's subsequent death, and not periodic payments from the former husband. ", " Additionally, Adair, as well as Schroeder, was decided in a community property state where, as the Tenth Circuit indicated, \"income from community property awarded to the wife as her sold and separate property [does not] constitute . . . ", "a contribution from her former husband.\" ", "421 F.2d at 654.", "\n\nIII\n\n17\nThe judgment of the district court is reversed, and the case is remanded for entry of a judgment in accordance with this opinion.", "\n\n\n18\nReversed and remanded.", "\n\n\n\n1\n It is said that the agreement also provided that if a decree was granted, Mr. Gershman would assign his interest in a house owned jointly by the parties to plaintiff, that he would convey to her certain personal property, and that he would assign to her certain life insurance polices. ", " The parties' formal agreement was received as an exhibit in the proceedings before the Secretary but, unfortunately, the copy included in the administrative record filed with the district court and the copy contained in the administrative record furnished to the members of this court is absolutely illegible. ", " The matter would seem of little moment, however, since plaintiff's testimony, totally undisputed, is that at the time the parties separated their house was being offered for sale and they had practically no equity in it. ", " The house was subsequently sold. ", " Plaintiff also testified that she received from her husband neither personal property nor insurance, as provided in this agreement\nSimilarly, the decree of divorce is illegible. ", " Apparently it was silent on the subject of alimony in accordance with Pennsylvania law.", "\n\n\n2\n The record contains evidence that because of the chronic illness of one of the children, she could not be absent from the home\n\n\n3\n The word is a misnomer. \"", "Trustee\" or \"guardian\" would have been more accurate\n\n\n4\n 42 U.S.C.A. Sec. ", "402(g) (1) (F) (i) then provided that a surviving divorced mother (not remarried) was entitled to benefits for herself if, inter alia, at the wage earner's death she was receiving at least one-half of her support from the deceased wage earner, \"pursuant to agreement or court order.\" ", " (emphasis supplied) The statute was amended in 1965 by Pub. ", "L. 89-97 Secs. ", "306(c) (7) and 308(d) (3)-(5); 79 Stat. ", "286\n\n\n5\n As a result of subsequent events, the future benefits would be small, although the record does not reflect their precise amount. ", " Michael ceased attending school in June, 1966, and became employed, and Lois reached the age of eighteen and married in May, 1967. ", " Plaintiff, therefore, could in no event be eligible for benefits after April, 1967, since this was the month preceding the month in which \"no child of such deceased individual is entitled to a child's insurance benefit . . . ,\" ", "a condition terminating eligibility. ", "42 U.S.C.A. Sec. ", "402(g) (1)\n\n\n6\n In fairness to the district court, it must be noted that throughout the proceedings on judicial review, the Secretary has evidenced considerable confusion as to the correct statute which governs the outcome. ", " It cannot be said with certainty that the 1965 amendments which we consider crucial were brought to the attention of the district judge\n\n\n7\n The regulations, adopted to flesh out p (I), state simply that a claimant is considered in receipt of one-half of her support from a wage earner at his death if, for the previous twelve months he \"made regular contributions, in cash or in kind, to such person's support and the amount of such contributions equaled or exceeded one-half of such person's support during such period.\" ", "20 C.F.R. Sec. ", "404.349(b) et seq\n\n\n" ]

{ "pile_set_name": "FreeLaw" }

[ 0.04504504504504504, 0, 0, 0.0425531914893617, 0, 0.04032258064516129, 0.08695652173913043, 0.08333333333333333, 0.06896551724137931, 0, 0.028169014084507043, 0.010256410256410256, 0, 0, 0, 0.010869565217391304, 0.045454545454545456, 0.0049261083743842365, 0, 0.00966183574879227, 0, 0.01639344262295082, 0.008620689655172414, 0, 0, 0.044444444444444446, 0, 0, 0, 0.013333333333333334, 0, 0.16666666666666666, 0, 0, 0, 0.0047169811320754715, 0, 0, 0.003389830508474576, 0, 0, 0, 0, 0, 0, 0.007194244604316547, 0, 0, 0.008, 0, 0, 0.005405405405405406, 0, 0.004484304932735426, 0.004098360655737705, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.020833333333333332, 0, 0, 0, 0, 0.0047169811320754715, 0.007518796992481203, 0.015625, 0, 0, 0.008368200836820083, 0, 0.0625, 0, 0, 0.0034129692832764505, 0, 0.0045045045045045045, 0, 0, 0, 0, 0.013333333333333334, 0, 0, 0, 0, 0, 0.015151515151515152, 0, 0, 0.058823529411764705, 0, 0, 0, 0 ]

[ "Según la denuncia por la que fue detenida, a la que tuvo acceso Infobae, la dirigente kirchnerista es sindicada como \"jefa\" de una organización constituida por cooperativas que se apropió de $1.634.444,21 que iban a utilizarse para obras y que no fueron ejecutadas." ]

{ "pile_set_name": "OpenWebText2" }

[ 0.018867924528301886 ]

[ "JAY-Z and Roc Nation has inked a deal with the NFL, The New York Times reports. ", "JAY and Roc Nation will now serve as the league’s “live music entertainment strategists,” which will see them consulting on entertainment, including the Super Bowl halftime performances. ", "They will also contribute to the NFL’s Inspire Change activism campaign, which launched this January following its controversial handling of players who kneel during the national anthem—most notably, former San Francisco 49ers quarterback Colin Kaepernick. ", "The two parties are set to announce the deal in a press conference Wednesday.", "\n\n“The N.F.L. has a great big platform, and it has to be all-inclusive,” JAY-Z told the Times. “", "They were willing to do some things, to make some changes, that we can do some good.”", "\n\nJAY has historically been vocal about his support for Kaepernick. ", "In fall 2017, he began dedicating “The Story of O.J.” to the former quarterback in live performances and wore a custom Kaepernick jersey during his “SNL” appearance. ", "He later called Kaepernick “an iconic figure” in an interview.", "\n\nThe rapper also declined to perform at the 2018 Super Bowl halftime show to stand in solidarity with Kaepernick. ", "He confirmed the action in “APESHIT,” his 2018 track with Beyoncé, when he raps: “I said no to the Super Bowl: you need me, I don't need you.”", "\n\nRead, “The Story of JAY-Z’s Ascent to Billionaire Status, as Told by JAY-Z Lyrics” on Levels." ]

{ "pile_set_name": "OpenWebText2" }

[ 0.05, 0.0106951871657754, 0.011673151750972763, 0, 0.03125, 0, 0.029411764705882353, 0.006024096385542169, 0.016129032258064516, 0.008695652173913044, 0.007042253521126761, 0.021052631578947368 ]

[ "Predictors of depression 12 months after cardiac hospitalization: the Identifying Depression as a Comorbid Condition study.", "\nTo determine characteristics which predict depression at 12 months after cardiac hospitalization, and track the natural history of depression. ", "Depressive symptoms were monitored at baseline, 3 and 12 months in a cohort of 785 patients, using the self-report Center for Epidemiological Studies Depression Scale. ", "Multinomial regression analyses of baseline clinical and demographic variables identified characteristics associated with depression at 12 months. ", "Three baseline variables predicted moderate to severe depression at 12 months: depression during index admission, past history of emotional health problems and current smoking. ", "For those who were depressed during cardiac hospitalization, 51% remained depressed at both 3 and 12 months. ", "Persistence was more evident in patients who had moderate to severe depressive symptoms when hospitalized. ", "Mild depression was as likely to persist as to remit. ", "Three clinically accessible characteristics at the time of cardiac hospitalization can assist in predicting depression at 12 months and may aid treatment decisions. ", "Depressive symptoms persist in a substantial proportion of cardiac patients up to 12 months after hospitalization." ]

{ "pile_set_name": "PubMed Abstracts" }

[ 0.016260162601626018, 0.006944444444444444, 0.005952380952380952, 0, 0, 0, 0, 0, 0, 0 ]

[ "3rd Kentucky Infantry\n\nThe 3rd Kentucky Infantry Regiment was a volunteer infantry regiment that served in the Confederate States Army during the American Civil War. ", "It was part of the First Kentucky Brigade through August 1862.", "\n\nService\nThe 3rd Kentucky Infantry was organized in July 1861, at Camp Boone in Montgomery County, Tennessee, under the command of Colonel Lloyd Tilghman.", "\n\nAt the Battle of Shiloh, the regiment was brigaded with the 4th Alabama Infantry, 31st Alabama Infantry, 4th Kentucky Infantry, 6th Kentucky Infantry, and 9th Kentucky Infantry. ", "In a charge on the Union Army lines, 174 men from the 3rd Kentucky Infantry were killed. ", "All regimental officers were either killed or wounded.", "\n\nThe regiment remained at Port Hudson, Louisiana, until August 20, 1862, when it was ordered to Jackson, Mississippi. ", " Major General John C. Breckinridge was ordered to take the 4th Kentucky Infantry, 6th Kentucky Infantry, and 9th Kentucky Infantry with him and report to General Braxton Bragg. ", " The 3rd Kentucky Infantry, 7th Kentucky Infantry, and 8th Kentucky Infantry became part of the Army of Tennessee and returned to Port Hudson. ", " The 3rd Kentucky Infantry were en route to Bragg at Tullahoma, Tennessee, when they were ordered to reinforce Lieutenant General John C. Pemberton in the defenses of Vicksburg, Mississippi.", "\n\nBy 1864, the regiment's strength was severely depleted. ", " The 3rd Kentucky Infantry was ordered to report to General Nathan Bedford Forrest. ", " Horses were unavailable, so the men followed Forrest on foot. ", " The Kentucky troops that accompanied Forrest were divided into four brigades. ", " The 3rd Kentucky Infantry was in the third brigade with the 7th Kentucky Infantry, and 8th Kentucky Infantry, commanded by Colonel A. P. Thompson. ", " On March 15, 1864 Forrest moved north toward Paducah, Kentucky. ", " Three miles from Paducah they encountered Union pickets and pushed them back to their camp on the outskirts of town. ", " Under fire from a nearby fort, the Kentuckians moved through the streets of Paducah. ", " The fort was discovered to be impenetrable, and a retreat was ordered. ", " Colonel Thompson was killed by cannon fire while leading his troops. ", " Forrest soon returned to Mississippi where the regiment was engaged at the Battle of Brice's Crossroads. ", " At some point in the campaign to Kentucky, the regiment was mounted, becoming the 3rd Kentucky Mounted Infantry.", "\n\nThe regiment participated in the Battle of Franklin and surrendered on May 6, 1865, at Columbus, Mississippi.", "\n\nCommanders\n Colonel Lloyd Tilghman - promoted to brigadier general\n Colonel Albert P. Thompson\n\nSee also\n\n List of Kentucky Civil War Confederate units\n Kentucky in the Civil War\n\nReferences\n Carvell, Frank R., Jr. The Kentucky Brave: A Study of the Activities of the 12th Tennessee Infantry, 22nd Tennessee Infantry, 3rd Kentucky Infantry and 7th Kentucky Infantry, 1861-1862 (Paducah, KY: S.B.C. Pub.), ", "1999.", "\n George, Henry. ", "History of the 3d, 7th, 8th and 12th Kentucky C.S.A. (Louisville, KY: C. T. Dearing), 1911.", "\n Thompson, Edwin Porter. ", "History of the First Kentucky Brigade (Cincinnati, OH: Caxton Pub. ", "House), 1868.", "\n Thompson, Edwin Porter. ", "History of the Orphan Brigade (Louisville, KY: L. N. Thompson), 1898.", "\n\nExternal links\n 3rd Kentucky Infantry living history organization\n\nCategory:Military units and formations established in 1861\nCategory:Military units and formations disestablished in 1865\nCategory:Kentucky Confederate Civil War regiments\nCategory:Orphan Brigade\nCategory:1861 establishments in Tennessee" ]

{ "pile_set_name": "Wikipedia (en)" }

[ 0.024096385542168676, 0.016129032258064516, 0.012903225806451613, 0.027777777777777776, 0.02247191011235955, 0, 0, 0.02247191011235955, 0.027972027972027972, 0.015789473684210527, 0, 0.023809523809523808, 0.015873015873015872, 0.012658227848101266, 0.02702702702702703, 0.015384615384615385, 0, 0, 0, 0.014285714285714285, 0, 0.008849557522123894, 0, 0.0196078431372549, 0, 0.058823529411764705, 0, 0.038461538461538464, 0.014705882352941176, 0.07692307692307693, 0.038461538461538464, 0.02857142857142857, 0.006557377049180328 ]

[ "Top Occasion\n\nClient Testimonials\n\nKord Schmidt Pismo Beach, California, USA\n\nI have to admit at first I was a little skeptical using this site in the beginning! ", "However the order process was convenient, prompt, and a great experience! ", "The delivery was right on time and my girlfriend was surprised and very happy to receive her package, thanks a lot and I will be a return customer in the very near future. ", "Great service!!!", "\n\nRobert William UK\n\nGreat service again! ", "Arrived on time and my girlfriend was very happy.", "\n\nMajor Miquie Singapore\n\nGreat Service.", "Thank you for the updates regarding the Order # FPG-001995 and FPG-001997. ", "The\nSender and Recepients in the Philippines are very greatful and happy. ", "Godbless!", "\n\nJose Isidro United States\n\nmy fiancé has the gift. ", "thank you and i will do more business in the future with you.", "\nRegards\nJose Isidro" ]

{ "pile_set_name": "Pile-CC" }

[ 0, 0, 0, 0, 0.023809523809523808, 0, 0.025, 0, 0, 0, 0.018867924528301886, 0, 0.05 ]

[ "Jeep Soft Tops\n\nShould you have a hardtop and want to switch over to a soft top, you can still choose from that variety of fabric such as Sailcloth, Twill, or multi-layer, but the top kit comes inclusive with all the hardware needed to attach on your Jeep.", "\n\nMost Jeep soft tops have detailed descriptions of their specifications and features, so you can be sure to find a product that meets all your needs. ", "We also offer all the installation hardware and accessories you need to install, maintain, and repair your Jeep soft top.", "\n\nJeep Soft Tops >> Jeep Soft Tops Extremeterrain\n\nThe Jeep soft tops available from Rampage, Pavement Ends and Smittybilt are built to OEM specs using reliable materials that are waterproof and wind-resistant. ", "Available for 2- and 4-door Jeeps, these Jeep soft tops add style and customizability to your Jeep, rain or shine.", "\n\nThe open air Jeep JK is one of the most exciting and capable off-road vehicles around. ", "However, the factory top should not be used in the outdoors without a replacement Soft Top. ", "As enjoyable as it is to feel the wind in your hair, the weather can, and will, turn bad quickly.", "\n\nJeep soft tops are useful accessories because they keep elements off your Jeep. ", "Having a soft top for your Jeep enables more accessibility and versatility than the counterpart, the hard top. ", "Soft tops are built with fabric that is specifically designed to stretch for quick and easy installation.", "\n\nRelated posts to jeep soft tops\n\nShould you have a hardtop and want to switch over to a soft top, you can still choose from that variety of fabric such as Sailcloth, Twill, or multi layer, but the top kit comes inclusive with all the hardware needed to attach on your Jeep..\n\nMost Jeep soft tops have detailed descriptions of their specifications and features, so you can be sure to find a product that meets all your needs. ", "We also offer all the installation hardware and accessories you need to install, maintain, and repair your Jeep soft top.." ]

{ "pile_set_name": "Pile-CC" }

[ 0.015625, 0.006622516556291391, 0.008264462809917356, 0.004739336492890996, 0.017543859649122806, 0.011235955056179775, 0.010869565217391304, 0, 0.024390243902439025, 0.009009009009009009, 0, 0.00936768149882904, 0.00819672131147541 ]

[ "@import \"common.css\";\n@import \"screen.css\";\n\nbody {\n font-family: Verdana, sans-serif;\n}\n\n#content {\n width: 40em;\n padding: 0.5em 1em 0.5em 1em;\n}\n\n.title {\n float: left;\n}\n\n.pagenr {\n float: right;\n}\n\n.authors {\n font-style: italic;\n padding-left: 1em;\n}\n\n.abstract {\n width: 80ex;\n text-align: justify\n padding-left: 1em;\n}\n" ]

{ "pile_set_name": "Github" }

[ 0.008771929824561403 ]

[ "Altered HCN4 channel C-linker interaction is associated with familial tachycardia-bradycardia syndrome and atrial fibrillation.", "\nHCN4 channels are involved in generation, regulation, and stabilization of heart rhythm and channel dysfunction is associated with inherited sinus bradycardia. ", "We asked whether dysfunctional HCN4 channels also contribute to the generation of cardiac tachyarrhythmias. ", "In a candidate gene approach, we screened 422 patients with atrial and/or ventricular tachyarrhythmias and detected a novel HCN4 gene mutation that replaced the positively charged lysine 530 with an asparagine (HCN4-K530N) in a highly conserved region of the C-linker. ", "The index patient developed tachycardia-bradycardia syndrome and persistent atrial fibrillation (AF) in an age-dependent fashion. ", "Pedigree analysis identified eight affected family members with a similar course of disease. ", "Whole-cell patch clamp electrophysiology of HEK293 cells showed that homomeric mutant channels almost are indistinguishable from wild-type channels. ", "In contrast, heteromeric channels composed of mutant and wild-type subunits displayed a significant hyperpolarizing shift in the half-maximal activation voltage. ", "This may be caused by a shift in the equilibrium between the tonically inhibited nucleotide-free state of the C-terminal domain of HCN4 believed to consist of a 'dimer of dimers' and the activated ligand-bound tetrameric form, leading to an increased inhibition of activity in heteromeric channels. ", "Altered C-linker oligomerization in heteromeric channels is considered to promote familial tachycardia-bradycardia syndrome and persistent AF, indicating that f-channel dysfunction contributes to the development of atrial tachyarrhythmias." ]

{ "pile_set_name": "PubMed Abstracts" }

[ 0, 0.006211180124223602, 0.009259259259259259, 0.007434944237918215, 0.007692307692307693, 0, 0, 0, 0.0033444816053511705, 0.0041841004184100415 ]

[ "Cubs Trade Starlin Castro to Yankees, Sign Ben Zobrist\n\nThe Chicago Cubs made two bold moves today, trading Starlin Castro to the New York Yankees for Adam Warren and Brendan Ryan.", "\nand signing 34 year old free agent Ben Zobrist to a 4 year $56 mil contract. ", "Addison Russell will play SS full time in 2016. ", "Didi Gregorius had a solid finish to the 2015 MLB season hittin .2954 after the All-Star break and Castro will play 2B for the Pinstripes.", "\n\nCastro, 26, is a three-time All-Star that struggled mightily for much of the 2015 campaign but had a strong finish to the season and an even better showing in the playoffs. ", "He has four years and $38MM remaining on a seven-year, $60MM contract extension he signed three years ago and will, presumably, step in as the Yankees’ everyday second baseman for the foreseeable future. - ", "MLB Trade Rumors" ]

{ "pile_set_name": "Pile-CC" }

[ 0.044444444444444446, 0.01282051282051282, 0.041666666666666664, 0.028985507246376812, 0.005714285714285714, 0.0048543689320388345, 0 ]

[ "As rumored, Steve Jobs announced today at the Apple Worldwide Developers Conference that the Macintosh will make a transition to Intel processors.", "Jobs reviewed the two previous major transitions, from Motorola 680x0 processors to the PowerPC in 1994 thru 1996 (before Steve Jobs was back at the helm), and from Mac OS 9 to Mac OS X in 2001 through 2003. ", "Saying \"It's time for a third transition,\" he explained that the need for the change was more than just the inability to deliver a 3.0GHz Power Mac, as he promised 2 years ago, but that Intel offers increased performance AND reduced power consumption (\"Intel chips runs cooler\"), a critical factor for PowerBooks, and an exceptional \"roadmap\" into 2006 and beyond.", "He said that Mac OS X has been living a secret double life for the past five years (see Marklar rumor) and gave a demonstration. ", "The design for Mac OS X has always been processor independent and cross-platform capable by design. ", "The technology to let existing PowerPC applications run on Intel is named Rosetta and performs dynamic translation transparent to users (see QuickTransit from Transitive ).Mac OS on Intel is to be given to developers (ADC \"Select\" and \"Premier\" members) now and to customers \"this time next year.\" ", "The transition will be completed in less than 2 years, by the end of 2007. ", "Dashboard widgets, scripts, and Java programs do not need porting. ", "With Xcode 2.1 (out today and distributed at the Keynote), developers can make a \"tweak\" and recompile for Cocoa applications, and port Carbon applications in a matter of weeks. ", "Mathematica was ported in 2 hours, although the porting team had direct support from Apple. ", "A universal version of MS Office is coming. ", "Photoshop and its plug-ins run with typical performance but take longer to load.", "All demonstrations during the Keynote were performed on a 3.6GHz Pentium 4, to the surprise of many in the audience.", "Article Link: Macintosh Moving to Intel Processors [Updated]" ]

{ "pile_set_name": "OpenWebText2" }

[ 0.0273972602739726, 0.009615384615384616, 0.008241758241758242, 0.007751937984496124, 0, 0.010067114093959731, 0, 0.029850746268656716, 0.011235955056179775, 0.021739130434782608, 0.022727272727272728, 0, 0.008620689655172414, 0.016666666666666666 ]

[ "// Copyright 2016 The Go Authors. ", "All rights reserved.", "\n// Use of this source code is governed by a BSD-style\n// license that can be found in the LICENSE file.", "\n\n// +build darwin dragonfly freebsd linux netbsd openbsd solaris\n// +build !", "gccgo\n\npackage unix\n\nimport \"syscall\"\n\nfunc Syscall(trap, a1, a2, a3 uintptr) (r1, r2 uintptr, err syscall.", "Errno)\nfunc Syscall6(trap, a1, a2, a3, a4, a5, a6 uintptr) (r1, r2 uintptr, err syscall.", "Errno)\nfunc RawSyscall(trap, a1, a2, a3 uintptr) (r1, r2 uintptr, err syscall.", "Errno)\nfunc RawSyscall6(trap, a1, a2, a3, a4, a5, a6 uintptr) (r1, r2 uintptr, err syscall.", "Errno)\n" ]

{ "pile_set_name": "Github" }

[ 0, 0, 0.019230769230769232, 0.012987012987012988, 0.018691588785046728, 0.06818181818181818, 0.038461538461538464, 0.06593406593406594, 0 ]

[ "Potential of treatment-specific protein biomarker profiles for detection of hormone abuse in cattle.", "\nTargeted protein biomarker profiling is suggested as a fast screening approach for detection of illegal hormone treatment in meat production. ", "The advantage of using biomarkers is that they mark the biological response and, thus, are responsive to a panel of substances with similar effects. ", "In a preliminary feasibility study, a 4-plex protein biomarker flow cytometric immunoassay (FCIA) previously developed for the detection of recombinant bovine somatotropin (rbST) was applied to cattle treated with steroids, such as estradiol, dexamethasone, and prednisolone. ", "Each treatment resulted in a specific plasma biomarker profile for insulin-like growth factor-1 (IGF-1), IGF binding protein 2, osteocalcin, and anti-rbST antibodies, which could be distinguished from the profile of untreated animals. ", "In summary, the 4-plex biomarker FCIA is, apart from rbST, also capable of detecting treatment with other growth-promoting agents and therefore clearly shows the potential of biomarker profiling as a screening method in veterinary control. ", "It is proposed to perform additional validation studies covering high numbers of treated and untreated animals to support inclusion or adaptation of protein biomarker approaches in future monitoring regulations." ]

{ "pile_set_name": "PubMed Abstracts" }

[ 0, 0, 0, 0.0036231884057971015, 0.00851063829787234, 0.004166666666666667, 0 ]

[ "We Deploy this services when our clients are in the process of creating or expanding their Leadership teams. ", "Right from sourcing Board level to CXO’s and or strategic level talent. ", "We have handled assignments across the industry verticals and in a broad spectrum of functional domains. ", "Our executive search process that our highly experienced team has developed and keeps refining has earned us trust and respect of a large number of our clients. ", "Milestone-wise the process is as follows" ]

{ "pile_set_name": "Pile-CC" }

[ 0, 0.027777777777777776, 0, 0, 0 ]

[ "Implantable Microchip Controls Appetite\n\nUK scientists have designed an implantable microchip that attaches to the vagus nerve, which helps to control a variety of body functions from heart rate to hunger. ", "The chip, which is just a few millimeteres in size, is designed to read electrical and chemical signatures of appetite. ", "The device then sends electrical signals to the brain to reduce or stop the urge to eat.", "\n\nThe work could provide an alternative to weight-loss surgery. ", "Sir Stephen Bloom, one of the researchers involved in the project, says that the chip could provide an alternative to “gross surgery” and reassures potential patients that “There will be a little tiny insert and it will be so designed as to have no side effects, but restrict appetite in a natural way”.", "\n\nAlthough this might sound revolutionary, there are other groups working on the vagus nerve to combat obesity. ", "American companies such as EnteroMedics and IntraPace both use vagus nerve stimulation to try to reduce food consumption." ]

{ "pile_set_name": "Pile-CC" }

[ 0, 0, 0, 0, 0.0033003300330033004, 0, 0.01652892561983471 ]

[ "Aglummyia\n\nAglummyia is a genus of flies in the family Tachinidae. ", "It contains only one species, Aglummyia percinerea.", "\n\nReferences\n\nFurther reading\n\nExternal links\n\n \n\nCategory:Tachinidae\nCategory:Monotypic Diptera genera\nCategory:Taxa named by Charles Henry Tyler Townsend" ]

{ "pile_set_name": "Wikipedia (en)" }

[ 0.014925373134328358, 0, 0.012903225806451613 ]

[ "Q:\n\nDrawing circle using Html 5\n\nI am working on a simple paint program. ", "I want to draw rectangle and circle dynamicly. ", "I mean I want to keep track of mouse. ", "I used the following code to draw rectangle and it worked.", "\n// The rectangle tool.", "\ntools.rect = function () {\nvar tool = this;\nthis.started = false;\n\nthis.mousedown = function (ev) {\n tool.started = true;\n tool.x0 = ev._x;\n tool.y0 = ev._y;\n};\n\nthis.mousemove = function (ev) {\n if (!", "tool.started) {\n return;\n }\n\n var x = Math.min(ev._x, tool.x0),\n y = Math.min(ev._y, tool.y0),\n w = Math.abs(ev._x - tool.x0),\n h = Math.abs(ev._y - tool.y0);\n\n context.clearRect(0, 0, canvas.width, canvas.height);\n\n if (!", "w || !", "h) {\n return;\n }\n\n context.strokeRect(x, y, w, h);\n};\n\nthis.mouseup = function (ev) {\n if (tool.started) {\n tool.mousemove(ev);\n tool.started = false;\n img_update();\n }\n};\n};\n\nI want to do the same for circle. ", "But I am having trouble, I used following code, but it does not work. ", "\n// The circle tool.", "\ntools.circle = function () {\nvar tool = this;\nthis.started = false;\n\nthis.mousedown = function (ev) {\n tool.started = true;\n tool.x0 = ev._x;\n tool.y0 = ev._y;\n tool.z0 = ev._z;\n};\n\nthis.mousemove = function (ev) {\n if (!", "tool.started) {\n return;\n }\n\n var x = Math.min(ev._x, tool.x0),\n y = Math.min(ev._y, tool.y0),\n r = Math.min(ev._z, tool.z0),\n w = Math.abs(ev._x - tool.x0),\n h = Math.abs(ev._y - tool.y0);\n\n context.clearRect(0, 0, canvas.width, canvas.height);\n\n context.beginPath();\n context.arc(x, y,r,0, 2*Math.", "PI,true);\n context.stroke();\n context.closePath();\n};\n\nthis.mouseup = function (ev) {\n if (tool.started) {\n tool.mousemove(ev);\n tool.started = false;\n img_update();\n }\n};\n};\n\nHow can I draw a circle in this case? ", "\n\nA:\n\nYou need to calculate the midpoint of the line connecting your start-drag and current-mouse-position.", "\nvar midX=(startingX+currentX)/2;\nvar midY=(startingY+currentY)/2;\n\nThen you need to calculate the radius of a circle that fits that line.", "\nvar dx= Math.abs(startinX-canMouseX);\nvar dy= Math.abs(startinY-canMouseY);\nvar r=Math.sqrt( dx*dx + dy*dy )/2;\n\nHere is code and a Fiddle: http://jsfiddle.net/m1erickson/QQPRx/\n<!", "doctype html>\n<html>\n<head>\n<link rel=\"stylesheet\" type=\"text/css\" media=\"all\" href=\"css/reset.css\" /> <!-- ", "reset css -->\n<script type=\"text/javascript\" src=\"http://code.jquery.com/jquery.min.js\"></script>\n<!", "--[if lt IE 9]><script type=\"text/javascript\" src=\"../excanvas.js\"></script><![endif]-->\n\n<style>\n body{ background-color: ivory; }\n canvas{border:1px solid red;}\n</style>\n\n<script>\n$(function(){\n\n var canvas=document.getElementById(\"canvas\");\n var ctx=canvas.getContext(\"2d\");\n var lastX;\n var lastY;\n var strokeColor=\"red\";\n var strokeWidth=2;\n var canMouseX;\n var canMouseY;\n var canvasOffset=$(\"#canvas\").offset();\n var offsetX=canvasOffset.left;\n var offsetY=canvasOffset.top;\n var isMouseDown=false;\n\n function handleMouseDown(e){\n canMouseX=parseInt(e.clientX-offsetX);\n canMouseY=parseInt(e.clientY-offsetY);\n\n // Put your mousedown stuff here\n lastX=canMouseX;\n lastY=canMouseY;\n isMouseDown=true;\n }\n\n function handleMouseUp(e){\n canMouseX=parseInt(e.clientX-offsetX);\n canMouseY=parseInt(e.clientY-offsetY);\n\n // Put your mouseup stuff here\n isMouseDown=false;\n }\n\n function handleMouseOut(e){\n canMouseX=parseInt(e.clientX-offsetX);\n canMouseY=parseInt(e.clientY-offsetY);\n\n // Put your mouseOut stuff here\n isMouseDown=false;\n }\n\n function handleMouseMove(e){\n canMouseX=parseInt(e.clientX-offsetX);\n canMouseY=parseInt(e.clientY-offsetY);\n\n // Put your mousemove stuff here\n if(isMouseDown){\n var dx= Math.abs(lastX-canMouseX);\n var dy= Math.abs(lastY-canMouseY);\n var midX=(lastX+canMouseX)/2;\n var midY=(lastY+canMouseY)/2;\n var r=Math.sqrt( dx*dx + dy*dy )/2;\n ctx.clearRect(0, 0, canvas.width, canvas.height);\n ctx.beginPath();\n ctx.arc(midX, midY,r,0, 2*Math.", "PI,true);\n ctx.stroke();\n }\n }\n\n $(\"#canvas\").mousedown(function(e){handleMouseDown(e);});\n $(\"#canvas\").mousemove(function(e){handleMouseMove(e);});\n $(\"#canvas\").mouseup(function(e){handleMouseUp(e);});\n $(\"#canvas\").mouseout(function(e){handleMouseOut(e);});\n\n}); // end $(function(){});\n</script>\n\n</head>\n\n<body>\n <canvas id=\"canvas\" width=300 height=300></canvas>\n</body>\n</html>\n\n" ]

{ "pile_set_name": "StackExchange" }

[ 0, 0, 0, 0, 0, 0, 0.0040650406504065045, 0, 0.004424778761061947, 0, 0, 0, 0.006060606060606061, 0.004405286343612335, 0, 0, 0.0055248618784530384, 0.009259259259259259, 0.01, 0.004149377593360996, 0.009592326139088728 ]

[ "/*\n * This is a manifest file that'll be compiled into application.css, which will include all the files\n * listed below.", "\n *\n * Any CSS and SCSS file within this directory, lib/assets/stylesheets, vendor/assets/stylesheets,\n * or vendor/assets/stylesheets of plugins, if any, can be referenced here using a relative path.", "\n *\n * You're free to add application-wide styles to this file and they'll appear at the top of the\n * compiled file, but it's generally better to create a new file per style scope.", "\n *\n *= require_self\n *= require_tree .", "\n */\n" ]

{ "pile_set_name": "Github" }

[ 0, 0.015, 0, 0, 0 ]

[ "C'était « Solfé ». ", "Près de 40 ans d'histoire politique sous le signe de la rose, 3 000 m² de souvenirs, de victoires et de défaites. ", "De larmes et de poings serrés. ", "Mis à genoux électoralement - et financièrement - à la présidentielle et aux législatives, le Parti socialiste a définitivement claqué la porte de son siège, vendu 45 millions d'euros, et tourné une page de son épopée.", "\n\nC'était le 10, rue de Solferino, dans le cossu VIIe arrondissement de Paris. ", "Les socialistes y posent le pied pour la première fois en 1980, alors que se lance la campagne présidentielle de François Mitterrand.", "\n\nSolferino (Paris VIIe), le 27 avril 1981. ", "De gauche à droite : Gaston Defferre, Jack Lang, Lionel Jospin, François Mitterrand, Pierre Mauroy, Michel Rocard, Véronique Neiertz, Jean-Pierre Chevènement./AFP/Georges Gobet\n\nLe bâtiment recèle déjà une histoire riche - maison de syndicats sous le Front populaire, ministère de l'Information pendant Vichy -, les socialistes aspirent à y construire la suite. ", "Elle se raconte par séquences, à travers les fragments de mémoire de ceux qui l'ont vécue. ", "Le « bouillonnement » des années 1980 et 1990, alors que les héritiers de Jaurès sont au pouvoir. ", "Le traumatisme de l'affaire Urba, sur le financement occulte du PS fin 1980. ", "Et déjà des perquisitions dans un siège de parti politique. « ", "Le juge Van Ruymbeke était là et ses assistants remplissaient de documents des sacs en plastique noirs. ", "On n'a pas bougé un cil, personne n'a rien dit… » se rappelle Lyne Cohen-Solal, jadis proche de Pierre Mauroy. ", "Glacial.", "\n\nLe 17 mai 1995 est évidemment gravé dans les mémoires. ", "À l'Elysée, Jacques Chirac succède à François Mitterrand, qui fait son retour à Solfé… à pied. « ", "Il y avait du monde partout, dans la rue, dans la cour », se rappelle la sénatrice Marie-Noëlle Lienemann. ", "Son nom est scandé. « ", "Il nous a dit de tenir bon », poursuit-elle. ", "Alors patron du PS, Henri Emmanuelli offre à Mitterrand une Twingo verte. ", "La gauche ne tardera pas à revenir au pouvoir.", "\n\nCoupe du monde et porno\n\nSolfé, c'est la maison commune. ", "Celle où chacun se rend quand l'actualité trébuche, que la politique s'emballe. ", "Les cadres y déferlent le mardi 11 septembre 2001, après l'effondrement des deux tours du World Trade Center. ", "Le ministre délégué à l'Enseignement professionnel, Jean-Luc Mélenchon, parmi les premiers. « ", "C'est incroyable ce qu'il se passe… » glisse-t-il alors au gardien dans son bocal, avant de filer rejoindre ses camarades.", "\n\nLe lieu n'est jamais vraiment désert. ", "À l'été 2002, c'est dans le bureau du chef, à l'époque François Hollande, absent, que l'on regarde les matchs de la Coupe du monde en Corée du Sud. ", "Au moment du scandale DSK, les socialistes s'y « serrent les coudes », raconte Dominique Bouissou, qui a dirigé le service de presse du PS, quand « 400 à 500 journalistes arrivent à Solfé » le 14 mai 2011 au matin, après avoir appris qu'outre-Atlantique, on venait de passer les menottes au patron du FMI. ", "Sofitel et gueule de bois. ", "On y rit également sous cape lorsqu'une figure, bien connue du siège, dont le bureau et surtout l'écran d'ordinateur donnent sur la cour pavée, est à plusieurs reprises surpris en train de regarder… des vidéos pornos.", "\n\nLe scooter de Hollande et la rue Royale\n\nLe lieu revêt aussi un caractère sacré. « ", "La première fois que j'y suis rentré, j'avais l'impression de pénétrer dans le saint des saints », raconte Olivier Faure, actuel premier secrétaire, marqué par « les discours de Pierre Mauroy, dans un silence de cathédrale ». « ", "C'était un lieu d'effervescence intellectuelle », assure Régis Juanico, ancien patron du MJS (Mouvement des jeunes socialistes). ", "À cette époque, les bureaux nationaux prennent des airs de spectacles. « ", "Emmanuelli et Mélenchon faisaient tonner les BN (NDLR : bureaux nationaux), réveillaient la foule ! » ", "se souvient Jean-Christophe Cambadélis. ", "Ségolène Royal, dans son tailleur immaculé, électrisera elle aussi la foule depuis la terrasse du siège, après sa défaite en 2007. « ", "Rien n'était prévu, elle est montée alors qu'on avait perdu ! » ", "se rappelle Bouissou.", "\n\nLe 6 mai 2007. ", "Ségolène Royal sur le toit du siège du PS le soir de sa défaite./LP/Olivier Corsan\n\nC'est la fin de l'ère Hollande, premier secrétaire de 1997 à 2008. ", "À son départ, c'est Benoît Hamon qui hérite du petit scooter noir qu'il garait chaque matin devant la lourde grille noire. « ", "J'ai eu un accident avec ce scooter… rue Royale! » ", "raconte-t-il en se marrant. ", "Aubry, elle, hérite de la maison, et de ses « toilettes bouchées », racontera-t-elle. ", "Puis Harlem Désir, puis Cambadélis. ", "Lui sent le crépuscule arriver quand, au premier tour de la présidentielle de 2017, Solfé est désert. « ", "J'étais seul, il n'y avait personne. »", "\n\nLe 26 juin 1998. ", "François Hollande, premier secrétaire du parti de 1997 à 2008/LP Frédéric Dugit\n\nNewsletter Politique Chaque jour, l'actualité politique vue par Le Parisien Chaque jour, l'actualité politique vue par Le Parisien Votre adresse mail est collectée par Le Parisien pour vous permettre de recevoir nos actualités et offres commerciales. ", "En savoir plus" ]

{ "pile_set_name": "OpenWebText2" }

[ 0, 0.008771929824561403, 0, 0.0045871559633027525, 0.02531645569620253, 0.007518796992481203, 0.022727272727272728, 0.03038674033149171, 0, 0, 0.012987012987012988, 0, 0.009615384615384616, 0.04504504504504504, 0, 0, 0.020618556701030927, 0.028037383177570093, 0, 0, 0.02702702702702703, 0, 0, 0.025, 0.00909090909090909, 0.010638297872340425, 0, 0, 0.02702702702702703, 0.0196078431372549, 0.037037037037037035, 0.004608294930875576, 0.011764705882352941, 0.008771929824561403, 0.015503875968992248, 0, 0, 0.05, 0.007518796992481203, 0.03125, 0, 0, 0.006622516556291391, 0.024, 0.0196078431372549, 0, 0, 0.05555555555555555, 0.009615384615384616, 0.02631578947368421, 0, 0.024096385542168676, 0 ]

[ "Luxwoude\n\nLuxwoude () is a small village in the municipality of Opsterland in the east of Friesland, the Netherlands. ", "It had a population of around 275 in January 2017.", "\n\nReferences\n\nCategory:Populated places in Friesland" ]

{ "pile_set_name": "Wikipedia (en)" }

[ 0, 0, 0 ]

[ "Yeniköy, Kurucaşile\n\nYeniköy is a village in the District of Kurucaşile, Bartın Province, Turkey. ", "As of 2010, it had a population of 118 people.", "\n\nReferences\n\nCategory:Populated places in Bartın Province\nCategory:Kurucaşile District\nCategory:Villages in Turkey" ]

{ "pile_set_name": "Wikipedia (en)" }

[ 0.02040816326530612, 0, 0 ]

[ "roseycheeks's Channelwww.godtube.comen-USSun, 02 Aug 2015 18:50:16 -0400KWYDGNNXhttp://www.godtube.com/watch/?v=KWYDGNNXCarry My Cross music by Third Day PASSION OF THE CHRIST<img src=\"http://cdn.salemweb.net/godtube/2008/03/17/34516-34516-tn.jpg\" alt=\"Preview\" /><p class=\"description\">Music video featuring The Passion of the Christ and the song Carry My Cross by Third Day.</p>2008-03-17T00:00:00-04:00YD7YPNNXhttp://www.godtube.com/watch/?v=YD7YPNNXPURITY-The Path to Purity-Ashley Reynolds<img src=\"http://cdn.salemweb.net/godtube/2008/03/17/51258-51258-tn.jpg\" alt=\"Preview\" /><p class=\"description\">This is a public service video on PURITY presented by pop/contemporary performing artists/speaker ASHLEY REYNOLDS. ", "Ashley is an advocate for PURITY and travels the country introducing the topic through her COMMITMENT TO PURITY workshop to youth ages 13-19. ", "This video was sponsored by PURITYRINGS.com\nTo book ASHLEY REYNOLDS at your church/school or homeschool group visit www.ashleyreynolds.net</p>2008-03-17T00:00:00-04:00GKWPPNNXhttp://www.godtube.com/watch/?v=GKWPPNNXChange Of Plans<img src=\"http://cdn.salemweb.net/godtube/2010/10/01/63488-63488-tn.jpg\" alt=\"Preview\" /><p class=\"description\">This Is A Song I wrote. ", "God Is Constantly giving me music and I hope to shine for him.</p>2010-10-01T22:16:43-04:0067GGWNNXhttp://www.godtube.com/watch/?v=67GGWNNXJesus Camp<img src=\"http://cdn.salemweb.net/godtube/2010/10/01/72664-72664-tn.jpg\" alt=\"Preview\" /><p class=\"description\">Jesus camp came under controversy for supposedly &quot;indoctrinating&quot; kids to believe in Jesus. ", "This CBN news vid shows why that's simply not true.</p>2010-10-01T22:28:39-04:00M1C2CNNUhttp://www.godtube.com/watch/?v=M1C2CNNUEvangelism Linebacker: No excuses<img src=\"http://cdn.salemweb.net/godtube/2008/03/05/75989-75989-tn.jpg\" alt=\"Preview\" /><p class=\"description\">He loves you...but it might hurt!</p>2008-03-05T00:00:00-05:002EM2JNNUhttp://www.godtube.com/watch/?v=2EM2JNNULIfehouse Drama<img src=\"http://cdn.salemweb.net/godtube/2010/10/01/86781-86781-tn.jpg\" alt=\"Preview\" /><p class=\"description\">an amazing video</p>2010-10-01T22:47:15-04:002CC9FNNUhttp://www.godtube.com/watch/?v=2CC9FNNUwarren barfield - love is not a fight - christianremix.com<img src=\"http://cdn.salemweb.net/godtube/2010/10/01/89923-89923-tn.jpg\" alt=\"Preview\" /><p class=\"description\">No God, no peace. ", "Know God, know peace.</p>2010-10-01T22:51:17-04:00CC0JJNNUhttp://www.godtube.com/watch/?v=CC0JJNNUAbortion....<img src=\"http://cdn.salemweb.net/godtube/2010/10/01/99411-99411-tn.jpg\" alt=\"Preview\" /><p class=\"description\">abortion</p>2010-10-01T23:04:40-04:00DLPL6GNXhttp://www.godtube.com/watch/?v=DLPL6GNXBaby Preacher<img src=\"http://cdn.salemweb.net/godtube/2010/10/01/108076-108076-tn.jpg\" alt=\"Preview\" /><p class=\"description\">Enjoy!</p>2010-10-01T23:16:31-04:00D7DDPGNXhttp://www.godtube.com/watch/?v=D7DDPGNXCasting Crowns - Slow Fade (Official Music Video)<img src=\"http://cdn.salemweb.net/godtube/2013/03/01/430423-004-tn.jpg\" alt=\"Preview\" /><p class=\"description\">Casting Crowns - Slow Fade Music Video. ", "</p>2010-10-01T23:33:50-04:00JF1C1JNUhttp://www.godtube.com/watch/?v=JF1C1JNUThe Stool<img src=\"http://cdn.salemweb.net/godtube/2010/10/01/135951-135951-tn.jpg\" alt=\"Preview\" /><p class=\"description\"><a href=\"http://tinyurl.com/5rdlot\">\nView \"The Challenge\"</a> <br> <br>\n<a href=\"http://tinyurl.com/6zjrop\">\nDownload - The Stool</a> <br> <br>\nAre you committed?</p>2010-10-01T23:52:18-04:00DW7GKGNXhttp://www.godtube.com/watch/?v=DW7GKGNXFireproof-The Cross<img src=\"http://cdn.salemweb.net/godtube/2010/10/02/142636-142636-tn.jpg\" alt=\"Preview\" /><p class=\"description\">This is an excellent scene from the movie Fireproof.</p>2010-10-02T00:01:13-04:00J0FB0CNUhttp://www.godtube.com/watch/?v=J0FB0CNUCreation vs. Evolution - Faith<img src=\"http://cdn.salemweb.net/godtube/2010/10/02/143049-143049-tn.jpg\" alt=\"Preview\" /><p class=\"description\">Spoofing Mac vs. PC commercials, this video has Evolution and Creation debating the evidence that supports evolution</p>2010-10-02T00:02:10-04:00J0FB21NUhttp://www.godtube.com/watch/?v=J0FB21NUCreation vs. Evolution - Random<img src=\"http://cdn.salemweb.net/godtube/2010/10/02/143085-143085-tn.jpg\" alt=\"Preview\" /><p class=\"description\">This humorous video has the theory of evolution and Creation debating the concept of designer versus random process.</p>2010-10-02T00:02:12-04:00J1MC91NUhttp://www.godtube.com/watch/?v=J1MC91NUMoving forward by letting go<img src=\"http://cdn.salemweb.net/godtube/2010/10/02/157925-157925-tn.jpg\" alt=\"Preview\" /><p class=\"description\">Pastor Paul discusses how to move forward in our Christian walk by letting go of the past, forgiving, and putting our faith in God.</p>2010-10-02T00:21:34-04:00DYPPYPNXhttp://www.godtube.com/watch/?v=DYPPYPNXDraw me close to you<img src=\"http://cdn.salemweb.net/godtube/2010/10/02/158858-158858-tn.jpg\" alt=\"Preview\" /><p class=\"description\">From a beautiful worship album<br />\n<br />\nLyrics:<br />\nDraw me close to You<br />\nNever let me go<br />\nI lay it all down again<br />\nTo hear You say that I'm Your friend<br />\nYou are my desire<br />\nNo one else will do<br />\n'Cause nothing else could take Your place<br />\nTo feel the warmth of Your embrace<br />\nHelp me find the way<br />\nBring me back to You<br />\n<br />\nYou're all I want<br />\nYou're all I've ever needed<br />\nYou're all I want<br />\nHelp me know You are near<br />\n<br />\nEnjoy!! ", "^__^</p>2010-10-02T00:22:52-04:00DGLLZPNXhttp://www.godtube.com/watch/?v=DGLLZPNXFireproof - Breaking Free<img src=\"http://cdn.salemweb.net/godtube/2010/10/02/160098-160098-tn.jpg\" alt=\"Preview\" /><p class=\"description\">Caleb Holt is addicted to pornography, but he recently surrendered his life to Christ. ", "While on the Internet, a pop-up ad tempts him to click on a porn site and he struggles with going back to his old habit. ", "After reading that an addiction is like a parasite that destroys lives &amp; marriages, Caleb decides to destroy the parasite instead.</p>2010-10-02T00:25:01-04:00JE0JCFNUhttp://www.godtube.com/watch/?v=JE0JCFNUAmazing Hero Dog!!!<img src=\"http://cdn.salemweb.net/godtube/2010/10/02/164193-164193-tn.jpg\" alt=\"Preview\" /><p class=\"description\">This is the most fantastic thing I have ever seen or heard. ", "It is less than a minute so enjoy! ", "If only we were this compassionate for human beings! ", "This is truly AMAZING!!!</p>2010-10-02T00:30:37-04:00D6LYZ7NXhttp://www.godtube.com/watch/?v=D6LYZ7NXJohn Waller - While I'm Waiting (Official Music Video)<img src=\"http://cdn.salemweb.net/godtube/2010/10/02/170592-170592-tn.jpg\" alt=\"Preview\" /><p class=\"description\">Official music video for John Waller's &quot;While I'm Waiting,&quot; featuring clips from the movie Fireproof.</p>2010-10-02T00:38:55-04:00D6DK7WNXhttp://www.godtube.com/watch/?v=D6DK7WNXRed Balloon<img src=\"http://cdn.salemweb.net/godtube/2010/10/02/171324-171324-tn.jpg\" alt=\"Preview\" /><p class=\"description\">Today there are so many different opinions about what is truth and what isn't, it's almost ridiculous.</p>2010-10-02T00:40:06-04:00" ]

{ "pile_set_name": "Pile-CC" }

[ 0.011095700416088766, 0.014084507042253521, 0.01092896174863388, 0.005509641873278237, 0.012642225031605562, 0.008368200836820083, 0.008864499788940482, 0.006514657980456026, 0, 0.009900990099009901, 0, 0, 0.0070126227208976155 ]

[ "Klingon language\n\nThe Klingon language (tlhIngan Hol, , in pIqaD ) is the constructed language spoken by the fictional Klingons in the Star Trek universe.", "\n\nDescribed in the 1985 book The Klingon Dictionary by Marc Okrand and deliberately designed to sound \"alien\", it has a number of typologically uncommon features. ", "The language's basic sound, along with a few words, was first devised by actor James Doohan (\"Scotty\") and producer Jon Povill for Star Trek: The Motion Picture. ", "That film marked the first time the language had been heard on screen. ", "In all previous appearances, Klingons spoke in English, even to each other. ", "Klingon was subsequently developed by Okrand into a full-fledged language.", "\n\nKlingon is sometimes referred to as Klingonese (most notably in the Star Trek: The Original Series episode \"The Trouble with Tribbles\", where it was actually pronounced by a Klingon character as \"Klingonee\" ), but among the Klingon-speaking community, this is often understood to refer to another Klingon language called Klingonaase that was introduced in John M. Ford's 1984 Star Trek novel The Final Reflection, and appears in other Star Trek novels by Ford.", "\n\nThe play A Klingon Christmas Carol is the first production that is primarily in Klingon (only the narrator speaks English). ", "The opera ʼuʼ is entirely in Klingon.", "\n\nA small number of people are capable of conversing in Klingon. ", "Its vocabulary, heavily centered on Star Trek-Klingon concepts such as spacecraft or warfare, can sometimes make it cumbersome for everyday use.", "\n\nHistory\nAlthough mentioned in the original Star Trek series episode \"The Trouble with Tribbles\", the Klingon language first appeared on-screen in Star Trek: The Motion Picture (1979). ", "According to the actor who spoke the lines, Mark Lenard, James Doohan recorded the lines he had written on a tape, and Lenard transcribed the recorded lines in a way he found useful in learning them.", "\n\nFor Star Trek III: The Search for Spock (1984), director Leonard Nimoy and writer-producer Harve Bennett wanted the Klingons to speak a structured language instead of random gibberish, and so commissioned a full language, based on the phrases Doohan had originated, from Marc Okrand, who had earlier constructed four lines of Vulcan dialogue for Star Trek II: The Wrath of Khan.", "\n\nOkrand enlarged the lexicon and developed a grammar based on Doohan's original dozen words. ", "The language appeared intermittently in later films featuring the original cast (for example, in Star Trek V: The Final Frontier (1989) and in Star Trek VI: The Undiscovered Country (1991), where translation difficulties served as a plot device).", "\n\nTwo \"non-canon\" dialects of Klingon are hinted at in the novelization of Star Trek III: The Search for Spock, as Saavik speaks in Klingon to the only Klingon officer aboard Cpt. ", "Kruge's starship after his death, as the survivors of the Enterprise's self-destruction transport up from the crumbling Genesis Planet to the Klingon ship. ", "The surviving officer, Maltz, states that he speaks the Rumaiy dialect, while Saavik is speaking to him in the Kumburan dialect of Klingon, per Maltz's spoken reply to her.", "\n\nWith the advent of the series Star Trek: The Next Generation (1987)—in which one of the main characters, Worf, was a Klingon—and successors, the language and various cultural aspects for the fictional species were expanded. ", "In the Star Trek: The Next Generation episode \"A Matter of Honor\", several members of a Klingon ship's crew speak a language that is not translated for the benefit of the viewer (even Commander Riker, enjoying the benefits of a universal translator, is unable to understand) until one Klingon orders the others to \"speak their [i.e., human] language\".", "\n\nA small number of non-Klingon characters were later depicted in Star Trek as having learned to speak Klingon, notably Jean-Luc Picard and Jadzia Dax.", "\n\nLanguage\nHobbyists around the world have studied the Klingon language. ", "Six Klingon translations of works of world literature have been published: ghIlghameS (the Epic of Gilgamesh), Hamlet (Hamlet), paghmoʼ tIn mIS (Much Ado About Nothing), pInʼaʼ qan paQDIʼnorgh (Tao Te Ching), Sun pInʼaʼ veS mIw (the Art of War) and taʼpuq mach (the Little Prince). ", "The Shakespearean choices were inspired by a remark from High Chancellor Gorkon in Star Trek VI: The Undiscovered Country, who said, \"You have not experienced Shakespeare until you have read him in the original Klingon.\" ", "In the bonus material on the DVD, screenwriter Nicholas Meyer and actor William Shatner both explain that this was an allusion to the German myth that Shakespeare was in fact German.", "\n\nThe Klingon Language Institute exists to promote the language.", "\n\nCBS Television Studios owns the copyright on the official dictionary and other canonical descriptions of the language. ", "While constructed languages (\"conlangs\") are viewed as creations with copyright protection, natural languages are not protected, excluding dictionaries and/or other works created with them. ", "Mizuki Miyashita and Laura Moll note, \"Copyrights on dictionaries are unusual because the entries in the dictionary are not copyrightable as the words themselves are facts, and facts can not be copyrighted. ", "However, the formatting, example sentences, and instructions for dictionary use are created by the author, so they are copyrightable.\"", "\n\nOkrand had studied some Native American and Southeast Asian languages, and phonological and grammatical features of these languages \"worked their way into Klingon, but for the most part, not by design.\" ", "Okrand himself has stated that a design principle of the Klingon language was dissimilarity to existing natural languages in general, and English in particular. ", "He therefore avoided patterns that are typologically common and deliberately chose features that occur relatively infrequently in human languages. ", "This includes above all the highly asymmetric consonant inventory and the basic word order.", "\n\nSpeakers \nA small number of people are capable of conversing in Klingon. ", "Arika Okrent guessed in her book In the Land of Invented Languages that there might be 20–30 fluent speakers. ", "Its vocabulary, heavily centered on Star Trek–Klingon concepts such as spacecraft or warfare, can sometimes make it cumbersome for everyday use. ", "For instance, while words for transporter ionizer unit (jolvoyʼ) or bridge (of a ship) (meH) have been known since close to the language's inception, the word for bridge in the sense of a crossing over water (QI) was unknown until August 2012. ", "Nonetheless, mundane conversations are possible among skilled speakers.", "\n\nOne Klingon speaker, d'Armond Speers, raised his son Alec to speak Klingon as a first language, whilst the boy's mother communicated with him in English. ", "Alec rarely responded to his father in Klingon, although when he did, his pronunciation was \"excellent\". ", "After Alec's fifth birthday, Speers reported that his son eventually stopped responding to him when spoken to in Klingon as he clearly did not enjoy it, so Speers switched to English.", "\n\nIn 2007, a report surfaced that Multnomah County, Oregon, was hiring Klingon translators for its mental health program in case patients came into a psychiatric hospital speaking nothing but Klingon. ", "Most circulations of the report seemingly implied that this was a problem that health officials faced before; however, the original report indicated that this was just a precaution for a hypothetical and that said translator would only be paid on an as needed basis. ", "After the report was misinterpreted, the County issued another release noting that releasing the original report was a \"mistake\".", "\n\nIn May 2009, Simon & Schuster, in collaboration with Ultralingua Inc., a developer of electronic dictionary applications, announced the release of a suite of electronic Klingon language software for most computer platforms including a dictionary, a phrasebook, and an audio learning tool.", "\n\nIn September 2011, Eurotalk released the \"Learn Klingon\" course in its Talk Now! ", "series. ", "The language is displayed in both Latin and pIqaD fonts, making this the first language course written in pIqaD and approved by CBS and Marc Okrand. ", "It was translated by Jonathan Brown and Okrand and uses the Hol-pIqaD TrueType font.", "\n\nIn August 2016, a company in the United Kingdom, Bidvine, began offering Klingon lessons as one of their services.", "\n\nIn March 2018, the popular language learning site Duolingo opened a beta course in Klingon.", "\n\nThere are Klingon language meetings and linguists or students are interested in researching this topic, even writing essays about the language or its users. ", "In the media (music, literature and television) Klingon is also used frequently as a reference to Star Trek.", "\n\nOther media\n\nIn 2010, a Chicago Theatre company presented a version of Charles Dickens' A Christmas Carol in Klingon language and a Klingon setting. ", "On September 25, 2010, the Washington Shakespeare Company (now known as WSC Avant Bard) performed selections from Hamlet and Much Ado About Nothing in the Klingon language in Arlington, Virginia. ", "The performance was proposed by Okrand in his capacity as chairman of the group's board. ", "This performance was reprised on February 27, 2011 featuring Stephen Fry as the Klingon Osric and was filmed by the BBC as part of a 5-part documentary on language entitled Fry's Planet Word.", "\n\nGoogle Search and Minecraft each have a Klingon language setting.", "\n\nThe 2003–2010 version of the puzzle globe logo of Wikipedia, representing its multilingualism, contained a Klingon character. ", "When updated in 2010, the Klingon character was removed from the logo, and substituted with one from the Ge'ez script. ", "A Klingon language Wikipedia was started in June 2004 at tlh.wikipedia.org. ", "It was permanently locked in August 2005 and moved to Wikia. ", "The Klingon Wiktionary was closed in 2008.", "\n\nThe file management software XYplorer has been translated into Klingon by its developer.", "\n\nMicrosoft's Bing Translator attempts to translate Klingon from and to other languages. ", "It can do a good job with individual words, and with phrases included in its training corpus, but it is not well tuned for Klingon's system of prefixes and suffixes. ", "For example, DaHaDnIS \"You must study it\" is rendered instead as \"They Must Study.\"", "\n\nIn July 2015, when Conservative Welsh Assembly Member Darren Millar formally asked the Welsh Economy Minister Edwina Hart about the Welsh Government's policy funding research into sightings of UFOs at Cardiff Airport, a press officer in the Minister's office issued a written reply in Klingon: jang vIDa je due luq. ", "ʼach ghotvamʼeʼ QIʼyaH-devolved qaS, which was translated as: \"The minister will reply in due course. ", "However this is a non-devolved matter.\"", "\n\nWith the digital only release of Star Trek: Discovery in 2017, streaming service Netflix announced it would provide Klingon subtitles for the entire first season. ", "They can be enabled like any other language provided by the streaming service, and are shown as the phonetic pronunciation rather than Klingon script.", "\n\nLanguage learning applications\nDuolingo features a course for Klingon, which was released on March 15, 2018 and is now in beta testing.", "\nThe Klingon Language Institute provides a Learn Klingon Online series of lessons to its members. ", "The first few lessons are free to sample.", "\n\nCanon\nAn important concept to spoken and written Klingon is canonicity. ", "Only words and grammatical forms introduced by Marc Okrand are considered canonical Klingon by the KLI and most Klingonists. ", "However, as the growing number of speakers employ different strategies to express themselves, it is often unclear as to what level of neologism is permissible. ", "New vocabulary has been collected in a list maintained by the KLI until 2005 and has since then been followed up by Klingon expert Lieven Litaer.", "\n\nInternal history\nWithin the fictional universe of Star Trek, Klingon is derived from the original language spoken by the messianic figure Kahless the Unforgettable, who united the Klingon home-world of QoʼnoS under one empire more than 1500 years ago. ", "Many dialects exist, but the standardized dialect of prestige is almost invariably that of the sitting emperor.", "\n\nSources\nThe Klingon Language Institute regards the following works as canon Klingon; they serve as sources of Klingon vocabulary and grammar for all other works.", "\n\n Books\nThe Klingon Dictionary (TKD)\nThe Klingon Way (TKW)\nKlingon for the Galactic Traveler (KGT)\nSarek, a novel which includes some tlhIngan Hol\nFederation Travel Guide, a pamphlet from Pocketbooks\npaqʼbatlh: The Klingon Epic (), ed. ", "Floris Schönfeld et al., ", "trans. ", "Marc Okrand. ", "Includes the first full edition of the paqʼbatlh and noʼHol fragments.", "\n\n Audio tapes\nConversational Klingon (CK)\nPower Klingon (PK)\nThe Klingon Way (TKW)\n\n Electronic resources\n The Klingon Language Suite, language-learning tools from Ultralingua with Simon & Schuster\n Star Trek: Klingon, a CD-ROM game (KCD, also STK). ", "The CD-ROM includes a Klingon learning module with speech recognition to train the player in Klingon pronunciation; this module was developed by Dragon Systems, Inc. (which is credited on the box and in the CD-ROM) in collaboration with Marc Okrand.", "\n Talk Now! ", "Learn Klingon a beginners' language course for Klingon by Eurotalk and translated by Jonathan Brown (also known as qeʼSan) and Marc Okrand. (", "2011)\n\n Other sources\n certain articles in HolQeD (the journal of the KLI) (HQ)\n certain Skybox Trading Cards (SKY)\n a Star Trek Bird of Prey poster (BoP)\n on-line and in-person text/speech by Marc Okrand (mostly newsgroup postings)\n\nThe letters in parentheses following each item (if any) indicate the acronym of each source - used when quoting canon.", "\n\nPhonology\n\nKlingon has been developed with a phonology that, while based on human natural languages, is intended to sound alien to human ears. ", "When initially developed, Paramount Pictures (owners of the Star Trek franchise) wanted the Klingon language to be guttural and harsh and Okrand wanted it to be unusual, so he selected sounds that combined in ways not generally found in other languages. ", "The effect is mainly achieved by the use of a number of retroflex and uvular consonants in the language's inventory. ", "Klingon has twenty-one consonants and five vowels. ", "Klingon is normally written in a variant of the Latin alphabet. ", "The orthography of this transliteration is case-sensitive, that is, upper and lower case letters are not interchangeable (uppercase letters mostly represent sounds different from those expected by English speakers), although with the exception of Q/q there are no minimal pairs between case. ", "In other words, while \"tlhingan hol\", meaning Klingon language, is incorrect, it cannot be misread as anything but a(n erroneous) form of \"tlhIngan Hol\", but \"Qat\" (be popular) is not the same as \"qat\" (accompany) . ", "In the discussion below, standard Klingon orthography appears in , and the phonemic transcription in the International Phonetic Alphabet is written between /slashes/.\n\nConsonants\nThe inventory of consonants in Klingon is spread over a number of places of articulation. ", "In spite of this, the inventory has many gaps: Klingon has no velar plosives, and only one sibilant fricative. ", "Deliberately, this arrangement is very different from that of most human languages. ", "The combination of an aspirated voiceless alveolar plosive and a voiced retroflex plosive is particularly unusual.", "\n\nThere are a few dialectal pronunciation differences (it is not known if the aforementioned non-canon Kumburan or Rumaiy dialects of tlhIngan Hol hinted at in the third Trek movie's novelization might differ):\n\n In the Krotmag dialect and are realized as nasal stops and \n In the Tak'ev dialect and are pre-nasalized oral stops and \nIn the Morskan dialect:\n is a central affricate \n is realized as glottal syllable-initially and deleted syllable-finally\n is realized as a velar fricative\n\nVowels\nIn contrast to its consonants, Klingon's inventory of vowels is simple, and similar to those of many human languages, such as Spanish or Japanese. ", "There are five vowels spaced more or less evenly around the vowel space, with two back rounded vowels, one back unrounded vowel, and two front or near-front unrounded vowels. ", "The vowel inventory is asymmetrical in that the back rounded vowels are tense and the front vowels are lax.", "\n\nThe two front vowels, and , represent sounds that are found in English, but are more open and lax than a typical English speaker might assume when reading Klingon text written in the Latin alphabet, thus causing the consonants of a word to be more prominent. ", "This enhances the sense that Klingon is a clipped and harsh-sounding language.", "\n\n Vowels\nopen back unrounded vowel (in English spa)\nopen-mid front unrounded vowel (in English bed)\nnear-close near-front unrounded vowel (in English bit)\nclose-mid back rounded vowel (in French eau)\nclose back rounded vowel (in Spanish tu)\n\nDiphthongs can be analyzed phonetically as the combination of the five vowels plus one of the two semivowels and (represented by and , respectively). ", "Thus, the combinations , , , , , , and are possible. ", "There are no words in the Klingon language that contain * or *.", "\n\nSyllable structure\nKlingon follows a strict syllable structure. ", "A syllable must start with a consonant (including the glottal stop) followed by one vowel. ", "In prefixes and rare other syllables, this is enough. ", "More commonly, this consonant-vowel pair is followed by one consonant or one of three biconsonantal codas: /-wʼ -yʼ -rgh/. Thus, ta \"record\", tar \"poison\" and targh \"targ\" (a type of animal) are all legal syllable forms, but *tarD and *ar are not. ", "Despite this, one suffix takes the shape vowel+consonant: the endearment suffix -oy.", "\n\nStress\nIn verbs, the stressed syllable is usually the verbal stem itself, as opposed to a prefix or any suffixes, except when a suffix ending with is separated from the verb by at least one other suffix, in which case the suffix ending in is also stressed. ", "In addition, stress may shift to a suffix that is meant to be emphasized.", "\n\nIn nouns, the final syllable of the stem (the noun itself, excluding any affixes) is stressed. ", "If any syllables ending in are present, the stress shifts to those syllables.", "\n\nThe stress in other words seems to be variable, but this is not a serious issue because most of these words are only one syllable in length. ", "There are some words which should fall under the rules above, but do not, although using the standard rules would still be acceptable.", "\n\nGrammar\n\nKlingon is an agglutinative language, using mainly affixes in order to alter the function or meaning of words. ", "Some nouns have inherently plural forms, such as jengvaʼ \"plate\" (vs. ngop \"plates\"), but most nouns require a suffix to express plurality explicitly. ", "Depending on the type of noun (body part, being capable of using language, or neither) the suffix changes. ", "For beings capable of using language, the suffix is -puʼ, as in tlhInganpuʼ, meaning \"Klingons,\" or jaghpuʼ, meaning \"enemies\". ", "For body parts, the plural suffix is -Duʼ, as in mInDuʼ, \"eyes\". ", "For items that are neither body parts nor capable of speech, the suffix is -mey, such as in Hovmey (\"stars\"), or targhmey (\"targs\") for a Klingon animal somewhat resembling a boar. (", "However, a plural suffix is never obligatory. ", "To say \"The stars are beautiful\", ʼIH Hovmey and ʼIH Hov are equally grammatical, although the second can also mean \"The star is beautiful\".)", "\n\nThe words loD and beʼ, which on their own mean \"man\" and \"woman\" respectively, can be used in compound words to refer to the referent's sex. ", "For example, from puq (\"child\") this process derives puqloD (\"son\") and puqbeʼ (\"daughter\").", "\n\nKlingon nouns take suffixes to indicate grammatical number. ", "There are three noun classes, two levels of deixis, and a possession and syntactic function. ", "In all, twenty-nine noun suffixes from five classes may be employed: jupoypuʼnaʼwIʼvaD \"for my beloved true friends\". ", "A word may carry no more than one suffix from each class, and the classes have a specific order of appearance.", "\n\nVerbs in Klingon take a prefix indicating the number and person of the subject and object, whereas suffixes are taken from nine ordered classes and a special suffix class called rovers. ", "Each of the four known rovers has a unique rule controlling its position among the suffixes in the verb. ", "Verbs are marked for aspect, certainty, predisposition and volition, dynamic, causative, mood, negation, and honorific. ", "The Klingon verb has two moods: indicative and imperative.", "\n\nThe most common word order in Klingon is object–verb–subject, and, in most cases, the word order is the exact reverse of English for an equivalent sentence:\n \n DaH mojaq-mey-vam DI-vuS-nIS-beʼ ʼeʼ vI-Har\n now suffix-PL-DEM 1PL.A.3PL.P-limit-need-NEG that 1SG.A.3SG.P-believe\n \"I believe that we do not need to limit these suffixes now.\"", "\n\n(Hyphens are used in the above only to illustrate the use of affixes. ", "Hyphens are not used in Klingon.)", "\n\nAn important aspect of Klingon grammar is its \"ungrammaticality\". ", "As with for example Japanese, shortening of communicative statements is common, and is called \"Clipped Klingon\" (tlhIngan Hol poD or, more simply, Hol poD) and Ritualized Speech. ", "Clipped Klingon is especially useful in situations where speed is a decisive factor. ", "Grammar is abbreviated, and sentence parts deemed to be superfluous are dropped. ", "Intentional ungrammaticality is widespread, and it takes many forms. ", "It is exemplified by the practice of pabHaʼ, which Marc Okrand translates as \"to misfollow the rules\" or \"to follow the rules wrongly\".", "\n\nWriting systems\n\nWhen written in the Latin alphabet, Klingon is unusual in being case-sensitive, with some letters written in capitals and others in lowercase. ", "In one contrast, q and Q, there is an actual case-sensitive pair representing two different consonants. ", "Capitals are generally reserved for uvular or retroflex consonants pronounced further back in the mouth or throat than is normal for the corresponding English sounds, as with D, Q, and S. However, H, pronounced like the in German \"ach\" or Scottish \"loch\", is further forward in the throat than English /h/. One phoneme, the vowel I, is written capital to look more like the IPA symbol for the sound /ɪ/, and can pose problems when writing Klingon in sans-serif fonts such as Arial, as it looks almost the same as the consonant l.\n\nThis has led some Klingon enthusiasts to write it lowercase like the other vowels (\"i\") to prevent confusion, but this use is non-canonical. ", "Instead, a serif font that clearly distinguishes \"I\" and \"l\", such as Courier or Courier New, has traditionally been employed for writing Klingon in the Latin alphabet. ", "In any case, it can be disambiguated through context, as I never occurs next to another vowel, unlike l. The apostrophe, denoting the glottal stop, is considered a letter, not a punctuation mark.", "\n a b ch D e gh H I j l m n ng o p q Q r S t tlh u v w y ʼ\n\nKlingon is often written in (in-universe, \"transliterated to\") the Latin alphabet as used above, but on the television series, the Klingons use their own alien writing system. ", "In The Klingon Dictionary, this alphabet is named as pIqaD, but no information is given about it. ", "When Klingon symbols are used in Star Trek productions, they are merely decorative graphic elements, designed to emulate real writing and create an appropriate atmosphere. ", "Enthusiasts have settled on the name pIqaD for this writing system.", "\n\nThe Astra Image Corporation designed the symbols currently used to \"write\" Klingon for Star Trek: The Motion Picture, although these symbols are often incorrectly attributed to Michael Okuda. ", "They based the letters on the Klingon battlecruiser hull markings (three letters) first created by Matt Jefferies and on Tibetan writing because the script has sharp letter forms—used as a testament to the Klingons' love for knives and blades.", "\n\nFor April Fools' Day in 2013, Nokia and typography company Dalton Maag claimed to have used \"communication devices to far-flung star systems\" to assist them in localizing the Nokia Pure font to the Klingon writing system. ", "Though the explanation was of course humorous in nature, as part of the practical joke a series of real fonts based upon the most commonly used pIqaD character mapping were in fact developed, and have been made available for free download.", "\n\nVocabulary\nA design principle of the Klingon language is the great degree of lexical-cultural correlation in the vocabulary. ", "For example, there are several words meaning \"to fight\" or \"to clash against,\" each having a different degree of intensity. ", "There is an abundance of words relating to warfare and weaponry and also a great variety of curses (cursing is considered a fine art in Klingon culture). ", "This helps lend a particular character to the language.", "\n\nThere are many in-jokes built into the language. ", "For example, the word for \"pair\" is changʼeng, a reference to the original \"Siamese twins\" Chang and Eng; a guitar is a leSpal (i.e. Les Paul); the word for \"torture\" is joy; \"hangover\" is ʼuH, and the word for \"fish\" is ghotIʼ.\n\nSources for the vocabulary include English (albeit heavily disguised), and also Yiddish: SaʼHut for \"buttocks\" (from תּחת tuches spelled backwards), and ʼoyʼ for \"ache, pain, sore\" (cf. ", "oy vey).", "\n\nMany English words do not have direct translations into Klingon. ", "To express \"hello\", the nearest equivalent is nuqneH, meaning \"What do you want?\", ", "with \"goodbye\" translated as Qapla', \"Success!\".", "\n\nExample sentences\n\ntlhIngan Hol Dajatlhʼaʼ?", "\nDo you speak Klingon?", "\njIyajbeʼ.\nI don't understand.", "\nDochvetlh vISoplaHbeʼ.\nI can't eat that thing.", "\nbIlughbeʼ.\nYou are wrong.", "\nbortaS bIr jabluʼDIʼ reH QaQquʼ nayʼ.\nRevenge is a dish best served cold. (", "lit: When cold revenge is served, the dish is always very good)\nHeghluʼmeH QaQ jajvam.", "\nToday is a good day to die.", "\n\nSee also\n\n Klingon culture\n Klingon grammar\n Stovokor, a death metal band whose lyrics are written in Klingon\n ʼuʼ, the first Klingon opera\n Klingon Christmas Carol, a staged adaptation of Charles Dickens's A Christmas Carol in Klingon\n\nNotes\n\nReferences\nBernard Comrie, 1995, \"The Paleo-Klingon numeral system\". ", "HolQeD 4.4: 6–10.", "\nKlingon ConScript Unicode Registry (CSUR)\npIqaD Support\nKlingon (pIqaD) Unicode font (U+F8D0–U+F8FF)\nKlingon text converter (transliteration)\n\nExternal links\n\n Klingon Language Institute\n Klingonska Akademien\n qepHom Saarbrücken The largest annual Klingon language meeting in Europe\n Klingon Language Wiki Open encyclopedia about the Klingon language\n Klingon and its User: A Sociolinguistic Profile, a sociolinguistics MA thesis\n \n Is Klingon an Ohlonean language? ", "A comparison of Mutsun and Klingon\n Omniglot: Klingon Alphabet\n Eatoni Ergonomics' Klingon page includes BDF, TTF fonts and a Klingon text entry demo\n paqʼbatlh: The Klingon Epic\n Klingon speaking chatbot\n Klingon word list and spell checker\n photo editor translated into Klingon\n\nCategory:Klingon language\nCategory:Agglutinative languages\nCategory:Object–verb–subject languages\nCategory:Constructed languages introduced in the 1970s\nCategory:1979 introductions\nCategory:Star Trek" ]

{ "pile_set_name": "Wikipedia (en)" }

[ 0.025974025974025976, 0.006134969325153374, 0.012345679012345678, 0, 0, 0.013513513513513514, 0.008658008658008658, 0.007936507936507936, 0, 0, 0, 0, 0.010050251256281407, 0.015789473684210527, 0, 0.0040650406504065045, 0.016666666666666666, 0.019230769230769232, 0.01744186046511628, 0.004424778761061947, 0.005698005698005698, 0.013245033112582781, 0.0136986301369863, 0.01773049645390071, 0.01809954751131222, 0.016483516483516484, 0.015625, 0.008264462809917356, 0, 0.00966183574879227, 0, 0, 0, 0, 0, 0, 0.00909090909090909, 0, 0, 0, 0.019230769230769232, 0.009523809523809525, 0.00546448087431694, 0.009950248756218905, 0, 0, 0.010344827586206896, 0.024096385542168676, 0, 0.013422818791946308, 0.011904761904761904, 0.017241379310344827, 0, 0, 0.018518518518518517, 0.019867549668874173, 0.01020408163265306, 0, 0.010471204188481676, 0, 0.015625, 0.01680672268907563, 0.02631578947368421, 0.01639344262295082, 0.023809523809523808, 0.011111111111111112, 0.033707865168539325, 0.006024096385542169, 0, 0.012578616352201259, 0, 0, 0.01818181818181818, 0.006666666666666667, 0.0072992700729927005, 0.02040816326530612, 0, 0.013513513513513514, 0.024, 0, 0.020689655172413793, 0.011811023622047244, 0, 0.012269938650306749, 0.03375527426160337, 0.04, 0, 0.07692307692307693, 0, 0.027888446215139442, 0.008032128514056224, 0, 0.02127659574468085, 0.011363636363636364, 0.006896551724137931, 0.007874015748031496, 0, 0, 0.015625, 0, 0.009216589861751152, 0.0037174721189591076, 0.009009009009009009, 0, 0, 0.007680491551459293, 0, 0, 0.003816793893129771, 0.01282051282051282, 0.0025252525252525255, 0, 0, 0.015151515151515152, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.00819672131147541, 0, 0, 0, 0, 0.01098901098901099, 0, 0.014184397163120567, 0, 0, 0.016129032258064516, 0, 0, 0, 0, 0, 0, 0.017241379310344827, 0.0029154518950437317, 0.013888888888888888, 0, 0, 0.00558659217877095, 0.011764705882352941, 0.012345679012345678, 0, 0.007407407407407408, 0.006172839506172839, 0, 0.008915304606240713, 0.011834319526627219, 0, 0.00847457627118644, 0, 0.011627906976744186, 0, 0.010309278350515464, 0.012345679012345678, 0.017857142857142856, 0, 0, 0, 0, 0, 0, 0.004807692307692308, 0, 0, 0.012048192771084338, 0.020833333333333332, 0.022222222222222223, 0.045454545454545456, 0, 0, 0, 0.013157894736842105, 0, 0, 0.015873015873015872, 0, 0.014989293361884369, 0.01875 ]

[ "Q:\n\nios swift 3 delete contents of each cell when reloading tableView\n\nI am creating a quizApp using DLRadioButton with a label in each cell of tableView, the label is set from the storyBoard(with a tag) but I have set radioButtons programmatically for better design when I click next button to pass to next question new Radiobutton overlaps with the old Radiobutton\nhere is the first question\n\nhere is the second image\n\nBelow is my code\nfunc tableView(_ tableView: UITableView, cellForRowAt indexPath: IndexPath) -> UITableViewCell {\n let cell : UITableViewCell = tableView.dequeueReusableCell(withIdentifier: \"cell\")!", "\n var reponse = rep[(indexPath as NSIndexPath).row]\n\n let content:UILabel=cell.viewWithTag(111) as! ", "UILabel\n //var ra:UIButton=cell.viewWithTag(112) as! ", "UIButton\n\n content.text=reponse[\"rep\"] as? ", "String\n content.sizeToFit()\n let repiii = reponse[\"rep\"] as? ", "String\n\n // var radio = DLRadioButton()\n if (self.type==\"case à cocher\"){\n // cell.contentView.delete(radioButtons)\n let frame = CGRect(x: 50, y: 20, width: 200, height: 40)\n let squareButton = self.createRadioButton(frame: frame, title:repiii!, ", "color: UIColor.red,compt: squareButtons.count,sqaure:1);\n\n squareButtons.append(squareButton)\n cell.contentView.addSubview(squareButton)\n }\n else{\n let frame = CGRect(x: 50, y: 20, width: 200, height: 40)\n\n let radioButton = self.createRadioButton(frame: frame, title:repiii!, ", "color: UIColor.blue,compt: radioButtons.count,sqaure:0);\n\n //radioButton.isMultipleSelectionEnabled = true\n print(radioButtons.count)\n radioButtons.append(radioButton)\n cell.contentView.addSubview(radioButton)\n }\n\n return cell\n}\n\nany suggestion is appreciated\n\nA:\n\nin your code, just after the line\nlet cell : UITableViewCell = tableView.dequeueReusableCell(withIdentifier: \"cell\")!", "\n\nadd this:\nfor subview in cell.contentView.subviews {\n subview.removeFromSuperView()\n}\n\n" ]

{ "pile_set_name": "StackExchange" }

[ 0.00964630225080386, 0.009345794392523364, 0.017857142857142856, 0.021739130434782608, 0, 0.003703703703703704, 0.003205128205128205, 0.002421307506053269, 0 ]

[ "The '80s were a transitional decade for country music: a time when artists could try out different styles and approaches -- and, by extension, adopt new traditions that would come to reverberate in the '90s and beyond." ]

{ "pile_set_name": "Pile-CC" }

[ 0 ]

[ "Twitter Updates\n\nTwitter Updates\n\nMonday, October 01, 2007\n\nXavier Lee becomes the first Seminole this season to take home an ACC Player of the Week honor when he was named co-offensive back of the week on Monday. ", "The redshirt junior QB came off the bench and in the second half rallied the Seminoles to a 21-14 win over No. ", "22 Alabama. ", "The win was FSU's first over a ranked opponent since September 4, 2006\n\n___\n\nJoining Lee as Co-Offensive Player of the Week is Maryland QB Chris Turner. ", "Turner showed impressive poise after entering the game for an injured Jordan Steffy late in the first half against No. ", "10 Rutgers on Saturday. ", "Turner completed 14 of 20 pass attempts for 149 yards, directing four scoring drives and leading the Terrapins back from an 11 point deficit at the half. ", "The 34-24 win gave Maryland its first win over a top 10 team since 2004.", "\n\n___\n\nAgainst Duke on Saturday, Calais Campbell had one of his best games of the season as the Hurricane defense held the Blue Devils to just 61 rushing yards and 14 points on the day. ", "For the game, Campbell totaled eight tackles, including 2.5 sacks, 3.5 tackles for loss and two forced fumbles. ", "He now places seventh in the conference in sacks, fourth in tackles for loss, and is tied for third in fumbles forced." ]

{ "pile_set_name": "Pile-CC" }

[ 0.014018691588785047, 0.009009009009009009, 0, 0.013071895424836602, 0.01680672268907563, 0, 0.012987012987012988, 0, 0.010752688172043012, 0.008928571428571428, 0 ]

[ "Various methods and apparatus for cleaning and sorting culinary items have been proposed heretofore. ", "See for example U.S. Pat. ", "Nos. ", "3,247,858; 3,483,877; and 3,486,939. ", "As pointed out in U.S. Pat. ", "No. ", "3,486,939 most of these prior proposals have had limitations in operational capacity because of the inherent handling time involved in mechanically sensing and sizing the configuration of the object to be sorted or classified. ", "Also, despite the use of various types of automated equipment these prior systems have required the presence of attendants to carry out manual sorting operations or the like.", "\nThe apparatus described in U.S. Pat. ", "No. ", "3,486,939 which is designed to overcome prior limitations on operational capacity and reduce the number of attendants required in the operation, involves separating magnetically responsive chinaware from magnetically responsive silverware by passing the silverware through a grid which retains the chinaware, and then passing the separated items through a number of stations whereby the various articles are classified and isolated from each other. ", "The silverware, for example, is passed through several magnetic stations of different field strengths, the effectiveness of the separations being dependent upon one type of silverware (e.g., spoons) being selectively removed from other magnetically responsive silverware by virtue of the strength of the particular magnetic field through which they pass. ", "Thus for the silverware alone the use of three different magnetic stations of different field strengths is described. ", "In addition, the system involves several operations in which operating personnel participate." ]

{ "pile_set_name": "USPTO Backgrounds" }

[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]

[ "/*\nCopyright (C) 2005-2011 Sergey A. Tachenov\n\nThis program is free software; you can redistribute it and/or modify it\nunder the terms of the GNU Lesser General Public License as published by\nthe Free Software Foundation; either version 2 of the License, or (at\nyour option) any later version.", "\n\nThis program is distributed in the hope that it will be useful, but\nWITHOUT ANY WARRANTY; without even the implied warranty of\nMERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. ", "See the GNU Lesser\nGeneral Public License for more details.", "\n\nYou should have received a copy of the GNU Lesser General Public License\nalong with this program; if not, write to the Free Software Foundation,\nInc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA\n\nSee COPYING file for the full LGPL text.", "\n\nOriginal ZIP package is copyrighted by Gilles Vollant, see\nquazip/(un)zip.h files for details, basically it's zlib license.", "\n*/\n\n#include <QFileInfo>\n\n#include \"quazipnewinfo.h\"\n\nstatic void QuaZipNewInfo_setPermissions(QuaZipNewInfo *info,\n QFile::Permissions perm, bool isDir)\n{\n quint32 uPerm = isDir ? ", "0040000 : 0100000;\n if ((perm & QFile::ReadOwner) !", "= 0)\n uPerm |= 0400;\n if ((perm & QFile::WriteOwner) !", "= 0)\n uPerm |= 0200;\n if ((perm & QFile::ExeOwner) !", "= 0)\n uPerm |= 0100;\n if ((perm & QFile::ReadGroup) !", "= 0)\n uPerm |= 0040;\n if ((perm & QFile::WriteGroup) !", "= 0)\n uPerm |= 0020;\n if ((perm & QFile::ExeGroup) !", "= 0)\n uPerm |= 0010;\n if ((perm & QFile::ReadOther) !", "= 0)\n uPerm |= 0004;\n if ((perm & QFile::WriteOther) !", "= 0)\n uPerm |= 0002;\n if ((perm & QFile::ExeOther) !", "= 0)\n uPerm |= 0001;\n info->externalAttr = (info->externalAttr & ~0xFFFF0000u) | (uPerm << 16);\n}\n\nQuaZipNewInfo::QuaZipNewInfo(const QString& name):\n name(name), dateTime(QDateTime::currentDateTime()), internalAttr(0), externalAttr(0)\n{\n}\n\nQuaZipNewInfo::QuaZipNewInfo(const QString& name, const QString& file):\n name(name), internalAttr(0), externalAttr(0)\n{\n QFileInfo info(file);\n QDateTime lm = info.lastModified();\n if (!", "info.exists()) {\n dateTime = QDateTime::currentDateTime();\n } else {\n dateTime = lm;\n QuaZipNewInfo_setPermissions(this, info.permissions(), info.isDir());\n }\n}\n\nvoid QuaZipNewInfo::setFileDateTime(const QString& file)\n{\n QFileInfo info(file);\n QDateTime lm = info.lastModified();\n if (info.exists())\n dateTime = lm;\n}\n\nvoid QuaZipNewInfo::setFilePermissions(const QString &file)\n{\n QFileInfo info = QFileInfo(file);\n QFile::Permissions perm = info.permissions();\n QuaZipNewInfo_setPermissions(this, perm, info.isDir());\n}\n\nvoid QuaZipNewInfo::setPermissions(QFile::Permissions permissions)\n{\n QuaZipNewInfo_setPermissions(this, permissions, name.endsWith('/'));\n}\n" ]

{ "pile_set_name": "Github" }

[ 0.010238907849829351, 0, 0.01694915254237288, 0.012096774193548387, 0.008, 0.005208333333333333, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.01583710407239819, 0.008645533141210375 ]

[ "(a) v (b) p (c) 0 (d) 2\nc\nLet t be ((-3)/10)/(84/(-11830))*-4. ", "Let n = -169 - t. Which is the closest to n? ", " (a) 5/7 (b) 4/5 (c) 0.3\nc\nLet h be (-3)/(-15) + 2/40. ", "Let y = 1799 - 1801. ", "What is the nearest to h in 2, -1/4, y?", "\n-1/4\nLet u = 61/39 + -74/39. ", "Which is the nearest to 2? ", " (a) u (b) 8 (c) -2\na\nSuppose 0 = -4*r + 8*r + 40. ", "Let j = 6766/9 + -2255/3. ", "Which is the closest to 10? ", " (a) r (b) 1 (c) -4 (d) j\nb\nLet m be 209/(-19) - -158*9/126. ", "Let l = 11 + -6. ", "What is the nearest to 5 in l, 4, m?", "\nl\nLet j = -3.4 - -3. ", "Let m = -9899/29691 - -2/29691. ", "What is the nearest to 3 in j, -1/9, m?", "\n-1/9\nLet w = -1.7935 + 0.1135. ", "What is the closest to 0 in -2/3, 4, -3/4, w?", "\n-2/3\nLet s = 1.5455 - 3.5455. ", "Which is the closest to 0? ", " (a) -2/9 (b) -4 (c) s (d) -5\na\nLet t(n) = -549*n + 5492. ", "Let o be t(10). ", "Which is the nearest to 1/5? ", " (a) 23/5 (b) o (c) -0.2 (d) 10\nc\nLet q = 17353 + -17358. ", "Which is the closest to -1? ", " (a) 1/4 (b) q (c) -27\na\nLet v = 4755.8 - 4756. ", "Let o be (29*(-1)/(-4))/(-1). ", "Let z = 7 + o. Which is the closest to z? ", " (a) 3 (b) -4 (c) v\nc\nLet b = 91 - 314. ", "Let v = -223 - b. What is the nearest to 1 in -0.7, 1, v?", "\n1\nSuppose -u = 3*t - 13, -3*t - 19 = 2*u - 6*t. ", "Let k = -10706 + 10705. ", "Which is the nearest to k? ", " (a) 1 (b) u (c) 0.5 (d) 4/5\nb\nLet x = 0.52 + 0.08. ", "Let c be (8 + -7)*1/3*(1 - 1). ", "What is the closest to 1 in 0.3, x, c?", "\nx\nLet j be (115/35 - 4)*4/10. ", "What is the nearest to 2 in -5, 5, j?", "\nj\nLet q = 2.06593 - 0.06593. ", "What is the nearest to 0.1 in 17, 0, q?", "\n0\nLet k = 1420.5 - 1420.7. ", "Which is the closest to k? ", " (a) 5.1 (b) -4 (c) -4/15\nc\nLet k be -1 + (-10 - (8 - 14)). ", "Let x = -7 + 14. ", "Suppose 3*h - 2*w - 17 = 0, -2*w - 10 = -3*h - x*w. ", "Which is the closest to 1? ", " (a) k (b) h (c) -0.22\nc\nLet i = 280 - 253.6. ", "Let g = i + -23.4. ", "Which is the closest to 0.01? ", " (a) 0.4 (b) g (c) -0.3\nc\nLet o = 9050 - 9054.7. ", "Which is the nearest to 3? ", " (a) 1/2 (b) 2/9 (c) o\na\nLet i = 5195 + -36359/7. ", "Let g be 110/132*4/5. ", "What is the nearest to 0.26 in 2/9, i, g?", "\n2/9\nSuppose -3*i - 8*d = -2, -465*i = -464*i + 3*d + 1. ", "What is the closest to -1/5 in 1, 3, i, -5?", "\n1\nLet x = -31.25 - -31.2. ", "Let d = -160.9 + 161. ", "What is the nearest to d in 0, x, 0.4?", "\n0\nSuppose -19*p - 29 = -10. ", "Let z = 6 - 13. ", "Let f = -0.2005 + 0.0005. ", "Which is the nearest to p? ", " (a) f (b) -3 (c) z\na\nLet g = 46/9 + -40/9. ", "Let k = -12425/8 - -1542. ", "Let h = 95/8 + k. Which is the closest to 1? ", " (a) -1/2 (b) h (c) g\nb\nLet t = 0.054701 - -0.065299. ", "Let p be (4/6)/((-4)/(-3)). ", "Which is the nearest to p? ", " (a) -1 (b) t (c) 3/4\nc\nLet q = -5.1979 + -0.8021. ", "Which is the closest to 1? ", " (a) -0.5 (b) q (c) -0.4 (d) -4\nc\nLet f = 17763 + -17764. ", "Which is the closest to -0.4? ", " (a) -2 (b) -59 (c) 2 (d) f\nd\nLet g = 1/20 + -3/10. ", "Let r = 0 - -0.2. ", "Let x be 84/8 + 26 + -35. ", "Which is the closest to x? ", " (a) 0.4 (b) r (c) g\na\nLet j = 4.324 - 0.024. ", "Let i = 22/4775 - 9704/33425. ", "What is the nearest to 0.1 in j, -2/19, i?", "\n-2/19\nLet m = 4/13 + 5/26. ", "Let u = -0.11697 - -0.41697. ", "What is the closest to 1/3 in 8/7, u, m?", "\nu\nLet p(o) = -o - 14. ", "Let r be p(-18). ", "Let i be 2 + -7 + r/2. ", "Let z be 1/(0 + 3 - (i + 4)). ", "What is the closest to 0 in z, -2, -1?", "\nz\nLet n = -22/85 + 20/51. ", "What is the nearest to 4/13 in -2.2, 0.8, -1/3, n?", "\nn\nLet w = -13.2 + 15. ", "Let m = 0.198 - 2.098. ", "Let v = w + m. Which is the closest to v? ", " (a) -14 (b) 5 (c) -2/5\nc\nSuppose -91 - 39 = -26*q. ", "What is the closest to 11 in 0.3, -2/7, -7, q?", "\nq\nLet s = -99.915648 + 0.029648. ", "Let j = s - 0.314. ", "Let q = j - -100. ", "Which is the nearest to 0? ", " (a) q (b) -0.4 (c) -3\na\nLet j be 12/(-54) + 56/9. ", "Let r be (-1)/3*j/(-18). ", "Let i = 1129 + -1129.03. ", "Which is the closest to 0.1? ", " (a) i (b) 2 (c) r\nc\nLet z = 14878855813/8988 + -9932479/6. ", "Let t = -2/749 + z. Which is the nearest to 1? ", " (a) 4 (b) 5 (c) t\nc\nLet g = 0 - 1. ", "Suppose -21*z + 26*z + 2*f = 1, -4*z - f + 5 = 0. ", "Which is the closest to g? ", " (a) -0.03 (b) z (c) 0.3\na\nLet p = 4.32 + -1.07. ", "Let f = p + -2.25. ", "Suppose 3*y + 3*k - 6 = 0, 0*k - 22 = -4*y + 3*k. ", "Which is the closest to -2/5? ", " (a) f (b) y (c) 0\nc\nLet r be 3/7 - (-5334)/(-29106). ", "Let b = -4/99 - r. Let j = -329/6 - -55. ", "What is the closest to -2 in b, j, 0.5?", "\nb\nLet k = 17.8 + -18. ", "Let y = -89.1 + 89. ", "Let g = -1 - -1.2. ", "Which is the nearest to y? ", " (a) g (b) -1/4 (c) k\nc\nLet q = -49 - -33. ", "Let k(v) = v**2 + 16*v + 2. ", "Let z be k(q). ", "What is the closest to 0.1 in z, 1/4, -1/21?", "\n-1/21\nLet o = 65.4 + -65.6. ", "Which is the nearest to o? ", " (a) -5 (b) -2/5 (c) 89\nb\nLet b be -5 + -2 - (0 - -12)*2600/(-4576). ", "What is the closest to 1/4 in 1/6, b, -2?", "\n1/6\nLet n = -3488 - -3491. ", "What is the closest to n in -3, -1, -5, 4?", "\n4\nSuppose 0 = -p + o - 2, 2*p + 20 = -4*o + 22. ", "What is the closest to p in -0.48, -1, 0.8?", "\n-1\nLet q = -11 + -6.7. ", "Let d = -13.7 - q. What is the nearest to 0 in -5, -0.051, d?", "\n-0.051\nSuppose 1131*l - 1160*l = 0. ", "Which is the closest to l? ", " (a) -2 (b) -42/13 (c) -0.03\nc\nLet w be 6*16/192*-2. ", "Let r = -0.2 - -0.5. ", "What is the closest to 39 in r, w, 2?", "\n2\nLet j = -3980 + 19898/5. ", "Let r = 8.15 + -0.15. ", "Let s = 7.9 - r. Which is the closest to 0.1? ", " (a) s (b) -3 (c) j\na\nLet v be ((-1281)/33)/(-1) + ((-720)/(-88) - 8). ", "Which is the closest to 2/5? ", " (a) -9 (b) v (c) -6/5\nc\nLet i = -124 - -156. ", "Let y = i - 28. ", "Which is the closest to y? ", " (a) -4 (b) -1/15 (c) 0.4\nc\nLet a = -298.99 - -298.69. ", "What is the closest to 2/7 in -0.34, a, -0.06, 1/5?", "\n1/5\nLet k = 81086/155 - 2616/5. ", "What is the nearest to k in -1, 0, 1/3?", "\n0\nLet l = -8.99 - -8.89. ", "What is the nearest to l in 4/3, 3/5, -4, 5?", "\n3/5\nLet r(o) = o**2 - 7*o + 6. ", "Let n be r(2). ", "Let i be 8/(-3) - 6/n*2. ", "Let y = -145 - -146. ", "Which is the closest to y? ", " (a) i (b) -6/11 (c) -0.4\na\nLet p be -4 + 5 + (-3)/(9/65). ", "Let y = -493/24 - p. Let o = 116.7 - 117. ", "Which is the closest to 1? ", " (a) 2/9 (b) y (c) o\na\nLet f = 2397 - 2396.9. ", "What is the nearest to -0.383 in 0.3, -1, f?", "\nf\nSuppose 16*z = 61*z. ", "Let d = -19 + 18. ", "Which is the closest to d? ", " (a) -1/2 (b) -1/47 (c) z\na\nLet g be (-960)/112 + 8 + 1. ", "Let n = 0.58 - 0.58. ", "Which is the nearest to 1? ", " (a) n (b) 10 (c) g\nc\nLet u = 5.82 + -10.58. ", "Let z = u - -4.26. ", "What is the closest to 35 in z, -2/17, -5?", "\n-2/17\nLet n = 28348 - 28349. ", "What is the nearest to -0.2 in 0.3, -2, -1/2, n?", "\n-1/2\nSuppose 19*p - g - 15 = 22*p, 2*g = -5*p - 25. ", "Let k = -8 - -5. ", "Which is the nearest to -1? ", " (a) 4 (b) p (c) k\nc\nLet u be ((-4)/((-48)/15))/(10/(-40)). ", "Which is the nearest to -1/19? ", " (a) -6 (b) -1/2 (c) u\nb\nSuppose -2*c - 15 = 7*h - 8, h = -4*c - 1. ", "What is the nearest to -0.8 in h, 4, -0.1, 2/7?", "\nh\nLet k = -43 - -43.073. ", "Let z = -0.327 - k. Let u = 3.6 + -3.6. ", "Which is the closest to u? ", " (a) -3/5 (b) 20 (c) z\nc\nLet h = 1053 - 780. ", "Let p = 272.9 - h. Which is the closest to p? ", " (a) -4 (b) -42 (c) -0.5 (d) -0.4\nd\nLet q = 57/49 + -611/441. ", "Which is the nearest to 1? ", " (a) -0.2 (b) q (c) 0.5 (d) -2\nc\nLet v = -0.184 + -0.016. ", "Let o = 304 + -300. ", "Which is the closest to v? ", " (a) 2/13 (b) o (c) -3 (d) -2/13\nd\nLet v = 77 - 33. ", "Suppose -j - 3*j = 2*x + 40, 2*j - 5*x + v = 0. ", "Let w be ((8/j)/2)/((-15)/(-18)). ", "Which is the nearest to -0.3? ", " (a) w (b) 6 (c) 5\na\nLet u be 7 - (2200/330 + 2/10). ", "Which is the closest to 0? ", " (a) -3 (b) -82 (c) u (d) -0.4\nc\nLet b = -99808/15 - -6654. ", "What is the closest to -0.5 in 2.6, b, -0.1, 0.4?", "\n-0.1\nLet l = -368.2 + 393.2. ", "What is the closest to l in -5, -2/13, -0.15?", "\n-0.15\nLet x = 3552 - 3551.6. ", "What is the closest to 10 in -1/7, 128, x?", "\nx\nLet z = 0.0045 - -363.9955. ", "Let k = 364 - z. What is the nearest to 10 in k, -1, -2?", "\nk\nLet q = 1.69 + -27.49. ", "Let g = 5.2 - q. Let y = 34 - g. What is the closest to y in 3, 0.3, 3/4?", "\n3\nLet n = 0.181 + 0.069. ", "Let s = -0.71 + n. Let j = s + 0.26. ", "What is the nearest to -0.1 in -0.9, 4, j?", "\nj\nLet f = -369/7 - -53. ", "Let l = 1.82 + -4.82. ", "Which is the closest to -1? ", " (a) f (b) 5 (c) l\na\nLet y = 240.8 - 246. ", "Let g = y - -6.3. ", "What is the nearest to g in -3/2, -0.3, -4?", "\n-0.3\nLet q = 6.769 - 1.769. ", "Let x = 5 + -8. ", "Let b be 1*3*1/(-3). ", "What is the closest to b in q, x, 0.5?", "\n0.5\nLet x = -0.3362 + 1.3362. ", "What is the nearest to 1/5 in -4, 15, x?", "\nx\nLet u be 2/(-3 + (-15)/(-6)). ", "Let n = u + 15/4. ", "Let w = 277 + -276.8. ", "Which is the nearest to 2/3? ", " (a) w " ]

{ "pile_set_name": "DM Mathematics" }

[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.022222222222222223, 0, 0, 0, 0, 0, 0, 0.03571428571428571, 0.02, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.016129032258064516, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.037037037037037035, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.018867924528301886, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.02631578947368421, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.047619047619047616, 0, 0.023255813953488372, 0.041666666666666664, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.02564102564102564, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.022727272727272728, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.03333333333333333, 0, 0, 0, 0.03571428571428571, 0, 0, 0.014285714285714285, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.029411764705882353, 0, 0, 0, 0, 0, 0, 0, 0.03333333333333333, 0, 0, 0.017857142857142856, 0, 0, 0, 0, 0, 0, 0, 0.03571428571428571, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]

[ "Yarygino\n\nYarygino () is the name of several rural localities in Russia:\nYarygino, Kursk Oblast, a selo in Yaryginsky Selsoviet of Pristensky District of Kursk Oblast\nYarygino, Moscow Oblast, a village in Vasilyevskoye Rural Settlement of Sergiyevo-Posadsky District of Moscow Oblast\nYarygino, Oryol Oblast, a village in Otradinsky Selsoviet of Mtsensky District of Oryol Oblast\nYarygino, Perm Krai, a village in Kungursky District of Perm Krai\nYarygino, Ryazan Oblast, a village in Bulgakovsky Rural Okrug of Kasimovsky District of Ryazan Oblast\nYarygino, Smolensk Oblast, a village in Subbotnikovskoye Rural Settlement of Sychyovsky District of Smolensk Oblast\nYarygino, Syamzhensky District, Vologda Oblast, a village in Zhityevsky Selsoviet of Syamzhensky District of Vologda Oblast\nYarygino, Tarnogsky District, Vologda Oblast, a village in Shebengsky Selsoviet of Tarnogsky District of Vologda Oblast\nYarygino, Velikoustyugsky District, Vologda Oblast, a village in Pokrovsky Selsoviet of Velikoustyugsky District of Vologda Oblast\nYarygino, Vologodsky District, Vologda Oblast, a village in Semenkovsky Selsoviet of Vologodsky District of Vologda Oblast\nYarygino, Yaroslavl Oblast, a village in Lyubimsky Rural Okrug of Lyubimsky District of Yaroslavl Oblast" ]

{ "pile_set_name": "Wikipedia (en)" }

[ 0.015810276679841896 ]

[ "We Do Things Differently\n\nAt ROCK IT Recycling we recycle technology equipment in line with WEEE Directives. ", "We provide data erasing services that meet the highest recognized standards in the UK, namely CESG; however from this point onwards ROCK IT is different.", "\n\nROCK IT is structured as a Community Interest Company (CIC). ", "The income generated by ROCK IT through WEEE services and donations is almost exclusively used to support employment and skills training for young people who are not in education, employment or training (NEET).", "\n\nWe are all about ‘Corporate Social Responsibility’ and helping you benefit from our activities.", "\n\nWe help businesses meet their Corporate Social Responsibility goals\n\nAt ROCK IT Recycling we process IT equipment in line with the WEEE Directive. ", "All our commercial services meet Government standards and our team deliver first-class customer service.", "\n\nSussex businesses can make a positive environmental impact by supporting sustainable recycling initiatives.", "\n\nWe offer a range of eco-friendly services, including data destruction and mobile shredding.", "\n\nOur aim is to help businesses across the South East of England with their corporate social responsibility objectives.", "\n\nWe intend to help businesses to recycle their obsolete or unwanted IT equipment. ", "We deliver sustainable solutions and guarantee full compliance with data security and environmental legislation. ", "Ensuring any data held on IT equipment is securely disposed of.", "\n\nAll the equipment we handle is securely disposed of through an environmentally responsible process.", "\n\nROCK IT Recycling believes in making a better future\n\nThere is a growing issue with unemployment in the UK, especially for those without formal qualifications or training. ", "Here at ROCK IT we are committed to supporting people by offering job opportunities through our apprenticeship scheme. ", "This provides people with the skill-set and work experience they need to help them build a better future for themselves.", "\n\nOur mission is to give back to communities through donating IT equipment to charities, schools and vulnerable people.", "\n\nOur work continues to promote a positive environmental message to businesses across Southern England, informing people that they do have an opportunity to make a difference by reducing waste that would otherwise go to landfill.", "\n\nWe all acknowledge there is a growing issue with youth unemployment, especially for those without any formal qualifications or training, and who find it difficult to see a worthwhile future.", "\n\nNo one person or organisation can resolve such matters, but working with ROCK IT you can help us play our part in a brighter future." ]

{ "pile_set_name": "Pile-CC" }

[ 0.009174311926605505, 0, 0.031746031746031744, 0, 0.010309278350515464, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]

[ "Introduction\n============\n\nA key objective of wildlife research is to determine how demographic parameters change over space and time. ", "Understanding reproduction, survival, and dispersal of animals is necessary to determine the status and viability of populations, and to identify critical or sensitive portions of a population. ", "These vital rate estimates can then be used to parameterize matrix models, or more complicated life cycle-based models, to assess whether populations are declining and determine the life stages that have the greatest influences on population growth rates and are thus most sensitive to change (Caswell [@b7]; Barker et al. [", "@b3]). ", "In an applied context, this information can help researchers and wildlife managers to determine optimal approaches for management and conservation activities including the life stages and demographic rates to target, when action is warranted (Williams et al. [", "@b49]).", "\n\nEstimating demographic parameters requires years of intensive data collection, most commonly through capture--recapture methods (Williams et al. [", "@b49]). ", "Capture--recapture models have a long history in ecology, starting with the Lincoln--Petersen model (Pollock [@b29]; Nichols [@b24]), which provided the first method for estimating population abundance, and the Cormack--Jolly--Seber (Cormack [@b10]; Jolly [@b18]; Seber [@b43]) models, which introduced approaches for estimating apparent survival (Lebreton et al. [", "@b22]) and immigration. ", "Since that time, a number of models have been developed to improve upon inferences from capture--recapture techniques by accounting for individual heterogeneity (e.g., Burnham and Overton [@b6]; Pledger et al. [", "@b27]; Royle [@b36]; Gimenez and Choquet [@b14]; Cubaynes et al. [", "@b11]). ", "The multistate models were developed to estimate state-specific demographic rates with the assumption that life stage (and sex) frequently influences survival, reproductive, and dispersal probabilities (Arnason [@b2];: Nichols et al. [", "@b25]; Schwarz et al. [", "@b42]; Nichols et al. [", "@b26]; Lebreton and Pradel [@b21]). ", "The continued relevance of capture--recapture methodologies has led to a host of recent advances, including those focused on spatially explicit methods (Efford et al. [", "@b13]; Royle et al. [", "@b37]), state misclassification (Kendall et al. [", "@b20]), state uncertainty (Pradel [@b32]), disease dynamics (Conn and Cooch [@b9]), density dependence (Lebreton & Gimenez [@b100]), and the incorporation of telemetry data (Powell et al. [", "@b31]; Sollmann et al. [", "@b47]) as well as other auxiliary information (Pollock [@b30]).", "\n\nWhile capture--recapture is the most direct way to attain detailed demographic information, these data can be expensive to collect and challenging to obtain at large spatial scales (Williams et al. [", "@b49]). ", "Many capture--recapture surveys are therefore limited to a small number of locations, often providing information for just one species in a single region. ", "As the pressure on wildlife populations increases, inexpensive and efficient approaches for estimating demographic rates that can be applied at large spatial and temporal scales are needed.", "\n\nWe build on N-mixture models (Royle [@b35]) to demonstrate an approach for estimating demographic rates using only state-structured count data while accounting for the imperfect detection of individuals during sampling. ", "Our framework is based on the open population extension of the N-mixture model by Dail and Madsen ([@b12]), which models abundance by separately accounting for apparent survival and population growth (reproduction and immigration) from count data over time. ", "Zipkin et al. ([", "@b50]) extended the Dail and Madsen ([@b12]) model to obtain estimates of state-specific survivorship, immigration, and recruitment using only count data where individuals can be appropriately identified as belonging to one of a number of discrete states. ", "Here, we expand this approach to incorporate data where the state is uncertain and apply our model to estimate sex-and (life) stage-specific survival as well as density-dependent recruitment rates for a population of black-throated blue warblers (*Setophaga caerulescens*). ", "We use data collected on breeding grounds in the Hubbard Brook Experimental Forest in New Hampshire, USA. ", "This warbler population has been studied extensively and, as a result, detailed information is available from capture--capture data (Sillett and Holmes [@b44]; Holmes [@b16]; Townsend et al. [", "@b48]), which we use for comparison.", "\n\nMaterials and Methods\n=====================\n\nStudy system\n------------\n\nLong-term demographic data on black-throated blue warblers were collected in the Hubbard Brook Experimental Forest, New Hampshire, U.S.A. (43°56′, 71°45′). ", "This 3160 ha forest is part of the 3039 km^2^ White Mountain National Forest and is comprised of unmanaged, relatively mature, second-growth northern hardwood (Holmes [@b17]). ", "Black-throated blue warblers, a sexually dichromatic passerine, were studied on three plots: from 1986 to 2010, a 65 ha, middle elevation site at 600 m above sea level, and from 1997 to 2010, a 85 ha low elevation site at 250--400 m, and a 35 ha high elevation site at 700--850 m above sea level. ", "The three plots were separated from one another by at least 500 m. Habitat quality and warbler density increases with elevation at Hubbard Brook (Rodenhouse et al. [", "@b34]) such that the three plots were designed to contain roughly the same number of warbler pairs. ", "Adult warblers were captured with mist nets and uniquely marked with colored leg rings. ", "Birds were aged using plumage characteristics (Pyle [@b33]) as either yearlings in their first breeding season or older adults. ", "Warbler territories were visited every two days to resight individuals and to monitor breeding activity. ", "A small number of birds eluded capture throughout the breeding season in some years. ", "In such cases, unmarked males were aged by visual observation of plumage characters (Graves [@b15]) when possible; unmarked females were not aged. ", "Further details about field methods are provided in Sillett and Holmes ([@b44], [@b45]) and Townsend et al. ([", "@b48]).", "\n\nWe collapsed this detailed capture--recapture dataset into stage-and sex-specific counts per year. ", "We included the counts of individuals that were observed but not captured, such that we had the total annual count (e.g., number of unique individuals observed at least once from May to August in a given year) for six groups: yearling (age one) males, yearling females, adult (age two and older) males, adult females, males of unknown age, and females of unknown age. ", "The number of males and females where age was unknown comprised a small portion of the data (\\<1% of males and 8% of females).", "\n\nPopulation model\n----------------\n\nOur model builds on Zipkin et al. ([", "@b50]), which demonstrates how state-specific demographic rates and abundance can be estimated from multistate count data. ", "For the black-throated blue warbler population, our interest lies in estimating the stage-(yearling or adult) and sex-specific survival rates and the annual number of yearlings and adults that recruit to the population. ", "We do this by assuming that abundance, *N*~*i,j,t*~, of each state *i* at plot *j* in year *t* is dependent only on abundance of the local population in the previous year, *t*−1. ", "Thus, we assume that dynamics in the three plots (high, middle, and low elevation) are independent of one another. ", "We define four states of the warbler population (Fig.", " [1](#fig01){ref-type=\"fig\"}): yearling males (*i *=* *1), yearling females (*i *=* *2), adult males (*i *=* *3), and adult females (*i *=* *4). ", "Because we have no information prior to the first year of sampling, we model abundance for each state in year *t *=* *1 as *N*~*i,j*,1~ ˜ Pois (*λ*~i~), where *λ*~i~ is the expected abundance of each state *i*, which we assume to be constant across the three plots. ", "For all other years of sampling (*t* ≥ 2), we model abundance by considering (1) the annual number of individuals that survive (*S*) and return to the plot after migrating south for the winter and (2) the new individuals that are gained (*G*) to plots through reproduction or immigration, which is assumed to be a density-dependent process based on local abundance in the previous year. ", "The number of surviving individuals, *S*~*i,j,t*~, in state *i* at time *t* at plot *j* is modeled as:\n\n{#fig01}\n\nwhere *ω*~*i*~ is the survival probability for each of the four *i* states. ", "To model the annual number gained at each plot, we considered the natural history of this population. ", "Individuals that fledge from these plots rarely return to the exact same plot; thus, yearlings that create breeding territories in each of the *j* plots are technically immigrants, at least on this very local scale (Sillett and Holmes [@b45]). ", "Fecundity (number of fledglings produced) and interannual variations in population abundance are density dependent, and yearlings are more likely to shift territory locations compared with adults (Rodenhouse et al. [", "@b34]). ", "As such, we assumed that the number of individuals gained annually, *G*~*i,j,t*~ is a density-dependent recruitment process that is the same for both sexes but possibly different for yearlings and adults where\n\n*N*~total,*j,t*−1~ is the total population size of all stages combined at plot *j* in year *t*−1, *γ*~1~ and *γ*~2~ are the per capita recruitment/immigration rates of yearlings and adults, and *K* (which is constant for all plots but could vary by year or plot if the quantity of data is sufficient) is the carrying capacity for each plot (Fig.", " [1](#fig01){ref-type=\"fig\"}). ", "Thus, *γ*~1~·*N*~total~ and *γ*~2~·*N*~total~ are the expected number of yearlings and immigrating adults that enter the plot when the population is at carrying capacity, *K*. ", "The annual state-specific abundances, *N*~*i,j,t*~, for *t* ≥ 2 are then:\n\nDetection model: imperfect observation of state\n-----------------------------------------------\n\nWe incorporated an additional component in this model to account for the fact that each of the *N*~*i,j,t*~ is detected imperfectly during the sampling process. ", "As described above, our data, *n*~*i,j,t*~, arise from six states: the four states described in the model as well as males of unknown age (*i *=* *5) and females of unknown age (*i* = 6). ", "We thus have two processes affecting the data recorded during sampling: the probability of detecting an individual and the probability of correctly classifying its state (conditional on detection). ", "We specified the detection processes separately for males and females based on the results of Sillett and Holmes ([@b44]), which suggest that detection may vary by sex. ", "Let *p*~1~ be the probability of detecting a male and *c*~1~ be the probability of being able to correctly classify that individual as either a yearling or an adult. ", "Then, the detection model for the male states can be specified for plot *j* in time *t* and repeated measure *k* as:\n\nAn analogous model is used for the female states where *p*~2~ is the detection probability of females and *c*~2~ is the probability of being able to classify the stage of that individual. ", "This model implicitly assumes that errors in the detection process arise only from a failure to detect individuals (e.g., no false positives or misclassifation of sex). ", "In our model, there is only one sampling event (*k *=* *1), but the same approach can be used when *k *\\>* *1.", "\n\nModel analysis\n--------------\n\nWe used Bayesian inference and MCMC as implemented in R and JAGS (Plummer [@b28]) to simulate posterior distributions of parameters. ", "For the process model, we set vague priors for survivorship, *ω*~*i*~ ˜ Uniform (0,1), per capita recruitment/immigration, *γ*~1,2~ ˜ Uniform (0,30), initial state-specific abundance, *λ*~*i*~ ˜ Uniform (0,30), and carrying capacity, *K* ˜ Uniform (0,150). ", "The upper bounds for *γ*, *λ*, and *K* parameters were well above biologically reasonable values. ", "For the detection model, we only had data from a single annual survey event, which represented the total number of observed individuals within states for each breeding season. ", "Although estimating a detection probability for an open population is possible with only one survey replicate over 25 years of data (Dail and Madsen [@b12]), the simulation results in Zipkin et al. ([", "@b50]) suggest that the limited number of plots in our study could lead to imprecise parameter estimates. ", "Therefore, we used informative priors on the detection probabilities of males, *p*~1~ ˜ Normal (0.926, 0.034)T(0,1), and females *p*~2~ ˜ Normal (0.869, 0.061)T(0,1), taken from annual detection/capture probabilities (mean and standard deviation) in Sillett and Holmes ([@b44]) derived using a Cormack--Jolly--Seber model (CJS) on a subset of these data on the mid-elevation plot from 1986 to 1999. ", "T(0,1) indicates that the distribution is truncated so that detection cannot be below zero or above one. ", "We set vague priors on both the male and female classification parameters where *c* ˜ Uniform (0,1). ", "We generated three Markov chains, each consisting of 20,000 iterations after a burn-in of 20,000 iterations, and we saved every 10th sample, such that we obtained 6000 posterior samples for each parameter. ", "We checked convergence by examining plots of the posterior distributions and the variance within and between chains to ensure that the Brooks--Gelman--Rubin diagnostic (i.e., statistic) was \\<1.05 for all parameters.", "\n\nResults\n=======\n\nSome parameter estimates produced by the state-structured model, such as those related to fecundity and carrying capacity, were consistent with capture--recapture studies as well as to inferences from other black-throated blue warblers studies in the region (Fig.", " [2](#fig02){ref-type=\"fig\"}), whereas other parameter estimates, such as survival, were less consistent (Fig.", " [3](#fig03){ref-type=\"fig\"}). ", "The carrying capacity, *K*, of the plots had a median value of 58.7 warblers (95% confidence interval, CI: 45.4--75.4). ", "This is consistent with estimates in Rodenhouse et al. ([", "@b34]; Fig.", " [1](#fig01){ref-type=\"fig\"}) showing that population growth rate is near zero when density of adults was around 10--11 breeding individuals per 10 hectare, which translates to 62.5--71.5 individuals on our middle elevation -- and medium habitat quality -- plot. ", "Although directly comparing the per capita rate of yearling recruitment from our model (top panels of Fig.", " [2](#fig02){ref-type=\"fig\"}) with available estimates of fecundity (e.g., young fledged per breeding pair) is difficult, these results are consistent in the negative impact of high density (Sillett and Holmes [@b45]). ", "Our estimates of *γ*~1~ (median: 0.16; 95% CI: 0.13--0.20) suggest that a breeding pair produces about 0.64 yearlings when the population is at carrying capacity (e.g., per capita recruitment of both male and female yearlings at *K* is 2*γ*~1~ and thus per capita recruitment per breeding pair is 4*γ*~1~). ", "Rodenhouse et al. ([", "@b34]; Fig.", " [2](#fig02){ref-type=\"fig\"}) estimated that approximately 2 fledglings were produced per breeding pair at similar densities (10 breeding individuals per 10 hectares). ", "This would indicate that approximately one-third of individuals survive from fledging to their first breeding season, similar to the 0.3 value that Sillett and Holmes ([@b45]) used to approximate observed warbler dynamics. ", "At carrying capacity, the expected number of yearlings (male and female) recruiting to a plot is approximately 18.8 (2*γ*~1~ · *K*), again similar to Sillett et al. ([", "@b46]) who showed that the number of yearling males entering a plot ranged from 2 to 14 based on the previous year\\'s fecundity (i.e., assuming an equal sex ratio, we would expect about 4--28 total yearlings annually). ", "Adult immigration at carrying capacity was approximately 12.2 individuals (2*γ*~2~ · *K*; *γ*~2~ median: 0.10, 95% CI: 0.06--0.15). ", "The recruitment rates of yearlings and adults suggest that more yearlings move into the plots than immigrating adults, which is consistent with existing knowledge of the system (Rodenhouse et al. [", "@b34]). ", "The temporal patterns of abundance as estimated in our model were consistent with those produced using territory maps and tended to capture observed variations well (Fig.", " [2](#fig02){ref-type=\"fig\"}).", "\n\n{#fig02}\n\n{#fig03}\n\nEstimates of sex-and stage-specific survival from our model (Fig.", " [3](#fig03){ref-type=\"fig\"}) were lower and had larger confidence intervals than those estimated using the complete capture--recapture information. ", "The 95% confidence intervals for yearling females (*ω*~2~ median: 0.25, 95% CI: 0.04--0.49) and adult females (*ω*~4~ median: 0.27, 95% CI: 0.06--0.49) contained the values produced using a Jolly--Seber model of the capture--recapture data over the same time period (0.42 \\[SE: 0.04\\] for yearling and 0.46 \\[SE: 0.02\\] for adult females). ", "However, survival estimates for males were more severely underestimated, with the 95% CI of yearling (*ω*~1~ median: 0.19, 95% CI: 0.04--0.35) and adult (*ω*~3~ median: 0.19, 95% CI: 0.01--0.41) survivorships not containing the capture--recapture estimates (0.50 \\[SE: 0.03\\] for yearling and 0.51 \\[SE: 0.02\\] for adult males). ", "The low rates of survival combined with the overestimation of adult immigration suggest that our model may have had difficulty distinguishing between these two processes for this dataset.", "\n\nThe posterior distribution for the probability of male detection (*p*~1~ median: 0.89; 95% CI: 0.83--0.96) was slightly lower, but still similar to its prior; the posterior distribution for the detection probability of females (*p*~2~ median: 0.75; 95% CI: 0.68--0.83) was more diffuse and lower than the prior (Fig.", " [3](#fig03){ref-type=\"fig\"}). ", "This result may not be surprising because the data include individuals of unknown age (*i *=* *5,6) that could not be included for capture--recapture analysis, and more of those individuals are female than male (8% compared with less than 1%). ", "Estimates for classification probabilities were quite high for both males (95% CI: 0.98--1.0) and females (95% CI: 0.90--0.94), with males having a slightly higher probability of correct classification (Fig.", " [3](#fig03){ref-type=\"fig\"}). ", "This is consistent with our expectation, given that noncaptured females cannot be accurately aged by visual observations (T. S. Sillett, pers. ", "obs.).", "\n\nDiscussion\n==========\n\nThe state-structured models developed in Zipkin et al. ([", "@b50]) and presented in this article represent an extension of the Dail and Madsen ([@b12]) open population model as well as an extension of multistate models to populations for which data on individual encounter histories are not available (Table [1](#tbl1){ref-type=\"table\"}). ", "Link et al. ([", "@b23]) developed a similar age-structured approach for estimating demographic rates from aggregate count data. ", "As with our approach, their method assumed a first-order Markovian structure to estimate annual age-specific survival probabilities in a population of whooping cranes. ", "In their case, whooping cranes were censused implying that there were no omissions during the sampling process and that detection probabilities did not need to be incorporated. ", "To our knowledge, all other multistate models in the literature were developed for use in marked populations. ", "Our state-structured model, which requires only count data, provides an inexpensive method for obtaining inferences on state-specific demographic rates, while accounting for imperfect detection. ", "The relative ease of collecting count data suggests that our modeling framework could be applied on broader spatial scales than is possible with intensive capture--recapture techniques. ", "However, the approach can have drawbacks in that estimates of demographic rates and population abundance could be inaccurate and/or imprecise if data are limited. ", "For example, Zipkin et al. ([", "@b50]) conducted a number of simulations for a theoretical two-stage population and found that estimates of recruitment were biased low while estimates of juvenile survivorship were biased high when only two years of data were available even with a large numbers of sampling locations (e.g., 100 sites). ", "Yet, their simulation results also demonstrated that median parameter estimates were unbiased when 20 years of data were available at only five locations. ", "In that scenario, precision on all parameters was improved with three sampling replicates as compared to only one. ", "These results indicate that parameter estimates can be improved by increasing the length of the time series and the number of replicate surveys, and not necessarily by the addition of more sampling locations. ", "This suggests that our 25 years of black-throated blue warbler data should be adequate for inference even though the number of sampling plots was limited.", "\n\n###### \n\nData structures and possible population models used to estimate abundance and demographic rates (in some cases) for instances where samples consist of live individuals.", "\n\n Data structure Population (stage/class) structure \n ---------------------- ------------------------------------------------------ ----------------------------------------------------------------------------\n Marked individuals Jolly--Seber models and Cormack--Jolly--Seber models Multistate models\n (Cormack [@b10]; Jolly [@b18]; Seber [@b43]) (Nichols et al. [", "@b25]; Schwarz et al. [", "@b42]; Lebreton and Pradel [@b21])\n Unmarked individuals N-mixture models State-structured open population N-mixture models\n (Royle [@b35]; Dail and Madsen [@b12]) (Zipkin et al. [", "@b50]; model presented in this article)\n\nTo improve our results and because the information was available, we included strong priors on detection probabilities. ", "As expected, parameter estimates were much more imprecise when the model was rerun with an uninformative prior on detection (results not shown) and model runs did not converge well, indicating that the interpretation of our results is sensitive to our decision to use an informative prior. ", "Our model of the black-throated blue warbler population produced less accurate and precise estimates of demographic rates as compared to a similar state-structured model in Zipkin et al. ([", "@b50]) of a northern dusky salamander population. ", "This is likely due to the relatively simple life cycle of these salamanders in which population abundances are largely driven by local dynamics and individuals are fairly sedentary. ", "If movement rates are high, as in our population of warblers (Cline et al. [", "@b8]), then estimates of apparent survival can be confounded with local immigration because individuals are not identifiable. ", "Similarly, black-throated blue warblers have low natal philopatry. ", "Nearly all yearlings that recruited into our study plots were likely fledged outside of the plots such that the population dynamics among sites are not completely independent. ", "Nevertheless, annual fecundity of warblers breeding on our study plots is positively correlated with the number of yearling recruits in the following spring (Sillett et al. [", "@b46]), indicating that demographic variation documented on our Hubbard Brook study plots is representative of breeding season dynamics occurring in the larger White Mountains region of New Hampshire and possibly areas beyond that (Jones et al. [", "@b19]). ", "Our model produced similar patterns of abundance as compared to estimates from territory maps (Fig.", " [2](#fig02){ref-type=\"fig\"}). ", "This suggests that state-structured models derived from count data can be useful for characterizing the general temporal patterns to estimate trends even when it is not possible to estimate all demographic parameters with complete accuracy.", "\n\nDuring development of our black-throated blue warbler model, we considered many forms of density dependence on the number of individuals gained (*G*) to the population. ", "We settled on the model presented here because it represented a biologically plausible description of black-throated blue warblers, demographic parameter estimates were insensitive to choice of priors (on those parameters), and it had the lowest deviance information criterion (DIC = 2119). ", "However, we note that another model which assumed that adult immigration was not density dependent was the second choice (DIC = 2218). ", "In this model, annual survival probabilities were slightly higher (median values: *ω*~1~ = 0.20, *ω*~2~ = 0.29, *ω*~3~ = 0.36, *ω*~4~ = 0.38), carrying capacity was lower (median *K *=* *51.7), and the number of immigrating adults, which was constant, was lower at carrying capacity (expected number of new adults annually: 7.4). ", "The expected number of yearlings to recruit into the population at carry capacity, 18.1 individuals, was quite similar. ", "A comparison of these models indicates that the choice of model structure can play an important role in the interpretation of results and that it can be difficult to distinguish between mechanistic processes when only count data are available. ", "Indeed, parameter estimates produced by open N-mixture models are model-based by definition (Dail and Madsen [@b12]; Zipkin et al. [", "@b50]), and thus, the utility of results depends on how closely the data conform to the parametric assumptions of the model. ", "For example, our model assumes that the number of individuals gained to the population is only dependent upon local abundance in the previous year, but it is quite possible that recruitment is dependent among a number of other factors such as abundance in adjacent locations and/or conditions during winter migration. ", "Parameter estimates could be imprecise or even biased if data do not conform to the assumptions of the model. ", "As such, it is important to consider the major processes governing dynamics within populations and to outline the assumptions made when estimating quantities from state-structured count data. ", "Similarly, parameter identifiability should be explored during model development. ", "In some cases, it may not be possible to estimate all parameters of interest.", "\n\nIn this article, we expanded the state-structured model of Zipkin et al. ([", "@b50]) by incorporating data where the state cannot be observed perfectly. ", "We demonstrated this approach in our detection model for the case where sex was known but life stage could not always be determined; but this method could be used when some individual states are unknown. ", "It might also be possible to improve inferences on detection if observation models other than the binomial (i.e., the simple counting model) are available. ", "For example, if data can be collected using a removal approach or distance sampling, a multinomial observation model could be used, which would likely result in better precision on estimates of detection and thus population abundance and demographic rates.", "\n\nThe use of capture--recapture techniques will continue to be important in estimating population abundance and demographic rates because of the high quality information that such methods can produce. ", "Yet, capture--recapture cannot be the only approach for obtaining demographic parameter estimates due to its limited spatial extent and relatively high cost. ", "While methodological advancements for unmarked populations -- such as the one presented in this article -- offer exciting alternatives, unmarked populations cannot provide the same detailed information as marked populations. ", "Thus, the most comprehensive approaches to estimate population parameters on large spatial and temporal scales may be to integrate intensive data (e.g., capture--recapture) with extensive data (e.g., counts of unmarked individuals). ", "Besbeas et al. ([", "@b4]) and Brooks et al. ([", "@b5]) developed integrated population models that use a combination of band recovery data and population indices to formulate more robust estimates of abundance and demographic rates than is possible using only the mark-recovery data. ", "More recently, a number of studies have used integrated population models to explore local population dynamics (Barker et al. [", "@b3]; Schaub et al. [", "@b39], [@b41]), determine the conservation status of threatened species (Schaub et al. [", "@b39], [@b10]), and improve parameter estimates when data are limited (Schaub et al. [", "@b38]; Abadi et al. [", "@b1]). ", "In most cases, capture--recapture or ring-recovery data provide the direct information for estimating demographic parameters. ", "The results of our study suggest that it may be possible to use count data in broader ways within integrated models, especially if it is possible to obtain counts of individuals in relevant life states (e.g., sex and stages). ", "This could lead to exciting opportunities for developing mechanistic-based integrated models for improved estimates of population processes and abundances.", "\n\nThe work in this manuscript was conducted as a part of the \"Modeling species response to environmental change: development of integrated, scalable Bayesian models of population persistence\" Working Group supported by the John Wesley Powell Center for Analysis and Synthesis, funded by the US Geological Survey. ", "We thank Jim Nichols, Richard Barker, Marc Kéry, and an anonymous reviewer for comments on the manuscript that greatly improved the final product. ", "This manuscript is a contribution of the Hubbard Brook Ecosystem Study. ", "Hubbard Brook is part of the Long-Term Ecological Research network, which is supported by the NSF. ", "The Hubbard Brook Experimental Forest is operated and maintained by the USDA Forest Service, Northern Research Station, Newtown Square, PA. ", "Any use of trade, product, or firm names is for descriptive purposes only and does not imply endorsement by the U.S. Government. ", "This is contribution number 464 of the U.S. Geological Survey Amphibian Research and Monitoring Initiative (ARMI).", "\n\nConflict of Interest\n====================\n\nNone declared.", "\n\nFunding Information\n===================\n\nWorking Group supported by the John Wesley Powell Center for Analysis and Synthesis, funded by the US Geological Survey. ", "Fieldwork was funded by U.S. National Science Foundation grants to R. T. Holmes (Dartmouth College), N. L. Rodenhouse (Wellesley College), TSS, and M. S. Webster (Cornell University).", "\n\n[^1]: **Present address**, Elise F. Zipkin, Department of Zoology, Michigan State University, East Lansing, Michigan, 48824\n" ]

{ "pile_set_name": "PubMed Central" }

[ 0, 0, 0.006172839506172839, 0.14285714285714285, 0.0038461538461538464, 0.14285714285714285, 0.006756756756756757, 0.125, 0.0273972602739726, 0.041666666666666664, 0.018957345971563982, 0.09090909090909091, 0.125, 0.01276595744680851, 0.08695652173913043, 0.08695652173913043, 0.1111111111111111, 0.005952380952380952, 0.09523809523809523, 0.02040816326530612, 0.031746031746031744, 0.08333333333333333, 0.031746031746031744, 0.004975124378109453, 0.125, 0, 0, 0.009009009009009009, 0.007751937984496124, 0, 0.0078125, 0, 0.009433962264150943, 0.020833333333333332, 0.027777777777777776, 0.004347826086956522, 0.017045454545454544, 0, 0.012121212121212121, 0.01, 0, 0.0078125, 0.009523809523809525, 0, 0.006802721088435374, 0.045454545454545456, 0.14285714285714285, 0, 0, 0, 0, 0.008130081300813009, 0, 0.0111731843575419, 0, 0.018867924528301886, 0, 0, 0.002583979328165375, 0.009433962264150943, 0, 0, 0, 0.00819672131147541, 0.004629629629629629, 0.125, 0.0035971223021582736, 0, 0, 0.009009009009009009, 0.005319148936170213, 0, 0.01775147928994083, 0, 0, 0, 0, 0.012048192771084338, 0.011673151750972763, 0, 0, 0.005, 0.009433962264150943, 0.012531328320802004, 0, 0.009900990099009901, 0.0048543689320388345, 0.009259259259259259, 0.0035460992907801418, 0.00909090909090909, 0, 0.008333333333333333, 0.017543859649122806, 0.18181818181818182, 0, 0.009433962264150943, 0.0091324200913242, 0.003257328990228013, 0.05, 0.18181818181818182, 0, 0.013452914798206279, 0.005988023952095809, 0.0045662100456621, 0.007575757575757576, 0.005076142131979695, 0.125, 0.0058823529411764705, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.004166666666666667, 0, 0.0058823529411764705, 0.0060790273556231, 0, 0.009433962264150943, 0, 0, 0.00966183574879227, 0, 0.006993006993006993, 0, 0, 0.007168458781362007, 0, 0.009009009009009009, 0, 0, 0, 0, 0, 0, 0, 0.003289473684210526, 0, 0, 0, 0, 0, 0.016091954022988506, 0.08695652173913043, 0.03065134099616858, 0.006211180124223602, 0, 0, 0.02, 0, 0.013157894736842105, 0.007936507936507936, 0, 0, 0.005747126436781609, 0.012195121951219513, 0.125, 0.010101010101010102, 0, 0, 0, 0.003436426116838488, 0.007407407407407408, 0, 0, 0, 0.007575757575757576, 0.008, 0, 0, 0, 0, 0, 0, 0.013333333333333334, 0, 0, 0, 0, 0, 0, 0, 0, 0.07692307692307693, 0.00425531914893617, 0, 0.09523809523809523, 0.03409090909090909, 0.03488372093023256, 0.09523809523809523, 0.14285714285714285, 0, 0, 0, 0.003194888178913738, 0.02040816326530612, 0, 0.030303030303030304, 0.014285714285714285, 0.007751937984496124, 0.008771929824561403, 0, 0.006097560975609756, 0.03825136612021858, 0.023809523809523808 ]

[ "1. ", "Field of the Invention\nThe present invention relates to an apparatus for producing a beverage and, more specifically, to a apparatus for producing a beverage from a liquid concentrate.", "\n2. ", "Description of the Prior Art\nMany beverages have been produced from concentrate including fruit juices and coffee and tea. ", "However, the production of coffee and tea from concentrate has been limited substantially to commercial apparatus that is too expensive and cumbersome for home or office usage. ", "An example of a beverage apparatus that produces beverages from two liquid concentrates is shown in the U.S. patent to Bardeau. ", "U.S. Pat. ", "No. ", "3,843,020.", "\nAnother example found in the U.S. Patent art, is the Burke et al Patent, U.S. Pat. ", "No. ", "6,752,069. ", "Burke et al adds water, either manually of automatically, to a beverage concentrate. ", "The device, which may perform well, is large and complex and thus, at least as to the area of home appliances, is too expensive.", "\nThe Shaver patent, U.S. Pat. ", "No. ", "4,579,048 initially brews a concentrate, specifically from tea leaves, to produce a concentrate. ", "The concentrate is then diluted to an acceptable strength and temperature by the timed addition of water. ", "Once again, what apparently is a desirable device for commercial use is economically not practical for home usage and is also far too large for home usage.", "\nThe Gorski dt al Patent, U.S. Pat. ", "No. ", "6,149,035 uses a dry concentrate for dispensing a food or beverage. ", "Once again an apparatus is taught which is economically unsuitable for home or office usage.", "\nToday, liquid concentrate is economically produced and supplies of liquid coffee concentrate as well as other concentrates are available. ", "Unfortunately, a practical apparatus for home or office use does not exist to produce coffee and tea from concentrates. ", "Liquid concentrates provide a superior beverage and a much neater operation for the production of a beverage. ", "When brewing coffee from liquid coffee concentrate there are no filters of used coffee grounds to clean up.", "\nThe use of a concentrate to produce coffee in a home or office from a concentrate has been recognized. ", "The Paoloni Patent, U.S. Pat. ", "No. ", "3,536,496 teaches a simplified method for producing concentrate and then using such concentrate for producing coffee. ", "The method, however, is not practical for use today and with the availability of liquid coffee concentrate, the concept is not suitable for home and office usage. ", "What is needed is an apparatus that is of a size and cost suitable for use in the home or office and which can brew a fresh cup of coffee one cup at a time on demand.", "\nEfforts have been made to produce a coffee maker that uses liquid concentrate for home and office use. ", "The Triola et al Patent, U.S. Pat. ", "No. ", "5,740,719 describes a coffee maker using liquid coffee concentrate that is intended for home and office usage. ", "Triola, et al continued with the concept of requiring a pump to deliver the concentrate. ", "This feature has been universally accepted in the prior art. ", "To eliminate an electromechanical pump, Triola et al uses a cylinder which is pressed down by hand to deliver concentrate. ", "Controlling the amount of concentrate when pressing on the cylinder is not a simple task and too much or too little concentrate can result only too easily. ", "The Triola et al Patent exemplifies the previous inability to produce a simple apparatus for making coffee from liquid coffee that operates on a gravity fed system free of pumps, whether manual or power operated.", "\nVitality Foodservice, Inc. of Tampa, Fla. offers dispensers for coffee and hot beverages. ", "The device includes a solenoid valve for controlling discharge of water from a water tank to an open channel. ", "Disposed above the open channel is a control valve for controlling discharge of concentrate into the water in the channel. ", "The resulting beverage is then discharged." ]

{ "pile_set_name": "USPTO Backgrounds" }

[ 0, 0, 0, 0, 0, 0.0078125, 0, 0, 0, 0.011904761904761904, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.027777777777777776, 0, 0, 0, 0, 0, 0, 0, 0, 0.03333333333333333, 0, 0, 0, 0, 0, 0.02857142857142857, 0, 0, 0.011235955056179775, 0, 0.008130081300813009, 0, 0.0047169811320754715, 0.01098901098901099, 0, 0, 0 ]

[ "Psychological differences between veterans with and without Gulf War unexplained symptoms. ", "Portland Environmental Hazards Research Center.", "\nThe objective of this study was to assess measures of psychological and neurobehavioral functioning to determine their association with unexplained symptoms in Gulf War veterans. ", "An epidemiological survey focusing on exposures and symptoms was mailed to a random sample of Gulf War veterans from Oregon and southwestern Washington. ", "Volunteers were recruited from survey respondents who agreed to undergo a thorough medical examination and psychological and neurobehavioral assessment. ", "Persistent symptoms with no medical explanation associated with service in the Persian Gulf (eg, fatigue, muscle pain, and memory deficits) that began during or after the war qualified respondents as cases. ", "The 241 veterans with unexplained symptoms were classified as case subjects, and the 113 veterans without symptoms were classified as control subjects. ", "All veterans completed a battery of computerized assessment tests consisting of 12 psychosocial and 6 neurobehavioral tests. ", "Differences between case and control subjects on neurobehavioral and psychological variables were assessed with univariate and multivariate statistical comparisons. ", "Case subjects differed substantially and consistently from control subjects on diverse psychological tests in the direction of increased distress and psychiatric symptoms. ", "Case subjects had small but statistically significant deficits relative to control subjects on some neurobehavioral tests of memory, attention, and response speed. ", "A logistic regression model consisting of four psychological variables but no neurobehavioral variables classified case and control subjects with 86% accuracy. ", "Our results revealed that Gulf War veterans who report symptoms associated with that conflict differed on multiple psychological measures in the direction of increased distress and performed more poorly on neurobehavioral measures when compared with control subjects who did not report symptoms. ", "This suggests that psychological differences have a prominent role in investigation of possible explanations of Gulf War symptoms." ]

{ "pile_set_name": "PubMed Abstracts" }

[ 0, 0.02127659574468085, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]

[ "Cell Cycle Synchronization of Primary Articular Chondrocytes Enhances Chondrogenesis.", "\nAlthough tissue engineering is a promising option for articular cartilage repair, it has been challenging to generate functional cartilaginous tissue. ", "While the synthetic response of chondrocytes can be influenced by various means, most approaches treat chondrocytes as a homogeneous population that would respond similarly. ", "However, isolated cells heterogeneously progress through the cell cycle, which can affect macromolecular biosynthesis. ", "As it is possible to synchronize cells within discrete cell cycle phases, the purpose of this study was to investigate the effects of cell cycle synchronization on the chondrogenic potential of primary articular chondrocytes. ", "Different methods of cell synchronization (serum starvation, thymidine, nocodazole, aphidicolin, and RO-3306) were tested for their ability to synchronize primary articular chondrocytes during the process of cell isolation. ", "Cells (unsynchronized and synchronized) were then encapsulated in alginate gels, cultured for 4 weeks, and analyzed for their structural and biochemical properties. ", "The double-thymidine method yielded the highest level of cell purity, with cells synchronized in S phase. ", "While the cells started to lose synchronization after 24 hours, tissue constructs developed from initially S phase synchronized cells had significantly higher glycosaminoglycan and collagen II amounts than those developed using unsynchronized cells. ", "Initial synchronization led to long-term changes in cartilaginous tissue formation. ", "This effect was postulated to be due to the rapid auto-induction of TGF-βs by actively dividing S phase cells, thereby stimulating chondrogenesis. ", "Cell synchronization methods may also be applied in conjunction with redifferentiation methods to improve the chondrogenic potential of dedifferentiated or diseased chondrocytes." ]

{ "pile_set_name": "PubMed Abstracts" }

[ 0, 0, 0, 0, 0, 0.004464285714285714, 0, 0, 0, 0, 0, 0 ]

[ "Trafficking of the potato spindle tuber viroid between tomato and Orobanche ramosa.", "\nViroids, small RNA pathogens capable of infecting flowering plants, coexist in the field with parasitic plants that infest many crops. ", "The ability of viroids to be exchanged between host and parasitic plants and spread in the latter has not yet been investigated. ", "We studied the interaction between the Potato spindle tuber viroid (PSTVd) and Branched bromrape (Orobanche ramosa) using the tomato, Solanum lycopersicon, as a common host. ", "We report the long distance trafficking of PSTVd RNA via the phloem from tomato to O. ramosa, but not vice versa. ", "Furthermore, we identify O. ramosa as a novel host with the ability to facilitate the replication and processing of PSTVd. ", "Finally, molecular variants of PSTVd with single nucleotide substitutions that replicate with different efficiencies in tomato were isolated from O. ramosa." ]

{ "pile_set_name": "PubMed Abstracts" }

[ 0.012048192771084338, 0.007352941176470588, 0, 0.022988505747126436, 0.017543859649122806, 0.008130081300813009, 0 ]

[ "An in vivo, label-free quick assay for xylose transport in Escherichia coli.", "\nEfficient use of xylose is necessary for economic production of biochemicals and biofuels from lignocellulosic materials. ", "Current studies on xylose uptake for various microorganisms have been hampered by the lack of a facile assay for xylose transport. ", "In this work, a rapid in vivo, label-free method for measuring xylose transport in Escherichia coli was developed by taking advantage of the Bacillus pumilus xylosidase (XynB), which cleaved a commercially available xylose analog, p-nitrophenyl-beta-d-xylopyranoside (pNPX), to release a chromogenic group, p-nitrophenol (pNP). ", "XynB was expressed alone or in conjunction with a Zymomonas mobilis glucose facilitator protein (Glf) capable of transporting xylose. ", "This XynB-mediated transport assay was demonstrated in test tubes and 96-well plates with submicromolar concentrations of pNPX. ", "Kinetic inhibition experiments validated that pNPX and xylose were competitive substrates for the transport process, and the addition of glucose (20 g/L) in the culture medium clearly diminished the transmembrane transport of pNPX and, thus, mimicked its inhibitory action on xylose uptake. ", "This method should be useful for engineering of the xylose transport process in E. coli, and similar assay schemes can be extended to other microorganisms." ]

{ "pile_set_name": "PubMed Abstracts" }

[ 0, 0, 0, 0, 0, 0, 0, 0 ]

[ "Business Proposal\n\nInternet Marketing\n\nSustainability\n\ninside\n\nStandard sales letters start off off with a incredibly powerful statement to capture the interest of the reader. ", "If you have enclosed any documents along with the letter, such as a resume, you indicate this merely by typing Enclosures 1 line below the closing. ", "If you prefer to use indents, attempt using the semi-block or modified semi-block format alternatively. ", "Order Letter = Order letters are specifically as they sound, they are utilised to order material that is running low and will be needed quickly. ", "Historically, business letters were sent by way of postal mail or courier, despite the fact that the World wide web is rapidly altering the way enterprises communicate.", "\n\nDisclaimer: The content on this web page is intended for educational use and not to be construed as legal or expert assistance. ", "The high-quality of details that is passed along from a single person to an additional tremendously impacts the success of a business. ", "Most business letters have a letterhead, which includes all the speak to information of the sender. ", "Ordinarily the men and women you write formal letters to are people who deserve your complete respect for the reason that these men and women are not on the exact same level as you. ", "It’s a shame, then, that so lots of businesspeople regard writing business letters as a chore.", "\n\nNow that you have acquainted oneself with the standard business letter writing suggestions and guidelines, you can check out our business letter samples to link theory with practice. ", "Is a letter that utilizes a format that is slightly diverse from the complete block letter. ", "Every business organization need to location careful consideration to appropriate corporate communication.", "\n\nWhen writing business letters, you should spend special interest to the format and font applied. ", "Cover letters, application letters, letters of acceptance, confirmation letters, letters of introduction, letters of appointment, and cancellation letters are distinctive sorts of business letters. ", "The generally accepted font is Instances New Roman, size 12, even though other fonts such as Arial might be applied. ", "A lot of organizations have their own style for writing a business letter, but right here are some prevalent examples. ", "Order letters are sent by shoppers or businesses to a manufacturer, retailer or wholesaler to order goods or services. ", "The title or heading is ordinarily brief and clear and written in capital letters.", "\n\nThis block format business letter template illustrates how fast and straightforward communications can be to type. ", "In some circumstances, individuals who favor to use this format start these components five spaces to the right of the center of the page. ", "You can study the finest business letter format, and you can use it to your benefit. ", "Written letters can convey the feelings of the writer a great deal greater than an e mail." ]

{ "pile_set_name": "Pile-CC" }

[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.008547008547008548, 0, 0, 0, 0, 0, 0, 0 ]

[ "[Social inequities in the use of primary care services: a long way to go].", "\nTo describe the relation between the main variables related with social inequality and the utilization of primary care services. ", "Socio-demographic variables and the number of consultations were collected in a cross-sectional study. ", "264 subjects were interviewed. ", "66% of the population belonged to social classes IV and V. There was statistical signification between age and number of visits (p = 0.0014) and between number of visits and monoparental families (p = 0.01). ", "Most of the attended population belonged to the low and middle socio-economic levels. ", "The relationship between non-structured families and hyper-utilization and the relationship between age and hyper-utilization is confirmed." ]

{ "pile_set_name": "PubMed Abstracts" }

[ 0, 0, 0, 0, 0, 0, 0 ]

[ "For some players in the National Hockey League, the sin bin has proven to be insufficient.", "\n\nThere is no denying it, hockey, especially at the elite level of the NHL, is a dangerous game with a multitude of ways one can be seriously injured. ", "And when during play a skater does something nefarious that increases the danger of the game or all-out threatens the physical well-being on an opponent, the league must step in and dole out suspensions.", "\n\nSome like Dale Hunter's hit on Pierre Turgeon in the 1993 playoffs, a hit out of frustration and anger at himself for goofing on the play, may not appear as vindictive as others, yet he still had to pay the price and sit. ", "It is a slippery slope if the league allows a hit resulting in injury after the play to go unpunished.", "\n\nAnd the length of these suspensions are only getting longer. ", "In the early 1990s, the longest was a mere 21 games. ", "now, after several 25-game punishments, repeat offenders must be worried that their next slip up might cost them their careers.", "\n\nNot all transgressions have occurred on the ice, with one of the longest suspensions still continuing with no end in the foreseeable future. ", "Though this instance is a very particular situation, but one the brass of the NHL hope never to see repeated.", "\n\nSome of the older disciplinary measures, like that used to punish Dan Maloney, might seem rather odd by today's standards. ", "It is important to note that suspensions have been handed out almost since the inception of the game.", "\n\nOthers, like Marty McSorley's one-year suspension would go on to tarnish his entire career; a career that saw him playing with Wayne Gretzky for much of it. ", "In fact his last game in the NHL was the game of his worst transgression. ", "There was no wave goodbye to fans on his retirement. ", "Just scorn from them for having scarred the game they love.", "\n\nShockingly, Todd Bertuzzi's sucker punch on Steve Moore only resulted in 20 total NHL games missed, though he was banned from playing anywhere by the IIHF throughout the NHL's 2004-05 lockout.", "\n\nIt is a great game, though, and the NHL police just hope to keep it that way and prevent it from becoming mired in controversy.", "\n\n15 Maurice Richard - 15 games\n\nWhile there are several suspensions of 15 games, this one is by far the most famous (or infamous) one.", "\n\nThe Canadiens icon Maurice Richard was in a fight with Hal Laycoe of the Bruins, in retaliation for Laycoe hitting Richard with a stick to the head. ", "While linesman Cliff Thompson tried to restrain Richard, The Rocket turned and knocked him out cold. ", "Richard was suspended the rest of the regular season, and as a result lost out on the scoring title. ", "He also missed all 12 playoff games, with the Habs dropping the final in seven games to Detroit. ", "This incident was also the catalyst for the infamous Richard Riot.", "\n\n14 Eddie Shore - 16 games\n\nvia flickr.com\n\nAs tragic as any incident on this list, Eddie Shore's sucker punch of Toronto Maple Leafs star Ace Bailey resulted in Bailey's career ending, due to a fractured skull. ", "On the evening of December 13th, 1933, Shore knocked Bailey down from behind, with Bailey's head hitting the ice. ", "Apparently the hit was in retaliation of Bailey taking down Bruins player Red Horner. ", "Either way the act was reckless and it's kind of shocking Shore would only get 16 games for ending a player's career.", "\n\n13 Matt Cooke - 16 games (with playoffs)\n\nHits like this made Matt Cooke the league's most hated player at one point. ", "The rulebook had to redefine a headshot due to the liberties Cooke would take with opposing players' heads. ", "In this case, he elbowed Rangers defenceman Ryan McDonagh. ", "It was as deliberate as an elbow could be, with Cooke sticking his elbow sideways to catch McDonagh's head. ", "Cooke wasn't going for the puck so much as he was head hunting Cooke. ", "Cooke was suspended for the remainder of the regular season and most of the Penguins' opening round series against Tampa.", "\n\n12 Todd Bertuzzi, Tom Lydsiak, Brad May, Steve Downie, - 20 games\n\nWe'll place Todd Bertuzzi's sucker punch on Steve Moore above the rest of the 20-game lot because it should have been longer. ", "Bertuzzi's total NHL games missed due to the incident was 20 games, due to the lockout after the 2004 season. ", "Bertuzzi was also banned from playing in any IIHF league, as they honor NHL suspensions. ", "Bertuzzi was reinstated by the league following the conclusion of the lockout.", "\n\n- Tom Lysiak was suspended for 20 games back in 1983 for intentionally tripping NHL linesman Ron Foyt.", "\n\n- Brad May slashed Steve Heinze in the nose\n\n- Steve Downie threw himself at Dean McAmmond behind the net\n\n11 Dale Hunter - 21 games\n\nThough known for racking up penalty minutes, this hit has left an asterisk beside an otherwise decent career.", "\n\nDuring Game 6 of the first round of the 1993 playoffs between the Washington Capitals and the New York Islanders, Hunter would exhibit one of the worst displays of unsportsmanlike behavior in NHL history.", "\n\nIslander Pierre Turgeon would strip Hunter of the puck in the Capitals' end and scored after going in all alone to put New York up 5-3 in the third. ", "Hunter, who was the Caps' leading scorer with seven goals in that series, became incensed and took his frustration out on a celebrating Turgeon, hitting him without warning into the boards.", "\n\nTurgeon sustained a concussion and a separated shoulder on the play and would not return to action until Game 7 of the next series against the Pittsburgh Penguins.", "\n\nThis hit was made example by new NHL Commissioner Gary Bettman to help curb injuries due to illegal hits and Hunter was handed a 21-game suspension.", "\n\n10 Raffi Torres - 21 games (reduced from 25)\n\nIf this hit happened during the high-wheeling days of the '80s, it would have been celebrated.", "\n\nHowever, in the marginally safer present-day NHL, this hit was deemed highly illegal and highly dangerous, garnering Phoenix Coyotes winger Raffi Torres a 25-game suspension later to be dropped to 21.", "\n\nOn April 17, 2012, during the third game of the first round of the playoffs between the Coyotes and the Chicago Blackhawks, Torres laid a hard hit on veteran Marian Hossa after the latter passed the puck off near centre ice.", "\n\nHossa was knocked unconscious and laid on the ice for several minutes before being put on a gurney and taken to a nearby hospital.", "\n\nNo penalty was called on the play, but it would later be reviewed, clearly showing that Torres had left the ice to make the hit with Hossa's head being the main point of contact. ", "It was a dangerous hit and to prevent more vicious plays NHL head cop Brendan Shanahan laid out a 25-game suspension. ", "Seventy-six days after the hit, his suspension was dropped to 21 games.", "\n\nTorres would lose $170,731 in salary for the hit.", "\n\n9 Gordie Dwyer - 23 games\n\nTampa Bay Lightning forward Gordie Dwyer would in fact earn himself three suspensions that together totaled 23 games.", "\n\nIn an exhibition match between the Lightning and the Washington Capitals on September 19, 2000, Dwyer fought Capital players Joe Murphy and Joe Reekie. ", "Once in the penalty box, Dwyer would illegally return to the ice for the purpose of trying to fight Reekie again.", "\n\nThough no injuries were sustained, Dwyer was awarded three game misconducts, each worth a 10-game suspension. ", "Two of those misconducts were for abusing the referees. ", "In trying to reach Reekie, Dwyer twice forced his way through the officials.", "\n\nFeatured Today\n\n8 Jesse Boulerice - 25 games\n\nIn a game where the Philadelphia Flyers were leading 8-2 over the Vancouver Canucks on October 10, 2007, Jesse Boulerice gave reason to continue the tradition of calling the team from the city of brotherly love the Broad Street Bullies.", "\n\nWith the game winding down, Boulerice caught Ryan Kesler behind the play as he rounded out from behind the net with a cross-check to the face sending the blue chipper to the ice.", "\n\nThe two had been squabbling all game and it appeared as if Boulerice was attempting to instigate a fight, however what he would get instead would be a 25-game suspension.", "\n\nKesler would return the next game after only receiving a swollen jaw and lip and bruising to the face.", "\n\n7 Chris Simon - 25 games\n\nNew York Islander Chris Simon's seventh suspension was as vicious as they come. ", "And he'd sure pay the price for it.", "\n\nWith under seven minutes left in the third period of a game between the Islanders and the New York Rangers on March 11, 2007, Simon's infamous temper would rear its ugly head.", "\n\nWith the play deep in the Islanders' zone, Ranger Ryan Hollweg gave Simon a good, hard hit in the corner. ", "Taking exception to it, moments later as Hollweg was rounding his way out of the zone, Simon would slash him in the face with both hands on his stick.", "\n\nThe slash was done with so much force that the announcer would remark that it looked like he was felling a tree.", "\n\nFor his actions, Simon was handed a 25-game suspension.", "\n\n6 Chris Simon - 30 games\n\nRepeat offender Chris Simon of the New York Islanders was suspended for an unprecedented 30 games following a malicious attempt to injure Jarkko Ruutu of the Pittsburgh Penguins on December 15, 2007.", "\n\nIn what at first appeared to be a rather benign scuffle between Tim Jackman and Ruutu near the teams' benches during a stoppage of play, Simon pulled Ruutu's right skate from under him with his own causing the Penguin player to follow to his knees. ", "Simon then proceeded to stomp on Ruutu's right ankle before heading off the ice on a line change.", "\n\nAt the time of the incident Simon was given a match penalty for attempting to injure and ejected from the game.", "\n\nThis was Simon's eight suspension in his NHL career.", "\n\n5 Slava Voynov - 80+ games and counting\n\nKirby Lee-USA TODAY Sports\n\nThis suspension is ongoing and looks to continue for sometime.", "\n\nVoynov was arrested on October 20, 2014 on suspicion of domestic violence and has since been suspended by the NHL with pay for the foreseeable future. ", "He is also prohibited from practicing with the Los Angeles Kings.", "\n\nAccording to court reports, Voynov's wife, Marta Varlamova, received a laceration over the left eye requiring eight stitches, was pushed into a flatscreen TV, sustained markings on her neck indicative of choking and is quoted as saying that she was kicked and pushed several times.", "\n\nHaving already surpassed the 65-game mark, Voynov's suspension is the longest in modern NHL history (based on games missed).", "\n\nThe trial, which has been postponed on at least one occasional, is set for April 1.", "\n\n4 Alexander Perezhogin - 89 games\n\nWhile this was an AHL game, it is too ugly of an incident to leave off. ", "The penalty was 89 games for Alexander Perezhogin of the Hamiltion Bulldogs (five remaining playoff games, 80 regular season games and four playoff games the following year). ", "Perezhogin missed all of the 2004-05 season for slashing, well more like baseball swinging Garrett Stafford in the face with his stick.", "\n\n3 Marty McSorley - One year\n\nBoston Bruins' tough guy Marty McSorley's 17-year career would end in infamy.", "\n\nIn the dying seconds of a game between the Bruins and the Vancouver Canucks on February 21, 2000, McSorley blatantly and viciously slashed Donald Brashear in the head causing the enforcer to fall backwards, hitting the back of his head on the ice. ", "Brashear would sustain a grade III concussion, forcing him to miss 20 games.", "\n\nMcSorley was originally suspended for the remainder of the season as well as the playoffs for the 1999-00 season (totaling 23 games). ", "His suspension would be lengthened to an entire year following a British Columbia court finding McSorley guilty of assault with a weapon on October 6, 2000.", "\n\nMcSorely would never play another game in the NHL.", "\n\n2 Dan Maloney - Two years\n\nvia bloodyhawks.ru\n\nProbably the most contentious inclusion on this list, Dan Maloney's attack on November 4, 1975 would be the first time in NHL history that an on-ice event would go to trial.", "\n\nThough there doesn't appear to be many reports from the game between the Detroit Red Wings and the Toronto Maple Leafs, apparently Maloney of the Wings attacked Leafs' Brian Glennie using his stick and throwing punches. ", "It should be known that Maloney was known as having one of the hardest punches during his time.", "\n\nAfter having subdued Glennie, getting him to the ice, Maloney continued to throttle the fallen defenceman repeatedly bashing his head into the ice.", "\n\nBecause of his on-ice attack, Maloney was charged with assault to cause bodily harm, in a move by the Ontario Attorney-General Roy McMurtry to curb violence in hockey.", "\n\nHis charge would later be dropped for community service, however because of the incident he was prohibited from playing in Toronto for two years.", "\n\n1 Billy Coutu - Life\n\nvia realclearsports.com\n\nAfter losing the Stanley Cup Final to the Ottawa Senators in four games on April 13, 1927, Billy Coutu of the Boston Bruins pursued referee Jerry Laflamme off the ice and accosted him and then threatened his linesman.", "\n\nAccording to reports, the former captain of the Montreal Canadiens was following the instructions of Bruins' head coach Art Ross. ", "However, Coutu was banned from the NHL for his actions and fined $100.", "\n\nCoutu would go on to play in minor leagues but he would never again play pro. ", "His suspension was eventually lifted five years later at the behest of Canadiens' head coach Leo Dandurand. ", "However, the ban would be lifted a year after he had retired." ]

{ "pile_set_name": "Pile-CC" }

[ 0.022222222222222223, 0.006622516556291391, 0, 0.008928571428571428, 0, 0, 0, 0, 0, 0.009174311926605505, 0.008, 0, 0.012578616352201259, 0.013513513513513514, 0, 0, 0.02577319587628866, 0.007751937984496124, 0.007407407407407408, 0.026490066225165563, 0.0297029702970297, 0.009900990099009901, 0.010309278350515464, 0.015151515151515152, 0.018779342723004695, 0.02631578947368421, 0.011627906976744186, 0.008547008547008548, 0.016666666666666666, 0, 0.01694915254237288, 0.018518518518518517, 0.014285714285714285, 0.008264462809917356, 0.03076923076923077, 0.01818181818181818, 0.033707865168539325, 0.01282051282051282, 0.028846153846153848, 0.0163265306122449, 0.019417475728155338, 0.019867549668874173, 0.010582010582010581, 0.012121212121212121, 0.02, 0, 0.01485148514851485, 0.01327433628318584, 0.007575757575757576, 0.011049723756906077, 0.01694915254237288, 0, 0, 0.0136986301369863, 0.025974025974025976, 0.017699115044247787, 0.008928571428571428, 0, 0.02631578947368421, 0.017605633802816902, 0.011111111111111112, 0.005813953488372093, 0.009615384615384616, 0.018518518518518517, 0, 0.005649717514124294, 0.018518518518518517, 0.006666666666666667, 0, 0, 0.022026431718061675, 0.01195219123505976, 0.010309278350515464, 0, 0.018518518518518517, 0.007518796992481203, 0.013071895424836602, 0.015384615384615385, 0.007067137809187279, 0.015873015873015872, 0, 0.01834862385321101, 0.011428571428571429, 0.007407407407407408, 0.009259259259259259, 0.016, 0.013157894736842105, 0.007352941176470588, 0.00641025641025641, 0.019230769230769232, 0.013513513513513514, 0.013513513513513514, 0.010526315789473684, 0.006711409395973154, 0.011834319526627219, 0, 0.011278195488721804, 0.022727272727272728, 0.02857142857142857, 0, 0.018518518518518517, 0 ]

[ "Q:\n\nreplace Statement to insert into specific columns only\n\nI am trying to use replace statement but only to replace data in specific columns, but the query i am using is replacing values in all the columns.", "\npublic boolean insertDataTable(String FileNumber, String Areas, String Level, String ProjectCode, String Year, String Department, String University, String Address, String City, String State, String Region, String UserId) {\n\n SQLiteDatabase sqLiteDatabase = this.getWritableDatabase();\n\n String query = \" REPLACE INTO DataTable (FileNumber, Areas, Level, ProjectCode, Year, Department, University, Address, City, State, Region, UserId) VALUES (?,?,?,?,?,?,?,?,?,?,?,?)\";", "\n\n sqLiteDatabase.execSQL(query,new String[]{FileNumber, Areas, Level, ProjectCode, Year, Department, University, Address, City, State, Region, UserId});\n sqLiteDatabase.close();\n return true;\n }\n\nI have table with 13 columns, i am trying to not update value in last column. ", "this is the code i am using.", "\n\nA:\n\nI think that you misunderstood the purpose of the REPLACE statement. ", "\nIt is not the same as UPDATE. ", "\nRead the above link and you will see that REPLACE: \n\ninserts a new row or deletes the row that conflicts with the new row\n and then adds the new row.", "\n\nI believe what you really want is to update a row in the table. ", "So do this:\nString query = \"UPDATE DataTable SET \" + \n\"FileNumber = ?, ", "Areas = ?, ", "Level = ?, ", "ProjectCode = ?, ", "Year = ?, ", "Department = ?, \" ", "+\n\"University = ?, ", "Address = ?, ", "City = ?, ", "State = ?, ", "Region = ?, ", "UserId = ? \" ", "+\n\"WHERE ......\";\n\nUse the WHERE clause at the end of the statement to specify which row to update, otherwise all the rows of the table will be updated.", "\n\n" ]

{ "pile_set_name": "StackExchange" }

[ 0, 0.020618556701030927, 0.023411371237458192, 0, 0.013333333333333334, 0, 0.006622516556291391, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]

[ "Q:\n\nWhat is $\\underbrace{555\\cdots555}_{1000\\ \\text{times}} \\ \\text{mod} \\ 7$ without a calculator\n\nIt can be calculated that $\\frac{555555}{7} = 79365$. What is the remainder of the number $5555\\dots5555$ with a thousand $5$'s, when divided by $7$?", "\n\nI did the following:\n$$\\begin{array}\n & 5 \\ \\text{mod} \\ 7=& &5 \\\\\n 55 \\ \\text{mod} \\ 7= & &6 \\\\\n 555 \\ \\text{mod} \\ 7= & &2 \\\\\n 5555 \\ \\text{mod} \\ 7= & &4 \\\\\n 55555 \\ \\text{mod} \\ 7= & &3 \\\\\n 555555 \\ \\text{mod} \\ 7= & &0 \\\\\n 5555555 \\ \\text{mod} \\ 7= & &5 \\\\\n 55555555 \\ \\text{mod} \\ 7= & &6 \\\\\n 555555555 \\ \\text{mod} \\ 7= & &2 \\\\\n 5555555555 \\ \\text{mod} \\ 7= & &4 \\\\\n\\end{array}$$\nIt can be seen that the cycle is: $\\{5,6,2,4,3,0\\}$. \n$$\\begin{array}\n & 1 \\ \\text{number =} &5 \\\\\n 7 \\ \\text{numbers =} &5 \\\\\n 13 \\ \\text{numbers =} &5 \\\\\n \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\vdots & \\\\\n 985 \\ \\text{numbers =} &5 \\\\\n 991 \\ \\text{numbers =} &5 \\\\\n 997 \\ \\text{numbers =} &5 \\\\\n 998 \\ \\text{numbers =} &6 \\\\\n 999 \\ \\text{numbers =} &2 \\\\\n \\color{red}{1000} \\ \\color{red}{\\text{numbers =}} &\\color{red}{4} \\\\\n\\end{array}$$\nFrom here, we can conclude that $\\underbrace{555\\cdots555}_{1000\\ \\text{times}} \\ \\text{mod} \\ 7 = 4$.\nHowever, I wasn't allowed to use a calculator and solved this in about 12 minutes. ", "Another problem was that there was a time limit of about 5 minutes. ", "My question is: Is there an easier and faster way to solve this?", "\nThanks a lot in advance!", "\n\nA:\n\n${\\rm mod}\\ 7\\!:\\,\\ \\overbrace{55\\cdots 55}^{1+3n\\rm\\,\\ fives}\\, =\\, \\dfrac{5(10^{1+3n}\\!-1)}9\\, \\equiv\\, \\dfrac{-2\\,(3^{1+3n}-1)}2 \\,\\equiv\\, -3(\\color{#c00}{3^3})^{n}\\!+1 \\equiv 4\\ $ by $\\ \\color{#c00}{3^3\\equiv -1},\\ n$ odd\n\nA:\n\nAfter noting $555555$ is divisible by $7$, note further that $555555\\times 10^r$ is divisible by $7$ for any positive integer $r$. So you can cast out groups of six $5$s starting at the most significant digit, without changing the remainder on division by $7$. This gets rid of $996$ of the $5$s, leaving $5555$. Then $4949$ is obviously divisible by $7$ leaving $606$, and simple division then gives the remainder $4$.\n\nA:\n\nNote that $111111$ is divisible by $7$. This follows either from $111111 = \\frac{10^6-1}{9}$ where $10^6-1$ is divisible by $7$ by Fermat's little theorem, or from the factorization $111111 = 111 \\cdot 1001 = 111 \\cdot 7 \\cdot 11 \\cdot 13$. This implies that $555555$ is also divisible by $7$, hence\n$$ \\underbrace{555 \\cdots 5}_{k \\text{ times } 5} \\mod 7 $$\nis periodic with period $6$: if $k = 6a+b$, then\n$$\n\\underbrace{555 \\cdots 5}_k = \\underbrace{5555}_b + 555555 \\cdot 10^b + 555555 \\cdot 10^{6+b} + \\cdots + 555555 \\cdot 10^{6(a-1)+b}\n$$\nwhere all terms (expect the first) are divisible by $7$.\n You can now draw the desired conclusion, after noting that $1000 \\equiv 4 \\mod 6$.\n\n" ]

{ "pile_set_name": "StackExchange" }

[ 0, 0.01745877788554801, 0, 0, 0, 0.003692762186115214 ]

[ "ctest_submit\n------------\n\nPerform the :ref:`CTest Submit Step` as a :ref:`Dashboard Client`.", "\n\n::\n\n ctest_submit([PARTS <part>...] [FILES <file>...]\n [SUBMIT_URL <url>]\n [HTTPHEADER <header>]\n [RETRY_COUNT <count>]\n [RETRY_DELAY <delay>]\n [RETURN_VALUE <result-var>]\n [CAPTURE_CMAKE_ERROR <result-var>]\n [QUIET]\n )\n\nSubmit results to a dashboard server.", "\nBy default all available parts are submitted.", "\n\nThe options are:\n\n``PARTS <part>...``\n Specify a subset of parts to submit. ", " Valid part names are::\n\n Start = nothing\n Update = ctest_update results, in Update.xml\n Configure = ctest_configure results, in Configure.xml\n Build = ctest_build results, in Build.xml\n Test = ctest_test results, in Test.xml\n Coverage = ctest_coverage results, in Coverage.xml\n MemCheck = ctest_memcheck results, in DynamicAnalysis.xml\n Notes = Files listed by CTEST_NOTES_FILES, in Notes.xml\n ExtraFiles = Files listed by CTEST_EXTRA_SUBMIT_FILES\n Upload = Files prepared for upload by ctest_upload(), in Upload.xml\n Submit = nothing\n Done = Build is complete, in Done.xml\n\n``FILES <file>...``\n Specify an explicit list of specific files to be submitted.", "\n Each individual file must exist at the time of the call.", "\n\n``SUBMIT_URL <url>``\n The ``http`` or ``https`` URL of the dashboard server to send the submission\n to. ", " If not given, the :variable:`CTEST_SUBMIT_URL` variable is used.", "\n\n``HTTPHEADER <HTTP-header>``\n Specify HTTP header to be included in the request to CDash during submission.", "\n This suboption can be repeated several times.", "\n\n``RETRY_COUNT <count>``\n Specify how many times to retry a timed-out submission.", "\n\n``RETRY_DELAY <delay>``\n Specify how long (in seconds) to wait after a timed-out submission\n before attempting to re-submit.", "\n\n``RETURN_VALUE <result-var>``\n Store in the ``<result-var>`` variable ``0`` for success and\n non-zero on failure.", "\n\n``CAPTURE_CMAKE_ERROR <result-var>``\n Store in the ``<result-var>`` variable -1 if there are any errors running\n the command and prevent ctest from returning non-zero if an error occurs.", "\n\n``QUIET``\n Suppress all non-error messages that would have otherwise been\n printed to the console.", "\n\nSubmit to CDash Upload API\n^^^^^^^^^^^^^^^^^^^^^^^^^^\n\n::\n\n ctest_submit(CDASH_UPLOAD <file> [CDASH_UPLOAD_TYPE <type>]\n [SUBMIT_URL <url>]\n [HTTPHEADER <header>]\n [RETRY_COUNT <count>]\n [RETRY_DELAY <delay>]\n [RETURN_VALUE <result-var>]\n [QUIET])\n\nThis second signature is used to upload files to CDash via the CDash\nfile upload API. ", "The API first sends a request to upload to CDash along\nwith a content hash of the file. ", "If CDash does not already have the file,\nthen it is uploaded. ", "Along with the file, a CDash type string is specified\nto tell CDash which handler to use to process the data.", "\n\nThis signature accepts the ``SUBMIT_URL``, ``HTTPHEADER``, ``RETRY_COUNT``,\n``RETRY_DELAY``, ``RETURN_VALUE`` and ``QUIET`` options as described above.", "\n" ]

{ "pile_set_name": "Github" }

[ 0, 0.002680965147453083, 0, 0, 0.016282225237449117, 0, 0, 0, 0.00909090909090909, 0, 0, 0, 0, 0.005263157894736842, 0, 0.009478672985781991, 0.022727272727272728, 0.016129032258064516, 0.01834862385321101, 0, 0 ]

[ "Hydrogen peroxide is a highly important commercial product widely used as a whitening agent in the textile or paper industries, as a disinfectant and as a basic product of the chemical industry, e.g. in the production of peroxide compounds (sodium perborate, sodium percarbonate, metallic peroxides or percarboxylic acids) in oxidation reactions (manufacture of amine oxides), epoxidation and hydroxylation (manufacture of plasticizers and stabilizers). ", "It is further used for cleaning surfaces in the semiconductor industry, chemical polishing of copper, tin and other copper alloy surfaces, etching electronic circuits, etc.", "\nThe industrial method currently most widely used for the production of hydrogen peroxide is the autoxidation of alkylanthrahydroquinones. ", "This process, which is comprised of a series of phases of reduction, oxidation, extraction, purification and concentration, is very complicated which makes the investments and variable costs very high. ", "A very attractive alternative to this process is the production of hydrogen peroxide directly from the reaction between hydrogen and oxygen in the presence of metal catalysts of the platinum group, using explosive hydrogen concentrations (U.S. Pat. ", "Nos. ", "4,681,751, 4,772,458, 4,832,938, 5,338,531), outside the explosivity limit (WO 99/41190, WO 01/05498, WO 01/05501, U.S. Pat. ", "No. ", "6,168,775 B1). ", "However, a high concentration of H+ and Br− ions is necessary in this process in the reaction medium to obtain high concentrations of hydrogen peroxide. ", "Those ions are obtained from strong acids, such as sulphuric, phosphoric, hydrochloric or nitric and inorganic bromides. ", "Nevertheless, working with high acid concentration solutions requires the use of special equipment to avoid corrosion. ", "Furthermore, the presence of acid solutions and halogenated ions favours the solution of active metals (platinum group) which causes, firstly, the deactivation of the catalyst and, due to the very low dissolved metals concentration, its recovery is non-viable.", "\nTo avoid these inconveniences alternative processes have been proposed without the presence of halogen ions and/or acids in the reaction medium. ", "For example, in the European patent no. ", "EP 492064, a palladium based catalyst supported on a resin functionalized with halogens is proposed. ", "The reaction medium is water with a hydrogen peroxide stabilising agent, but the H2O2 concentrations reached were only around 0.58% in weight. ", "Another alternative (EP 504741), is the use of palladium catalysts supported on superacid inorganic solids, such as molybdenum, zirconium or wolfram, however, the hydrogen peroxide concentration reached did not exceed 1% in weight. ", "In the European patent EP 978316, a process to obtain hydrogen peroxide solutions using palladium catalysts supported on active carbon functionalized with sulphonic groups is described. ", "Nevertheless, said method requires many stages, it is very complicated to control the quality of the initial active carbons and the catalysts are difficult to reproduce.", "\nThus, there is the necessity to have new catalysts available which permit obtaining hydrogen peroxide by means of a direct reaction with hydrogen and oxygen in the presence of said catalysts, easily preparable and reproducible, and of a solvent, to obtain high concentration non-corrosive hydrogen peroxide solutions with high selectivity." ]

{ "pile_set_name": "USPTO Backgrounds" }

[ 0.0022026431718061676, 0, 0, 0, 0, 0, 0.024, 0, 0, 0, 0, 0, 0, 0.00684931506849315, 0, 0, 0, 0, 0.005376344086021506, 0, 0 ]

[ "Q:\n\nconfused for setup angularjs.", "Many dependency found\n\nI google for setup angularjs.", "I found many tutorial but i am confused.", "I found\n\nangular-seed \nYeoman\nbower\netc.", "\n\nit is necessary to use this dependency. ", "\nthere is any scratch for start angularjs.", "\n\nA:\n\nFor Angularjs you don't need any dependency. ", "Just to include angularjs library (like jquery or any other library). ", "Have look here:\n<!", "doctype html>\n<html ng-app=\"todoApp\">\n<head>\n<script src=\"https://ajax.googleapis.com/ajax/libs/angularjs/1.5.8/angular.min.js\"></script>\n<script src=\"todo.js\"></script>\n<link rel=\"stylesheet\" href=\"todo.css\">\n</head>\n<body>\n<h2>Todo</h2>\n<div ng-controller=\"TodoListController as todoList\">\n <span>{{todoList.remaining()}} of {{todoList.todos.length}} remaining</span>\n [ <a href=\"\" ng-click=\"todoList.archive()\">archive</a> ]\n <ul class=\"unstyled\">\n <li ng-repeat=\"todo in todoList.todos\">\n <label class=\"checkbox\">\n <input type=\"checkbox\" ng-model=\"todo.done\">\n <span class=\"done-{{todo.done}}\">{{todo.text}}</span>\n </label>\n </li>\n </ul>\n <form ng-submit=\"todoList.addTodo()\">\n <input type=\"text\" ng-model=\"todoList.todoText\" size=\"30\"\n placeholder=\"add new todo here\">\n <input class=\"btn-primary\" type=\"submit\" value=\"add\">\n </form>\n </div>\n </body>\n</html>\n\nAnd your app.js which contains angularjs code:\nangular.module('todoApp', [])\n.controller('TodoListController', function() {\n var todoList = this;\n todoList.todos = [\n {text:'learn angular', done:true},\n {text:'build an angular app', done:false}];\n\n todoList.addTodo = function() {\n todoList.todos.push({text:todoList.todoText, done:false});\n todoList.todoText = '';\n };\n\n todoList.remaining = function() {\n var count = 0;\n angular.forEach(todoList.todos, function(todo) {\n count += todo.done ? ", "0 : 1;\n });\n return count;\n };\n\n todoList.archive = function() {\n var oldTodos = todoList.todos;\n todoList.todos = [];\n angular.forEach(oldTodos, function(todo) {\n if (!", "todo.done) todoList.todos.push(todo);\n });\n };\n });\n\n(I took this example from https://angularjs.org/ ) so that you can understand easily.", "\nBut if you want to extend angular functionality with other library then you need to include those dependency, like you said\n\n" ]

{ "pile_set_name": "StackExchange" }

[ 0, 0, 0, 0, 0, 0, 0.0196078431372549, 0, 0, 0.004219409282700422, 0, 0.007194244604316547, 0 ]

[ "Q:\n\nGA - filtering in some profiles work in others not\n\nWe use measurement protocol for measurements in Google Analytics. ", "We have a \"Main profile\" (view) for official measurements including some IP address and bot filters. ", "However in this \"Main profile\" we see no measurement protocol (MP) hits. ", "Other hits are visible there.", "\nIf we create a new profile without any filters, measurement protocol hits start to work. ", "If we recreate the same filters in the new profile as in the main profile, then the MP works again.", "\nWe tried also to duplicate our main profile, but even if we remove the filters there, the MP hits are still not there.", "\nDoes somebody know what else besides filters should we analyze in order to find out what is behind this strange GA behavior?", "\n\nA:\n\nFor anyone else who might encounter the same issue - we found out that in our case it is caused by the \"Exclude all hits from known bots and spiders\" checkbox in the view settings. ", "However I am not sure how exactly this option works, maybe we send too many hits at one point of time, because we use MP hits.", "\n\n" ]

{ "pile_set_name": "StackExchange" }

[ 0.00819672131147541, 0.009900990099009901, 0, 0, 0, 0, 0, 0.008, 0, 0, 0 ]

[ "Salomon Lefmann\n\nSalomon Lefmann (born in Telgte, Westphalia, December 25, 1831; died in Heidelberg, January 14, 1912) was a German Jewish philologist.", "\n\nHe was educated at the Jewish school of his native town, at the seminary and academy at Münster, and at the universities of Heidelberg, Berlin, and Paris (Ph.D., Berlin, 1864). ", "In 1866 he became privat-docent of Sanskrit at Heidelberg, where he later became an associate professor (1870) and honorary professor (1901).", "\n\nLefmann's principal philological works were:\n\"De Aristotelis in Hominum Educatione Principiis\", Berlin, 1864.", "\n\"August Schleicher : Skizze\", Leipzig, 1870 (biography of linguist August Schleicher). ", "\n\"Lalita Vistara\" (edited and translated; Lalita-vistara), Halle, 1883, 1902.", "\n\"Geschichte des Alten Indiens\", Berlin, 1879–90; 2nd edition, 1898 (\"History of ancient India\").", "\n\"Franz Bopp : sein Leben und seine Wissenschaft\" 2 volumes., ", "Berlin, 1891–97 (\"Franz Bopp; his life and science\").", "\n\nThrough his \"Ueber Deutsche Rechtschreibung\" (in \"Virchow und Holzendorff's Wissenschaftliche Vorträge\", 1871) and \"Zur Deutschen Rechtschreibung\" (in \"Münchner Allgemeine Zeitung\", 1871, nos. ", "136, 209, 274) Lefmann took part in the movement for the establishment of a uniform system of spelling in German.", "\n\nLefmann took part in Jewish communal affairs. ", "While preparing himself for the university and during his employment as a public teacher he held also the positions of tutor and school-master in several small communities of Westphalia; and at Heidelberg in 1887 he was president of the Zedaka Verein, a society for the aid of the poor.", "\n\nReferences\n\nExternal links\n \n \n\nCategory:1831 births\nCategory:1912 deaths\nCategory:German orientalists\nCategory:German academics\nCategory:German Sanskrit scholars\nCategory:German Jews\nCategory:German male non-fiction writers\nCategory:Heidelberg University faculty\nCategory:People from Warendorf (district)" ]

{ "pile_set_name": "Wikipedia (en)" }

[ 0.013245033112582781, 0, 0.0070921985815602835, 0.018018018018018018, 0, 0, 0, 0.04838709677419355, 0, 0.005128205128205128, 0.008849557522123894, 0.020833333333333332, 0.0034965034965034965, 0.003257328990228013 ]

[ "\n557 F.Supp. ", "1178 (1983)\nJadean SIEREVELD, an infant by her mother Eula SIEREVELD, as next friend, et al., ", "Plaintiffs,\nv.\nPeter CONN, Cabinet for Human Resources, Frankfort, Kentucky, et al., ", "Defendants.", "\nCiv. ", "A. No. ", "77-29.", "\nUnited States District Court, E.D. Kentucky, Covington Division.", "\nFebruary 23, 1983.", "\n*1179 Richard Cullison, Northern Kentucky Legal Aid Society, Inc., Covington, Ky., for plaintiffs.", "\nPaul F. Fauri, Ann T. Hunsaker, Dept. ", "for Human Resources, Frankfort, Ky., for defendants.", "\n\nOPINION AND ORDER\nBERTELSMAN, District Judge.", "\nThe main issue in this case is whether the practice of the Kentucky Cabinet for Human Resources of removing children who have been committed to it from the homes of their natural parents violates constitutional due process where the Cabinet provides *1180 no standards limiting its discretion, no advance notice to the family of the removal and no opportunity to be heard. ", "Also, to the extent it authorizes such practices, the constitutionality of section 208.430(2) of Kentucky Revised Statutes must be resolved.", "\n\nCHR'S REMOVAL PRACTICES\nUnder Kentucky law, children who have been found to be dependent or neglected are sometimes committed to the Cabinet for Human Resources (hereinafter CHR).[1] Ky. Rev.Stat. §§ ", "208.020; 199.011(5), (6); 208.200 (Baldwin's 1982). ", "Sometimes a child who has been committed to CHR is placed in the home of his or her natural parents under CHR supervision. ", "At other times, CHR places the child in some other custodial situation such as in a group home or in foster care placement. ", "Frequently thereafter, CHR places the committed child in the home of his or her natural parents with continuing CHR supervision. ", "Until an injunction was issued in this case, CHR's practice was to remove a committed child from the home of the natural parent, if the social worker assigned to the case and his or her supervisor determined that it was advisable to do so. ", "CHR had no standards governing social worker discretion in arriving at this decision; no written notice of the reasons for the removal was afforded the family prior to the removal; and no pre-removal or post-removal hearing was provided to determine whether removal of the child was an appropriate course of action.", "\nCHR's authority for this type of removal was ostensibly under the auspices of section 208.430(2) of Kentucky Revised Statutes, which provides:\nUnless the child has been discharged from commitment, or the Court has specifically ordered otherwise, any disposition of a child made under this section may at any time during the period of his commitment be changed and other disposition made in accordance with the provision of this section.", "\nThe defendants' interpretation of this statute was that CHR was free to remove children committed to it from the homes of their natural parents without reference to standards and without providing notice and a hearing for the family. ", "It is not disputed by the parties that the defendants were acting in good faith at all times.", "\n\nFACTUAL SUMMARY\nPlaintiff Jadean Siereveld was found to be a dependent child and was committed to CHR pursuant to an order of the Juvenile Court, Campbell County, Kentucky, on June 5, 1975. ", "At that time she was fourteen (14) years old. ", "The commitment was to last for an indeterminate period of time not to exceed her attaining twenty-one years of age. ", "Following the commitment, CHR placed Jadean in the home of her natural mother, plaintiff Eula Siereveld.", "\nOn February 17, 1977, CHR, through its local social service worker and her supervisor, removed Jadean from the home of her natural mother. ", "The Plaintiffs did not receive any written notice of CHR's intention to remove the child nor of the reasons for the removal, but they did have one week's oral notice. ", "The plaintiffs were never afforded an opportunity for any kind of administrative or judicial hearing relative to the merits of Jadean's removal from the home. ", "Defendants' social workers who decided that Jadean should be removed from the home did not refer to any official standards or criteria to be utilized as guidelines in making this decision.", "\nAfter Jadean was removed, she was placed in a group foster home. ", "During her stay there, plaintiff Eula Siereveld had less access to and control over her daughter than when they had lived together, and Jadean was subjected to greater restrictions than she had been while living at home. ", "This lawsuit was filed April 25, 1977, by Jadean and Eula Siereveld for themselves and as class representatives of similarly situated *1181 persons. ", "By agreement of all concerned, plaintiff Jadean Siereveld was returned to her natural home and physical custody of her mother on May 27, 1977.", "\n\nCLASS ACTION, MOOTNESS, ABSTENTION\nThe court has heretofore certified this case to proceed as a class action under F.R.Civ.", "P. 23(b)(2). ", "The class is comprised of those families who could be affected by this CHR policy and the pertinent statute.[2]\nThe court has also heretofore overruled a motion to dismiss this case for mootness after Jadean attained her majority. ", "The court was of the opinion that the plaintiffs continued to have a sufficient stake in the outcome of the action to be adequate representatives of the class and that the class action status of this case insured the continued existence of a present controversy. ", "See United States Parole Commission v. Geraghty, 445 U.S. 388, 100 S.Ct. ", "1202, 63 L.Ed.2d 479 (1980).", "\nThe court also declined to abstain from deciding the questions presented herein. ", "This case does not involve Younger abstention, in which particularly delicate issues of comity are involved, in that an injunction curtailing state court proceedings is sought from a federal court. ", "See Younger v. Harris, 401 U.S. 37, 91 S.Ct. ", "746, 27 L.Ed.2d 669 (1971). ", "Here, if abstention were appropriate at all, it would be Pullman abstention. ", "See Railroad Commission of Texas v. Pullman Company, 312 U.S. 496, 61 S.Ct. ", "643, 85 L.Ed. ", "971 (1941). ", "This Pullman type of abstention comes into play when the interpretation of the state law being constitutionally challenged is ambiguous. ", "Field, Abstention and Constitutional Cases: The Scope of the Pullman Abstention Doctrine, 122 U.Pa.", "L.Rev. ", "1071 (1974).", "\nAs the foregoing article clearly points out, there are two requirements for the invocation of Pullman abstention: (1) The state law must be unclear, and (2) it must be subject to an interpretation that will avoid the federal constitutional question. ", "Field, supra, at 1088; Lake Carriers' Association v. MacMullan, 406 U.S. 498, 92 S.Ct. ", "1749, 32 L.Ed.2d 257 (1972); Harman v. Forssenius, 380 U.S. 528, 534, 85 S.Ct. ", "1177, 1181, 14 L.Ed.2d 50 (1965). ", "The principal reason for this dual requirement is that federal courts are primarily responsible for interpreting federal law.", "\nIt is an insufficient reason for abstention, nevertheless, that a federal court might, as a matter of comity, wish to give the state courts the first opportunity to pass on the federal constitutionality of a state statute. ", "Field, supra, at 1088 ff. ", "Therefore, it being admitted that the state statute under consideration is neither unclear nor subject to an interpretation which would resolve the federal constitutional problem, the court determined that abstention was inappropriate in this case.", "\n\nDUE PROCESS\nFor reasons more fully set out below, on May 19, 1981, this court ruled that section 208.430(2) of Kentucky Revised Statutes is unconstitutional to the extent that it permits CHR to remove committed children from the physical custody of their natural parents without delineating standards for such removal and without affording the parents and children any prior written notice and prior opportunity for a hearing. ", "The statute is violative of the fourteenth amendment to the United States Constitution in that it deprives the parents and children of their rights to liberty and family *1182 integrity without due process of law. ", "Similarly, the defendants' acts, practices and policies of removing children under such circumstances are unconstitutional.", "\nThis court issued an injunction on May 19, 1981, prohibiting the defendants from removing committed children from the physical custody of their natural parents without first providing the family with written notice and an opportunity for a fair hearing. ", "The defendants were further enjoined from removing children in this situation without first establishing written standards that would adequately advise parents and children of the circumstances under which removal might occur and that would properly limit CHR's discretion. ", "The court permitted the defendants a reasonable time to submit recommendations to the court regarding the notices, procedures and standards. ", "It is important to understand that this injunction did not apply in full force if a child were faced with a genuine emergency. ", "If the social worker had probable cause to believe that it was necessary to remove the child because the child faced imminent death or serious bodily injury, then removal was authorized, although CHR was then required to provide the family with a prompt post-removal fair hearing.", "\nIn analyzing what process, if any, was due the plaintiffs in this case under the fourteenth amendment, the court employed the factors set out in Mathews v. Eldridge, 424 U.S. 319, 96 S.Ct. ", "893, 47 L.Ed.2d 18 (1976). ", "Under the Mathews test, the first consideration is the type of private interest being affected. ", "It has been recognized in numerous cases that family integrity is an interest of the very strongest type. ", "See, e.g., Stanley v. Illinois, 405 U.S. 645, 92 S.Ct. ", "1208, 31 L.Ed.2d 551 (1972); Smith v. Organization of Foster Families for Equity and Reform, 431 U.S. 816, 97 S.Ct. ", "2094, 53 L.Ed.2d 14 (1977); Santosky v. Kramer, 455 U.S. 745, 102 S.Ct. ", "1388, 71 L.Ed.2d 599 (1982). ", "These cases derive from the same body of case law as Meyer v. Nebraska, 262 U.S. 390, 43 S.Ct. ", "625, 67 L.Ed. ", "1042 (1923); Pierce v. Society of Society of Sisters, 268 U.S. 510, 45 S.Ct. ", "571, 69 L.Ed. ", "1070 (1925); Griswold v. Connecticut, 381 U.S. 479, 85 S.Ct. ", "1678, 14 L.Ed.2d 510 (1965); and Moore v. City of East Cleveland, 431 U.S. 494, 97 S.Ct. ", "1932, 52 L.Ed.2d 531 (1977). ", "Although it sometimes permits the state to intrude into family matters, the Constitution of the United States quite properly recognizes that the right of a person to raise his or her own family is an interest of profound and fundamental importance.", "\nThe second factor to be considered under Mathews is the value of an individual hearing in the particular situation involved. ", "Common sense indicates that factual disputes will occur frequently concerning the quality of parental care. ", "For example, authorities might discover that a child is not attending school. ", "Upon further investigation, however, it may be revealed that there is some misunderstanding with the teacher and that the parents are not really culpable. ", "Perhaps the parents are facing a financial crisis of a temporary nature, or perhaps the parent and a particular social worker have a personality conflict that is creating a problem. ", "The logic of providing some form of a hearing in such situations, where one may be deprived of an important interest, has been recognized by the United States Supreme Court in Goss v. Lopez, 419 U.S. 565, 95 S.Ct. ", "729, 42 L.Ed.2d 725 (1975), a school expulsion case.", "\nThe third factor employed in Mathews is the public burden as compared with the private benefit. ", "The requirement of a due process hearing prior to the removal of a child in a non-emergency situation would impose no significant burden on the public. ", "This is not a case, for example, where millions of dollars in welfare benefits might never be recovered if they are improperly paid. ", "Moreover, the interest to be protected is a weighty one.", "\nTested by the principles set out in Mathews, section 208.430(2) of Kentucky Revised Statutes fails to provide due process of law. ", "The previously cited cases dictate that families be afforded a pre-removal hearing in non-emergency cases and a prompt post-removal hearing following an emergency removal of a child. ", "Thus, to the *1183 extent that this statute would permit a removal without such protection, it is violative of the fourteenth amendment.", "\nSimilarly, the procedures employed by the defendants, which permit removal of children from the homes of their natural parents without proper findings of fact, are also unconstitutional. ", "This principle was recognized in Roe v. Conn, 417 F.Supp. ", "769, 778 (M.D.Ala.1976), in which it was asserted that, \"before intrusion into the affairs of the family is allowed, the State should have reliable evidence that a child is in need of protective care.\" ", "Id. at 778. ", "The court indicated that \"this fact finding process, as a matter of basic fairness, should provide notice to the parents and child of the evidence ... and provide them with an opportunity for rebuttal at a hearing before an impartial tribunal.\" ", "Id. This does not mean, however, that a formal hearing before a judge is always required. ", "In some situations, a judicial hearing may not be suitable. ", "What the Constitution requires is a fundamentally fair hearing, which sometimes may be accomplished outside of the judicial context.", "\nThe statute and the practices employed by defendants pursuant to section 208.430(2) are further unconstitutional for failing to include standards to govern the removal of children from their homes. ", "Due process requires that there be some limits on social worker discretion in this regard and that the parents be given adequate notice of the circumstances under which their children may be removed. ", "See Alsager v. District Court of Polk County, 406 F.Supp. ", "10 (S.D.Iowa 1975); Roe v. Conn, 417 F.Supp. ", "769 (M.D.Ala.1976). ", "While this court has determined that there must be standards which are communicated to the family and which limit the discretion of the defendants, the court does not think it proper to implement its views. ", "Therefore, defendants have been ordered to develop standards, relying upon their expertise, and to submit them to the court for approval.", "\nDefendants and plaintiffs have joined in devising and have tendered a set of standards in a proposed consent decree which the court has reviewed carefully. ", "In its order of November 5, 1982, the court tentatively approved the standards, the procedures providing for notice to families who have children committed to CHR, and the procedure providing for due process hearings, all of which were embodied in the proposed consent decree. ", "This tentative approval was subject to notice of this proposed settlement to the class of persons affected in accordance with F.R.Civ.", "P. 23(e). ", "The court ordered CHR to provide reasonable notice to the class of the proposed settlement. ", "Accordingly, the class has been afforded an opportunity to comment on the proposed consent decree.", "\nSince more than two months have elapsed and no objection has been received from any class member concerning the proposed consent decree, it is the ruling of the court that the consent decree fully addresses the concerns that the court had as to the constitutionality of the defendants' practices and of section 208.430(2). ", "Therefore, the consent decree appended hereto is approved and the defendants are ordered to follow its terms.", "\n\nAPPENDIX\n\nUNITED STATES DISTRICT COURT EASTERN DISTRICT OF KENTUCKY COVINGTON NO. ", "77029\nJADEEN SIEREVELD, ET AL. ", " PLAINTIFFS\nvs.\nPETER CONN, ET AL. ", " DEFENDANTS\n PROPOSED CONSENT DECREE REGARDING\n POLICY, STANDARDS AND PROCEDURES\n FOR REMOVAL OF COMMITTED JUVENILES\n FROM HOME OF PARENTS\n ====================================\n\nPOLICY\nWhen a child committed to the Department as dependent, neglected, or abused at some point afterwards is placed in the home of his/her parent(s), the child may not be removed by the Department except in accordance with the standards and procedures detailed below. ", "In addition, the parents must be informed in writing at the time of *1184 placement of the criteria that will be used to determine if removal is necessary.", "\n\nPROCEDURE AND STANDARDS\n1. ", "At the time a committed child is placed in the home of its natural parent(s) by the Department, the parent(s) shall be informed of the conditions of the placement by letter (Exhibit A).", "\n2. ", "If the social worker believes that the committed child continues to be dependent, neglected, or abused, but immediate removal is unnecessary to protect the child from imminent death or serious injury, the casework situation and evidence will be reviewed with the Field Office Supervisor to make a determination to continue work with the family intact or to remove the child. ", "There shall be documentation that the social worker, prior to the court hearing, made an effort to contact the parents to inform them of the specific problems that could lead to removal so that they have an opportunity to take corrective action; if the parents are unavailable or will not respond to attempts to communicate, documentation to this effect will meet the requirement.", "\n3. ", "If it appears that the child's health or welfare or physical, mental, or emotional condition is subjected to or threatened with real and substantial harm and there is not reasonably available an alternative less drastic than removal of the child from the home which would adequately protect the child, the DSS staff shall petition the court to review the case pursuant to KRS 208.205 in relation to the Department's intention to remove the child from the parent(s) home. ", "If the court fails to find that the child's health or welfare or physical, mental, or emotional condition is subjected to or threatened with real and substantial harm, or recommends a less drastic alternative that is reasonably available, the child shall not be removed from the home.", "\n4. ", "The petition shall set forth the facts which constitute the need for removal and the time and place for a hearing to be held. ", "The court is responsible for serving notice of the petition and hearing on the parent(s).", "\n5. ", "If a social worker finds a child unattended who is too young to take care of himself/herself, the social worker shall make reasonable efforts to arrange for an emergency caretaker in the child's home until the parent(s) returns or fails to return within a reasonable time. ", "In the event no in-home caretaker is available for the child, the DSS shall request any appropriate law enforcement officer to take the child into protective custody during such emergency. ", "If, after a reasonable time, it appears the child has been abandoned, the Department shall petition the District Court to review the case.", "\n6. ", "If there exist reasonable grounds to believe that the child is in danger of imminent death or serious injury or is being sexually abused and that the parent(s) is unable or unwilling to protect the child, the social worker may immediately remove the child prior to filing a petition for review. ", "Within 72 hours after such removal, DSS shall cause a petition for review to be filed in District Court pursuant to KRS 208.205 with a request for an expeditious hearing thereon pursuant to paragraph 3.", "\n7. ", "The parents of a committed child placed at home must receive prior notice of all treatment planning conferences concerning the child. ", "The notice must inform them of their right to be accompanied by a representative or legal counsel. ", "If the court provides notice (through summons or other method) the social worker should contact the parents to be sure they received the notice and that the parent is aware of the right to be represented by counsel.", "\nWhen a parent's whereabouts are unknown, notice may be mailed to the last known address of an adult who is a near relative.", "\n\nDEFINITIONS\nA. \"Dependent child\" means any child who is under improper care, control, or guardianship that is not due to the negligence of the parent or guardian, provided that the child is not an abused or neglected child.", "\nB. \"Abused or neglected child\" means a child whose health or welfare is harmed or *1185 threatened with harm when his parent, guardian, or other person who has the permanent or temporary care, custody, or responsibility for the supervision of the child: inflicts or allows to be inflicted upon the child physical or mental injury to the child by other than accidental means; commits or allows to be committed an act of sexual abuse upon the child; willfully abandons or exploits such child; does not provide the child with adequate care and supervision, food, clothing and shelter, education, or medical care necessary for the child's well-being; provided, however, that a parent or guardian legitimately practicing his religious beliefs who thereby does not provide specified medical treatment for a child, for that reason alone shall not be considered a negligent parent or guardian. ", "This exception, however, shall not preclude a court from ordering that medical services be provided to the child, where his health requires it.", "\nC. \"Physical harm\" means physical pain or any impairment of physical condition.", "\nD. \"Emotional harm\" means an injury to the mental or psychological capacity or emotional stability of a child as may be evidenced by a substantial and observable impairment in his ability to function within a normal range of performance and behavior with due regard to his culture, which injury may be directly attributable to the failure, refusal or incapacity of the parent or guardian to exercise a minimum degree of parental care and supervision toward the child.", "\nE. \"Serious injury\" means physical injury which creates a substantial risk of death or which causes serious and prolonged disfigurement, prolonged impairment of health or prolonged loss or impairment of the function of any bodily organ.", "\nHAVE SEEN AND APPROVED:\n/s/ Stanley A. Stratford /s/ James Rogers \n STANLEY A. STRATFORD JAMES ROGERS\n COUNSEL FOR COUNSEL FOR\n DEFENDANTS PLAINTIFFS\n/s/ Paul F. Fauri /s/ Richard Cullison \n PAUL F. FAURI RICHARD CULLISON\n COUNSEL FOR COUNSEL FOR\n DEFENDANTS PLAINTIFFS\n\nEXHIBIT A\n ______________________________\n Name of Child\nTO: Parents\nYour child, named above, has been committed to Cabinet For Human Resources by order of the District Court and Cabinet For Human Resources is placing your child in your custody as parents.", "\nIf the Cabinet receives information that your child has become dependent, abused or neglected during this home placement, but the Cabinet determines the situation is not an emergency requiring immediate removal of the child, an effort will be made to contact you and inform you of the situation that needs to be corrected. ", "A child is considered abused, neglected or dependent when any of the following conditions exist:\na. The child is harmed or threatened with harm through physical or mental injury by other than accidental means.", "\nb. The child is not provided appropriate food, medical care, shelter, clothing or education.", "\nc. The child is caused or permitted to engage in any practice of danger to its health, safety, welfare or morals, including incest or sexual exploitation.", "\nd. The child is abandoned.", "\nIn the event of an emergency which requires immediate removal of the child to prevent imminent death or serious bodily injury to the child, the Cabinet will remove the child without notice or Court order. ", "After an emergency removal, the case will be reviewed by the District Court as soon as possible. ", "For additional information, you may contact the Department For Social Services or the Social Worker named below.", "\n Sincerely yours,\nNOTES\n[1] Throughout the pendency of this action the Department for Human Resources was the Kentucky agency charged with providing services for committed children. ", "Recently, this office became a cabinet office and is now known as the Cabinet for Human Resources (CHR).", "\n[2] The class certification order, filed November 3, 1980, indicated the class was comprised of these members:\n\n(a) All parents who have had their natural children committed to the Kentucky Department for Human Resources as dependent or neglected, and who, after having said children placed in their homes, have had in the past or will have in the future, said children removed from their physical custody by the Department for Human Resources or its employees without first affording parents and children written notice of the removal, and without establishing standards to limit discretion regarding such removal.", "\n(b) The children of parents described in subsection (a) above.", "\n" ]

{ "pile_set_name": "FreeLaw" }

[ 0, 0.02127659574468085, 0.011764705882352941, 0, 0, 0, 0, 0.03076923076923077, 0, 0.020202020202020204, 0.05128205128205128, 0.019230769230769232, 0, 0.0053475935828877, 0, 0.009900990099009901, 0, 0.016260162601626018, 0.008064516129032258, 0.015503875968992248, 0.004166666666666667, 0.0031746031746031746, 0.002288329519450801, 0.00425531914893617, 0, 0.010416666666666666, 0, 0, 0.019230769230769232, 0.007142857142857143, 0.011976047904191617, 0, 0, 0, 0.00904977375565611, 0.006711409395973154, 0.007042253521126761, 0.008, 0, 0.004329004329004329, 0, 0.0136986301369863, 0, 0, 0, 0.022222222222222223, 0, 0, 0.02631578947368421, 0, 0, 0, 0, 0, 0, 0, 0.022988505747126436, 0.012658227848101266, 0, 0, 0, 0, 0, 0.004662004662004662, 0, 0, 0, 0.0036496350364963502, 0, 0, 0.0035714285714285713, 0, 0, 0.010416666666666666, 0, 0.01818181818181818, 0.008620689655172414, 0.013888888888888888, 0, 0.021052631578947368, 0, 0.012987012987012988, 0, 0, 0.011235955056179775, 0, 0, 0.007936507936507936, 0, 0, 0, 0, 0.009345794392523364, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.034482758620689655, 0.009900990099009901, 0, 0, 0, 0, 0, 0, 0, 0.017241379310344827, 0.044444444444444446, 0.05, 0, 0, 0, 0.0036101083032490976, 0, 0, 0.010869565217391304, 0, 0, 0, 0.011904761904761904, 0.03225806451612903, 0.047619047619047616, 0.004246284501061571, 0, 0, 0.005405405405405406, 0, 0.0026666666666666666, 0, 0, 0.006369426751592357, 0, 0, 0, 0, 0, 0, 0.005291005291005291, 0.014492753623188406, 0, 0, 0.01485148514851485, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.009536784741144414, 0.006172839506172839, 0, 0, 0, 0, 0.009708737864077669, 0.010309278350515464, 0.017857142857142856, 0.004830917874396135, 0.019230769230769232, 0.0032414910858995136, 0, 0 ]

[ "What would be the next move be in a full central bank pivot? ", "QE4, let the free money flow.", "\n\nWhat was once experimental and temporary, is now being demanded to keep the overvalued markets roaring. ", "Or perhaps it’s really because everyone knows the next crisis is near and a good dose of QE money printing might just be enough to usher it in. ", "After all, for most, if you know you’re about to declare bankruptcy and you get a new credit card in the mail, the most likely outcome would be to take advantage of any credit you’re given.", "\n\nCalling for the Fed to cut rates and buy more bonds and MBS derivatives, the theory is that taking on more debt will actually encourage the economic expansion and pay for itself over time, which can be true for self-liquidating debt. ", "But governments typically take on non-self-liquidating debt relying on growing tax receipts and inflated wages to enable governments to fund even more debt. ", "For corporations, debt used for stock buybacks, dividends that leave the companies, does nothing to repay the debt. ", "This is why the world is saddled with unpayable debt that inflated the markets but did not “stimulate” the global economies.", "\n\nIn fact, the IMF (International Monetary Fund) has lowered the global growth outlook for the third time in six months, confirming that the trillions in new debt did not have the stated outcome and did not stimulate the economy. ", "It is critically important to understand that the global slowdown is deflationary, so is a falling market. ", "There is only one way to fight deflation and that is with inflation, that is the long-term central bank playbook. ", "But the problem is the dwindling effect of central bank stimulus, particularly since 2007.", "\n\nInsanity is doing the same thing and expecting different results. ", "Is additional QE insanity or is it designed to force a global monetary reset?", "\n\nIf it is about forcing a monetary reset, could it make some sense to have on the Fed board, some members that understand what a savings-based money is? ", "Could this be why President Trump nominated Stephen Moore, who supports both QE4 and a commodity backed currency, and Herman Cain, who wrote in 2012, “A gold standard is to the moochers and looters in government what sunlight and garlic are to vampires” to the Fed board? ", "Perhaps we’ll need them to help the USD regain the confidence of the public after hyperinflation resets the unpayable debt?", "\n\nOne look at the BIS (Bank for International Settlements) Money Flower tells you why gold is most likely to shine once again. ", "It is the only money accessible to you that is widely accepted in peer-to-peer transactions AND is out of the sphere of the central banks. ", "It is the only real, tangible money. ", "Since QE is really about devaluing money, wouldn’t it make sense to hold the kind of money that has proven to hold value for 5,000 years?", "\n\nWhat would be the next move be in a full central bank pivot? ", "QE4, let the free money flow.", "\n\nInsanity is doing the same thing and expecting different results. ", "Is additional QE insanity or is it designed to force a global monetary reset?", "\n\nIf it is about forcing a monetary reset, could it make some sense to have on the Fed board, some members that understand what a savings-based money is?", "\n\nOne look at the BIS (Bank for International Settlements) Money Flower tells you why gold is most likely to shine once again. ", "It is the only money accessible to you that is widely accepted in peer-to-peer transactions AND is out of the sphere of the central banks. ", "It is the only real, tangible money. ", "Since QE is really about devaluing money, wouldn’t it make sense to hold the kind of money that has proven to hold value for 5,000 years?" ]

{ "pile_set_name": "Pile-CC" }

[ 0, 0, 0, 0, 0, 0.00847457627118644, 0, 0, 0, 0.004347826086956522, 0, 0, 0, 0, 0, 0.006493506493506494, 0.014705882352941176, 0.008130081300813009, 0.015748031496062992, 0, 0, 0, 0, 0, 0, 0, 0.006535947712418301, 0.015748031496062992, 0, 0, 0 ]

[ "Today, I’m staring down the initial order deadline for titles releasing in November. ", "The initial order deadline is something I neglect to realize is coming until a few days before they’re due – and while there’s always a lot of prep that is done ahead of time, going through the order book will still take a full work day of mostly uninterrupted thought to get through. ", "Every month is a completely new challenge, with different series popping up all the time, and new incentive programs to ponder all the way through. ", "The goal: make sure you have enough for shelf when the comic hits the stands. ", "The reality: you will never ever succeed at doing this. ", "There are hundreds of titles, and many of them you will have to much of, or too little of. ", "Sometimes all it takes is for one or two people to come in from out of town or to try out your shop for the first time, and suddenly your carefully crafted system is in shambles for one or two of the books on your shelf. ", "Inevitably, this is the one period of time when you suddenly get… I don’t know, let’s say 10 people walking through your door, looking for issues of Spawn when you rarely, if ever, sell copies from the shelf. ", "They know you are out. ", "They can smell the blood in the water, and they want to punish you for it.", "\n\nHi. ", "My name is Brandon Schatz. ", "Welcome to my irregular retail therapy session.", "\n\nThis week, considering the fact that initial orders are due and I’m looking at the order book already, I figured it would be a great time to discuss variants and the poisonous culture that surrounds them. ", "As always, this is going to be full of laffs. ", "I hope your chuckle muscles are ready.", "\n\nDEGREE OF VARIANTS\n\nNovember is the second month in Marvel’s big All-New, All-Different launch cycle, and as such, we are in the eye of the storm. ", "Much like DC’s DC You initiative, Marvel is doing this all in a sizeable chunk, albeit in nearly bite-sized morsels over the course of several months. ", "At this point in time, while DC tends to flail and pump out new initiatives in fits and starts, Marvel has produced a relaunch program that nearly hums like clockwork. ", "They pick a linchpin title, and get that one out the gate first – in this case, it’s the Brian Michael Bendis penned Invincible Iron Man title. ", "They let that launch with relatively little noise surrounding it – which in this case means setting the Final Order Cut-Off date unseasonably early for its date of release, giving retailers one clear choice for where to put their money, thus ensuring a healthy launch for the book. ", "From there, they do the gradual roll out, focusing on tiers of books. ", "A Spider-Man book launches. ", "An Avengers series launches. ", "A Guardians of the Galaxy series launches. ", "An X-Men book launches. ", "One or two second tier books relaunch. ", "One or two fresh titles launch. ", "Any one area is not flooded with content, letting retailers and readers alike focus their attention on certain areas of the publishing schedule. ", "The process repeats each month until the line stabilizes. ", "In a few months, new titles will be launched in a secondary, smaller blast to fill in holes left by under performing books in the publishing schedule, and more often than not, these titles are a bit more risky. ", "If they don’t hit, another season of launches is just a few months to a year away. ", "The cycle continues on a seasonal basis.", "\n\nIt’s a system that seems to frustrate long time readers and retailers, but one that I quite enjoy. ", "It borrows the language of television – a medium dealing with millions on a regular basis, rather than thousands – offering seasons of stories that ebb and flow, always offering something new when titles inevitably start losing steam. ", "Unfortunately, this marketing system is paired with a highly destructive variant program that is dripping poison into the veins of the industry.", "\n\nNow a quick side note: yes, the store I co-own is called Variant Edition. ", "It’s a name we chose quite deliberately, because it sounds very put together and responsible, and offers us the opportunity to pitch the store to people regularly. ", "If you’re reading this, there is a high chance that you are neck deep in the industry, and understand all the lingo – but the majority of the people out there have no idea what a “variant edition” is. ", "When they ask about the store, they inevitably ask why we called it Variant Edition, and we explain: a variant edition is a comic that features an alternative cover image, but contains the same contents. ", "We liked the name Variant Edition because we are a comic store, and we have similar contents to other comic stores, but we’re not the stereotype – we’re something different.", "\n\nAnd in a way, that’s one of the only things that I like about variants – they offer the consumer a choice. ", "What aesthetic do they like best? ", "What speaks to them more? ", "That, I like. ", "The culture that has sprung up around variants? ", "Not so much.", "\n\nIn the current order book, Marvel alone are offering 134 variant covers (this doesn’t include a few announced retroactively, which I’ll be adjusting during the final order cut-off period). ", "All but one of these variants comes with a qualifier. ", "Sometimes you just need to order ten copies of a certain book to get the aforementioned cover. ", "Other times, you have to order 100. ", "Then there’s the ones where you have to exceed 150% (or whatever number they’re using) of a different comic you ordered in order to unlock a particular variant. ", "After you meet that qualification, you can order whatever you want. ", "You just have to spend a lot of money for that “privilege”. ", "The problem with that is simple: whereas the variant should be treated as the means for a customer to further connect with the product, it’s usually treated as collector bait, or worse: blackmail.", "\n\nTake a look at this modified look at some of Marvel’s upcoming hip-hop variants, as made by Strange Adventures:\n\nThe hip-hop covers have garnered a lot of attention for Marvel, both positive and negative. ", "I don’t want to gloss over the negative part too much, but I’m definitely not the voice who needs to be heard regarding this matter – so please see the collection of links at the end of this article for more information. ", "Suffice to say, the result of all of this attention means there are people champing at the bit to get their hands on these covers. ", "The only problem? ", "Marvel has some hoops that need to be jumped through to get them. ", "This is where the blackmail comes in: if you want your customers to get these covers, you have to jump through those hoops – which means you are ordering copies you know you probably won’t sell in order to get these in-demand covers in. ", "So, how do you cover the cost of this? ", "Well, by increasing the price of those sought after covers. ", "Or worse: say you’re a store that qualifies for some of these cover naturally. ", "They are in quite a high demand, and again, you already have your orders covered by the copies of the regular cover you’ve brought in – so you don’t order a whole lot of the variant. ", "Low supply. ", "High demand. ", "What happens?", "\n\nThis variant scheme is built to make sure there is a low supply of higher demand product – with the by-product being increased, and often unsustainable level of regular product on the market. ", "Retailers have been trained to combat this by increasing the price of the sought after comics – but the byproduct of that is a situation where people are paying a much higher price for a product that speaks to them, for a terrible, unsustainable reason. ", "What’s more, it creates the appearance where Marvel, and the retailer, are attempting to unjustly profit from an appropriated culture. ", "And hey – they are, and we are, and that’s something to talk about, but at a base level, having the comic stickered up well over cover price certainly isn’t going to help appearances. ", "It’s honestly one of the main reasons we don’t chase after variants that we qualify for – and even when we do qualify, we sometimes opt out, unless it’s a particularly great image. ", "Regardless, the whole thing is a bad situation – and that’s before you even get to the clear over-reliance this industry has on variant culture in general.", "\n\nRemember when I said that Marvel was offering 134 variant covers for November? ", "Well, they are only shipping 63 titles – and a few of those are two issues of one book. ", "So easy math says there’s more than two variants for every single issue released on average – or rather, the market is supporting the weight of an immense amount of product with a third of the unique product as a base. ", "This is not a sustainable model, but one that’s born out of the ever increasing pressure that the companies are under to keep profits and volume up. ", "I absolutely understand why they need to do it – there is a demand in place to show more and more and more from shareholders or higher ups, and the growth rate expected often far outstrips what can be achieved organically. ", "I don’t envy anyone at the big two whose job it is to meet these quotas either directly, or indirectly. ", "That said, it’s clearly building a flawed system – one that will surely collapse given the slightest amount of pressure in the wrong areas, at the wrong times.", "\n\nThis doesn’t even begin to touch the truly decedent qualifying structures of some recent variants. ", "For issue one of DC’s Dark Knight III, they are offering a 1 for 5000 variant. ", "To be fair to them, this variant will feature an original sketch from Jim Lee on it. ", "Marvel on the other hand, is offering a 1 for 4999 copy variant for Deadpool #1 that I believe is just a black-and-white reproduced “sketch” version of another one of their Deadpool #1 variants. ", "There are a few others than have 1 for 500 qualifiers on them, a few others that clock in at 1 for 100, and a slew of covers that need you to order 25 copies in order to get just one of a certain other cover. ", "All of this contributes to a glut of product – the kind that clearly cannot be sustained in this fashion – and has some pretty dark portents for the future of the industry – but honestly, I’m running a little low on time to dig both hands into that for this week, and there’s another thing I want to discuss as well.", "\n\nBACK MATTER\n\nBecause of all of that meandering nonsense wasn’t enough already.", "\n\nLast time in The Retailer’s View, I talked about how DC’s marketing for their new line-up really failed to connect with retailers and readers. ", "Well, since that column went up, a few things happened. ", "First, the publisher published their December solicitations wherein they cancelled a swath of books, including Justice League United, Omega Men, Gotham by Midnight, Lobo, Sensation Comics featuring Wonder Woman, and Batman ’66. (", "In the week that has passed, Omega Men was granted a stay of execution, letting the series play out its originally scheduled 12 issues.) ", "There was also the notable absence of Doomed and Green Lantern: Lost Army, which representatives said were always intended to be six issue stories – which I think is kind of hilarious, just… in a really depressing way.", "\n\nDoomed and Green Lantern: Lost Army were both solicited and treated like ongoing series, right up until now. ", "It’s a strategy that I said would have benefited a book like Prez, as retailers are honestly less likely to support anything labelled as a mini-series. ", "The fact that DC is now claiming these books to have been secret minis all along means one of two things: one, they are attempting to save face with two ongoing that under performed and are being fairly disingenuous about it – or two, they had a slate of mini-series, and decided to act inconsistently towards marketing them, giving Doomed and Lost Army the tiniest extra push by giving the appearance of an ongoing status. ", "Whichever scenario is true, it shows how very chaotic the publishing and marketing plan is for the company at this moment – and how they have no clue how to fully utilize the tools at their disposal.", "\n\nAlmost all projects should be solicited as ongoing concerns. ", "A lot of people don’t like that idea, because it supposedly makes ordering comics harder. ", "How do you know when to taper off a series when it’s going to end? ", "How do you know you should order heavier on a first issue so that you can sell it through the series’ two to five year run? ", "Simply put: you don’t. ", "Ordering in this fashion is a remnant of an old system where comic shops were the only place people could get their hands on stories, and the single issue format was the be-all, end-all. ", "Today, stories are collected with regularity, often right around the time a storyline has wrapped. ", "These stories are also available digitally in perpetuity, and often at a far lesser price than the physical copy (after a few months have passed). ", "For the reader, what is the benefit of having the single issues available to purchase years from now, when there are easier and cheaper formats to grab to help bring you up to speed? ", "Yes, some people prefer the single issue format – but those readers are usually in either every week or every month to grab those single copies – and the ones that aren’t are generally pretty happy with a second or third printing to bring them up to speed. ", "The only reason to use older ordering models, is to placate the collector’s market, which is often volatile and always, always, always unsustainable.", "\n\nI’ve always believed that ordering for readers is the right way to go. ", "They’re the ones who always come back for the books that they love. ", "They’re not just buying things to flip, they’re buying things to enjoy, and when you work up a nice relationship with them, they will be with you for as long as you and the medium maintain their interest. ", "These people are the beating heart of the industry, the ones who will stick with you through thick and thin as gimmicks bloom and die. ", "They are more than happy to get a second or third printing, because they just want to read the story. ", "They also don’t really care if a story is ongoing, or just a few issues – they just want to be entertained – and when they’re not being entertained, they’ll walk away from the series. ", "Issue numbers don’t matter. ", "Series length doesn’t matter. ", "It’s story – and it’s ordering to sustain match the interest of your regular readers. ", "And honestly, if you’re really concerned about having back stock, by the time a story or series is wrapped up, you’ll get issues trickling back towards you as some people tour around the various comic shops, looking to get rid of some books they read, but no longer need in their collection – and since it’s back stock, a retailer can often pick that product up for cheaper than they paid Diamond for their initial orders. ", "Or at least, that’s my take. ", "I’m only five months into running my own store after eight years of thinking I could do better, so we’ll see how that all shakes out. ", "Currently, things are going far better than we’d originally projected, so there’s that.", "\n\nPICS OR IT DIDN’T HAPPEN\n\nFor what it means, DC isn’t even consistent with how they present their mini-series to readers. ", "Some of the number ones have the “of six” denotation. ", "Prez doesn’t. ", "Most of the others lose this demarkation as of issue #2, with only Bizarro continuing its numbering. ", "The reason for this? ", "Who knows. ", "Regardless, they aren’t being consistent with their message – if they even know what message they’re trying to convey at all.", "\n\nThey also retroactively placed twelve issue limiters on Telos and Superman: Lois and Clark after previously announcing them as ongoings alongside Titans Hunt. ", "Why? ", "Who knows. ", "Maybe they were always twelve issue minis, or maybe these titles were approved before the final numbers came back on Convergence (including returns) and they decided to talk things back. ", "Honestly, there doesn’t seem to be a rhyme or reason for how DC is presenting or marketing their series these days, and that lack of concrete confidence is really hurting them. (", "Plus, a Telos series? ", "Really? ", "Go ahead and try to pitch that to a person on the street. ", "You can’t.)", "\n\nTO BE CONTINUED…\n\nThere’s another edition of The Retailer’s View on tap for next week. ", "If nothing crazy happens, it will be about how comic shops became clubhouses, and how the clubhouse mentality is bad for the industry. ", "If something crazy happens, it will probably be about that instead. ", "Working ahead is a hell of a thing.", "\n\nUntil next time…\n\n[Brandon Schatz is an owner of Variant Edition in Edmonton, Alberta and has spent the past nine years working behind the comic book counter. ", "In his spare time, he writes about the comics and culture. ", "You can find him on twitter @soupytoasterson and at his website, Submetropolitan. ", "The opinions expressed are those of Schatz and do not necessarily reflect those of The Beat.]" ]

{ "pile_set_name": "OpenWebText2" }

[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.037037037037037035, 0, 0, 0, 0, 0.006711409395973154, 0.013245033112582781, 0.005952380952380952, 0.013888888888888888, 0.0035460992907801418, 0, 0.03571428571428571, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.005235602094240838, 0, 0, 0, 0, 0, 0, 0, 0.014492753623188406, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.007407407407407408, 0, 0, 0, 0.012345679012345678, 0, 0, 0, 0, 0, 0, 0, 0.02531645569620253, 0.011764705882352941, 0, 0, 0, 0, 0, 0, 0.026200873362445413, 0.0072992700729927005, 0, 0, 0, 0.0023584905660377358, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.008, 0.024844720496894408, 0, 0, 0.0053475935828877, 0, 0.045454545454545456, 0, 0, 0, 0, 0, 0, 0, 0.006211180124223602, 0, 0.012195121951219513, 0.010752688172043012 ]

[ "Q:\n\nAdd string to url on page load with jQuery?", "\n\nI'm trying to add this specific string to the end of my url on page load:\n?", "aa_campaign=f45632\n(http://examplesite.com/test.html)\nIt's for marketing and tracking. ", "\nI've tried this:\nif window.location.href.indexOf(\"http://examplesite.com/test.html\") {\n window.location = \"http://examplesite.com/test.html?aa_campaign=f45632\";\n}\n\nThat straight up didn't work but the idea is what I'm looking for. ", "Any thoughts?", "\n\nA:\n\nNo need for jQuery, you can do this with pure JavaScript in most \"modern\" browsers, i.e.:\nif (window.location.href === \"http://examplesite.com/test.html\") {\n window.history.pushState(\"object or string\", \"Title\", \"http://examplesite.com/test.html?aa_campaign=f45632\");\n}\n\nThe pushState() method\n\npushState() takes three parameters: a state object, a title (which is\n currently ignored), and (optionally) a URL. ", "Let's examine each of\n these three parameters in more detail:\nstate object — The state object is a JavaScript object which is associated with the new history entry created by pushState(). ", "Whenever\n\nthe user navigates to the new state, a popstate event is fired, and\n the state property of the event contains a copy of the history entry's\n state object.", "\nThe state object can be anything that can be serialized. ", "Because Firefox saves state objects to the user's disk so they can be restored\n\nafter the user restarts the browser, we impose a size limit of 640k\n characters on the serialized representation of a state object. ", "If you\n pass a state object whose serialized representation is larger than\n this to pushState(), the method will throw an exception. ", "If you need\n more space than this, you're encouraged to use sessionStorage and/or\n localStorage.", "\ntitle — Firefox currently ignores this parameter, although it may use it in the future. ", "Passing the empty string here should be safe\n\nagainst future changes to the method. ", "Alternatively, you could pass a\n short title for the state to which you're moving.", "\nURL — The new history entry's URL is given by this parameter. ", "Note that the browser won't attempt to load this URL after a call to\n\npushState(), but it might attempt to load the URL later, for instance\n after the user restarts the browser. ", "The new URL does not need to be\n absolute; if it's relative, it's resolved relative to the current URL.", "\n The new URL must be of the same origin as the current URL; otherwise,\n pushState() will throw an exception. ", "This parameter is optional; if it\n isn't specified, it's set to the document's current URL.", "\n\nSRC : https://developer.mozilla.org/en-US/docs/Web/Guide/API/DOM/Manipulating_the_browser_history\n\nA:\n\nYou can add the string to window.location.search instead, for a more general solution.", "\n\nif (location.origin + location.pathname === 'your url here') {\r\n location.search += 'additional data here';\r\n}\n\nThe advantage of this approach is that you can apply this code to multiple pages with less changes to the same code.", "\nNote that this will cause a page reload, which might not be optimal to user experience. ", "Since you said you are doing this for tracking, you can instead ping the page by appending an image with the new url to DOM. ", "Something like this:\n\nvar pinger = new Image(0,0); // keep the size of the image 0\r\npinger.src = 'changed url here, with the new query param appended';\r\ndocument.body.appendChild(pinger); // ping sent\r\npinger.parentNode.removeChild(pinger); // remove the node when ping is sent\n\nHope that helps :)\n\n" ]

{ "pile_set_name": "StackExchange" }

[ 0.02127659574468085, 0, 0.011494252873563218, 0.008583690987124463, 0, 0.009501187648456057, 0.005291005291005291, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.005235602094240838, 0, 0, 0, 0.006688963210702341 ]

[ "I wanted to play Miss Havisham because she's an iconic character who pervades our world in various forms. ", "So many people have written about her or based other characters on her over many decades.", "\n\nI was interested in what it was that was so appealing about her, what it is that seems to get under people's skin.", "\n\nGillian Anderson as Miss Havisham in Great Expectations\n\nWe're talking about a woman who is deeply, almost psychotically manipulative and potentially really psychologically damaging to Pip and Estella, the two children that we see her have this direct impact on.", "\n\nThere was a curiosity there for me. ", "Also reading the scripts and appreciating the adaptation but then also going back and reading Great Expectations and kind of falling in love with her complexities.", "\n\nI don't know how much of that was about falling in love with my interpretation of her, or what I was getting off the page of the script.", "\n\nI've tried to remember what my innocent reader's eyes were picking up on when I first took a look at Great Expectations when I was younger and whether she still held that position for me in terms of awe, as she does now.", "\n\nI have a feeling it was probably different, a very uncomfortable take I had on her really early on.", "\n\nI don't know whether my ideas are based on other people's ideas of how she's been built up over time.", "\n\nThe bottom line was knowing that the BBC would do a spectacular production.", "\n\nIn order to see this content you need to have both Javascript enabled and Flash installed. ", "Visit BBC Webwise for full instructions\n\nTrailer: 'Your eyes have been opened... and now you cannot close them'\n\nI think probably my favourite room on the set was the drawing room of Satis House because of the depth of it, the depth of the history, the muted colours, the butterflies, the birds and then the decay on top of all of that, the vastness, the height of the ceilings and the shafts of light just barely peeking through the windows... all of that.", "\n\nI also really admired Sarah Phelps' adaptation and felt this was the one I wanted to be involved in.", "\n\nGreat Expectations is my favourite Charles Dickens book, because I feel like it has a humanity to it that has always moved me.", "\n\nThat starts at the very beginning with Magwitch being moved by Pip's bravery, of identifying the fact that this young boy is going to save a stranger by stealing the file from the one person he loves, and the person who loves him.", "\n\nThe heartbreak of Pip deciding to do that act and then at the last minute, grabbing a piece of pie for Magwitch.", "\n\nIt's recognised in that moment as Pip hands the pie over, that it also breaks Magwitch's heart.", "\n\nThat moment of pure innocence and humanity not only transforms Pip's life - unfortunately also in a negative way - but transforms those two human beings.", "\n\nIt opens Magwitch's heart in a way it has not been opened up before. ", "It also carries you through the rest of the book, because it's a pure moment of one human being's kindness to another against everything he knows, up until that point.", "\n\nI think Dickens' novels endure because there are common recognisable themes.", "\n\nHis characters are so complex, so multifaceted, painful and tragically human. ", "But also he draws such interesting stories - he is a wonderful storyteller.", "\n\nIn order to see this content you need to have both Javascript enabled and Flash installed. ", "Visit BBC Webwise for full instructions\n\nMiss Havisham interrogates Pip\n\nI am sure it also matters when somebody read the book and what their situation was at that particular time.", "\n\nA lot of people I know who said Great Expectations is their favourite book are men.", "\n\nDid they read it when they were pre-pubescent and feeling lost and misunderstood? ", "Pip is feeling the awe of the wider world, the world beyond, and how Miss Havisham draws him into that, and opens his eyes and his heart, ultimately to crush it.", "\n\nI can imagine being a young man, and reading Pip's journey, falling in love in a mysterious way in this magical house where you have come from the hardship of working in a forge and having lost all of your brothers and sisters save one.", "\n\nAnd here's hope, here is a door to the rest of the world - and then having that shut and then reopened.", "\n\nI can imagine that journey as a young kid, especially a young boy, must be unbelievably exciting.", "\n\nIt was the journey pre-Harry Potter. ", "Of course it was longer ago, but I can imagine young people having the same kind of magical response to Great Expectations that we did when Harry Potter books first started to come out.", "\n\nThat's if it does get introduced at an early age, in school or through a parent or whatever and the child is able to crack the density of it.", "\n\nThis wasn't my experience of it. ", "My experience of it was dipping into it here and there and probably reading most of it in my late 20s.", "\n\nI can only imagine the magic of it and the immersion in that world at a younger age.", "\n\nGillian Anderson plays Miss Havisham in Great Expectations.", "\n\nGreat Expectations starts on BBC One and BBC One HD on Tuesday, 27 December at 9pm.", "\n\nFor further programme times, please visit the upcoming episodes page.", "\n\nWatch Gillian (in costume) talking further about the Great Expectations script and set.", "\n\nRead an article by Mike Osborn on the 'youthful' air of Gillian Anderson's Miss Havisham.", "\n\nComments made by writers on the BBC TV blog are their own opinions and not necessarily those of the BBC.", "\n\n" ]

{ "pile_set_name": "OpenWebText2" }

[ 0.009433962264150943, 0, 0, 0.015151515151515152, 0, 0.006134969325153374, 0, 0, 0, 0, 0.012987012987012988, 0.021505376344086023, 0.002188183807439825, 0.00980392156862745, 0.0078125, 0.008620689655172414, 0.008771929824561403, 0.010309278350515464, 0.0064516129032258064, 0.014084507042253521, 0, 0.01282051282051282, 0, 0, 0.021505376344086023, 0.016666666666666666, 0.011764705882352941, 0, 0.006211180124223602, 0.004201680672268907, 0, 0, 0, 0.010810810810810811, 0, 0, 0, 0, 0.03278688524590164, 0.03529411764705882, 0, 0, 0.03296703296703297, 0.018867924528301886, 0 ]

[ "Q:\n\nPostgreSQL Full Text Search and reserved words, preserving some words\n\nI am using Postgresql with full test search with english dict. ", "When I want to receive records with some english words I get verid results.", "\nAnd so:\nSELECT id FROM table1 WHERE ts_vector1 @@ to_tsquery('it')\n\nreturns 0 results.", "\nSELECT id FROM table1 WHERE ts_vector1 @@ to_tsquery('specialist & it')\n\nreturns more than 0 results (word 'it' exists in table and index). ", "ts_vector1 is created as follow:\nts_vector1 = to_tsvector('english', some_text_column)\n\nIs 'it' a reserved word? ", "If so, what is the best way to 'escape' reserved words?", "\n\nA:\n\n'It' is ignored as a stop word, per the relevant docs:\nhttp://www.postgresql.org/docs/current/static/textsearch-controls.html\n\nIn the example above we see that the resulting tsvector does not contain the words a, on, or it, the word rats became rat, and the punctuation sign - was ignored.", "\n\nYou can change the list of stop words by configuring the needed dictionaries:\nhttp://www.postgresql.org/docs/current/static/textsearch-dictionaries.html\n\n" ]

{ "pile_set_name": "StackExchange" }

[ 0.007246376811594203, 0, 0, 0.0070921985815602835, 0, 0, 0.003389830508474576, 0.00641025641025641 ]

[ "Governor Briggs\n\nGovernor Briggs may refer to:\n\nAnsel Briggs (1806–1881), 1st Governor of Iowa\nFrank A. Briggs (1858–1898), 5th Governor of North Dakota\nGeorge N. Briggs (1796–1861), 19th Governor of Massachusetts" ]

{ "pile_set_name": "Wikipedia (en)" }

[ 0.028169014084507043 ]

[ "White Privilege Conference: Being white is like being an alcoholic\n\nThe 15th annual National White Privilege Conference took place in Madison, Wisconsin, last week — subjecting attendees to informational sessions that explained why everything they did was inherently racist and oppressive.", "\n\nThe conference was funded in part by hotel tax revenues, the University of Wisconsin and the City of Madison — in other words, by taxpayer dollars. ", "It was a colorful week, according to an account by the MacIver Institute\n\nKim Radersma, a former high school English teacher and current activist, hosted a session titled, “Stories from the front lines of education: Confessions of a white, high school English teacher.”", "\n\n“Teaching is a political act, and you can’t choose to be neutral,” said Radersma. “", "You are either a pawn used to perpetuate a system of oppression or you are fighting against it. ", "And if you think you are neutral, you are a pawn.”", "\n\nAll teachers who do not actively confront the system are promoting white supremacy, said Radersma.", "\n\nShe also said that white people fighting oppression is akin to alcoholic trying to resist the temptation to drink. ", "The dark sickness of racism is at the heart of all the actions of white people.", "\n\nShe also articulated the view that black students were better off being taught by black teachers, since white people have little to offer them.", "\n\n“You need to learn feminism from a woman,” she said. “", "You need to learn what it is like to be a woman from a woman. ", "I can’t teach students of color nearly as well as a person of color can.”", "\n\nRadersma is white, as were the vast majority of the participants, according to a photograph of the event.", "\n\nThe price tag for attending WPC varies depending on whether you are a student and when you apply, but it can run as high as $440. ", "At its cheapest, it still costs $200.", "\n\nConference organizers did not respond to a request for comment.", "\n\nWhen white people give charity to black people, it’s because they are racist.", "\n\nA white attendee shared an anecdote with participants: Her family donated school supplies to a disadvantaged minority family. ", "The attendeed realized–and Radersma agreed–that her family had perpetrated racism against the minority family.", "\n\n“It’s that savior mentality… ‘we need to think of them and give them our sympathy and our charity and our generosity,’ which is so demeaning to the people on the receiving end,” said Radersma. “", "It’s so demoralizing and disempowering to be receiving it.”" ]

{ "pile_set_name": "Pile-CC" }

[ 0.006920415224913495, 0.006666666666666667, 0.0037174721189591076, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.007575757575757576, 0, 0, 0, 0, 0, 0, 0 ]

[ "Q:\n\nIs prefix scan CUDA sample code in gpugems3 correct?", "\n\nI've written a piece of code to call the kernel in the book GPU Gems 3, Chapter 39: Parallel Prefix Sum (Scan) with CUDA.", "\nHowever the results that I get are a bunch of negative numbers instead of prefix scan.", "\nIs my kernel call wrong or is there something wrong with the code from the GPU Gems 3 book?", "\nHere is my code:\n#include <stdio.h>\n#include <sys/time.h>\n#include <cuda.h>\n\n__global__ void kernel(int *g_odata, int *g_idata, int n, int dim)\n{\n extern __shared__ int temp[];// allocated on invocation\n int thid = threadIdx.x;\n int offset = 1;\n\n temp[2*thid] = g_idata[2*thid]; // load input into shared memory\n temp[2*thid+1] = g_idata[2*thid+1];\n for (int d = n>>1; d > 0; d >>= 1) // build sum in place up the tree\n {\n __syncthreads();\n if (thid < d)\n {\n int ai = offset*(2*thid+1)-1;\n int bi = offset*(2*thid+2)-1;\n temp[bi] += g_idata[ai];\n }\n offset *= 2;\n }\n if (thid == 0) { temp[n - 1] = 0; } // clear the last element\n for (int d = 1; d < n; d *= 2) // traverse down tree & build scan\n {\n offset >>= 1;\n __syncthreads();\n if (thid < d)\n {\n int ai = offset*(2*thid+1)-1;\n int bi = offset*(2*thid+2)-1;\n int t = temp[ai];\n temp[ai] = temp[bi];\n temp[bi] += t;\n }\n }\n __syncthreads();\n g_odata[2*thid] = temp[2*thid]; // write results to device memory\n g_odata[2*thid+1] = temp[2*thid+1];\n}\n\nvoid Initialize(int *h_in,int num_items)\n{\n int j;\n for(j=0;j<num_items;j++)\n\n h_in[j]=j;\n printf(\" input: \");\n printf(\"\\n\\n\");\n}\n\nint main(int argc, char** argv)\n{\n int num_items = 512;\n\n int* h_in = new int[num_items];\n\n // Initialize problem \n Initialize(h_in, num_items);\n\n int *d_in = NULL;\n cudaMalloc((void**)&d_in, sizeof(int) * num_items);\n\n if(cudaSuccess !", "= cudaMemcpy(d_in, h_in, sizeof(int) * num_items, cudaMemcpyHostToDevice)) fprintf(stderr,\"could not copy to gpu\");\n\n // Allocate device output array\n int *d_out = NULL;\n cudaMalloc((void**)&d_out, sizeof(int) * (num_items+1));\n\n kernel<<<1,256,num_items*sizeof(int)>>>(d_out, d_in,num_items, 2);\n\n int* h_out= new int[num_items+1];\n if(cudaSuccess !", "= cudaMemcpy(h_out,d_out,sizeof(int)*(num_items+1),cudaMemcpyDeviceToHost))fprintf(stderr,\"could not copy back\");\n int i;\n printf(\" \\n\");\n for(i=0;i<num_items;i++)\n printf(\" ,%d \",h_out[i]);\n // Cleanup\n if (h_in) delete[] h_in;\n if (h_out) delete[] h_out;\n if (d_in) cudaFree(d_in);\n if (d_out) cudaFree(d_out);\n\n printf(\"\\n\\n\");\n\n return 0;\n}\n\nA:\n\nIt seems that you've made at least 1 error in transcribing the code from the GPU Gems 3 chapter into your kernel. ", " This line is incorrect:\ntemp[bi] += g_idata[ai];\n\nit should be:\ntemp[bi] += temp[ai];\n\nWhen I make that one change to the code you have now posted, it seems to print out the correct (exclusive-scan) prefix sum for me. ", " There's a few other things I would mention:\n\nEven without that change, I get some results that are close to correct. ", " So if you're getting widely different stuff (e.g. negative numbers) you may have a problem with your machine setup or CUDA install. ", " I would suggest using more rigorous cuda error checking than what you have now (although a machine setup problem should have been indicated in one of your checks.)", "\nThe routine as crafted will have some limitations. ", " It can only be used in a single threadblock, it will have bank conflicts on shared memory access, and it will be limited in data set size to what can be handled by a single threadblock (this routine produces two output elements per thread, so the data set size is expected to be equal to twice the number of threads). ", " As has been already covered, the dynamic shared memory allocation needs to be as large as the data set size (ie. ", "twice the thread size, in number of elements).", "\nThis may be useful for learning, but if you want a robust, fast prefix scan, you are advised to use a routine from thrust or cub instead of your own code, even if derived from this (old) article.", "\n\nThe following code is similar to yours, but it has the above issues fixed, and I have templated the kernel for use with various datatypes:\n#include <stdio.h>\n#define DSIZE 512\n#define cudaCheckErrors(msg) \\\n do { \\\n cudaError_t __err = cudaGetLastError(); \\\n if (__err !", "= cudaSuccess) { \\\n fprintf(stderr, \"Fatal error: %s (%s at %s:%d)\\n\", \\\n msg, cudaGetErrorString(__err), \\\n __FILE__, __LINE__); \\\n fprintf(stderr, \"*** FAILED - ABORTING\\n\"); \\\n exit(1); \\\n } \\\n } while (0)\n\ntypedef int mytype;\n\ntemplate <typename T>\n__global__ void prescan(T *g_odata, T *g_idata, int n)\n{\n extern __shared__ T temp[]; // allocated on invocation\n int thid = threadIdx.x;\n int offset = 1;\n temp[2*thid] = g_idata[2*thid]; // load input into shared memory\n temp[2*thid+1] = g_idata[2*thid+1];\n for (int d = n>>1; d > 0; d >>= 1) // build sum in place up the tree\n {\n __syncthreads();\n if (thid < d)\n {\n int ai = offset*(2*thid+1)-1;\n int bi = offset*(2*thid+2)-1;\n temp[bi] += temp[ai];\n }\n offset *= 2;\n }\n if (thid == 0) { temp[n - 1] = 0; } // clear the last element\n for (int d = 1; d < n; d *= 2) // traverse down tree & build scan\n {\n offset >>= 1;\n __syncthreads();\n if (thid < d)\n {\n int ai = offset*(2*thid+1)-1;\n int bi = offset*(2*thid+2)-1;\n T t = temp[ai];\n temp[ai] = temp[bi];\n temp[bi] += t;\n }\n }\n __syncthreads();\n g_odata[2*thid] = temp[2*thid]; // write results to device memory\n g_odata[2*thid+1] = temp[2*thid+1];\n}\n\nint main(){\n\n mytype *h_i, *d_i, *h_o, *d_o;\n int dszp = (DSIZE)*sizeof(mytype);\n\n h_i = (mytype *)malloc(dszp);\n h_o = (mytype *)malloc(dszp);\n if ((h_i == NULL) || (h_o == NULL)) {printf(\"malloc fail\\n\"); return 1;}\n cudaMalloc(&d_i, dszp);\n cudaMalloc(&d_o, dszp);\n cudaCheckErrors(\"cudaMalloc fail\");\n for (int i = 0 ; i < DSIZE; i++){\n h_i[i] = i;\n h_o[i] = 0;}\n cudaMemset(d_o, 0, dszp);\n cudaCheckErrors(\"cudaMemset fail\");\n cudaMemcpy(d_i, h_i, dszp, cudaMemcpyHostToDevice);\n cudaCheckErrors(\"cudaMemcpy 1 fail\");\n prescan<<<1,DSIZE/2, dszp>>>(d_o, d_i, DSIZE);\n cudaDeviceSynchronize();\n cudaCheckErrors(\"kernel fail\");\n cudaMemcpy(h_o, d_o, dszp, cudaMemcpyDeviceToHost);\n cudaCheckErrors(\"cudaMemcpy 2 fail\");\n mytype psum = 0;\n for (int i =1; i < DSIZE; i++){\n psum += h_i[i-1];\n if (psum !", "= h_o[i]) {printf(\"mismatch at %d, was: %d, should be: %d\\n\", i, h_o[i], psum); return 1;}\n }\n return 0;\n}\n\n" ]

{ "pile_set_name": "StackExchange" }

[ 0.017857142857142856, 0.008130081300813009, 0, 0, 0.001314060446780552, 0.01358695652173913, 0.004024144869215292, 0, 0, 0.007518796992481203, 0, 0, 0, 0, 0, 0, 0.0034602076124567475, 0.0068212824010914054, 0 ]

[ "Microwave conductivity of very thin graphene and metal films.", "\nThe surface resistance of Ag, Au and A1 thin conducting films deposited on low loss dielectric substrates at microwave frequencies using TE011 mode single post-dielectric resonator (10-13.22 GHz) was measured to calculate their conductivity in relation to layers thickness. ", "This method enabling measurements near metal-insulator percolation transition was also applied for epitaxial graphene deposited on semi-insulating SiC. Moreover, effective microwave conductivity has been determined for intentionally made aluminum island structure where the DC conductivity is equal to zero. ", "Special attention was paid to films thickness measurements which is critical for accuracy of sheet resistance calculation. ", "Conductivity of thin metal layers and very thin graphene was compared." ]

{ "pile_set_name": "PubMed Abstracts" }

[ 0, 0.014545454545454545, 0.003246753246753247, 0, 0 ]

[ "---\nabstract: 'It is discussed the singular string associated to the gauge field of monopoles must be a physical observable if the monopole charge $g$ is different from zero, $g\\neq 0$. It is naturally found that if the gauge is to be an observable, it is possibly connected to gravity.'", "\nauthor:\n- Dario Sassi Thober\n- 'Center for Research and Technology CPTec - Unisal'\n- 'thober@fnal.gov thober@cptec.br'\n- 'Phone.55-19-7443107 Fax.55-19-7443036'\ntitle: The definition of a magnetic monopole in Electrodynamics combined with Gravitation\n---\n\nIntroduction\n============\n\nSome non solved fundamental theoretical questions are involved in the definition of the magnetic charge or monopole in Quantum Electrodynamics. ", "One of these questions is the non - observable singular gauge string (many times called Dirac string). ", "Electric charges must never touch such strings according to the original Dirac’s proposal, \\[1,2\\]. ", "In section 2 it is discussed the general problems related to Dirac monopoles \\[3,4\\] and the topologycal solution of Wu and Yang \\[5,6,7\\] where the gauge theory is identified to a Fiber - Bundle geometric structure. ", "According to this view Dirac strings are said to be non - observable. ", "In the same section we cite the important recent work of He, Qiu and Tze \\[8\\] in which it is proven no magnetic charge different from zero in Quantum Electrodynamics is possible if the string is not a physical observable. ", "This cleary shows that pure Quantum Electrodynamics (as we know it) does not supports monopoles in any way.", "\n\nWe follow identifying that in general the monopole string may have some volume in the three - dimensional flat world. ", "This implies that for $g\\neq 0$ (the monopole’s charge different from zero) one has to consider a reduced physical world for the particles and fields in interaction with the monopole. ", "The string is the place where the gauge potential is not defined, and as a consequence (in the general case of volumetric string) the monopole’s magnetic field is also not defined in this region. ", "In section 3 we consider Gravity as seen in a three - dimensional flat world, showing there are forbidden places for particles and fields in the case even a small spherical mass is present. ", "Defining the electromagnetic vector potential as having a volumetric singular string, it is the same as to define it in a reduced physical space relative to the three - dimensional flat space. ", "As the physical spacetime in the presence of some mass can be seen as this smaller or reduced space (subspace in some formulations, \\[6\\]), the monopole is defined in the combined theory of Electromagnetism and Gravity. ", "This means monopole gauge strings are observable as spacetime distortions. ", "Other interpretations and studies on this connection are addressed to a future work in the concluding subsection of section 3.", "\n\nThe definition of a monopole\n============================\n\nMagnetic charge or monopole is a open theoretical and experimental question. ", "The original version of the monopole proposed by Dirac \\[1\\] never found a place in Nature as we know it: It has never been found by any tangible experiment and the theoretical machinery used to define its properties never fulfil all requirements in terms of what we understand by a particle in Electrodynamics.", "\n\nThe string of singularities has been a problem of non - natural assumptions in Quantum Electrodynamics since Dirac’s proposal \\[1\\]. ", "In order to avoid the string Dirac defined a [*[nodal line]{}*]{}, a region of the spacetime where all Schroedinger wave functions associated to the particles in the Universe are identically zero. ", "In the Schroedinger equation, $(-i\\mathbf{\\nabla }-e%\n\\mathbf{A})^{2}\\psi =2m\\mathcal{E}\\psi ,$ it is necessary for $\\psi $ to be zero or discontinous over the string of singularities. ", "The nodal line is then a constraint on the places the particles can be found - no particle is allowed to be in some determined (by the strings positions) places of the Universe.", "\n\nAfter some time of theoretical existence, the monopole idea was improved by Dirac himself in terms of a variational principle formulation and the problems related to it, \\[2\\]. ", "The source of problems again came related to the definition of the singularity line of the vector potential. ", "It is necessary to assume that a string of such type never pass through a charged particle if the equations of motion are to be derived from an action principle. ", "In trying a quantized version of the theory via a Hamiltonian formulation, Dirac \\[2\\] found that the Poisson Brackets for the vector - potential field is directly dependent on an arbitrary function which, in its turn, is related to the mechanism used to define a possible action principle (i.e., without the divergences that arise from the singular strings). ", "Up to that point the string was the theoretical difficulty which required something the basic principles in Electrodynamics could not give: A topologycal explanation in which the string could find a place as a gauge artifact.", "\n\nAlmost twenty years later, Rohrlich \\[3\\] and Rosenbaum \\[4\\] showed in a different approach the conditions for the existence of a variational principle valid in the case of monopoles. ", "It is interesting to quote the problem put forward by Rohrlich that a system of particle equations can be derived only from a nonlocal action integral and that no action integral exists from which both the particle and field equations can be derived. ", "As in Rosenbaum work, the idea is to have a non - natural contraint (not derived from the action principle) about the dynamics of charges and monopoles: Charges must never touch monopoles; Since Lorentz force can be derived from a principle which states that a charge approaching a monopole along a straight line will collide, it is in contradiction with the necessity of a charge never pass through a monopole. ", "These considerations indicated that something strange to Electrodynamics should be assumed in order to not fall into contradiction about the theoretical existence of the monopole. ", "In fact, some years later t ’Hooft and Polyakov \\[5\\] proposed that a natural condition for the monopole to exist will arise when other topologies are involved, i.e., when other forces (associated to broken non - Abelian gauge theories) of Nature are in consideration.", "\n\nAbout the same time Wu and Yang \\[6\\] gave a clever topologycal description of the problem in non - Abelian as well as in the Abelian case. ", "Using the concept of Fiber Bundles their proposal is that along a path of some charged particle (in the $U(1)$ case), the gauge can be changed in order to avoid the string of singularities. ", "Each gauge changing is well defined if Dirac Quantization Condition is respected - which is quite obvious since a phase changing of $2\\pi $ will not alter Physics. ", "In this view no singularities are seen by any particle’s path and a beautifull connection to geometric concept of fields is naturally given.", "\n\nSoon after Wu and Yang’s work, Brandt and Primack \\[7\\] showed that original Dirac’s theoretical formulation \\[1\\] of the monopole is equivalent to the Wu and Yang’s one \\[6\\]. ", "Showing that the Dirac string attached to the monopole can be arbitrarily moved by a gauge transformation valid everywhere and that it can be completely removed at the cost of introducing a non - global topology in space, Brandt and Primack accomplished to demonstrate the equivalence of the formulations.", "\n\nRecently He, Qiu and Tze \\[8\\] proposed the inconsistency of Quantum Electrodynamics in the presence of monopoles. ", "These authors \\[8\\] formally show that the gauge coupling associated with the unphysical longitudinal photon field is non - observable and has an arbitrary value in Quantum Electrodynamics. ", "In deriving Dirac Quantization Condition in $U(1)$ case it was found that this derivation involves only the unphysical longitudinal coupling constant. ", "This work was focused on Dirac point - monopoles in the standart Dirac formulation \\[1,2\\]. ", "It is interesting to observe that according to Brandt - Primack \\[7\\] and He - Qiu - Tze \\[8\\] works, Quantum Electrodynamics is inconsistent in the presence of monopoles in whichever formulation. ", "The singular Dirac string in the monopole gauge potential is a purely gauge artifact, it is just a gauge freedom which allows one to arbitrarily move the string around without any physical effect, provided Dirac Quantization Condition is satisfied. ", "He, Qiu and Tze \\[8\\] observed that by introducing another unphysical pure gauge field into Quantum Electrodynamics, it is possible to attribute part of the singularities to this pure - gauge field, and thus the corresponding Quantization Condition involves the unphysical gauge coupling associated with this pure - gauge field. ", "After Dirac monopoles are introduced in whichever way, the exact $U(1)\n$ gauge invariance must be respected, so that fixing any specific physical value for an unphysical gauge coupling will violate the exact $U(1)$ gauge invariance. ", "Conversely, [*[if we assume]{}*]{} $g\\neq 0$ *the string must be observable* according to reference* *\\[8\\]. ", "It is impossible to have $g\\neq 0$ and require no physical effects due to the singular string as Dirac \\[1,2\\] or Wu and Yang \\[6\\] claimed, \\[8\\]. ", "This implies that some new fundamental principle should exist, which gives this pure - gauge coupling (and consequently to the longitudinal photon field) a physical meaning so that it become observable \\[8\\]. ", "Accordingly, He, Qiu and Tze thought this is most unlikely and set $g=0$ as the only possible solution in pure Quantum Electrodynamics.", "\n\nAharonov and Bohm proposed an experimental test for the quantization of the magnetic flux related to the discret value of the electron’s charge, \\[9\\]. ", "A magnetized iron filament called whisker is positioned inside the volume of the environment where electrons are allowed to perform trajectories, i.e., these electric charges are not allowed to go inside the whisker region. ", "This simple case has no problem to be defined theoretically: The reason is because there is a physical limitation (some material in the whisker region) for the electric charges to not cross over the magnetized filament.", "\n\nIt turns out to be impossible to define a singularity - free potential $%\nA^{\\mu }$ over all the flat three - dimensional world (i.e., over all $%\n\\bf{R}^{3},$\\[6\\]). ", "In fact as in reference \\[6\\] any fiber of the physical environment is smaller than $\\bf{R}^{3}$, the physical space cannot be defined as the entire $\\bf{R}^{3}$ flat world for a given gauge.", "\n\nThe problem related to the monopole’s string can be understood in terms of the singular region associated to the electromagnetic potential $A^{\\mu }$, without which no quantization of the angular momentum $eg/c$ is defined ($%\ne $ is the quantum of electric charge and $g$ is the quantum of magnetic charge). ", "The main problem is that this singular part of the $A^{\\mu }$ potential implies an infinite amount of interaction energy (self or mutual). ", "A simple example of a vector potential is: $${\\bf{A}}=-g\\frac{1+\\cos \\theta }{r\\sin \\theta step\\left[ \\theta\n-\\delta \\right] }{\\bf{\\phi }}$$\n\nwhere $\\bf{\\phi }$ is the unitary vector associated to the spherical coordinate $\\phi ,$ and $\\theta $ is the other spherical coordinate in $%\n\\bf{r}=\\left( r,\\theta ,\\phi \\right) $ defined in a *three - dimensional flat spacetime* ($\\bf{R}^{3}$ according to the terminology of this work). ", "The “step” function is defined as $step\n[x-x_{0}]=0(x<x_{0});1/2(x=x_{0});1(x>x_{0})$, and $\\delta $ is a vanishing angle, $\\delta \\rightarrow 0$. The magnetic field derived from this potential ($\\bf{B=\\nabla }\\times \\bf{A})$ is: $${\\bf{B}}=g2\\pi (1+\\cos \\delta )\\frac{\\bf{r}}{r^{3}}$$\n\nif $\\delta <\\theta \\leq \\pi $, any $\\phi $, otherwise the magnetic field is not defined. ", "The energy proportional to $\\int \\bf{B}_{i}\\cdot \\bf{B}%\n_{j}d^{3}x$ (the indices refer to different sources $i\\neq j$, or the same source $i=j$) is not defined for $\\theta \\leq \\delta $, any $\\phi $ (the string region), as well as the momentum proportional to $\\int \\bf{E}%\n_{i}\\times \\bf{B}_{j}d^{3}x$.\n\nWhen $\\delta =0$ it is said that $\\bf{A}$ remains singular but $\\bf{B%\n}$ is well defined everywhere. ", "The general situation happens when the singular string has some volume however ($\\delta \\neq 0$ in the example).", "\n\nThe theoretical question about Dirac monopoles can be described in two items: *i*) The general formulation in terms of an action principle which allows an Hamiltonian formulation and consequent quantization, and *ii*) The problem involved in defining a hidden (non observable) string of singularities. ", "The main pourpose of the present work is to deal with the string problem (*ii*) and address to the first (*i*) in another work.", "\n\nLets consider the magnetic field is given by the rotational of the vector potential, $\\bf{B=\\nabla }\\times \\bf{A}$, in the example as given in equations (1) and (2). ", "If it is said $g\\neq 0$ then it must be assumed the physical space where the magnetic flux is measured, $\\oint \\bf{B\\cdot\nd\\sigma }$ ($\\bf{d\\sigma }$ the elementary oriented area surface), is smaller than the $\\bf{R}^{3}$. *In saying this flux has a non - zero net value, one is assuming the space is no longer the entire three - dimensional flat because nor particles or fields are allowed to be in string region*. ", "The direction of the singular string in $\\bf{R}^{3}$ world has no physical meaning since now it is considered no hole exists in the *reduced space* (the actual physical space where $g\\neq 0$).", "\n\nThe strings have some three - dimensional volume in general. ", "The general case for bosons and fermions particles studied by Weisskopf \\[10\\] put limitations on this particles radii even in the general quantum - relativistic formulation. ", "Of course the radius of some particle is related to the not - well defined interaction between two points which are the same in spacetime. ", "This issue is a specific part of the definition of particles which is not the focus in the present work, and it will be considered in general that a string which is to be attached to a particle must have some nonzero volume accordingly, \\[10\\]. ", "Observe that the problem Dirac \\[1,2\\] faced with the strings is of the same kind Weisskopf did, \\[10\\]: The fields must (in Dirac’s words, \\[2\\]) *go out of existence* at some places in order to define particles. ", "The news in the monopole case is that this is an extended region in space.", "\n\nIn the next section we intend to provide a definition of $g\\neq 0$ in the combined situation of having Electromagnetism and Gravitation. ", "This conjunction provides a natural place for the singular string of the gauge fields. ", "This formulation is different from that of Dirac \\[1,2\\] or Wu - Yang \\[6\\] because the effect of the string is a physical observable.", "\n\nThe observable singular string\n==============================\n\nIn the last section it was discussed that the existence of a monopole in $%\nU(1)$ case ($g\\neq 0$ in Quantum Electrodynamics) implies in general the space ones takes as physical is in fact smaller than that known as the flat $%\n\\bf{R}^{3}$. The direction of the undefined region in $\\bf{R}^{3}$ has no physical meaning once one accepts $g\\neq 0$. It is very interesting and important to observe that this comes from the fact $\\bf{A}$ *is not defined* in the string region - the value $1/0$ (one over zero) has no physical or mathematical meaning in describing fields.", "\n\nIn order to consider $g\\neq 0$ it is necessary to have a physical reason to the fields and particles never be defined in the string region. ", "We found gravity is a possible candidate to hide the string.", "\n\nA physical place for the singular string\n----------------------------------------\n\nNow it is considered the effects of Einstein’s gravity in terms of deformations in spacetime as viewed in the flat three - dimensional world. ", "This is a known valid and feasible way to see gravity, \\[11\\].", "\n\nThe curved spacetime interval outside the region of some matter distribution can be written as: $$ds^{2}=A(r)dt^{2}-B(r)dr^{2}-C(r)r^{2}d\\theta ^{2}-C(r)r^{2}\\sin ^{2}\\theta\nd\\phi ^{2}$$\n\nwhere $r$, $\\theta $, $\\phi $ are regarded as spherical coordinates and $%\nA(r) $, $B(r)$, $C(r)$ are given functions of $r$. It is possible to show that for $r=R$ the corresponding physical area $\\Delta $ for $R$ fixed is: $${\\Delta }=4\\pi R^{2}C(R)$$\n\nand that the physical distance $\\Lambda $ between the points $r=R_{0}$ and $%\nr=R$ on a given radial line is: $$\\Lambda =\\int_{R_{0}}^{R}\\sqrt{B(r)}dr.$$\n\nConsider a spherical mass $m$ at the center of the coordinate system with some given radial matter distribution function. ", "In this particular case the interval for $r>2m$ is: $$ds^{2}=(1-\\frac{2m}{r})dt^{2}-(1-\\frac{2m}{r})^{-1}dr^{2}-r^{2}d\\theta\n^{2}-r^{2}\\sin ^{2}\\theta d\\phi ^{2}$$\n\naccording to Schwarzschild. ", "In this particular case the function $C(r)$ is equal to one. ", "We are interested in to study this metric as seen in the $%\n\\bf{R}^{3}$ world (three - dimensional flat). ", "For the parameter $r=R,$ the physical area ${\\Delta }$ is $4\\pi R^{2}.$ Let us determine the physical radius $\\Lambda $: $$\\Lambda =\\int_{R_{0}}^{R}r/\\sqrt{r^{2}-2mr}dr=\\left[ \\sqrt{\\left(\nr^{2}-2mr\\right) }+m\\ln \\left( r-m+\\sqrt{\\left( r^{2}-2mr\\right) }\\right)\n\\right] \\allowbreak _{R_{0}}^{R},$$\n\nwhere $R_{0}$ is some internal radius ($R_{0}<R$) in the region of the matter distribution. ", "We assume that the resulting value of the expression above for the constant parameter $R_{0}$ is vanishingly small (of the order of $2m$) compared to the one for $R$, so that the physical radius is: $${\\Lambda }=\\sqrt{\\left( R^{2}-2mR\\right) }+m\\ln \\left( R-m+\\sqrt{%\n\\left( R^{2}-2mR\\right) }\\right)$$\n\nand for $R>>2m$, $${\\Lambda }=R+m\\ln \\left( 2R-2m\\right)$$\n\ni.e., the physical distance ${\\Lambda }$ is larger than the parameter $R$.\n\nThe conclusion is that for some physical distance ${\\Lambda }$ the area avaliable to cover a sphere of this radius is $4\\pi R^{2}$, with $R<{\\Lambda }$, in the $\\bf{R}^{3}$ world. ", "In the three - dimensional flat world it is impossible to close the surface of radius $%\n{\\Lambda }$ in this case. ", "For a particle in the physical avaliable world no hole occurs, it is all continuous, but in the $\\bf{R}^{3}$ world there is a region where the spacetime is not defined. ", "As each spherical surface has this non - physical region, it performs a volume of forbidden places for all particles and fields in $\\bf{R}^{3}$.\n\nIt is known that for a flat three - dimensional world it is possible to define an average curvature by means of a defect from $4\\pi r^{2}$ of the measured area of some surface of radius $r$. The connection of this idea to the theory of gravitation is via a conceptual significance of the $G_{4}^{4}$ component of the stress - energy tensor. ", "It is the average curvature $%\nR_{12}^{12}+R_{23}^{23}+R_{13}^{13}$ of the three - space, which is perpendicular to the time. ", "This is a known valid interpretation of the theory of gravitation, \\[11\\].", "\n\nNow we have two physical results in $\\bf{R}^{3}$: The electromagnetic potential $\\bf{A}$ according to Maxwell’s Electromagnetic theory and the physical region for particles and fields according to Einstein’s gravitational theory. ", "The electromagnetic potential is physical only outside the singular (in general volumetric) string region. ", "The spacetime is only physical outside some region defined by the holes on each spherical surface starting from the monopole of mass $m$, as viewed in the flat $\\bf{R}%\n^{3} $.", "\n\n*The two forbidden regions in the* $\\bf{R}^{3}$* world can be set to be the same*. ", "It is only necessary to define a volumetric string as source for the electromagnetic potential (where $\\bf{A}$ is not defined) exactly in the region the physical space is also not defined in the flat world. ", "The measure $\\oint \\bf{A\\cdot dl}$ can be set to be a constant for any closed loop around the string (in the physical region already) if we require a constant flux at the string for any distance from the monopole.", "\n\nThis only means that in order to define a monopole the spacetime must be modified accordingly. ", "The same situation happened to Weisskopf \\[10\\], who defined a forbidden spherical region in spacetime where [*all*]{} the fields are non - existent. ", "In the monopole case this forbidden region is extended in spacetime.", "\n\n A fiber - bundle formulation\n-----------------------------\n\nIt is possible to describe the resulting physical situation of a reduced space due to gravitation in a fiber - bundle formalism when we identify the gauge given by $\\bf{A}$ in $\\bf{R}^{3}$ as determining the region of the singular string (or the forbidden region in $\\bf{R}^{3}$). ", "As in Wu - Yang formalism \\[6\\], each gauge determines a fiber or subspace which is smaller than the flat three - dimensional world.", "\n\nThe view in Wu and Yang’s work is that by the gauge freedom it is possible for a particle to be defined in all $\\bf{R}^{3}$ since it is possible to rotate some subspace (which is smaller than the entire $\\bf{R}^{3}$) to turn it into another, making some forbidden region avaliable.", "\n\nIn interpreting the effect of gravity as a reduction of the physical space regarded to the flat three - dimensional world, there exists a forbidden region for particles in this world. ", "This region can be arbitrarily set on some direction in the referred space with no physical consequences whatsoever. ", "We defined a gauge where the singular string is at the same region in $\\bf{R}^{3}$ where particles are forbidden to go due to gravity, so that a gauge is associated to the position of the string in flat three - dimensional space.", "\n\nIn any of the two descriptions (the present one or Wu - Yang’s) each gauge is associated to a reduced space relative to the flat three - dimensional one. ", "The difference between the two formalisms comes from the fact that in the present case the interpretation is so that the reduced space for some gauge means in fact the physical avaliable space is reduced, i.e., the spacetime is distorted (and strings are observable); Changings on the string position will not result all $\\bf{R}^{3}$ can be visited.", "\n\nThe fundamental question and conclusions\n----------------------------------------\n\nThe fundamental question about a non - physically observable gauge string is that $g$ must be exactly null if gauge invariance is to be respected in Quantum Electrodynamics. ", "This is one of the main causes all theoretical formulations about Dirac monopoles are inconsistent \\[8\\].", "\n\nThe present work proposes a definition of the monopole in a combined situation where Gravity and Electrodynamics are considered at the same time. ", "It is discussed the electric charges and fields never touch a monopole string due to Gravity, i.e., Gravity becomes the physical observable if $%\ng\\neq 0$. It is in agreement with the conclusions in reference \\[8\\] where it is shown $g\\neq 0$ implies the string must be a physical observable.", "\n\nHe, Qiu and Tze, \\[8\\], discussed also that in the case of a point monopole the physical observable is connected to the longitudinal photon field. ", "In ordinary Quantum Electrodynamics this field is not physical and consequently $g$ must be zero in pure QED (because the longitudynal photon field is not a physical observable). ", "In view of the present result we can confirm that string is physical when $g\\neq 0$ in the general case when it has some volume in $\\bf{R}^{3}$, but it is not clear if in this case the longitudinal photon field has some direct role. ", "This deserves more investigation in a future work.", "\n\nAcknowledgements\n================\n\nI would like to thank Professors P. S. Letelier (University of Campinas), W. A. Rodriguez Jr. (Unisal) and H. -J. He (University of Michigan) for very usefull comments. ", "I am also in debt to Centro Universitário Salesiano Unisal for the finantial support.", "\n\nReferences\n==========\n\n.", "\n\nP. A. M. Dirac, Proc. ", "Roy. ", "Soc. **", "A133** (1931) 60\n\n\\[2\\] P. A. M. Dirac, Phys. ", "Rev. **74** (1948) 817\n\n\\[3\\] F. Rohrlich, Phys. ", "Rev. **150** (1966) 1104\n\n\\[4\\] D.Rosenbaum, Phys. ", "Rev. **147** (1966) 891\n\nG. t ’Hooft, Nucl. ", "Phys.**", " B79** (1974) 276;\n\nA. M. Polyakov, Sov. ", "Phys. ", "JETP Lett.**", " 20** (1974) 194\n\n\\[6\\] T. T. Wu and C. N. Yang, Phys. ", "Rev. **D12** (1975) 3845\n\n\\[7\\] R. A. Brandt and J. R. Primack, Phys. ", "Rev. **D15** (1977) 1175\n\n\\[8\\] H. -J. He, Z. Qiu and C. -H. Tze, Zeits. ", "Phys. **", "C65** (1995),\n\n**hep-ph/9402293**\n\n\\[9\\] Y. Aharonov and D. Bohm, Phys. ", "Rev. [**115**]{} (1959) 485\n\n\\[10\\] V. F. Weisskopf, Phys. ", "Rev. **56** (1939) 72\n\n\\[11\\] R. P. Feynman, F. B. Morinigo and W. G. Wagner,\n\n*Feynman Lectures on Gravitation*,\n\nBrian Hatfield Ed. ", "Addison-Wesley Pub. ", "Company (1995), Lecture 11.", "\n" ]

{ "pile_set_name": "ArXiv" }

[ 0, 0.011682242990654205, 0, 0.01, 0.009216589861751152, 0, 0.008968609865470852, 0.009345794392523364, 0, 0, 0, 0, 0, 0.004545454545454545, 0, 0, 0, 0.006430868167202572, 0.014814814814814815, 0.005076142131979695, 0.005405405405405406, 0, 0, 0, 0, 0.005555555555555556, 0.0044444444444444444, 0.0053475935828877, 0.00398406374501992, 0.0048543689320388345, 0.005555555555555556, 0.0037313432835820895, 0.014084507042253521, 0, 0.012195121951219513, 0, 0.027932960893854747, 0.003278688524590164, 0.02564102564102564, 0.005263157894736842, 0, 0, 0.005076142131979695, 0.004016064257028112, 0.0060790273556231, 0, 0, 0.013513513513513514, 0, 0.014814814814814815, 0.01948051948051948, 0, 0, 0.005917159763313609, 0, 0, 0, 0.0023148148148148147, 0.005319148936170213, 0.0024509803921568627, 0, 0.003289473684210526, 0, 0.005952380952380952, 0, 0, 0, 0.005714285714285714, 0, 0, 0.014018691588785047, 0, 0.007194244604316547, 0, 0.007462686567164179, 0.0031645569620253164, 0, 0, 0, 0, 0, 0, 0, 0, 0.002551020408163265, 0, 0.008695652173913044, 0, 0, 0, 0, 0.008620689655172414, 0, 0, 0, 0, 0, 0, 0.006666666666666667, 0, 0, 0.007575757575757576, 0.007067137809187279, 0, 0, 0, 0.00641025641025641, 0, 0.003861003861003861, 0.009523809523809525, 0.006756756756756757, 0, 0.006711409395973154, 0.0111731843575419, 0, 0, 0.024271844660194174, 0.011764705882352941, 0, 0.041666666666666664, 0.2, 0, 0.021739130434782608, 0, 0, 0, 0, 0.024390243902439025, 0, 0.08333333333333333, 0.01818181818181818, 0.04285714285714286, 0.0136986301369863, 0, 0.027777777777777776, 0, 0.029850746268656716, 0.05, 0, 0 ]

[ "Bassment\n\nProduct Description\n\nB.U.P. was formed in 1998. ", "The music is mainly Drum n Bass. ", "Each song makes defines the mood, emotion, time and place. ", "The music varies from Industrial to downright Jungle, and everything in between. ", "In the year 2000 B.U.P. participated in the Mixdown . ", "This show is hosted by DJB on WRVU, FM voice of the Vanderbilt University community in Nashville, TN. ", "The Mixdown features underground and experimental electronic music contributed by artists from around the world, many of them unsigned and heard exclusively over the air on this show. ", "At the end of the year B.U.P. there is a contest in which listeners vote for their favorite artist who has not just good mixes, but consistently contribute to the show on a weekly basis. ", "B.U.P. came in 3rd for 2000. ", "In 2001 they won 1st place. ", "B.U.P.'s music has been featured in commercials and used for adds. ", "This includes SKYKING motorcycle parts, and featured music for SOCALRPM's videos. ", "Music from B.U.P. has been posted and featured on MP3.com and many CDs have been bought all over the world, including Brazil, France, UK, the Netherlands, and America. ", "If you like Drum n Bass, you will love B.U.P. Let the music sink in- it will eventually grow on ya. ", "See below comments on B.U.P.'s music/songs from people just like you!: ", "From: Liable Nice made! ", "Cool start. ", "The bassgroove is cool, and when the drums came in it even cooler. ", "Like ambient sounds, and u got a lot of that. ", "It sounds like early synthmusic back in the 80's. ", "Like it. ", "Nice drum groove. ", "Also like that fact it is the same groove thru the song but it isn't monotony!! ", "great work! ", "Song: PLANET-E From: thedrownies AMAZING! ", "This track shows a lot of attention to detail, and it is AMAZING! ", "This is one of the best songs I have heard from this genre for a long time. ", "Cool trippy effects and beat change-ups kept me interested. ", "VERY cool stuff Now it's time to give your ears something good to listen 2. ", "Enjoy!", "\n\nB.U.P. was formed in 1998. ", "The music is mainly Drum n Bass. ", "Each song makes defines the mood, emotion, time and place. ", "The music varies from Industrial to downright Jungle, and everything in between. ", "In the year 2000 B.U.P. participated in the Mixdown . ", "This show is hosted by DJB on WRVU, FM voice of the Vanderbilt University community in Nashville, TN. ", "The Mixdown features underground and experimental electronic music contributed by artists from around the world, many of them unsigned and heard exclusively over the air on this show. ", "At the end of the year B.U.P. there is a contest in which listeners vote for their favorite artist who has not just good mixes, but consistently contribute to the show on a weekly basis. ", "B.U.P. came in 3rd for 2000. ", "In 2001 they won 1st place. ", "B.U.P.'s music has been featured in commercials and used for adds. ", "This includes SKYKING motorcycle parts, and featured music for SOCALRPM's videos. ", "Music from B.U.P. has been posted and featured on MP3.com and many CDs have been bought all over the world, including Brazil, France, UK, the Netherlands, and America. ", "If you like Drum n Bass, you will love B.U.P. Let the music sink in- it will eventually grow on ya. ", "See below comments on B.U.P.'s music/songs from people just like you!: ", "From: Liable Nice made! ", "Cool start. ", "The bassgroove is cool, and when the drums came in it even cooler. ", "Like ambient sounds, and u got a lot of that. ", "It sounds like early synthmusic back in the 80's. ", "Like it. ", "Nice drum groove. ", "Also like that fact it is the same groove thru the song but it isn't monotony!! ", "great work! ", "Song: PLANET-E From: thedrownies AMAZING! ", "This track shows a lot of attention to detail, and it is AMAZING! ", "This is one of the best songs I have heard from this genre for a long time. ", "Cool trippy effects and beat change-ups kept me interested. ", "VERY cool stuff Now it's time to give your ears something good to listen 2. ", "Enjoy!" ]

{ "pile_set_name": "Pile-CC" }

[ 0, 0.030303030303030304, 0, 0, 0.018518518518518517, 0.029411764705882353, 0, 0, 0.034482758620689655, 0, 0.014925373134328358, 0.012195121951219513, 0.005952380952380952, 0.02, 0.014084507042253521, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.030303030303030304, 0, 0, 0.018518518518518517, 0.029411764705882353, 0, 0, 0.034482758620689655, 0, 0.014925373134328358, 0.012195121951219513, 0.005952380952380952, 0.02, 0.014084507042253521, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]

[ "If it makes you feel better MGK, Canada gets almost all the good cartoons a while before the US does. ", "Crap, for that I’d agree not to air Chopped at all. ", "But I’d agree to that anyway, because I’m so very sick of reality cooking shows.", "\n\nFair enough. ", "But Iron Chef has more cheesiness and less judges wagging fingers at the chefs for not being able to invent a perfect dessert out of Scotch Bonnets and packing peanuts in 30 minutes. ", "So I actually watch Iron Chef.", "\n\nWould’ve disagreed with you about this being a strong season for How I Met Your Mother, but tonight’s ep was easily the best of the season and very good in general; HIMYM is at its best when plotted and scripted to the bursting point, and tonight was a prime example of such.", "\n\nI think Chuck’s one saving grace is that its ratings while down are better than any new NBC show other than the Event- I mean its not like the network can plausibly say- “we can do better, screw a reasonably established audience”\n\nAlso, given that tonight’s Chuck had a commercial for the newest NBC series, School Pride, which is basically Extreme Makeover for schools, it doesn’t seem to me that NBC’s got much in the way of hour long series on the bench.", "\n\nChuck has finally scraped and clawed its way to the point, narratively speaking, where I feel it should have been in mid-season 1. ", "Now they just need to tick off a few items:\n\n1) Chuck can kick ass any time, all the time. ", "If he can’t just flash and take out a bitch there better be a DAMN GOOD REASON. ", "Buffy had an accepted level of combat ability that was rather high and yet the writers found plenty ways to challenge her without her going all “OMG I totally forgot how to fight and now I am all clumsy and nerdy for no reason, blerk!!”", "\n\n2) We’ve almost got the whole cast in on the Big Secret, so let’s get Ellie on board already for fuck’s sake. ", "Jeffster can stay oblivious.", "\n\n3) Chuck & Sarah have been through 35,000 relationship crises, so ENOUGH. ", "Maybe 1 a year, not every damned week.", "\n\n4) No more “wacky” music during the “wacky” scenes so I know they’re “wacky”! ", "IT’S PRETTY DAMNED OBVIOUS ALREADY." ]

{ "pile_set_name": "Pile-CC" }

[ 0.00980392156862745, 0.019230769230769232, 0, 0, 0.00546448087431694, 0.03333333333333333, 0.0036101083032490976, 0.015250544662309368, 0.007518796992481203, 0.01098901098901099, 0, 0, 0.008928571428571428, 0.03571428571428571, 0.013157894736842105, 0, 0, 0 ]

[ "Q:\n\nURLStream and unicode\n\nI am trying to send info using USLStream from flash client to JAVA server.", "\nSome of the info is Chinese so i have to use Unicode.", "\nHow can i do that? ", "now the Unicode info retrieved in the server is corrupted.", "\n\nA:\n\nAs far as I know, Flash uses Unicode natively. ", "Perhaps the endian property of the URLStream object is set incorrectly, you could try changing its value.", "\n\n" ]

{ "pile_set_name": "StackExchange" }

[ 0.009900990099009901, 0, 0, 0, 0.018867924528301886, 0, 0 ]

[ "Assassin's Creed IV On PS4 Needs An Update Before It Can Hit 1080p\n\nCurrently, Assassin's Creed IV on the PlayStation 4 runs at 900p, but an update will bump it up to 1080p soon.", "\n\nAccording to the game's associate producer Sylvain Trottier, speaking on the Ubisoft blog, a patch to bump the game's resolution will be available \"shortly after release\".", "\n\nAccording to Trottier, most will not notice the difference, but those who can will see that it is, \"slightly less crisp but a tiny bit smoother.\" ", "The 1080p delay is a product of making sure the game could ship at 30 frames per second in time for the PlayStation 4's launch. ", "Since work completed on the PlayStation 4 version of the game, a small team continued to refine it and were able to increase the game's resolution, and come up with a new anti-aliasing technique – a term that refers to the smoothing of jagged edges on pixelated models.", "\n\nUbisoft was not able to offer an exact date for the patch's availability, and while the post does confirm the new anti-aliasing technique will be available on Xbox One, it doesn't mention whether Microsoft's console will also run in native 1080p.", "\n\nOur TakeResolution has become increasingly important in the Xbox One versus PlayStation 4 console debate. ", "Infinity Ward recently confirmed that the Xbox One version of Call of Duty: Ghosts will be running in upscaled 720p, as opposed to native 1080p, which is where it will be running on the PlayStation 4. ", "The whole Call of Duty resolution issue has been referred to as ResolutionGate online, so it's understandable that Ubisoft would want to be clear on its resolution specs for Assassin's Creed IV: Black Flag." ]

{ "pile_set_name": "Pile-CC" }

[ 0.011235955056179775, 0.011560693641618497, 0.006756756756756757, 0, 0, 0.008064516129032258, 0, 0.004975124378109453, 0.009708737864077669 ]

[ " u be d(-12). ", "Put u, 0, 22 in descending order.", "\n22, u, 0\nLet s = -160/17 + -2281/34. ", "Sort -0.3, s, 0.5 in increasing order.", "\ns, -0.3, 0.5\nSuppose 0*r - 3 = -p - 3*r, -5*p + 5*r = -15. ", "Let a be 54 + -52 + (0 - 3/1). ", "Sort a, -2, p.\n-2, a, p\nLet t = 3.8 - 7.8. ", "Let z = -4 - -7. ", "Let k be ((-6)/(-2))/z + -3. ", "Put t, k, -5 in decreasing order.", "\nk, t, -5\nLet r = -223 - -226.76. ", "Let w = r + 0.24. ", "Suppose -3*u + 5*s = -35, -3*s - 3 = -2*u + 19. ", "Sort w, -0.4, u in descending order.", "\nu, w, -0.4\nLet n be -2*2*(-4)/88. ", "Sort 3, n, -4, 0.1 in ascending order.", "\n-4, 0.1, n, 3\nLet h = 0.87 - -0.53. ", "Let c = 32 + -32.5. ", "Sort h, 1/5, c in ascending order.", "\nc, 1/5, h\nLet r = 1 + -11. ", "Let y be r/(-6)*(5 - 2). ", "Put -5, y, -8 in increasing order.", "\n-8, -5, y\nLet l be (2/(-6))/(4/60). ", "Let f = -2 + 5. ", "Suppose -2*t + 5*t = -v + 4, -2*t = -f*v + 12. ", "Sort -3, l, v in decreasing order.", "\nv, -3, l\nLet g = -2 - -4. ", "Let a be ((3 - 1) + 1 - -2)*-2. ", "Put 0.4, a, g in ascending order.", "\na, 0.4, g\nLet s be (12/(-28)*-2)/31. ", "Let c = s - -356/2821. ", "Sort -1/8, c, 3 in descending order.", "\n3, c, -1/8\nLet g(j) = 15 + 4*j - 7*j - 19 - 15. ", "Let b be g(-7). ", "Sort -1, b, -3.", "\n-3, -1, b\nSuppose 16 = -5*c + m, -8*c - m - 24 = -3*c. ", "Sort c, -33, 5, -3 in ascending order.", "\n-33, c, -3, 5\nLet r = -132 + 135.02. ", "Let b = 0.02 - r. Let y = -5 - b. Put 1, -1, y in increasing order.", "\ny, -1, 1\nLet q be 57/(-76)*(-16)/(-150). ", "Sort q, -0.5, 25, -4 in increasing order.", "\n-4, -0.5, q, 25\nSuppose 28 = -i + 4*i + 4*o, 4*o + 56 = 4*i. ", "Let b be (-520)/i - 4/2. ", "Let j = -45 - b. Put -5/6, j, 0 in ascending order.", "\n-5/6, 0, j\nSuppose -18*t + 49 = -11*t. ", "Suppose 6*i + t = -i. ", "Put 0, 1, i in descending order.", "\n1, 0, i\nSuppose 1 = 3*l - 5. ", "Suppose 4*p + 12 = l*p. ", "Put p, 1/3, 2 in decreasing order.", "\n2, 1/3, p\nSuppose -7*g + 3*g + 16 = 0. ", "Put 3, -0.19, g in increasing order.", "\n-0.19, 3, g\nSuppose -5*o + 24 = 3*w - 2*o, -3*w + 25 = 4*o. ", "Let f(t) = 8*t - 1. ", "Let r be f(2). ", "Let s = 11 - r. Sort 2, w, s in descending order.", "\nw, 2, s\nSuppose -1347 + 1359 = 3*j. ", "Put j, -5, 3 in descending order.", "\nj, 3, -5\nLet a be 3 + 40/(-15) + 7/(-3). ", "Sort 2, -7, -5, a.\n-7, -5, a, 2\nLet c be 3/(-2)*-3*(-8)/36. ", "Sort -17, -2/5, 3, c in descending order.", "\n3, -2/5, c, -17\nLet r be (-280 - -293) + -12 + 2. ", "Let t be (-4)/18 + 56/9. ", "Put -4, r, t in increasing order.", "\n-4, r, t\nLet k = 0.2 - 0.3. ", "Let h be -5 - (-203)/42 - (-2)/3. ", "Sort -3, h, k in decreasing order.", "\nh, k, -3\nSuppose 0 = -21*y + 16*y - 25. ", "Sort y, -3, 1 in increasing order.", "\ny, -3, 1\nSuppose -6*s - 72 = -0*s. ", "Sort s, -2, -3 in increasing order.", "\ns, -3, -2\nLet m = 44 + -131/3. ", "Let i(w) = w**3 + 3*w**2 + w + 25. ", "Let x be i(-4). ", "Put m, x, -2/13 in decreasing order.", "\nx, m, -2/13\nLet p(d) = 4*d**2 + d - 2. ", "Let k be p(1). ", "Let v be (k/(-3) - 2)/1. ", "Let j = 1/51 - 37/153. ", "Sort v, 4, j.\nv, j, 4\nSuppose 39*w = 46*w + 28. ", "Put w, -1, 0, 3 in ascending order.", "\nw, -1, 0, 3\nSuppose -3*g = 161 - 158. ", "Sort 4, 5, -5, g in descending order.", "\n5, 4, g, -5\nLet f(g) = g - 23. ", "Let k be f(25). ", "Sort -5, -4, -15, k in descending order.", "\nk, -4, -5, -15\nLet w be 184/(-44)*-1 - 4. ", "Let t = w - -3/44. ", "Sort t, 0.3, -1/3.", "\n-1/3, t, 0.3\nLet x = 0.05 + -3.05. ", "Let d be (-8)/12*3/(-96)*-18. ", "Sort x, 1, d in descending order.", "\n1, d, x\nLet s(v) = -v**3 - 6*v**2 - 6*v - 3. ", "Let b be s(-5). ", "Put b, -2, -1, 7 in decreasing order.", "\n7, b, -1, -2\nLet s = -3.9 - -2.3. ", "Let n = 3 - 3.6. ", "Let x = s - n. Put x, 1, 5 in decreasing order.", "\n5, 1, x\nLet h be -4 + 5/((-15)/(-21)). ", "Suppose -4*d - 14 = 2. ", "Sort h, d, -6, 5 in descending order.", "\n5, h, d, -6\nLet n(j) = -5*j. ", "Let f be n(1). ", "Let t be 3/(-4) - ((-405)/4)/(-5). ", "Let h(w) = -w**3 - 20*w**2 + 23*w + 47. ", "Let b be h(t). ", "Sort 0, f, b in ascending order.", "\nf, 0, b\nLet x = -0.09 + -15.91. ", "Let b = 14 + x. Suppose 2*u + 5 = -1. ", "Put b, u, -0.03 in descending order.", "\n-0.03, b, u\nLet w = 618 - 602. ", "Put 1, w, 3, 4 in increasing order.", "\n1, 3, 4, w\nLet q = 41.9 + -45.9. ", "Sort 0.2, q, -0.3, 6.9 in increasing order.", "\nq, -0.3, 0.2, 6.9\nSuppose 2*a = w + 45, -5*a + 52 = 4*w - 28. ", "Suppose 0*u + a = 5*u. ", "Let l(j) = -48*j + 45. ", "Let m be l(1). ", "Sort u, 0, m in decreasing order.", "\nu, 0, m\nLet d = -19.83 - -20. ", "Let y = 0.47 - d. Sort -5, y, 0.5 in increasing order.", "\n-5, y, 0.5\nLet v = -4.9 - -5. ", "Suppose -3*o - g = -0*o + 10, 2*g = -5*o - 18. ", "Sort v, 1, o, -3/5.", "\no, -3/5, v, 1\nLet i be -1 - 2/(6/(-21)). ", "Let k be 1/((i/(-15))/2). ", "Suppose 60 = 14*q + q. Put q, 8, k in descending order.", "\n8, q, k\nLet r(q) be the second derivative of 23*q**4/12 + q**3/2 - q**2 + 3*q. ", "Let x be r(1). ", "Let o = -21 + x. Sort -4, 5, o in increasing order.", "\n-4, o, 5\nSuppose 0 = 3*c, 2*c - 3 = -3*d + 15. ", "Suppose -27 = 11*j + d. Sort -2, 6, -5, j in decreasing order.", "\n6, -2, j, -5\nLet a = -355 + 1419/4. ", "Let i be (-72)/105 + 2/5. ", "Put 1/6, a, i in increasing order.", "\ni, a, 1/6\nLet a = -12 - -12.4. ", "Sort -4/3, -0.06, a.\n-4/3, -0.06, a\nSuppose -6 = 3*z - 3*x, -16 = 3*z + 5*x + 6. ", "Let m = -5327 + 5332. ", "Sort z, -1, m, -5.", "\n-5, z, -1, m\nLet h = 163 - 160. ", "Sort -4, 1, h in increasing order.", "\n-4, 1, h\nLet w(f) = -f + 22. ", "Let n be w(19). ", "Sort -10, n, 1, -2 in ascending order.", "\n-10, -2, 1, n\nLet d be -2 + 11 - 6 - 3. ", "Sort 6, -4, -1, d.\n-4, -1, d, 6\nLet u = -952 + 948. ", "Sort -353, 2, u, 0 in descending order.", "\n2, 0, u, -353\nLet x = -83.33 - -84. ", "Let u = x + -0.87. ", "Put 2, u, -0.01, -2/9 in decreasing order.", "\n2, -0.01, u, -2/9\nLet k be (-5 - (-1 + -4)*1) + 153. ", "Put -5, k, -1, 1 in ascending order.", "\n-5, -1, 1, k\nLet p = 392 - 392.2. ", "Sort 11, -5, p, 2 in decreasing order.", "\n11, 2, p, -5\nLet z(a) = 3*a**3 + 3. ", "Let h be z(3). ", "Let p be (-16)/h*(-6)/(-4). ", "Put -1/2, p, 1 in descending order.", "\n1, p, -1/2\nLet a be 2/2 + (-2 - 0 - -1). ", "Sort 1, a, -5, 5 in descending order.", "\n5, 1, a, -5\nSuppose -b + 4*a = 14, -b - 4*a = 3*b + 16. ", "Let o = -89 - -86. ", "Sort 0.2, b, o, 3/2 in ascending order.", "\nb, o, 0.2, 3/2\nLet g(s) = -s**2 + 5*s + 7. ", "Let w be g(6). ", "Let j be w - 3 - (-24)/4. ", "Suppose 5*f - 5*o + 5 + 0 = 0, 0 = 5*f - o - 11. ", "Sort f, j, -1 in increasing order.", "\n-1, f, j\nLet q = 0.3 + -0.1. ", "Let r = 152.7 + -148.7. ", "Sort q, 15/8, r in descending order.", "\nr, 15/8, q\nLet m be 3/(9/(-3))*(-15)/(-5). ", "Let k be 1 - (m + (-200)/(-52)). ", "Put -3, -1/3, 0, k in ascending order.", "\n-3, -1/3, 0, k\nLet n = -120.1 - -119.1. ", "Put 0, -45, 1, n in ascending order.", "\n-45, n, 0, 1\nLet a = -112.2 - -112. ", "Sort 5, a, -3, -0.3.", "\n-3, -0.3, a, 5\nLet w(j) = -j**3 - 11*j**2 - 14*j + 3. ", "Let c be w(-8). ", "Let q be (-242)/c + 3/(-21). ", "Suppose -7*p + 4 = -3*p. ", "Sort 5, q, p.\np, q, 5\nLet o = 0.034 - 0.534. ", "Let k = -199 + 198.6. ", "Put o, k, 26 in ascending order.", "\no, k, 26\nLet i(x) = -x + 2. ", "Let y be i(-1). ", "Suppose -y*o - 17 = -2*j - 0*o, -4*j + 5*o + 29 = 0. ", "Sort -2, 13, j in decreasing order.", "\n13, j, -2\nSuppose -n - 3*n + 12 = 0, -5*y + 2*n - 76 = 0. ", "Let l(s) = -s + 3. ", "Let a be l(2). ", "Put y, a, 2 in ascending order.", "\ny, a, 2\nLet d = 1 + 1. ", "Let v be d/(-3) + 8/12. ", "Let h be -2 + 3 + 3 - v. Put h, -2, -0.1 in increasing order.", "\n-2, -0.1, h\nLet x = 17.1 + -17. ", "Sort 5, x, 2/5, 0.5 in decreasing order.", "\n5, 0.5, 2/5, x\nLet d = 5 + -9.6. ", "Let l = d + -0.4. ", "Suppose 63*h = 56*h. ", "Sort l, h, -2/9 in descending order.", "\nh, -2/9, l\nLet s = 0.052 - 43.052. ", "Let f = -41 - s. Let i be 3*(-1 - (-2 - -4)). ", "Put i, f, -3 in decreasing order.", "\nf, -3, i\nSuppose 4*g + 4 = -8. ", "Sort g, 3, -4.", "\n-4, g, 3\nSuppose -q + i = 0, -q - 2 = 5*i - 8. ", "Let a(u) = -u**3 - 4*u**2 - 4*u - 2. ", "Let n be a(-4). ", "Let c be (-2)/4 + (-7)/n. ", "Sort 3, c, q in descending order.", "\n3, q, c\nLet k = 4.7 - 0.7. ", "Let r = -601 + 598. ", "Let u be (-12*6/(-264))/((-6)/(-4)). ", "Put r, u, k in increasing order.", "\nr, u, k\nLet l = -0.9 + 4.9. ", "Let q = -3 + 8. ", "Let p = 0.5512 + -0.0512. ", "Sort p, q, l in ascending order.", "\np, l, q\nLet o = 139 - 142. ", "Let t(z) = -z**2 - 2*z - 1. ", "Let s be t(-2). ", "Let w = -34 - -36. ", "Put w, s, o in increasing order.", "\no, s, w\nLet j(z) = -4*z + 2. ", "Let f be j(-2). ", "Let m be 1 + (-4 - 1*-6). ", "Suppose -m*w = 2*w - f. Put -3, -0.3, w in descending order.", "\nw, -0.3, -3\nLet i(s) = 13*s**2 + 41*s - 4. ", "Let y be i(-4). ", "Put -3, -5, y in increasing order.", "\n-5, -3, y\nLet o(p) = -p**2 + p - 2. ", "Let n be o(2). ", "Suppose a = 4*y + 11, -52*a + 50*a - 3*y = 0. ", "Put 0, a, -2/5, n in decreasing order.", "\na, 0, -2/5, n\nLet d(k) = 3*k + 33. ", "Let c be d(-10). ", "Put 4, 9, c in increasing order.", "\nc, 4, 9\nLet f = 8112 - 8139. ", "Let s be (3/8)/(1/2). ", "Put f, 4, s in decreasing order.", "\n4, s, f\nLet d(j) = 2" ]

{ "pile_set_name": "DM Mathematics" }

[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.020833333333333332, 0, 0.02857142857142857, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.02127659574468085, 0, 0.037037037037037035, 0, 0, 0, 0, 0, 0, 0, 0.06666666666666667, 0.017857142857142856, 0.02631578947368421, 0, 0.014925373134328358, 0.023809523809523808, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.027777777777777776, 0, 0.03125, 0, 0, 0, 0, 0, 0, 0, 0.020833333333333332, 0.02857142857142857, 0.02564102564102564, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.02702702702702703, 0.02857142857142857, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.06666666666666667, 0, 0, 0.02631578947368421, 0, 0, 0, 0, 0, 0, 0, 0, 0.06666666666666667, 0, 0, 0, 0, 0, 0, 0.023809523809523808, 0, 0, 0, 0.06666666666666667, 0, 0, 0.016129032258064516, 0, 0, 0, 0, 0.012345679012345678, 0, 0.05555555555555555, 0.030303030303030304, 0, 0, 0, 0, 0, 0.038461538461538464, 0, 0, 0, 0, 0, 0.027777777777777776, 0.02857142857142857, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.029411764705882353, 0.03333333333333333, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.018867924528301886, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.03125, 0.034482758620689655, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]

[ "In a large pot, heat olive oil over medium heat. ", "Toss in half a chopped onion, a clove of chopped garlic, and 1 1/2 to 2 peeled and sliced carrots. ", "Saute until tender. ", "Toss in half a can of cannelli white beans and half a large can of diced tomatoes with their juice. ", "Cover with chicken or vegetable broth. ", "Bring to a boil then reduce heat to low. ", "Add in sea salt, pepper, and a dash of red pepper flakes to taste. ", "Sprinkle with a big pinch each of chopped fresh parsley and basil. ", "Simmer for 25-35 minutes or until the flavors are well-blended.* ", "Before serving, add a splash {use sparingly} of balsamic vinegar.", "\n\nThis is a pretty basic bean soup recipe but the splash of balsamic vinegar really kicks up the flavor and adds a unique element for your taste buds!", "\n\n——–\n\n*Have you ever tossed soup ingredients into a pot and tried a bite? ", "It most likely tasted a bit…off, like the flavors hadn’t quite blended. ", "Maybe you could taste the basil or the cayenne or other spice, but all together, the soup didn’t seem to suit your taste buds in the right way.", "\n\nGenerally I find that simmering the soup for longer gives it a flavor with more well-blended depth. ", "You may still be able to taste the different flavors, but the soup feels more coherent, for lack of a better word." ]

{ "pile_set_name": "Pile-CC" }

[ 0, 0, 0, 0, 0, 0, 0, 0, 0.015384615384615385, 0, 0, 0, 0, 0.006993006993006993, 0, 0 ]

[ "Los Angeles police are asking for the public’s help in finding a man who reportedly attacked an elderly woman in Koreatown, leaving the 85-year-old with a cracked skull and badly bruised face.", "\n\nPolice said Mi Reum Song was walking on the sidewalk when a man approached her and hit her. ", "At a news conference Monday afternoon, LAPD Capt. ", "David Kowalski said Song was struck in the head and face before she fell unconscious.", "\n\nThe suspect is described as a 35-year-old man, about 5 feet 5 and 150 pounds, according to the LAPD. ", "Kowalski said police obtained a video from a nearby smoke shop that shows a man running away.", "\n\nThe man is a “person of interest,” Kowalski said.", "\n\n\n“He was clearly running from that area,” he said. “", "That elevates the probability that he was probably involved.”", "\n\nPolice said Song was not robbed, but noted that there have been multiple attacks on elderly people in the area before.", "\n\n“Somebody saw this crime. ", "It happened in the middle of the day in one of the busiest parts of Los Angeles,” Kowalski added. “", "Please have the courage to come forward.”", "\n\nIn a Facebook post that has been shared thousands of times since Sunday, Song’s granddaughter, Yujin Ko, said her grandmother was on the sidewalk near Olympic Boulevard and Vermont Avenue when she was “struck in her head” by an unknown assailant.", "\n\n\nThe attack occurred between 2 and 3 p.m. Saturday, Ko said.", "\n\n“There seemed to be no motive as he had no relation to her nor did he take any of her belongings,” Ko wrote. ", "Photos show Song with a knot in the middle of her forehead and both eyes swollen shut with deep purple bruising. ", "A brown medical wrap is covering the top of her skull, which Ko said was “split open.”", "\n\n“She told me to let this go because she wants to forgive the man that did this but I can not and I am livid,” Ko wrote, pleading for witnesses who may have seen the attack to call police.", "\n\n\n“In the least, let this be a lesson to everyone living in this area to please be vigilant and report any suspicious activity. ", "You can’t be too safe,” she said.", "\n\njoseph.serna@latimes.com\n\nsarah.parvini@latimes.com\n\n\nUPDATES:\n\n7:45 p.m.: This article was updated with the name of the victim.", "\n\n3:30 p.m.: This article was updated with additional details from a police press conference.", "\n\nThis article was originally published at 9:50 a.m." ]

{ "pile_set_name": "OpenWebText2" }

[ 0, 0.010638297872340425, 0.02, 0.023529411764705882, 0.009708737864077669, 0.010752688172043012, 0.0196078431372549, 0, 0, 0.008333333333333333, 0, 0.010101010101010102, 0, 0.008064516129032258, 0.016129032258064516, 0.009009009009009009, 0, 0.011627906976744186, 0.005291005291005291, 0, 0, 0.015384615384615385, 0, 0 ]

[ "The content relating to real estate for sale in this web site comes in part from the Internet Data eXchange (\"IDX\") program of METROLIST INC® Real estate listings held by brokers other than Brokers Guild Real Estate are marked with the IDX Logo. ", "This information is being provided for the consumers' personal, non-commercial use and may not be used for any other purpose. ", "All information subject to change and should be independently verified. ", "Click here for the full Terms of Use.", "\n\nWant to purchase or sell your Colorado home, townhouse, condo, loft, acreage or horse property in the Denver Metro, Colorado Springs or Northern Colorado areas? ", "Call the Kinkade Team at Brokers Guild Real Estate at (303) 482-2344. ", "Our team of experienced real estate agents are ready and able to assist you with all your realty needs." ]

{ "pile_set_name": "Pile-CC" }

[ 0.02032520325203252, 0, 0, 0, 0, 0.02857142857142857, 0 ]

[ "Color Block Dinosaur Planter Decor\n\nSo, you might remember last month’s project, featuring a teensy birdhouse, an even small dinosaur and an airplant (or click here to see it now!) ", "Well, the cute little dinosaur I used came in a package with several other cute little dinosaurs, and I couldn’t let them do to waste. ", "I had to make something with them. ", "So, today I’m bringing you Color Block Dinosaurs. ", "A little gold spray paint and these dinosaurs turn into perfectly unique additions to any terrarium or potted plant. ", "And they couldn’t be easier to make.", "\n\nFirst, tape off the part of your dinosaur that you don’t want to end up gold. ", "I recommend isolating a certain feature (like I did the armored back plate on the little blue guy) or blocking off half or a third to give your dinosaur a paint dipped look.", "\n\nLay your dinosaurs in a shallow box or on a piece of cardboard to spray paint them. ", "It should only take one coat. ", "Let everything dry thoroughly before peeling off the tape. ", "Depending on how thick you sprayed the paint on, drying time should be around 10-20 minutes.", "\n\nYou might notice that the red dinosaur didn’t end up with a neatly defined section of gold – I didn’t stick the tape on tight enough :( But, this was easily remedied by just giving him another coat of spray paint, from the top only. ", "I actually kind of like the gradient look it gave him – the gold fading out as it gets closer to his feet is pretty cool I think.", "\n\nOnce everything is dry, you are ready to add your dinosaurs to your favorite pots and plants. ", "Get creative here! ", "You can certainly set them next to a cute succulent, but finding ways to nestle or even partially conceal them is even more fun.", "\n\nYour friends will definitely be in for a surprise when they notice these sweet, shiny little guys peaking out at them!", "\n\nI hope everyone has a great holiday weekend! ", "And please let me know what you think of the dinosaurs!!", "\n\nPrimary Sidebar\n\nsearch\n\nMy Latest Videos\n\nLove Silhouette Projects?", "\n\nI would love for you to share my projects on your own blog or website. ", "Please limit yourself to use of 1 or 2 images including a link that leads directly to the post you borrowed them from. ", "Anything else will be considered copyright infringement. ", "For the full privacy, disclosure, copyright & disclaimer policy please click here." ]

{ "pile_set_name": "Pile-CC" }

[ 0, 0, 0, 0.02, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]

[ "A Windows program for pyroxene-liquid thermobarometry\n\nFuat Yavuz, Demet Kıran Yıldırım\n\nAbstract\n\nA Windows program (WinPLtb) has been developed to calculate wet–chemical and microprobe pyroxene analyses based on the standard International Mineralogical Association (IMA-88) nomenclature scheme. ", "The program allows the user to enter clinopyroxene, orthopyroxene and associated composition of liquid or whole-rock and some calculated components in the Data Entry Screen as well as loading the Microsoft® Excel files including pyroxene and liquid analyses. ", "Although, WinPLtb is essetially aimed to estimate the clinopyroxene–liquid and orthopyrpxene–liquid thermobarometers it also calculates the clinopyroxene-based hygrometers and depths where pyroxene-bearing rocks crystallized. ", "Calculation of pressure- and temperature-dependent thermobarometers is carried out using the previously entered input P-T values or calculated P-T values by program depending on the selected options from pull-down menu. ", "The input values for calculations are percentage of clinopyroxene and orthopyroxene analyses, liquid or whole-rock compositions, P (GPa) for temperature–dependent orthopyroxene–liquid thermometers, and T (K)–P (kbar) for clinopyroxene–liquid thermobarometers. ", "All the calculated results by program are stored in an output Excel file. ", "This file can be used for further general data manipulation and graphing purposes. ", "The compiled program described herein is distributed as a self–extracting setup file, including the necessary support files used by program, a help file, and sample data files." ]

{ "pile_set_name": "Pile-CC" }

[ 0.006734006734006734, 0.011583011583011582, 0, 0, 0.011538461538461539, 0, 0, 0 ]

[ "The Saratoga Sun -\n\nTigers shine at cloudy meet\n\nWyoming’s mercurial spring weather brought cold temperatures and snow to track and field state finals in Casper over the weekend, but neither the cold nor the wet could stop the Encampment Tigers who had four of nine athletes take home first place, All-State honors.", "\n\nThree of six Lady Tigers returned with All-State honors in six events, and of six boys who traveled to Casper, one earned All-State with plenty others taking top-five and top-10 spots in a wide variety of events. ", "For such a small group comparatively, the Tigers punched well above their weight, with the girls’ team taking second place and the boys coming in sixth.", "\n\nSenior McKenzie Powell competed in the 400-meter dash, the 800-meter dash, the triple jump and the 1,600-meter run. ", "McKenzie Powell took second in the 400 and 800, third in the triple jump and fourth in the 1,600.", "\n\nMcKenzie Powell’s younger sister, Paige Powell, competed as well, besting her older sister in the triple jump. ", "McKenzie Powell, for her part, encouraged her younger sister, challenging the junior Powell to beat her in the jump. ", "Paige did by 3 inches, taking second place in the event.", "\n\nThose are the sorts of team dynamics that gave Encampment the edge over other schools, said Kegan Willford, head coach of the Encampment Tigers’ track and field team.", "\n\n“These guys see each other in practice all the time, they compete against each other all the time,” Willford said. “", "I think that carries over into the meets and we have a leg up on the competition because these guys are competing with each other night in and night out.”", "\n\nRising Encampment star Hailey Barkhurst also brought home the gold for the Tigers, earning first place All-State honors in the shot put with a throw of 35’9.75.” ", "Barkhurst also finished first in discus with her 188’2” throw.", "\n\nOverall, the Lady Tigers fielded six athletes, and all finished every event in the top 10, with most finishes being in the top five. ", "The girls earned second place in team scores at State, punching well above the school’s weight considering the size of the Tiger contingent.", "\n\nThe boys’ team, likewise, had a spate of finishes in the top 10, with most being in the top five. ", "Of six athletes who traveled to Casper, they competed in 12 individual events with seven top 10 finishes. ", "The boys of Encampment also turned in strong performances on two team events, the 4x800-meter relay and the 4x400-meter relay.", "\n\nThe gentlemen Tigers took second in the 4x800 and seventh in the 4x400.", "\n\nLike the girls’ team, there were also All-State honors bestowed on the team. ", "Freshman Reid Schroeder took first place in the State in the 3,200-meter run, and followed up his performance with a seventh-place finish in the 1,600-meter.", "\n\nThe youth of the team, coupled with the exemplary results they turned in at State bodes well for Encampment school going into the future. ", "This year’s team only had two seniors, yet the Tigers made up for a lack of experience with hard work.", "\n\nWhile reluctant to take too much credit for the hard work of the students, Willford said the team’s method of individual short-and-long-term goal setting worked well for the team, allowing athletes to show consistent improvement over the course of the season.", "\n\nThe Tigers also peaked right on time, Willford said, allowing them to hit their best performances during regionals and State when it mattered most.", "\n\nBecause the team is young and still improving, Willford predicts fans of Encampment track and field will have a lot to look forward to when the season rolls around again for the next few years." ]

{ "pile_set_name": "Pile-CC" }

[ 0.0031746031746031746, 0.004651162790697674, 0.006578947368421052, 0.00847457627118644, 0.010309278350515464, 0.008849557522123894, 0.017094017094017096, 0, 0.017857142857142856, 0.00847457627118644, 0, 0.012195121951219513, 0.016129032258064516, 0, 0.007142857142857143, 0, 0, 0.007936507936507936, 0.0136986301369863, 0, 0.012738853503184714, 0.014285714285714285, 0.00980392156862745, 0.0038314176245210726, 0.020134228187919462, 0.010256410256410256 ]

[ "Both main opposition parties have an opportunity, say analysts: the Tories to hammer the message that the Liberals are bad managers, and the New Democrats to show they say one thing and do another." ]

{ "pile_set_name": "OpenWebText2" }

[ 0 ]

[ "Many-body effects for critical Casimir forces.", "\nWithin mean-field theory we calculate the scaling functions associated with critical Casimir forces for a system consisting of two spherical colloids immersed in a binary liquid mixture near its consolute point and facing a planar, homogeneous substrate. ", "For several geometrical arrangements and boundary conditions we analyze the normal and the lateral critical Casimir forces acting on one of the two colloids. ", "We find interesting features such as a change of sign of these forces upon varying either the position of one of the colloids or the temperature. ", "By subtracting the pairwise forces from the total force we are able to determine the many-body forces acting on one of the colloids. ", "We have found that the many-body contribution to the total critical Casimir force is more pronounced for small colloid-colloid and colloid-substrate distances, as well as for temperatures close to criticality, where the many-body contribution to the total force can reach up to 25%." ]

{ "pile_set_name": "PubMed Abstracts" }

[ 0.021739130434782608, 0.00390625, 0.006329113924050633, 0, 0, 0.010638297872340425 ]

[ "Pharmacokinetics of intramuscular microparticle depot of valdecoxib in an experimental model.", "\nWe did a prospective study to investigate pharmacokinetics of a single intramuscularly (i.m.) ", "administered Valdecoxib (VC) polymeric microparticles in New Zealand white rabbits. ", "Poly[lac(glc-leu)] microparticles encapsulating a potent cyclooxygenase-2- selective inhibitor, VC, were prepared by emulsion and solvent evaporation technique and administered i.m. ", "to rabbits for pharmacokinetic study. ", "A single i.m. ", "dose of drug-loaded poly[lac(glc-leu)] microparticles resulted in sustained therapeutic drug levels in the plasma for 49 days. ", "The relative bioavailability was increased severalfold as compared with unencapsulated drug. ", "Injectable poly[lac(glc-leu)] microparticles hold promise for increasing drug bioavailability and reducing dosing frequency for better management of rheumatoid arthritis." ]

{ "pile_set_name": "PubMed Abstracts" }

[ 0, 0, 0.023809523809523808, 0.005494505494505495, 0, 0, 0, 0, 0.0058823529411764705 ]

[ "Postnatal changes in the distribution and morphology of rat substantia nigra dopaminergic neurons.", "\nSignificant changes in the neurophysiology and neuropharmacology of nigral dopaminergic neurons take place in the first postnatal month. ", "In order to correlate these changes with the postnatal development of dopaminergic neuron morphology and substantia nigra cytoarchitecture, brains from Sprague-Dawley rat pups of age postnatal days 1, 7, 14, 21 and 28 and adult rats were sectioned and processed for tyrosine hydroxylase immunocytochemistry. ", "At postnatal day 1, pars compacta and pars reticulata were not clearly delineated; tyrosine hydroxylase positive neurons and a dense plexus of fibers were scattered throughout the substantia nigra. ", "By day 7 the density of tyrosine hydroxylase positive neurons decreased markedly in ventral substantia nigra, and a dopaminergic pars compacta and a non-dopaminergic pars reticulata could be more clearly distinguished. ", "By day 14 the substantia nigra appeared essentially as it does in the adult. ", "Cell counts during development revealed that the number of tyrosine hydroxylase positive neurons/section in both pars compacta and pars reticulata decreased significantly from postnatal day 1 to postnatal day 14, while those in pars lateralis did not change. ", "Tyrosine hydroxylase-positive somatic size increased modestly but significantly from postnatal day 1 to day 14 as did the diameter of the proximal and distal dendrites. ", "However, even at day 1, the morphology of tyrosine hydroxylase positive neurons appeared essentially the same as in adults. ", "Dendritic arborizations were well developed. ", "The dendrites were non-varicose and modestly branched, with some of the longer ventrally directed dendrites passing through pars reticulata into the crus cerebri.(ABSTRACT TRUNCATED AT 250 WORDS)" ]

{ "pile_set_name": "PubMed Abstracts" }

[ 0, 0, 0.006493506493506494, 0, 0, 0.012987012987012988, 0, 0, 0, 0, 0 ]

[ "Q:\n\nWhat's the difference with or without backtick \"`\"?", "\n\ntype level =\n[ `Debug\n| `Info\n| `Warning\n| `Error]\n\nCan i remove the \"`\" here ?", "\nSincerely!", "\n\nA:\n\nIt's hard to answer this question yes or no.", "\nYou can remove the backticks and the square brackets. ", " Then you would have\ntype level2 = Debug | Info | Warning | Error\n\nIn the simplest cases, this type is is very similar to your type level. ", " It has 4 constant constructors.", "\nIn more complex cases, though, the types are quite different. ", " Your type level is a polymorphic variant type, which is more flexible than level2 above. ", " The constructors of level can appear in any number of different types in the same scope, and level participates in subtyping relations:\n# type level = [`Debug | `Info | `Warning | `Error]\n# type levelx = [`Debug | `Info | `Warning | `Error | `Fatal]\n\n# let isfatal (l: levelx) = l = `Fatal;;\nval isfatal : levelx -> bool = <fun>\n# let (x : level) = `Info;;\nval x : level = `Info\n# isfatal (x :> levelx);;\n- : bool = false\n\nThe point of this example is that even though x has type level, it can be treated as though it were of type levelx also, because level is a subtype of levelx.", "\nThere are no subtyping relations between non-polymorphic variant types like level2, and in fact you can't use the same constructor name in more than one such type in the same scope.", "\nPolymorphic variant types can also be open-ended. ", " It's a big topic; if you're interested you should see section 4.2 of the OCaml manual, linked above.", "\n\n" ]

{ "pile_set_name": "StackExchange" }

[ 0, 0.012345679012345678, 0, 0, 0, 0, 0, 0, 0, 0.003436426116838488, 0, 0, 0, 0 ]

[ "Silver (TV channel)\n\nSilver was a movie television channel broadcasting to the Nordic countries broadcasting quality movies, \"World cinema\" and independent films. ", "The channel was managed by Scandinavian television broadcaster NonStop Television, part of Turner Broadcasting.", "\n\nThe owners NonStop Television applied for a license to broadcast a channel with the working name \"NonStop Filmfestival\" in the Swedish digital terrestrial network in the autumn of 2005. ", "The government gave the channel a license in February 2006, at the expense of the owner's other movie channel, Showtime Scandinavia. ", "NonStop Filmfestival had to launch before the end of May and Showtime was allowed to continue broadcasting until the new channel started.", "\n\nNonStop Filmfestival was named \"Silver\" in April and could start broadcasting on May 26, 2006 during the Cannes Film Festival. ", "The opening night included Velvet Goldmine, Wild at Heart and Millennium Hambo. ", "Initially, the channel was only available in Sweden on the Boxer terrestrial platform and it wasn't available on from any other distributor until April 2, 2007, when it launched on the Swedish Com Hem cable network.", "\n\nIn February 2007, it was announced that the channel would launch on the 3 mobile phone platform in Sweden. ", "This launch occurred on April 16 and NonStop claimed that Silver was the first movie channel in Europe to be available on a mobile platform. ", "On the same day, it was announced that Silver would launch on satellite from Canal Digital in Finland, Sweden, Norway and Denmark on May 1 and that a high-definition version called \"Silver HD\" would launch on September 1, 2007. ", "After the launch on Canal Digital satellite, it has expanded to other cable networks such as LumoTV in Finland and Get in Norway.", "\n\nIt was on Astra for the South African market. ", "It was being bought by Top TV, a division of On Digital Media (ODM). ", "It was launched in May 2010.", "\n\nSilver ceased operations on July 15, 2015;\n\nReferences\n\nExternal links\n NonStop Television \"Silver\" channels on October 2011:\n Silver, launched April 2007\n Silver HD\n Silver on demand, launched in November 2007\n Silver Baltic(s), launched October 1, 2008\n Silver Africa, launched on May 1, 2010\n\nCategory:Movie channels\nCategory:Pan-Nordic television channels\nCategory:Television stations in Denmark\nCategory:Television channels and stations established in 2006" ]

{ "pile_set_name": "Wikipedia (en)" }

[ 0.006134969325153374, 0.018018018018018018, 0.005319148936170213, 0.007518796992481203, 0.014598540145985401, 0, 0.025, 0.009302325581395349, 0, 0.0070921985815602835, 0.0043859649122807015, 0.007751937984496124, 0.020833333333333332, 0.043478260869565216, 0, 0.0021598272138228943 ]

[ "Short-segment fixation without fusion for thoracolumbar burst fractures with neurological deficit can preserve thoracolumbar motion without resulting in post-traumatic disc degeneration: a 10-year follow-up study.", "\nProspective consecutive series. ", "To evaluate the post-traumatic disc degeneration and range of motion 10 years after short-segment fixation without fusion for thoracolumbar burst fractures with neurological deficit. ", "Early clinical results of short-segment fixation without fusion for thoracolumbar burst fractures were satisfactory. ", "However, the long-term results have not been reported, and post-traumatic disc degeneration and preservation of thoracolumbar motion have not been elucidated. ", "Twelve patients who had thoracolumbar burst fractures and associated incomplete neurological deficit, operatively treated within 4 days of admission and had their implants removed within 1 year, were prospectively followed for at least 10 years. ", "Following indirect reduction and pedicle screw fixation, transpedicular intracorporeal hydroxyapatite grafting to the fractured vertebrae was performed. ", "Sagittal alignment was improved from a mean preoperative kyphosis of 17° to -2° (lordosis) by operation, but was found to have slightly deteriorated to 2° at the final follow-up observation. ", "With respect to back pain, 8 patients did not report back pain. ", "Three reported occasional minimal pain, and 1 reported moderate pain. ", "None reported severe pain or needed daily dosages of analgesics.", "Regarding disc degeneration, the shape of the disc adjacent to the fractured vertebra had not changed from the preoperative to the 10-year postoperative magnetic resonance image (MRI). ", "Although signal intensity of the disc had decreased by 1 grade from the preoperative to the 2-year postoperative MRI, the intensity had not changed from the 2-year postoperative MRI to the 10-year postoperative MRI. ", "At the 10-year follow-up, flexion-extension radiographs revealed that a mean range of motion at the disc adjacent to the fractured vertebra was 12º (range; 5-19). ", "This unprecedented 10-year follow-up study demonstrated that posterior indirect reduction, transpedicular hydroxyapatite grafting, and pedicle screw fixation does not require fusion to a segment, thereby preserves thoracolumbar motion without resulting in post-traumatic disc degeneration. ", "4." ]

{ "pile_set_name": "PubMed Abstracts" }

[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]

[ "\n60 Ill. App.2d 295 (1965)\n210 N.E.2d 20\nPeople of the State of Illinois, Defendant in Error,\nv.\nBernie A. Ilg, Plaintiff in Error.", "\nGen. No. ", "49,987.", "\nIllinois Appellate Court — First District, Second Division.", "\nApril 27, 1965.", "\n*296 John L. White, of Chicago, for plaintiff in error.", "\nDaniel P. Ward, State's Attorney of Cook County, of Chicago (Elmer C. Kissane and Kenneth L. Gillis, Assistant State's Attorneys, of counsel), for defendant in error.", "\nMR. ", "JUSTICE LYONS delivered the opinion of the court.", "\nThis is an appeal from an order denying a petition in the nature of a writ of coram nobis entered on July 31, 1964.", "\nDefendant, Bernie A. Ilg, was arrested in the vicinity of North Avenue and Austin Boulevard in the City of Chicago on January 22, 1964. ", "When arrested, he was given a summons in the form of a traffic citation charging him with \"driving under the influence.\" ", "The summons was labeled \"Notice to Appear — Copy of Complaint.\" ", "In the lower left hand corner of the ticket was printed: \"You are further notified that the officer whose signature appears hereon will file a sworn complaint in this court charging you with the offense set forth above.\" ", "On the \"Notice to Appear — Copy of Complaint\" appeared the statement, \"did then and there unlawfully violate section 47 UART — State of Illinois, By Driving Under Influence.\"", "\nAdmittedly filed with the First Municipal District of the Circuit Court of Cook County was an information *297 corresponding to the \"Notice to Appear\" given defendant. ", "The information described the charge as, \"did then and there unlawfully violate section 47 UART — State of Illinois, by ... Driving a motor vehicle while under the influence of intoxicating liquor.\" ", "It was subscribed, sworn to and filed before a deputy clerk on January 22, 1964. ", "In the upper left hand corner of the information were the words: \"In the name and by the authority of the People of the State of Illinois....\" At the end of the information were the words, \"... against the peace and dignity of the people of the State of Illinois.\" ", "Near the top of the ticket were two boxes; one preceding the phrase, \"People of the State of Illinois,\" the other preceding the phrase, \"City of Chicago, a Municipal Corporation, Plaintiff, v.\" Neither of the boxes were checked or designated.", "\nDefendant was found guilty of driving under the influence of intoxicating liquor on April 1, 1964. ", "He was fined $100 and $5 costs and his driver's license was revoked.", "\nDefendant then filed a petition in the nature of a writ of error coram nobis, which was denied on July 31, 1964. ", "In that petition he only raised evidentiary points and did not question the validity of the information.", "\nOn July 31, 1964, he filed a notice of appeal from the \"judgment entered ... on the 31st day of July, 1964.\" ", "He did not appeal the conviction of April 1, 1964.", "\nThe sole contention advanced by defendant on appeal is that the information or complaint under which the defendant was charged, tried and convicted was void ab initio as it did not charge a crime and was not brought in the authority of the People of the State of Illinois.", "\n*298 At the outset, the State contends defendant may not seek review of a conviction, where appeal was not properly perfected. ", "The State maintains that defendant filed a petition in the nature of a writ of coram nobis which was denied on July 31, 1964; that he then filed a notice of appeal from \"the judgment entered ... on the 31st day of July, 1964\"; that he did not file a notice of appeal from the April 1, 1964, finding; that in the petition in the nature of a writ of coram nobis, he did not question the sufficiency and validity of the complaint, but argued only evidentiary matters; that since defendant failed to perfect his appeal from the judgment of April 1, 1964, he cannot now raise matters at issue in that trial as Supreme Court Rule 27 (7) (a) states no appeals may be taken after expiration of 30 days from entry of judgment and as he filed no notice of appeal from the April 1, 1964, conviction, he cannot appeal this conviction.", "\n[1] We agree with the position taken by the State. ", "Defendant could have perfected his appeal from the order of April 1, 1964, either by filing a notice of appeal within 30 days of the conviction or by filing a petition for leave to appeal in this court. ", "Defendant did not comply with the prerequisites of Supreme Court Rule 27(7)(a) and thus his appeal as to the order of conviction is ineffectual. ", "Johnson v. Cook County, 368 Ill. 160, 13 NE2d 169 (1938). ", "Walton v. Winter & Hirsch, Inc., 18 Ill. App.2d 540, 152 NE2d 602 (1958).", "\n[2, 3] Defendant contends that the State made no attempt to dismiss his appeal and thus is estopped from alleging that this court has no jurisdiction. ", "We disagree with defendant. ", "Failure to file a notice of appeal cannot be waived by agreement of the parties or by an estoppel arising out of the conduct of either *299 party. ", "Wishard v. School Directors of Dist. ", "No. ", "11, 279 Ill. App. ", "333 (1935).", "\n[4, 5] Defendant further contends that even if no appeal was taken from the order of April 1, 1964, this court, because an appeal was filed from the order of July 31, 1964, should review both matters. ", "We disagree with this contention for two reasons. ", "The first is that review of the order denying the coram nobis petition only reaches matters contained therein and the petition did not question the validity of the information. ", "People v. Thon, 374 Ill. 624, 30 NE2d 54 (1940). ", "The second reason is that a party, upon failing to perfect his appeal within 30 days, could circumvent Supreme Court Rule 27(7) (a) by filing a petition under section 72 of the Civil Practice Act and appealing from that order as a matter of right.", "\n[6, 7] Finally, defendant contends that the validity of an information or indictment can be reviewed for the first time on appeal citing, People v. Fain, 30 Ill. App.2d 270, 173 NE2d 825 (1961). ", "This is a correct rule of law, but it has application only when the sufficiency of the information or indictment is not raised in the trial court and not upon the failure to perfect an appeal. ", "For the above reasons the appeal is dismissed.", "\nAppeal dismissed.", "\nBURKE, P.J. and BRYANT, J., concur.", "\n" ]

{ "pile_set_name": "FreeLaw" }

[ 0.015267175572519083, 0, 0, 0.03333333333333333, 0, 0.017857142857142856, 0.029940119760479042, 0, 0, 0, 0.014598540145985401, 0, 0, 0.004524886877828055, 0.005747126436781609, 0.011834319526627219, 0.005025125628140704, 0, 0.0037735849056603774, 0.004132231404958678, 0, 0, 0, 0, 0, 0, 0, 0.0078125, 0.0024330900243309003, 0.019230769230769232, 0, 0.006896551724137931, 0.017241379310344827, 0.0273972602739726, 0.006578947368421052, 0, 0, 0.02702702702702703, 0, 0, 0, 0, 0, 0, 0, 0.008097165991902834, 0.00510204081632653, 0, 0, 0, 0.027777777777777776, 0 ]

[ "2006 Croatia Open Umag – Singles\n\nGuillermo Coria was the defending champion but lost in the first round to Robin Vik.", "\n\nStanislas Wawrinka won the title, after Novak Djokovic retired in the final while leading 3–1 in the first set tiebreak.", "\n\nSeeds\n\nDraw\n\nFinals\n\nTop Half\n\nBottom Half\n\nReferences\n\nExternal links\nMain Draw\n\nCroatia Open Umag" ]

{ "pile_set_name": "Wikipedia (en)" }

[ 0.00847457627118644, 0.01639344262295082, 0 ]

[ "All relevant data are within the paper and its Supporting Information files.", "\n\nIntroduction {#sec001}\n============\n\nDiffuse large B-cell lymphoma (DLBCL) is the most common type of non-Hodgkin lymphoma and has a poor prognosis in approximately 50% of patients \\[[@pone.0172364.ref001],[@pone.0172364.ref002]\\]. ", "DLBCL is biologically heterogeneous and shows variable responses to conventional chemotherapy and rituximab \\[[@pone.0172364.ref001],[@pone.0172364.ref002]\\]. ", "Recent advances in next generation sequencing (NGS) have provided a better understanding of the biology of DLBCL and have implicated potential targets to improve diagnosis and therapy \\[[@pone.0172364.ref003]--[@pone.0172364.ref005]\\]. ", "A variety of signaling pathways are involved in the pathogenesis of DLBCL including those involving the B-cell receptor (BCR), NFκB, NOTCH, Toll-like receptor (TLR), PI3 kinase, MAP kinase, immunity, cell cycle/apoptosis, and chromatin modification \\[[@pone.0172364.ref003],[@pone.0172364.ref005]--[@pone.0172364.ref007]\\]. ", "A number of recurrent mutations lead, either directly or indirectly, to pathway activation, and components of various signaling pathways are attractive targets in the clinical setting \\[[@pone.0172364.ref003]\\].", "\n\nBased on cell-of-origin (COO) gene signatures studies, DLBCL can be stratified into prognostically relevant subtypes, with the activated B-cell (ABC) type being associated with an inferior outcome compared with the germinal center B-cell (GCB) type \\[[@pone.0172364.ref008]--[@pone.0172364.ref010]\\]. ", "With regard to BCR signaling inhibition, fostamatinib, a SYK inhibitor, showed activity against relapsed DLBCL in an early phase I/II study \\[[@pone.0172364.ref011]\\], and evaluable tumor responses were observed in two of seven DLBCL patients treated with the BTK inhibitor, ibrutinib, as part of a phase I study for relapsed or refractory B-cell non-Hodgkin lymphoma \\[[@pone.0172364.ref012]\\]. ", "In a subsequent phase II study of fostamatinib, the overall response rate was only 3% and no patient with stable disease or response had ABC type tumors \\[[@pone.0172364.ref013]\\]. ", "However, ibrutinib continues to hold promise as an effective strategy for BCR signal inhibition, at least in certain DLBCL subtypes: in a recent phase I/II clinical trial of relapsed or refractory DLBCL, ibrutinib achieved 37% complete or partial responses in ABC subtype but only 5% response in GCB DLBCL, underscoring the importance of BCR signaling in the pathogenesis of ABC type tumors \\[[@pone.0172364.ref014]\\]. ", "Interestingly, this study showed that the highest number of responses occurred in ABC tumors that lacked BCR mutations (9/29; 31%) implying that BCR signaling in ABC DLBCL is not dependent on the presence of BCR mutations and may be activated via other mechanisms \\[[@pone.0172364.ref014]\\]. ", "Genetic and transcriptional analyses are not yet widely available in routine practice, and although paraffin-based methods are on the horizon \\[[@pone.0172364.ref015]\\], these analyses represent only an indirect measure of protein expression. ", "Immunohistochemistry (IHC) is a time-tested and widely available method to evaluate both protein amount and phosphorylation. ", "Thus, immunohistochemical analysis of BCR signaling components should be an effective and accurate tool for selection of DLBCL cases that would respond to anti-BCR therapies, such as ibrutinib.", "\n\nWe have previously identified a robust signature of active BCR signaling in DLBCL on formalin-fixed paraffin-embedded specimens based on quantitative immunofluorescence (qIF) of phosphorylated BCR-associated kinases SYK, LYN and BTK \\[[@pone.0172364.ref016]\\]. ", "We used DLBCL cell lines as a model system, and identified and validated active BCR signaling in 46% (71/154) of primary DLBCL patient specimens in two clinical cohorts. ", "Additional analysis revealed increased nuclear exclusion of forkhead transcription factor FOXO1, a downstream effect of BCR signaling and AKT activation leading to increased cell survival, among DLBCL with qIF evidence of active BCR signaling compared with those without (*p* = 0.004). ", "There was no difference between any qIF variable for GCB versus non-GCB cases, nor was there any enrichment for GCB or non-GCB COO within BCR-positive or negative cases \\[[@pone.0172364.ref016]\\]. ", "Our data underscored the importance of immunohistochemical analysis to detect active BCR signaling at the level of protein expression and supported the utility of qIF as a tool to identify patients who could potentially benefit from anti-BCR therapies such as ibrutinib.", "\n\nRearrangements of the oncogenes *BCL6*, *BCL2*, as well as *MYC* are well documented in DLBCL, and *MYC* translocations are recognized to confer a worse prognosis in patients treated with cyclophosphamide, doxorubicin, vincristine, and prednisone (CHOP), with or without rituximab (R) \\[[@pone.0172364.ref017]--[@pone.0172364.ref020]\\]. ", "The poor outcome of double-hit DLBCL, defined by rearrangements affecting the *MYC* locus in combination with another breakpoint, mainly *BCL2*, appears to be the result of the combination of MYC and BCL2 overexpression \\[[@pone.0172364.ref021]--[@pone.0172364.ref023]\\]. ", "While double-hit DLBCL is relatively uncommon, found in 5--10% of cases, concurrent high expression of MYC and BCL2 proteins by IHC, termed double-expressor lymphoma (DEL), is detected in approximately 20% of DLBCL \\[[@pone.0172364.ref022],[@pone.0172364.ref024],[@pone.0172364.ref025]\\]. ", "DEL is characterized by an aggressive clinical course and inferior response to R-CHOP therapy, indicating the need for more individualized therapeutic approaches targeting particular signaling pathways \\[[@pone.0172364.ref023]--[@pone.0172364.ref030]\\]. ", "MYC overexpression by IHC does not correlate perfectly with the presence of a *MYC* rearrangement, as other mechanisms of *MYC* activation can lead to overexpression, including copy number amplification, upstream regulation by microRNA and oncogenic mutations. ", "However, *MYC* gene activation has been associated with poor outcome and thus, these alternate pathways that activate *MYC* may have similar biological consequences as *MYC* rearrangement. ", "Indeed, some studies have shown that B-cell lymphomas with concurrent *MYC* and *BCL2* abnormalities, other than translocations, appear to behave similarly to *MYC/BCL2* double-hit lymphomas \\[[@pone.0172364.ref027]--[@pone.0172364.ref029]\\]. ", "In addition, it has been proposed that the poor prognosis of ABC vs. GCB type in DLBCL may be largely explained by MYC/BCL2 double-expression rather than COO per se \\[[@pone.0172364.ref026]\\], although COO assignment using an RNA-based expression platform designed for formalin-fixed paraffin-embedded tissue appears to support the prognostic impact of COO independent of MYC/BCL2 double-expression \\[[@pone.0172364.ref031]\\]. ", "Currently, these IHC studies are increasingly used as part of risk stratification of DLBCL but do not directly impact therapy \\[[@pone.0172364.ref025],[@pone.0172364.ref026]\\]. ", "In this study, we further characterize the clinicopathological significance of active BCR signaling, as determined by qIF, in a cohort of primary DLBCL samples (*N* = 93) by correlating signaling intensity with clinical features and tumor cell characteristics. ", "We demonstrate that concurrent high expression of MYC and BCL2 by IHC is positively correlated with previously studied markers of activated BCR signaling. ", "These findings imply that the BCR signaling pathway is more active in DEL compared to other DLBCL subgroups and may represent a rational therapeutic target in this aggressive subgroup of DLBCL.", "\n\nMethods {#sec002}\n=======\n\nCase selection {#sec003}\n--------------\n\nTo analyze clinicopathologic features associated with activated BCR signaling in a cohort of primary DLBCL samples, we obtained clinical follow-up data from electronic medical records of patients from the original validation cohort from the previously published study \\[[@pone.0172364.ref016]\\]. ", "This cohort consisted of 144 consecutive DLBCL patients diagnosed at the Massachusetts General Hospital between 2000 and 2006. ", "Patients were identified via a computer-assisted search of electronic pathology reports and only cases with sufficient tissue for tissue microarray (TMA) construction were selected for further study following Institutional Review Board approval. ", "Tumors were classified according to the 2008 World Health Organization classification \\[[@pone.0172364.ref001]\\].", "\n\nTissue microarray construction, immunofluorescence and immunohistochemistry {#sec004}\n---------------------------------------------------------------------------\n\nTMA construction was conducted as described previously \\[[@pone.0172364.ref032]\\]. ", "Briefly, three 0.6 mm diameter tissue cores were punched from representative regions of each donor tissue block and inserted into a recipient paraffin block using a semiautomatic robotic precision instrument. ", "Immunofluorescent staining and quantification on the TMA was performed as described previously \\[[@pone.0172364.ref016]\\] and as detailed in [S1 Text](#pone.0172364.s001){ref-type=\"supplementary-material\"}. ", "Tumors were further characterized by IHC for various antigens previously shown to be prognostic in DLBCL. ", "TMA sections 4 μm thick were prepared, deparaffinized and rehydrated according to laboratory protocols. ", "Staining was performed using Leica BOND Polymer Refine DAB Detection kits on a Leica BOND-III Autostainer (Leica Biosystems, Buffalo Grove, IL) using validated staining protocols. ", "On line antigen retrieval was performed prior to incubation with the primary antibodies. ", "Antibodies studied, and their clones, dilutions and sources were as follows: MYC (clone Y69, 1:50, Epitomics), BCL2 (clone bcl-2/100/D5, prediluted, Leica), CD10 (clone 56C6, prediluted, Leica), BCL6 (clone LN22, prediluted, Leica), MUM1 (clone EAU32, prediluted, Leica), Ki67 (clone MIB-1, 1:200, Dako), CD30 (clone BerH2, 1:50, Dako) and p53 (clone DO-7, prediluted; Leica).", "\n\nAll immunohistochemical stains were evaluated via consensus review by two hematopathologists (AEK and ARS), who were blinded to the results of qIF and to patient outcome. ", "Stains for MYC, BCL2, Ki67, CD30 and p53 were scored on tumor cells in increments of 10%. ", "Based on prior data examining optimum survival cutoffs for dichotomizing levels of expression, 40% positivity was used as a cut-off for MYC and 50% positivity for BCL2 overexpression \\[[@pone.0172364.ref025]\\]. ", "Therefore, DEL was defined as tumors demonstrating ≥40% MYC and ≥50% BCL2 expression. ", "COO (GCB vs. non-GCB) was determined using the Hans classifier (CD10, BCL6, MUM1), with positive expression for each antibody defined as ≥30% tumor cell staining \\[[@pone.0172364.ref033]\\].", "\n\nFluorescence In Situ Hybridization (FISH) {#sec005}\n-----------------------------------------\n\nFISH was performed on 4μm thick TMA sections as described previously \\[[@pone.0172364.ref034]\\]. ", "Rearrangements involving the following loci were assessed using the probes indicated (each from Abbot Molecular, Des Plaines, IL): *MYC*/8q24 (Vysis LSI *MYC* Dual Color Break-Apart Rearrangement Probe), *BCL2*/18q21 (Vysis LSI *BCL2* Dual Color Break-Apart Rearrangement Probe), and *BCL6*/3q27 (Vysis LSI *BCL6* Dual Color Break-Apart Rearrangement Probe). ", "Fifty to 100 nuclei were scored per case, and a case was considered positive for the rearrangement if 20% or more nuclei exhibited a break-apart signal.", "\n\nStatistical analysis {#sec006}\n--------------------\n\nThe initial statistical analysis of qIF data has been previously described \\[[@pone.0172364.ref016]\\]. ", "The mean and standard deviation of pLYN+(%), combined score of pSYK+(%) and pBTK+(%) expression derived from linear regression using a maximum-likelihood algorithm (〈pSYK,pBTK〉), and cytoplasmic localization score of FOXO1 (F~cyt~), a surrogate marker of AKT activation, were calculated. ", "Results from untransformed data are based upon arithmetic means, and transformed data are based upon medians, of two to three samples per clinical specimen. ", "Details regarding transformation and reanalysis of BCR signaling classification are provided in [S1 Text](#pone.0172364.s001){ref-type=\"supplementary-material\"}. ", "Welch\\'s unequal variances *t*-test was used to compare qIF markers (pLYN, pSYK, pBTK, FOXO1), adjusted where noted by the Holm-Bonferroni correction. ", "Pearson's χ^2^ test with Yates' correction was used to compare nominal variables. ", "Overall survival (OS) was defined as the time from diagnosis to death from any cause. ", "OS was analyzed using the Kaplan-Meier method with censoring. ", "The log-rank test used to compare differences in survival between groups.", "\n\nResults {#sec007}\n=======\n\nOf 144 clinical specimens examined, 93 fulfilled criteria for measurement of pLYN, 〈pSYK,pBTK〉 and *F*~cyt~ and were evaluable for BCR signaling by qIF. ", "Among the immunohistochemical markers studied, high MYC expression (27/93 cases, 29%) and DEL (21/93 cases, 23%) were found to be positively correlated with markers of activated BCR signaling by qIF ([Table 1](#pone.0172364.t001){ref-type=\"table\"}). ", "The significance of the association increased progressively for markers further downstream of the BCR, from pLYN (*p* = 0.08), to 〈pSYK,pBTK〉 (*p* = 0.02), to *F*~cyt~ (*p* = 4×10^−5^). ", "Examples of BCR+ and BCR- cases and their differences in MYC and BCL2 expression are illustrated in [Fig 1](#pone.0172364.g001){ref-type=\"fig\"}.", "\n\n10.1371/journal.pone.0172364.t001\n\n###### Clinicopathologic and qIF characteristics of DEL vs. non-DEL.", "\n\n![](", "pone.0172364.t001){#pone.0172364.t001g}\n\n Category All MYC+[^1^](#t001fn001){ref-type=\"table-fn\"} MYC-[^1^](#t001fn001){ref-type=\"table-fn\"} DEL[^2^](#t001fn002){ref-type=\"table-fn\"} non-DEL[^2^](#t001fn002){ref-type=\"table-fn\"} MYC+ vs. MYC-[^3^](#t001fn003){ref-type=\"table-fn\"} DEL vs. non-DEL[^3^](#t001fn003){ref-type=\"table-fn\"}\n ---------------------------------------------------------- --------- -------------------------------------------- -------------------------------------------- ------------------------------------------- ----------------------------------------------- ----------------------------------------------------- -------------------------------------------------------\n *N* 93 27 66 21 72 \n Clinical parameters \n  Age[^4^](#t001fn004){ref-type=\"table-fn\"} 62±16 64±16 61±16 66±14 61±16 ns ns\n  Male 57 19 38 15 42 \n  Female 36 8 28 6 30 ns ns\n Treatment \n  CHOP 16 5 11 5 11 \n  R-CHOP 56 14 42 11 45 \n  R-other 6 2 4 2 4 \n  Other 5 1 4 1 4 \n  Unknown 10 5 5 2 8 \n Immunophenotype \n  pLYN^+^ (%)[^4^](#t001fn004){ref-type=\"table-fn\"} 36±32 51±35 30±28 48±35 33±30 0.008 0.08\n  〈pSYK,pBTK〉 (%)[^4^](#t001fn004){ref-type=\"table-fn\"} 29±29 44±30 24±27 44±32 25±27 0.005 0.02\n  *F*~cyt~[^4^](#t001fn004){ref-type=\"table-fn\"} 52±30 70±22 45±30 73±21 47±30 4×10^−5^ 4×10^−5^\n  GCB 50 10 40 8 42 \n  non-GCB 43 17 26 13 30 ns ns\n  BCL2 (%)[^4^](#t001fn004){ref-type=\"table-fn\"} 45±37 69±36 36±34 86±16 34±34 2×10^−4^ 6×10^−15^\n  CD30 (%)[^4^](#t001fn004){ref-type=\"table-fn\"} 8±18 4±13 10±19 4±13 10±19 ns ns\n  Ki67 (%)[^4^](#t001fn004){ref-type=\"table-fn\"} 63±24 73±23 59±23 69±23 62±23 0.009 ns\n  p53 (%)[^4^](#t001fn004){ref-type=\"table-fn\"} 19±28 29±33 14±25 27±30 16±23 0.05 ns\n FISH (+ve/-ve/ND)[^5^](#t001fn005){ref-type=\"table-fn\"} \n  *MYC* 7/81/5 5/19/3 2/62/2 4/14/3 3/67/2 ns ns\n  *BCL2* 13/79/1 3/23/1 10/56/0 3/17/1 10/62/0 ns ns\n  *BCL6* 8/76/9 3/20/4 5/56/5 2/15/4 6/61/5 ns ns\n\n^1^ MYC ≥ 40%.", "\n\n^2^ MYC ≥ 40%, BCL2 ≥ 50%.", "\n\n^3^ *p*-values are uncorrected for multiple comparisons. ", "Holm-Bonferroni corrections (MYC+ vs. MYC-): *p* = 0.02 (pLYN), *p* = 0.02 (〈pSYK,pBTK〉), *p* = 2×10^−4^ (*F*~cyt~), *p* = 0.001 (BCL2), *p* = 0.02 (Ki67), *p* = 0.05 (p53). ", "Holm-Bonferroni corrections (DEL vs. non-DEL): *p* = 0.08 (pLYN), *p* = 0.04 (〈pSYK,pBTK〉), *p* = 1×10^−4^ (*F*~cyt~), *p* = 2×10^−14^ (BCL2).", "\n\n^4^ Expressed as mean +/- standard deviation.", "\n\n^5^ No cases of *MYC/BCL2* or *MYC/BCL6* double-hit lymphoma were identified.", "\n\nAbbreviations: CHOP---cyclophosphamide, doxorubicin, vincristine, and prednisone; COO---cell of origin; DEL---double-expressor lymphoma; FISH---fluorescence in situ hybridization; GCG---germinal center B-cell type; IHC---immunohistochemistry; ns---not significant; R-CHOP---rituximab, cyclophosphamide, doxorubicin, vincristine, and prednisone; R-other---rituximab alone or other rituximab-containing regimen; qIF---quantitative immunofluorescence.", "\n\n{#pone.0172364.g001}\n\nNo correlation was observed between BCR signaling markers and the other clinical or pathological parameters studied, including age; sex; COO as assessed by the Hans classifier; expression of BCL2 alone, BCL6, Ki67, CD30 or p53 by IHC; or *MYC*, *BCL2* or *BCL6* rearrangement status as determined by FISH. ", "Of note, only 8% of cases harbored a *MYC* rearrangement and no cases of *MYC/BCL2* or *MYC/BCL6* double-hit lymphoma were identified.", "\n\nBased on previously established criteria \\[[@pone.0172364.ref016]\\], we initially classified cases with \\>15% pLYN and \\>15% 〈pSYK,pBTK〉 as BCR-positive (BCR+), and cases with \\<15% pLYN and \\<15% 〈pSYK,pBTK〉 as BCR-negative (BCR-). ", "Despite the observed association of BCR signaling markers with DEL, we found no significant association of DEL with classification as BCR+, although there was a significant association of DEL with *F*~cyt~ ([Table 2](#pone.0172364.t002){ref-type=\"table\"}). ", "We therefore re-examined our criteria for BCR classification. ", "Two problems are evident: first, the use of percentage positive cells is not optimal because the data is not evenly distributed over the range of 0--100%; and second, the definition of BCR+ and BCR- excludes cases with \\>15% pLYN but \\<15% 〈pSYK,pBTK〉, or *vice versa*, corresponding to 18/93 (19%) of cases in the current cohort.", "\n\n10.1371/journal.pone.0172364.t002\n\n###### Association of DEL with BCR and *F*~cyt~ classification (untransformed).", "\n\n![](", "pone.0172364.t002){#pone.0172364.t002g}\n\n DEL non-DEL Pearson's χ^2^ *p* value\n -------------------------------------------- ----- --------- ---------------- -----------\n All cases 21 72 \n BCR+ 13 29 3.75 0.15\n BCR- 4 29 \n Other[\\*](#t002fn001){ref-type=\"table-fn\"} 4 14 \n *F*~cyt~+ (\\>50) 17 30 10.04 0.001\n *F*~cyt~- (\\<50) 4 42 \n\n\\*Cases with \\>15% pLYN but \\<15% 〈pSYK,pBTK〉 or *vice versa* that are unclassified based on previously established criteria for BCR positivity.^16^\n\nAbbreviations: BCR---B-cell receptor; DEL---double-expressor lymphoma.", "\n\nAccordingly, we returned to the original qIF data for BCR signaling markers in activated DLBCL cell lines \\[[@pone.0172364.ref016]\\] and applied a modified logit transformation to correct the uneven distribution of data ([S1 Fig](#pone.0172364.s002){ref-type=\"supplementary-material\"}). ", "Unsupervised normal mixture modeling readily clustered known BCR+ and BCR- cell lines ([S2 Fig](#pone.0172364.s003){ref-type=\"supplementary-material\"}). ", "We then defined a hyperplane equally weighted according to the three transformed BCR markers, pLYN, pSYK and pBTK, in order to separate the two clusters for unambiguous assignment of all specimens as either BCR+ or BCR- ([S1 Text](#pone.0172364.s001){ref-type=\"supplementary-material\"}).", "\n\nWe applied the same transformation to the 93 clinical samples of DLBCL. ", "The untransformed data were unevenly distributed, being clustered near the origin and 100% ([S3 Fig](#pone.0172364.s004){ref-type=\"supplementary-material\"}). ", "The logit transformed data were more evenly distributed ([Fig 2](#pone.0172364.g002){ref-type=\"fig\"}), in closer agreement with a standard error distribution assumed by a standard *t*-test. ", "Following logit transformation, DEL cases showed significantly higher levels for each individual BCR signaling marker compared to non-DEL cases, including after Holm-Bonferroni correction for multiple hypotheses testing ([Table 3](#pone.0172364.t003){ref-type=\"table\"}).", "\n\n{ref-type=\"supplementary-material\"}).](pone.0172364.g002){#pone.0172364.g002}\n\n10.1371/journal.pone.0172364.t003\n\n###### Association of DEL with BCR classification according to logit transformation.", "\n\n![](", "pone.0172364.t003){#pone.0172364.t003g}\n\n DEL Non-DEL *t*-test[\\*](#t003fn001){ref-type=\"table-fn\"}\n ---------- ------- --------- -----------------------------------------------\n pLYN 0.027 -1.59 *p* = 0.02 (0.02)\n pSYK -0.66 -2.36 *p* = 4×10^−3^ (8×10^−3^)\n pBTK 0.025 -2.21 *p* = 2×10^−3^ (5×10^−3^)\n *F*~cyt~ 70 47 *p* = 7×10^−4^ (3×10^−3^)\n\n\\**p* values in parentheses adjusted for Holm-Bonferroni correction.", "\n\nAbbreviations: BCR---B-cell receptor; DEL---double-expressor lymphoma.", "\n\nWe tested recursive partitioning to generate a decision tree ([S4 Fig](#pone.0172364.s005){ref-type=\"supplementary-material\"}), but this was not an effective means for selecting DEL cases on the basis of BCR signaling markers. ", "We also applied unsupervised clustering by normal mixture modeling to the qIF data of the TMA ([S1 Text](#pone.0172364.s001){ref-type=\"supplementary-material\"}). ", "Two clusters were generated for putative BCR+ and BCR- cases, but no significant association between BCR status and DEL was detected. ", "However, when the hyperplane derived from reanalysis of DLBCL cell lines was applied to classify BCR+ and BCR- cases, a significant association was observed between BCR status and both DEL and *F*~cyt~ via this revised classification ([Table 4](#pone.0172364.t004){ref-type=\"table\"}).", "\n\n10.1371/journal.pone.0172364.t004\n\n###### Association of DEL with BCR (transformed) and of BCR (transformed) with *F*~cyt~ classification.", "\n\n![](", "pone.0172364.t004){#pone.0172364.t004g}\n\n DEL Non-DEL Pearson's χ^2^ *p* value\n ------------------ ---------- ---------- ---------------- -----------\n BCR+ 15 28 5.68 0.02\n BCR- 6 44 \n **BCR+** **BCR-** \n *F*~cyt~+ (\\>50) 33 15 18.40 2×10^−5^\n *F*~cyt~- (\\<50) 10 35 \n\nAbbreviations: BCR---B-cell receptor; DEL---double-expressor lymphoma.", "\n\nTreatment information was known in 83/93 patients (89%), the largest proportion of whom received R-CHOP (56/83, 67%) ([Table 1](#pone.0172364.t001){ref-type=\"table\"}). ", "Survival data were available in 88/93 patients (95%), with a median follow-up of 60 months. ", "Patients with DEL had significantly shorter OS compared to those with non-DEL (median OS 21 months vs. not reached, *p* = 0.03, [Fig 3A](#pone.0172364.g003){ref-type=\"fig\"}). ", "The difference between DEL and non-DEL was no longer significant when analysis was restricted to R-CHOP-treated patients, likely due to the smaller sample size ([Fig 3B](#pone.0172364.g003){ref-type=\"fig\"}). ", "In addition, no significant OS difference was seen between BCR+ vs. BCR- cases ([Fig 3C](#pone.0172364.g003){ref-type=\"fig\"}), or between cases with net cytoplasmic localization of FOXO1 (*F*~cyt~\\>50 vs. F~cyt~\\<50, [Fig 3D](#pone.0172364.g003){ref-type=\"fig\"}). ", "There were also no statistically significant differences in OS between DEL/BCR-, DEL/BCR+, non-DEL/BCR- and non-DEL/BCR+ cases ([S5 Fig](#pone.0172364.s006){ref-type=\"supplementary-material\"}). ", "Hence, while active BCR signaling and FOXO1 cytoplasmic localization were associated with DEL, they showed no apparent association with OS in the cohort comprising this study.", "\n\n{#pone.0172364.g003}\n\nDiscussion {#sec008}\n==========\n\nIn this study, we demonstrate that among several pathological features assessed by IHC and FISH, MYC expression by IHC was the only one positively correlated with markers of active BCR signaling as determined by qIF. ", "In addition, DEL showed greater BCR activation as compared to non-DEL based on individual phosphomarker expression, FOXO1 cytoplasmic localization, and overall BCR activity classification. ", "Overall, our findings suggest that the BCR signaling pathway is more active in DEL compared with other DLBCL subgroups and raise the possibility for targeting the BCR signaling pathway with agents, such as ibrutinib, in this inferior prognostic subgroup of DLBCL.", "\n\nAlthough DEL correlated with both OS and activated BCR signaling, we were unable to demonstrate a direct association between active BCR signaling and OS, which may be related to the retrospective nature of our study, the relatively small number of patients within different immunohistochemical subgroups, and the non-uniform treatment received (as treatment was not a selection criterion for inclusion in our TMA), all important limitations of our analysis. ", "However, our findings suggest that study of a larger number of uniformly treated patients may help to clarify the prognostic and predictive implications, if any, of activated BCR signaling in DLBCL and DEL. ", "In addition, as with immunohistochemical studies of a similar nature, pre-analytical variables and inter- and intraobserver variability in scoring tissue sections may confound the results. ", "Therefore, validation of these findings is warranted following the development of multiplex quantitative IHC assays for simultaneous and objective scoring of multiple markers.", "\n\nThe exact mechanisms linking BCR signaling to MYC expression have yet to be elucidated. ", "The *MYC* oncogene is a transcription factor that has a broad effect on gene expression: it regulates more than 15% of human genes, including a number of microRNA (miRNAs), and contributes to the pathogenesis of many human cancers \\[[@pone.0172364.ref035],[@pone.0172364.ref036]\\]. ", "Activation of MYC has a profound role in a variety of cellular processes including proliferation, DNA replication, metabolism, and protein and nucleotide biosynthesis. ", "Hence, its dysregulation is associated with genomic instability and oncogenic potential. ", "Studies of P493-6, a human B-lymphoid cell line with tet-repressible *MYC* gene and enrichment of *MYC*-repressed genes, show evidence for the role of miR-17\\~92, a MYC-regulated miRNA, as a major regulator of BCR pathway components \\[[@pone.0172364.ref037]\\]. ", "The miR-17\\~92 cluster has a strong oncogenic role: it is known to regulate multiple cellular processes that contribute to malignant transformation, cell survival and rapid cell proliferation, and it has been implicated in various B-cell malignancies, including DLBCL \\[[@pone.0172364.ref038]--[@pone.0172364.ref041]\\]. ", "In the P493-6 cell line, many of the direct targets of miR-17\\~92 were found to be immunoreceptor tyrosine inhibitory motif (ITIM)-containing proteins, including CD22 \\[[@pone.0172364.ref037]\\]. ", "Interestingly, either MYC or miR-17\\~92 expression was necessary to sustain phosphorylation of SYK and B-cell linker protein (BLNK) upon BCR activation. ", "Furthermore, BCR stimulation by miR-17\\~92 resulted in elevated MYC protein levels and enhanced calcium influx, while inhibition of the miR-17\\~92 diminished the BCR response as measured by SYK and BLNK phosphorylation. ", "Thus, it appears that the MYC-miR-17\\~92-BCR axis may constitute a novel lymphomagenic feed-forward loop in which MYC amplifies BCR signaling and increases its own protein levels via upregulation of miR-17\\~92 and targeting of ITIM proteins. ", "This study also showed that human DLBCLs of the BCR subtype by molecular profiling express higher levels of *MYC* transcript and *MIR17HG*, the precursor transcript derived from the *miR-17\\~92* gene, compared to other subtypes \\[[@pone.0172364.ref042]\\]. ", "Other data suggest that MYC may act as a universal amplifier of expressed genes in lymphocytes and embryonic stem cells by enhancing preexisting transcriptional programs rather than being an on/off specifier \\[[@pone.0172364.ref043],[@pone.0172364.ref044]\\]. ", "Therefore, it is possible that our results simply reflect increased BCR-mediated gene transcription that is present to some extent in all DLBCL but further regulated and enhanced by overexpression of MYC. ", "A recent study in precursor B-cell acute lymphoblastic leukemia revealed that pre-BCR signaling regulates PI3K/AKT, FOXO1 and MYC and can be a target of SYK inhibition \\[[@pone.0172364.ref045]\\]. ", "Interestingly, this report shows that the pre-BCR regulates MYC in a FOXO1-dependent manner. ", "Finally, early data show that MYC and BCR signaling may also be interconnected through regulation of MYC stability via post-translational modification and phosphorylation at specific MYC residues \\[[@pone.0172364.ref046]\\].", "\n\nDEL is characterized by an aggressive clinical course and inferior response to R-CHOP therapy, indicating the need for more individualized therapeutic approaches targeting particular signaling pathways \\[[@pone.0172364.ref023]--[@pone.0172364.ref026]\\]. ", "Active BCR signaling can be detected using qIF of phosphorylated forms of BCR-associated kinases LYN, SYK and BTK in nearly 50% of DLBCL and can be used as a tool in formalin-fixed paraffin-embedded tissue samples to identify patients who may benefit from anti-BCR therapies \\[[@pone.0172364.ref016],[@pone.0172364.ref047],[@pone.0172364.ref048]\\]. ", "Our findings suggest that the BCR signaling pathway as assessed by qIF shows higher activity in MYC-high DLBCL and DEL compared with other DLBCL subgroups. ", "We also confirm the utility of MYC and BCL2 IHC, tests that are more readily available and less costly than FISH, to identify DLBCL cases with an unfavorable prognosis. ", "Our preliminary findings suggesting the potential utility of BCR signaling inhibitors in DEL require validation in prospective studies incorporating MYC/BCL2 double-staining and qIF of BCR signaling molecules to identify patients most likely to respond to such agents. ", "Such a strategy may also help to clarify the interplay between BCR signaling and MYC overexpression in DLBCL.", "\n\nSupporting information {#sec009}\n======================\n\n###### Supporting methods.", "\n\n(PDF)\n\n###### \n\nClick here for additional data file.", "\n\n###### Logistic transform as a function of percentage.", "\n\nPlot of logit(*p*) vs. *p*.", "\n\n(TIF)\n\n###### \n\nClick here for additional data file.", "\n\n###### Logistic transform and cluster analysis of BCR signaling markers in DLBCL cell lines.", "\n\n\\(A\\) Pairwise scatterplots of untransformed data for %pLYN+, %pSYK+, %pBTK+ in ten DLBCL cell lines. ", "Uneven distribution with crowding at the origin is evident. (", "B) Pairwise scatterplots of transformed (logit) data for %pLYN+, %pSYK+, %pBTK+. (", "C) Pairwise scatterplots of transformed (logit) data for %pLYN+, %pSYK+, %pBTK+, with centroids for two clusters generated by unsupervised normal mixture modeling. ", "BCR+ (blue), BCR- (red). (", "D) Pairwise scatterplots of aggregated (median) transformed data for %pLYN+, %pSYK+, %pBTK+, with centroids for two clusters generated by unsupervised normal mixture modeling. ", "BCR+ (blue), BCR- (red).", "\n\n(TIF)\n\n###### \n\nClick here for additional data file.", "\n\n###### Untransformed data for BCR signaling markers in primary DLBCL specimens.", "\n\nPairwise scatterplots of untransformed data for %pLYN+CD20+, %pSYK+CD20+, %pBTK+CD20+ in tissue microarray of primary DLBCL specimens. ", "Uneven distribution with crowding at the origin and near 100% is evident.", "\n\n(TIF)\n\n###### \n\nClick here for additional data file.", "\n\n###### Recursive partitioning of DEL vs. non-DEL cases according to BCR signaling markers.", "\n\nDecision tree based on unsupervised recursive partitioning of DLBCL primary specimens according to BCR signaling markers. ", "Each intersection within the tree is labeled based on the majority of cases, and the number of DEL cases (left) and non-DEL cases (right) given below and the percent (%) of all cases within the cohort. ", "Below the tree are one- and two-dimensional scatterplots of cases based on single or pairwise classification by the four BCR signaling markers pLYN, pSYK, pBTK and Fcyt. ", "Cases are assigned as either DEL (red) or non-DEL (blue), and cut-offs determined by recursive partitioning indicated by step function (1-D) or black/white masking (2D). ", "Note: logistic transform for generation of plots used ε = 1×10--3, resulting in slight reduction in overall data range compared to other Figs.", "\n\n(TIF)\n\n###### \n\nClick here for additional data file.", "\n\n###### Kaplan-Meier analysis of overall survival (OS) based on DEL and BCR classification.", "\n\nOS for DEL/BCR- (solid black), OS for DEL/BCR+ (dashed black line), non-DEL/BCR- (red solid) and non-DEL/BCR+ (dashed red).", "\n\n(TIF)\n\n###### \n\nClick here for additional data file.", "\n\n[^1]: **Competing Interests:**The authors have declared that no competing interests exist.", "\n\n[^2]: **Conceptualization:** AMB AEK DF RHGB ARS.**Data curation:** AMB DF RHGB ARS.**Formal analysis:** AMB AEK LPL DF RHGB ARS.**Investigation:** AMB AEK LPL DF RHGB ARS.**Methodology:** AMB AEK LPL DF RHGB ARS.**Project administration:** AMB AEK LPL DF RHGB ARS.**Resources:** AMB AEK LPL DF RHGB ARS.**Software:** AMB AEK LPL DF RHGB ARS.**Supervision:** AMB ARS.**Validation:** AMB AEK LPL DF RHGB ARS.**Visualization:** AMB AEK LPL RHGB ARS.**Writing -- original draft:** AMB RHGB ARS.**Writing -- review & editing:** AMB AEK LPL DF RHGB ARS.", "\n" ]

{ "pile_set_name": "PubMed Central" }

[ 0.013157894736842105, 0.008547008547008548, 0.012578616352201259, 0.012711864406779662, 0.021604938271604937, 0.004739336492890996, 0.0165016501650165, 0.012626262626262626, 0.016574585635359115, 0.011933174224343675, 0.0136986301369863, 0.00411522633744856, 0.008, 0.0051813471502590676, 0.019011406844106463, 0.0058823529411764705, 0.013986013986013986, 0.025380710659898477, 0.003703703703703704, 0.0058997050147492625, 0.011029411764705883, 0.020761245674740483, 0.011811023622047244, 0.0038314176245210726, 0, 0.00823045267489712, 0.0234192037470726, 0.01694915254237288, 0.007662835249042145, 0.01935483870967742, 0.010362694300518135, 0.00546448087431694, 0.007874015748031496, 0.008130081300813009, 0.017699115044247787, 0.008064516129032258, 0, 0.014492753623188406, 0.009433962264150943, 0.009615384615384616, 0.016666666666666666, 0, 0.031914893617021274, 0, 0, 0.009478672985781991, 0.011627906976744186, 0.031746031746031744, 0.010309278350515464, 0.008356545961002786, 0, 0.012658227848101266, 0.010416666666666666, 0, 0.012345679012345678, 0.019867549668874173, 0.024390243902439025, 0, 0, 0, 0.016483516483516484, 0.012, 0.010752688172043012, 0.027777777777777776, 0.02857142857142857, 0, 0.0003520713531275672, 0.03571428571428571, 0, 0.017241379310344827, 0.02112676056338028, 0, 0, 0.011111111111111112, 0, 0.013468013468013467, 0.024096385542168676, 0, 0.03571428571428571, 0.011655011655011656, 0, 0.00851063829787234, 0.011673151750972763, 0.016129032258064516, 0.0030303030303030303, 0, 0, 0.003194888178913738, 0.006920415224913495, 0, 0.003484320557491289, 0, 0, 0, 0.011111111111111112, 0, 0.003816793893129771, 0.010582010582010581, 0, 0.00823045267489712, 0.013888888888888888, 0.008733624454148471, 0.018518518518518517, 0.022388059701492536, 0.01056338028169014, 0.014285714285714285, 0, 0.0017513134851138354, 0, 0, 0.011428571428571429, 0.009615384615384616, 0.007575757575757576, 0.010309278350515464, 0.017142857142857144, 0, 0.020618556701030927, 0.02247191011235955, 0.019230769230769232, 0.013888888888888888, 0.021164021164021163, 0.015209125475285171, 0.008695652173913044, 0.00966183574879227, 0, 0.005714285714285714, 0, 0.0070921985815602835, 0.005952380952380952, 0, 0.011494252873563218, 0.00625, 0.005128205128205128, 0.0196078431372549, 0.022727272727272728, 0.004132231404958678, 0.0078125, 0.011583011583011582, 0.00975609756097561, 0.025510204081632654, 0.010752688172043012, 0.02242152466367713, 0.01171875, 0.02005730659025788, 0.019230769230769232, 0.011834319526627219, 0.011152416356877323, 0.01834862385321101, 0, 0.018518518518518517, 0, 0, 0.018518518518518517, 0.010638297872340425, 0, 0, 0, 0, 0.038461538461538464, 0, 0.041666666666666664, 0.018518518518518517, 0.012345679012345678, 0, 0, 0.018518518518518517, 0.021739130434782608, 0.008064516129032258, 0.0049504950495049506, 0.011764705882352941, 0.011764705882352941, 0.007042253521126761, 0.018518518518518517, 0.03260869565217391, 0.024, 0.018518518518518517, 0, 0.02181818181818182, 0 ]

[ "Weber says team needs to focus on being tough\n\nWednesday\n\nIllinois basketball coach Bruce Weber scanned the Final Four teams and noticed the similarities. \"", "To me, the biggest things are they have toughness and they guard,'' Weber said Wednesday.", "\n\nIllinois basketball coach Bruce Weber scanned the Final Four teams and noticed the similarities.", "\n\n\"To me, the biggest things are they have toughness and they guard,'' Weber said Wednesday. \"", "You can say there's parity in college basketball. ", "It wasn't the best year. ", "It didn't have quite the stars. ", "That's what these guys had.''", "\n\nWeber will employ a Get Tough policy from here on out. ", "It's what he learned as a longtime assistant to Purdue coach Gene Keady. ", "A team filled with delicate psyches and egos will get pushed rather than pampered. ", "Toughness, bulk, defense and competitive drive are all ''musts'' for the Illini, who finished with a 21-15 record after an NIT quarterfinal loss.", "\n\n\"I tried to coddle them,'' Weber said. \"", "At the end, we went back to competitive drills, hard-nosed practices and competing in everything we did. ", "That's how you get tougher instead of worrying about egos and being fragile, worrying about if they break. ", "We have to get after them. ", "That doesn't mean yelling all the time. ", "It's being demanding of them. ", "They have to be demanding of themselves.''", "\n\nIt's a \"no-brainer'' that Illinois should be a top 25 team next year, Weber said.", "\n\n\"But some things definitely have to change,'' he said. \"", "It's going to start with a lot of competition through spring, motivated workouts throughout the summer. ", "In all of that, mental and physical toughness will be emphasized.", "\n\n\"The most important thing is we get in the weight room. ", "We get stronger. ", "The workouts have to be competitive, and we set a great foundation for the fall to make a big jump next season. ", "This next six months are going to be very important.''", "\n\nMike Davis and Mike Tisdale already made appearances in the weight room. ", "There's no question the Illini need more bulk. ", "But every player needs to grow his game: Davis must put the ball on the floor, Tisdale must battle inside, Demetri McCamey should continue to improve his conditioning and explosiveness, and play defense. ", "Bill Cole needs more strength. ", "Freshmen guards should create off the dribble. ", "Tyler Griffey can expect more from himself.", "\n\n\"I told Tyler to go beat out Mike Davis,'' Weber said. \"", "That should be your goal. ", "Put fear into the older guys. ", "If that happens, those guys get better, and (Griffey) gets better. ", "That's the fire we need from guys.''", "\n\nIn other news:\n\n- Weber met with McCamey again about the NBA evaluation process. ", "A return from the league is expected in two weeks. ", "Weber didn't initiate paperwork for any other Illini player.", "\n\n- Weber was unsure if redshirt freshman Stan Simpson would return. ", "Simpson logged 17 minutes this season. ", "Said Weber: \"We'll just have to wait and see as the spring goes along where he kind of sits and stands with us and his own thoughts.''", "\n\n- The annual United Center game next season still looks like a date with Illinois-Chicago, a possibility that excited Weber about as much as Illini fans in Chicago, who would prefer a high-profile opponent. ", "Illinois will also play a road game at Western Michigan.", "\n\n- Illinois was still taking a look at adding another player this spring. ", "Toughness would be a priority. ", "If so, one possibility could be James Siakam, an undersized power forward who learned he has enough credits to graduate from Brehm Prep in Carbondale. ", "Siakam missed most of the season with broken bones in his face.", "\n\nJohn Supinie can be reached at Johnsupinie@aol.com.", "\n\nNever miss a story\n\nChoose the plan that's right for you.", "\nDigital access or digital and print delivery." ]

{ "pile_set_name": "Pile-CC" }

[ 0.01282051282051282, 0.011235955056179775, 0.01020408163265306, 0.010638297872340425, 0, 0, 0, 0, 0, 0.0273972602739726, 0, 0.006896551724137931, 0.023809523809523808, 0, 0, 0, 0, 0, 0, 0.012048192771084338, 0, 0, 0, 0, 0, 0, 0, 0.02666666666666667, 0, 0.00980392156862745, 0.03225806451612903, 0, 0.023255813953488372, 0.034482758620689655, 0, 0, 0.014925373134328358, 0, 0.024096385542168676, 0, 0, 0.014492753623188406, 0, 0.007462686567164179, 0.009569377990430622, 0, 0, 0, 0.013245033112582781, 0, 0.03773584905660377, 0, 0 ]

[ "Q:\n\nHow to embed evince in firefox 4?", "\n\nI installed mozplugger and created the file mozpluggerrc with the following content according to this post but when I open a .pdf it opens in a separate evince window. ", "\nis there a way I can truly embed it in Firefox like the chrome pdf reader?", "\napplication/pdf: pdf: PDF file\napplication/x-pdf: pdf: PDF file\ntext/pdf: pdf: PDF file\ntext/x-pdf: pdf: PDF file\napplication/x-postscript: ps: PostScript file\napplication/postscript: ps: PostScript file\napplication/x-dvi: dvi: DVI file\n : evince $file\n\nA:\n\nEvince is a GTK+ PDF and PS viewer to replace gpdf/xpdf/acroread and ggv, and it's open source. ", "Using mozplugger you can embed all sorts of stuff into Mozilla and/or Firefox like media players and openoffice. ", "\nFirst make sure you have Evince and mozplugger installed.", "\nNow open up~/.mozilla/mozpluggerrc in your favorite text editor. ", "Here's how to do it with gedit Press Alt + Ctrl + T and paste\ngedit ~/.mozilla/mozpluggerrc\nWherever you see this:\napplication/pdf: pdf: PDF file\napplication/x-pdf: pdf: PDF file\ntext/pdf: pdf: PDF file\ntext/x-pdf: pdf: PDF file\n\nand\napplication/x-postscript: ps: PostScript file\napplication/postscript: ps: PostScript file\n\nadd this on the next line:\nrepeat noisy swallow(evince) fill: evince \"$file\"\n\nClose Firefox and Thats it! ", "\nHERE mine :\napplication/pdf: pdf: PDF file\napplication/x-pdf: pdf: PDF file\ntext/pdf: pdf: PDF file\ntext/x-pdf: pdf: PDF file\napplication/x-postscript: ps: PostScript file\napplication/postscript: ps: PostScript file\n repeat noisy swallow(evince) fill: evince \"$file\"\n\n# Also load the default configuration\nsinclude(/etc/mozpluggerrc)\n\nNote : this plug-ins embed MPlayer Totem OpenOffice ... Too\n\n" ]

{ "pile_set_name": "StackExchange" }

[ 0, 0, 0, 0.030726256983240222, 0.008849557522123894, 0, 0.015151515151515152, 0.025522041763341066, 0.0225 ]

[ "---\nabstract: 'Khovanov-Lauda-Rouquier algebras $R_\\theta$ of finite Lie type are affine quasihereditary with standard modules ${\\Delta}(\\pi)$ labeled by Kostant partitions $\\pi$ of $\\theta$. In type $A$, we construct explicit projective resolutions of standard modules ${\\Delta}(\\pi)$.'\naddress:\n- |\n Department of Mathematics\\\n University of Oregon\\\n Eugene\\\n OR 97403, USA\n- |\n Department of Mathematics\\\n University of Oregon\\\n Eugene\\\n OR 97403, USA\n- |\n Department of Mathematics\\\n University of Oregon\\\n Eugene\\\n OR 97403, USA\nauthor:\n- Doeke Buursma\n- Alexander Kleshchev\n- 'David J. Steinberg'\ntitle: Resolutions of standard modules over KLR algebras of type $A$\n---\n\n[^1]\n\nIntroduction {#SIntro}\n============\n\nLet $R_{\\theta,{{\\mathbb F}}}$ be a Khovanov-Lauda-Rouquier (KLR) algebra of finite Lie type over a field ${{\\mathbb F}}$ corresponding to $\\theta\\in Q_+$. It is known that $R_{\\theta,{{\\mathbb F}}}$ is affine quasihereditary [@Kato; @BKM; @Kdonkin; @KlL]. ", "In particular, it has finite global dimension and comes with a family of [*standard modules*]{} $\\{{\\Delta}(\\pi)_{{\\mathbb F}}\\mid \\pi\\in{\\operatorname{KP}}(\\theta)\\}$ and [*proper standard modules*]{} $\\{\\bar{\\Delta}(\\pi)_{{\\mathbb F}}\\mid \\pi\\in{\\operatorname{KP}}(\\theta)\\}$, where ${\\operatorname{KP}}(\\theta)$ denotes the set of the Kostant partitions of $\\theta$. The (proper) standard modules have well-understood formal characters. ", "Moreover, $L(\\pi)_{{\\mathbb F}}:={\\operatorname{head}}{\\Delta}(\\pi)_{{\\mathbb F}}\\cong {\\operatorname{head}}\\bar{\\Delta}(\\pi)_{{\\mathbb F}}$ is irreducible, and $\\{L(\\pi)_{{\\mathbb F}}\\mid \\pi\\in {\\operatorname{KP}}(\\theta)\\}$ is a complete set of irreducible $R_{\\theta,{{\\mathbb F}}}$-modules up to isomorphism and degree shift. ", "Finally, the projective cover $P(\\pi)_{{\\mathbb F}}$ of $L(\\pi)_{{\\mathbb F}}$ has a finite ${\\Delta}$-filtration and the (graded) decomposition number $d_{{\\sigma},\\pi}^{{\\mathbb F}}:=[\\bar{\\Delta}({\\sigma})_{{\\mathbb F}}:L(\\pi)_{{\\mathbb F}}]_q$ equals the (well-defined) multiplicity $(P(\\pi)_{{\\mathbb F}}:{\\Delta}({\\sigma})_{{\\mathbb F}})_q$, see [@BKM Corollary 3.14].", "\n\nThe KLR algebra is defined over the integers, so we have a ${\\mathbb{Z}}$-algebra $R_\\theta=R_{\\theta,{\\mathbb{Z}}}$ with $R_{\\theta,{{\\mathbb F}}}=R_\\theta\\otimes_{\\mathbb{Z}}{{\\mathbb F}}$. The standard modules have natural integral forms ${\\Delta}(\\pi)$ with ${\\Delta}(\\pi)_{{\\mathbb F}}\\cong {\\Delta}(\\pi)\\otimes_{\\mathbb{Z}}{{\\mathbb F}}$, see [@KS §4.2]. ", "Moreover, as illustrated in [@KS §4], understanding $p$-torsion in the ${\\mathbb{Z}}$-module ${\\operatorname{Ext}}_{R_\\theta}^m({\\Delta}(\\pi),{\\Delta}({\\sigma}))$ is relevant for comparing decomposition numbers $d_{{\\sigma},\\pi}^{{\\mathbb C}}$ and $d_{{\\sigma},\\pi}^{{\\mathbb F}}$ for a field ${{\\mathbb F}}$ of characteristic $p$. This motivates our interest in ${\\operatorname{Ext}}_{R_\\theta}^m({\\Delta}(\\pi),{\\Delta}({\\sigma}))$ and projective resolutions of (integral forms of) standard modules.", "\n\nThe problem of constructing a projective resolution of ${\\Delta}(\\pi)$ reduces easily to the semicuspidal case. ", "To be more precise, let us fix a convex total order $\\preceq$ on the set $\\Phi_+$ of positive roots. ", "A [*Kostant partition*]{} of $\\theta$ is a sequence $\\pi = (\\beta_1^{m_1}, \\ldots, \\beta_t^{m_t})$ such that $m_1,\\dots, m_t\\in {\\mathbb{Z}}_{>0}$, $\\beta_1 \\succ \\cdots \\succ \\beta_t$ are positive roots, and $m_1\\beta_1 + \\cdots + m_t\\beta_t = \\theta$. Then ${\\Delta}(\\pi)\\cong {\\Delta}(\\beta_1^{m_1})\\circ\\dots\\circ {\\Delta}(\\beta_t^{m_t})$ where ‘$\\circ$’ stands for induction product. ", "Since induction product preserves projective modules, it is enough to resolve the standard modules of the form ${\\Delta}({\\beta}_s^{m_s})$, which are exactly the [*semicuspidal standard modules*]{}. ", "Moreover, the case where ${\\beta}_s$ is a simple root is easy: the algebra $R_{m{\\alpha}_i}$ is the nil-Hecke algebra of rank $m$ and the standard module ${\\Delta}({\\alpha}_i^m)$ is the projective indecomposable module $P({\\alpha}_i^m)=R_{m{\\alpha}_i}1_{i^{(m)}}$ for an explicit primitive idempotent $1_{i^{(m)}}\\in R_{m{\\alpha}_i}$, see [@KL1 §2.2].", "\n\nLet us now specialize to Lie type $A_\\infty$. Then every non-simple positive root is of the form ${\\alpha}={\\alpha}_a+{\\alpha}_{a+1}+\\dots+{\\alpha}_{b+1}$ for integers $a\\leq b$, and we will work with the lexicographic convex order on the positive roots. ", "Let $\\theta:=m{\\alpha}$. We consider the set of compositions $${\\Lambda}:=\\{{\\lambda}=({\\lambda}_a,\\dots,{\\lambda}_b)\\mid 0\\leq {\\lambda}_a,\\dots,{\\lambda}_b\\leq m\\}.$$ Let ${\\Lambda}(n):=\\{{\\lambda}\\in{\\Lambda}\\mid {\\lambda}_a+\\dots+{\\lambda}_b=n\\}$. In Section \\[SDPR\\], for each ${\\lambda}\\in {\\Lambda}$, we define explicit idempotents $e_{\\lambda}\\in R_{\\theta}$ as concatenations of ‘divided power idempotents’ of the form $1_{i^{(m)}}$ mentioned above. ", "We define projective modules $P_{\\lambda}:=q^{s_{\\lambda}}R_\\theta e_{\\lambda}$, where $q^{s_{\\lambda}}$ stands for the grading shift by an explicitly defined integer $s_{\\lambda}$. For every $\\mu\\in{\\Lambda}(n+1)$ and $\\mu\\in {\\Lambda}(n)$ we then define explicit elements $d_n^{\\mu,{\\lambda}}\\in e_\\mu R_\\theta e_{\\lambda}$ so that $$P_\\mu\\mapsto P_{\\lambda},\\ xe_\\mu\\mapsto xe_\\mu d_n^{\\mu,{\\lambda}}$$ is an $R_\\theta$-module homomorphism. ", "Taking direct sum over all such gives us a homomorhism $$d_n:P_{n+1}:=\\bigoplus_{\\mu\\in {\\Lambda}(n+1)}P_\\mu\\longrightarrow P_{n}:=\\bigoplus_{{\\lambda}\\in{\\Lambda}(n)}P_{\\lambda}.$$ We note that $P_n=0$ for $n>m(b-a+1)$ and that $d_n^{\\mu,{\\lambda}}=0$ unless the compositions $\\mu$ and ${\\lambda}$ differ in just one part. ", "We also have a natural map $${\\sf p}:P_0=q^{s_0}R_\\theta e_0 \\longrightarrow {\\Delta}({\\alpha}^m),\\ xe_0\\mapsto xv_{{\\alpha}^m},$$ where $v_{{\\alpha}^m}$ is the standard generator of ${\\Delta}({\\alpha}^m)$ of weight $a^m(a+1)^m\\cdots (b+1)^m$, see (\\[ESG\\]).", "\n\n\\[TA\\] We have that $$0\\longrightarrow P_{m(b-a+1)}\\longrightarrow \\dots \\longrightarrow P_{n+1}\\stackrel{d_n}{\\longrightarrow} P_n\\longrightarrow\\dots \\stackrel{d_0}{\\longrightarrow} P_0\\stackrel{\\sf p}{\\longrightarrow} {\\Delta}({\\alpha}^m)\\longrightarrow 0$$ is a projective resolution of the standard module ${\\Delta}({\\alpha}^m)$.\n\nWhen $m=1$ this is a version of the resolution constructed in [@BKM Theorem 4.12], and our resolution can be thought of as the ‘thick calculus generalization’ (cf. [", "@KLMS]) of that resolution.", "\n\nFor an arbitrary $\\theta$, we denote ${\\Delta}:=\\bigoplus_{\\pi\\in{\\operatorname{KP}}(\\theta)}{\\Delta}(\\pi)$. In [@BKSTwo], we will use the resolution from Theorem \\[TA\\] to describe the algebra ${\\operatorname{Ext}}_{R_\\theta}^*({\\Delta},{\\Delta})$ in two special cases: (1) $\\theta$ is a positive root in type $A$ and (2) Lie type is $A_2$, i.e. $\\theta$ is of the form $r{\\alpha}_1+s{\\alpha}_2$.\n\nWe now describe the contents of the paper and the main idea of the proof. ", "After reviewing KLR algebras and standard modules in Section \\[SPrelim\\], we introduce the necessary combinatorial notation and define the resolution $P_\\bullet$ in Section \\[SDPR\\].", "\n\nIn order to prove that $P_\\bullet$ is a resolution of ${\\Delta}({\\alpha}^m)$, we want to show that it is a direct summand of a resolution $Q_\\bullet$ of $q^{m(m-1)/2}{\\Delta}({\\alpha})^{\\circ m}$ introduced in §\\[SQdef\\]. ", "The resolution $Q_\\bullet$ is obtained by taking the $m$th induced power of the resolution constructed in [@BKM Theorem 4.12].", "\n\nTo check that $P_\\bullet$ is a direct summand of $Q_\\bullet$, in §\\[SSComp\\] we construct what will end up being a pair of chain maps $f:P_\\bullet\\to Q_\\bullet$ and $g:Q_\\bullet\\to P_\\bullet$ with $g\\circ f={\\operatorname{id}}$. The main difficulty is to verify that $f$ and $g$ are indeed chain maps. ", "This verification occupies Sections \\[SF\\] and \\[SG\\]. ", "Modulo the fact that $f$ and $g$ are chain maps, Theorem \\[TA\\] is proved in §\\[SSProof\\].", "\n\nPreliminaries {#SPrelim}\n=============\n\nBasic notation\n--------------\n\nThroughout, we work over an arbitrary commutative unital ground $\\k$ (since everything is defined over ${\\mathbb{Z}}$, one could just consider the case $\\k={\\mathbb{Z}}$).", "\n\nFor $r,s\\in{\\mathbb{Z}}$, we use the segment notation $[r,s]:=\\{t\\in{\\mathbb{Z}}\\mid r\\leq t\\leq s\\},\\ [r,s):=\\{t\\in{\\mathbb{Z}}\\mid r\\leq t< s\\},\\ \\text{etc.}", "\n$\n\nLet $q$ be a variable, and ${\\mathbb{Z}}((q))$ be the ring of Laurent series. ", "For a non-negative integer $n$ we define $\n[n]:=(q^n-q^{-n})/(q-q^{-1})$ and $[n]^!:=[1][2]\\cdots [n].", "\n$ We denote by $\\Si_d$ the symmetric group on $d$ letters. ", "It is a Coxeter group with generators $\\{s_r:=(r,r+1)\\mid 1\\leq r<d\\}$ and the corresponding length function $\\ell$. The longest element of $\\Si_d$ is denoted $w_0$ or $w_{0,d}$. An element $w\\in \\Si_d$ is called fully commutative if it is possible to go between any two reduced decompositions of $w$ using only the relations of the form $s_r s_t=s_ts_r$ for $|r-t|>1$. By definition, $\\Si_d$ acts on $[1,d]$ on the left. ", "For a set $I$ the $d$-tuples from $I^d$ are written as words $\\bi=i_1\\cdots i_d$. The group $\\Si_d$ acts on $I^d$ via place permutations as $w\\cdot \\bi=i_{w^{-1}(1)}\\cdots i_{w^{-1}(d)}$.\n\nGiven a composition ${\\lambda}=({\\lambda}_1,\\dots,{\\lambda}_k)$ of $d$, we have the corresponding standard parabolic subgroup $\\Si_{\\lambda}:=\\Si_{{\\lambda}_1}\\times \\dots\\times \\Si_{{\\lambda}_k}\\leq \\Si_d$. For compositions ${\\lambda}$ and $\\mu$ of $d$, we denote by ${{\\mathscr D}}^{\\lambda}$ (resp. ", "${}^\\mu{{\\mathscr D}}$, resp. ", "${}^\\mu{{\\mathscr D}}^{\\lambda}$) the set of the shortest coset representatives for $\\Si_d/\\Si_{\\lambda}$ (resp. ", "$\\Si_\\mu\\backslash\\Si_d$, resp. ", "$\\Si_\\mu\\backslash\\Si_d/\\Si_{\\lambda}$). ", "The following is well-known and can be deduced for example from [@DJ Lemma 1.6]:\n\n\\[LDJ\\] Let ${\\lambda},\\mu$ be compositions of $d$ and $w\\in {}^\\mu{{\\mathscr D}}$. Then there exist unique elements $x\\in {}^\\mu{{\\mathscr D}}^{\\lambda}$ and $y\\in\\Si_{\\lambda}$ such that $w=xy$ and $\\ell(w)=\\ell(x)+\\ell(y)$.\n\nKLR Algebras {#SSKLR}\n------------\n\nFrom now on, we set $I:={\\mathbb{Z}}$. If $i,j \\in I$ with $|i-j|=1$ we set $\\eps_{i,j}:=j-i\\in\\{1,-1\\}$. For $i,j\\in I$, we set $$\\label{ECN}\n\\cc_{i, j}:=\n\\left\\{\n\\begin{array}{ll}\n2 &\\hbox{if $i=j$,}\\\\\n-1 &\\hbox{if $|i-j|=1$,}\\\\\n0 &\\hbox{otherwise.}", "\n\\end{array}\n\\right.$$\n\nWe identify $I$ with the set of vertices of the Dynkin diagram of type $A_\\infty$ so that the numbers $\\cc_{i,j}$ are the entries of the corresponding Cartan matrix. ", "The corresponding simple roots are denoted $\\{{\\alpha}_i\\mid i\\in I\\}$ and set of the positive roots is $\\Phi_+:= \\{{\\alpha}_r+\\dots+{\\alpha}_s\\mid r\\leq s\\}$. The root lattice is $Q:=\\bigoplus_{i\\in I}{\\mathbb{Z}}\\cdot{\\alpha}_i$, and we set $Q_+:=\\{\\sum_i m_i{\\alpha}_i\\in Q\\mid m_i\\in{\\mathbb{Z}}_{\\geq 0}\\ \\text{for all $i$}\\}$. For $\\theta=\\sum_i m_i{\\alpha}_i\\in Q_+$, we define its height $\\height(\\theta):=\\sum_i m_i$. For $\\theta\\in Q_+$ of height $d$, we define $I^\\theta:=\\{\\bi=i_1\\cdots i_d\\in I^d\\mid {\\alpha}_{i_1}+\\dots+{\\alpha}_{i_d}=\\theta\\}$. If $\\bi\\in I^\\theta$ and $\\bj\\in I^\\eta$ then the concatenation of words $\\bi\\bj$ is an element of $ I^{\\theta+\\eta}$.\n\nLet $\\theta\\in Q_+$ be of height $d$. The [*KLR algebra*]{} [@KL1; @Ro] is the unital $\\k$-algebra $R_\\theta$ (with identity denoted $1_\\theta$) with generators $$\\{1_\\bi \\mid \\bi \\in \\words^\\theta \\} \\cup \\{ y_1, \\dots, y_d\\} \\cup \\{\\psi_1, \\dots, \\psi_{d-1}\\}$$ and defining relations $$\\begin{aligned}\n &\\y_r \\y_s = \\y_s \\y_r; \\\\\n &1_\\bi1_\\bj={\\delta}_{\\bi,\\bj}1_\\bi \\quad \\text{and} \\quad \\sum_{\\bi\\in\\words^\\theta}1_\\bi=1_\\theta; \\\\\n &\\y_r 1_\\bi = 1_\\bi\\y_r \\quad \\text{and} \\quad \\psi_r 1_\\bi = 1_{s_r\\cdot \\bi}\\psi_r; \\\\\n &(\\psi_r y_t - y_{s_r(t)} \\psi_r)1_\\bi = {\\delta}_{i_r,i_{r+1}}({\\delta}_{t,r+1}-{\\delta}_{t,r})1_\\bi; \\\\\n &\\psi_r^2 1_\\bi =\n \\begin{cases}\n 0 & \\text{if } i_r=i_{r+1}, \\\\\n \\eps_{i_r,i_{r+1}}({y_r}-{y_{r+1}})1_\\bi & \\text{if } |i_r-i_{r+1}|=1, \\\\\n 1_\\bi & \\text{otherwise};\n \\end{cases} \\\\\n &\\psi_r \\psi_s = \\psi_s \\psi_r \\text{ if } |r-s|>1; \\\\\n &(\\psi_{r+1} \\psi_{r} \\psi_{r+1} - \\psi_{r}\\psi_{r+1}\\psi_{r}) 1_\\bi =\n \\begin{cases}\n \\eps_{i_r,i_{r+1}}1_\\bi & \\text{if } |i_r-i_{r+1}|=1 \\text{ and } i_r = i_{r+2}, \\\\\n 0 & \\text{otherwise}.", "\n \\end{cases} $$ The algebra $R_\\theta$ is graded with $\\deg 1_{\\bi}=0$; $\\deg (y_s)= 2$; $\\deg (\\psi_{r}1_{\\bi})=-\\cc_{i_r,i_{r+1}}$.\n\nWe will use the Khovanov-Lauda [@KL1] diagrammatic notation for elements of $R_\\theta$. In particular, for $\\bi=i_1\\cdots i_d\\in I^\\theta$, $1\\leq r<d$ and $1\\leq s\\leq d$, we denote $$1_\\bi=\n \\begin{tikzpicture}[baseline=6mm,black,line width=1pt, scale=0.32,\n draw/.append style={rounded corners},\n every node/.append style={font=\\fontsize{5}{5}\\selectfont}] \\tikzset{baseline=0mm}\n\n\\draw(0,1) node[above]{$i_1$}--(0,-1);\n\\draw(1,1) node[above]{$i_2$}--(1,-1);\n\\draw(2,1.1) node[above]{$\\cdots$};\n\\draw(3,1) node[above]{$i_d$}--(3,-1);\n\n\\end{tikzpicture}\n,\\quad\n1_\\bi\\psi_r=\n \\begin{tikzpicture}[baseline=6mm,black,line width=1pt, scale=0.32,\n draw/.append style={rounded corners},\n every node/.append style={font=\\fontsize{5}{5}\\selectfont}] \\tikzset{baseline=0mm}\n\n\\draw(0,1) node[above]{$i_1$}--(0,-1);\n\\draw(1,1.1) node[above]{$\\cdots$};\n\\draw(2.5,1) node[above]{$i_{r-1}$}--(2.5,-1);\n\\draw(4,1.05) node[above]{$i_{r}$}--(5.3,-1);\n\\draw(5.3,1) node[above]{$i_{r+1}$}--(4,-1);\n\\draw(7,1) node[above]{$i_{r+2}$}--(7,-1);\n\\draw(8.5,1.1) node[above]{$\\cdots$};\n\\draw(9.5,1) node[above]{$i_{d}$}--(9.5,-1);\n\n\\end{tikzpicture}\n\n,\\quad\n1_\\bi y_s=\n \\begin{tikzpicture}[baseline=6mm,black,line width=1pt, scale=0.32,\n draw/.append style={rounded corners},\n every node/.append style={font=\\fontsize{5}{5}\\selectfont}] \\tikzset{baseline=0mm}\n\n\\draw(0,1) node[above]{$i_1$}--(0,-1);\n\\draw(1,1.1) node[above]{$\\cdots$};\n\\draw(2.5,1) node[above]{$i_{s-1}$}--(2.5,-1);\n\\draw(4,1.05) node[above]{$i_{s}$}--(4,-1);\n\\draw(5.3,1) node[above]{$i_{s+1}$}--(5.3,-1);\n\\draw(7.5,1.1) node[above]{$\\cdots$};\n\\draw(8.5,1) node[above]{$i_{d}$}--(8.5,-1);\n\\blackdot(4,0);\n\n\\end{tikzpicture}\n$$ For each element $w \\in \\Si_n$, fix a reduced expression $w=s_{r_1}\\cdots s_{r_l}$ which determines an element $\\psi_w = \\psi_{r_1} \\cdots \\psi_{r_l}$ (depending on the choice of a reduced expression).", "\n\n\\[TBasis\\][[@KL1 Theorem 2.5]]{}, [@Ro Theorem 3.7] Let ${\\theta}\\in Q_+$ and $d=\\height({\\theta})$. Then the following sets are $\\k$-bases of $R_{\\theta}$: $$\\begin{aligned}\n \\{\\psi_w y_1^{k_1}\\dots y_d^{k_d}1_\\bi\\mid w\\in \\Si_d,\\ k_1,\\dots,k_d\\in{\\mathbb{Z}}_{\\geq 0}, \\ \\bi\\in I^{\\theta}\\},\n\\\\\n \\{y_1^{k_1}\\dots y_d^{k_d}\\psi_w 1_\\bi\\mid w\\in \\Si_d,\\ k_1,\\dots,k_d\\in{\\mathbb{Z}}_{\\geq 0}, \\ \\bi\\in I^{\\theta}\\}.\\end{aligned}$$\n\nParabolic subalgebras and divided power idempotents\n---------------------------------------------------\n\nLet $\\theta_1,\\dots,\\theta_t\\in Q_+$ and set $\\theta:=\\theta_1+\\dots+\\theta_t$. Set $$1_{\\theta_1,\\dots,\\theta_t}:=\\sum_{\\bi^1\\in I^{\\theta_1},\\dots,\\bi^t\\in I^{\\theta_t}}1_{\\bi^1\\cdots\\bi^t}\\in R_\\theta.$$ Then we have an algebra embedding $$\\label{EEmb}\n\\iota_{\\theta_1,\\dots,\\theta_t}: R_{\\theta_1}\\otimes\\dots\\otimes R_{\\theta_t}\\into 1_{\\theta_1,\\dots,\\theta_t}R_{\\theta_1+\\dots+\\theta_t}1_{\\theta_1,\\dots,\\theta_t}$$ obtained by horizontal concatenation of the Khovanov-Lauda diagrams. ", "For $r_1\\in R_{\\theta_1},\\dots, r_t\\in R_{\\theta_t}$, when there is no confusion, we often write $$r_1\\circ\\dots\\circ r_t:=\\iota_{\\theta_1,\\dots,\\theta_t}(r_1\\otimes\\dots\\otimes r_t).$$ For example, $$\\label{E240918}\n1_{\\bi^1}\\circ\\dots\\circ 1_{\\bi^t}=1_{\\bi^1\\cdots \\bi^t}\\qquad(\\bi^1\\in I^{\\theta_1},\\dots,\\bi^t\\in I^{\\theta_t}).$$\n\nWe fix for the moment $i\\in I$, $d\\in{\\mathbb{Z}}_{>0}$ and take $\\theta=d{\\alpha}_i$, in which case $R_{d{\\alpha}_i}$ is isomorphic to the rank $d$ nil-Hecke algebra ${\\mathcal{NH}}_d$. Following [@KL1], we consider the following elements of $R_{d{\\alpha}_i}$: $$y_{0,d}:=\\prod_{r=1}^d y_r^{r-1},\\quad\n1_{i^{(d)}}:=\\psi_{w_{0,d}}y_{0,d},\\quad\\text{and}\\quad\n1_{i^{(d)}}':=y_{0,d}\\psi_{w_{0,d}}.$$\n\nThe following is well-known, see for example [@KL1 §2.2]:\n\n\\[LW0Y0\\] In $R_{d{\\alpha}_i}$, the elements $1_{i^{(d)}}$ and $1_{i^{(d)}}'$ are idempotents. ", "Moreover,\n\n1. ", " \\[LW0Y0i\\] $\\psi_{w_{0,d}}f\\psi_{w_{0,d}}=0$ for any polynomial $f$ in $y_1,\\dots,y_d$ of degree less than $d(d-1)/2$.\n\n2. ", " \\[LW0Y0ii\\] $\\psi_{w_{0,d}}y_{0,d}\\psi_{w_{0,d}}=\\psi_{w_{0,d}}$.\n\nNow, let $\\theta\\in Q_+$ be arbitrary. ", "We define $I^{\\theta}_{{\\mathrm{div}}}$ to be the set of all expressions of the form $i_1^{(d_1)} \\cdots i_r^{(d_r)}$ with $d_1,\\dots,d_r\\in {\\mathbb{Z}}_{\\ge 0}$, $i_1,\\dots,i_r\\in I$ and $d_1 {\\alpha}_{i_1} + \\cdots + d_r {\\alpha}_{i_r} = \\theta$. We refer to such expressions as [*divided power words*]{}. ", "We identify $I^\\theta$ with the subset of $I^\\theta_{\\mathrm{div}}$ which consists of all divided power words as above with all $d_k=1$. We use the same notation for concatenation of divided power words as for concatenation of words. ", "For $\\bi = i_1^{(d_1)}\\cdots i_r^{(d_r)} \\in I^{\\theta}_{{\\mathrm{div}}}$, we define the [*divided power idempotent*]{} $$1_{\\bi}=1_{i_1^{(d_1)}\\cdots i_r^{(d_r)}}:=1_{i_1^{(d_1)}}\\circ\\dots\\circ 1_{i_r^{(d_r)}} \\in R_{\\theta}.$$ Then we have the following analogue of (\\[E240918\\]): $$\\label{E240918_2}\n1_{\\bi^1}\\circ\\dots\\circ 1_{\\bi^t}=1_{\\bi^1\\cdots \\bi^t}\\qquad(\\bi^1\\in I^{\\theta_1}_{{\\mathrm{div}}},\\dots,\\bi^t\\in I^{\\theta_t}_{{\\mathrm{div}}}).$$ To be used as part of the Khovanov-Lauda diagrammatics, we denote $$\\psi_{w_{0,d}}=:\n \\begin{tikzpicture}[baseline=6mm,black,line width=1pt, scale=0.32,\n draw/.append style={rounded corners},\n every node/.append style={font=\\fontsize{5}{5}\\selectfont}] \\tikzset{baseline=0mm}\n\\draw(1,-0.7) node[above]{\\small $w_0$};\n\n\\draw [rounded corners,color=gray] (-0.2,0.8)--(2.2,0.8)--(2.2,-0.4)--(-0.2,-0.4)--cycle;\n\n\\end{tikzpicture}\n,\\quad\ny_{0,d}=:\n \\begin{tikzpicture}[baseline=6mm,black,line width=1pt, scale=0.32,\n draw/.append style={rounded corners},\n every node/.append style={font=\\fontsize{5}{5}\\selectfont}] \\tikzset{baseline=0mm}\n\\draw(1,-0.7) node[above]{\\small $y_0$};\n\n\\draw [rounded corners,color=gray] (-0.2,0.8)--(2.2,0.8)--(2.2,-0.4)--(-0.2,-0.4)--cycle;\n\n\\end{tikzpicture}\n,\\quad\n1_{i^{(d)}}=\n \\begin{tikzpicture}[baseline=6mm,black,line width=1pt, scale=0.32,\n draw/.append style={rounded corners},\n every node/.append style={font=\\fontsize{5}{5}\\selectfont}] \\tikzset{baseline=0mm}\n\\draw(0,2.5)node[above]{$i$}--(0,1.5);\n\\draw(1,2.5) node[above]{$\\cdots$};\n\\draw(2,2.5)node[above]{$i$}--(2,1.6);\n\n\\draw(1,-2) node[above]{\\small $y_0$};\n\n\\draw(1,0.1) node[above]{\\small $w_0$};\n\n\\draw [rounded corners,color=gray] (-0.2,1.6)--(2.2,1.6)--(2.2,0.4)--(-0.2,0.4)--cycle;\n\n\\draw(0,0.5)--(0,-0.5);\n\\draw(2,0.5)--(2,-0.5);\n\\draw(1,-0.7) node[above]{$\\cdots$};\n\n\\draw [rounded corners,color=gray] (-0.2,-0.5)--(2.2,-0.5)--(2.2,-1.7)--(-0.2,-1.7)--cycle;\n\n\\end{tikzpicture}\n=:\n \\begin{tikzpicture}[baseline=6mm,black,line width=1pt, scale=0.32,\n draw/.append style={rounded corners},\n every node/.append style={font=\\fontsize{5}{5}\\selectfont}] \\tikzset{baseline=0mm}\n\\draw(0,-0.7) node[above]{\\small $i$};\n\\draw(1,-0.7) node[above]{\\small $\\cdots$};\n\\draw(2,-0.7) node[above]{\\small $i$};\n\\draw [rounded corners,color=gray] (-0.4,0.8)--(2.4,0.8)--(2.4,-0.4)--(-0.4,-0.4)--cycle;\n\\end{tikzpicture}\n\n=\n \\begin{tikzpicture}[baseline=6mm,black,line width=1pt, scale=0.32,\n draw/.append style={rounded corners},\n every node/.append style={font=\\fontsize{5}{5}\\selectfont}] \\tikzset{baseline=0mm}\n\\draw(1,-0.7) node[above]{\\small $i^{d}$};\n\\draw [rounded corners,color=gray] (-0.4,0.8)--(2.4,0.8)--(2.4,-0.4)--(-0.4,-0.4)--cycle;\n\\end{tikzpicture}\n$$\n\nFor example, if $d=3$, we have $$1_{i^3}\\psi_{w_0}=\n \\begin{tikzpicture}[baseline=6mm,black,line width=1pt, scale=0.32,\n draw/.append style={rounded corners},\n every node/.append style={font=\\fontsize{5}{5}\\selectfont}] \\tikzset{baseline=0mm}\n\\draw(0,1) node[above]{$i$}--(0,0);\n\\draw(1,1) node[above]{$i$}--(1,0);\n\\draw(2,1) node[above]{$i$}--(2,0);\n\\draw(1,-1.3) node[above]{\\small $w_0$};\n\\draw [rounded corners,color=gray] (-0.2,0)--(2.2,0)--(2.2,-1)--(-0.2,-1)--cycle;\n\\end{tikzpicture}\n\n=\n \\begin{tikzpicture}[baseline=6mm,black,line width=1pt, scale=0.32,\n draw/.append style={rounded corners},\n every node/.append style={font=\\fontsize{5}{5}\\selectfont}] \\tikzset{baseline=0mm}\n\\draw(0,1) node[above]{$i$}--(2,-2);\n\\draw(1,1) node[above]{$i$}--(0,-0.5)--(1,-2);\n\\draw(2,1) node[above]{$i$}--(0,-2);\n\\end{tikzpicture}\n,\\quad\n1_{i^3}y_0=\n \\begin{tikzpicture}[baseline=6mm,black,line width=1pt, scale=0.32,\n draw/.append style={rounded corners},\n every node/.append style={font=\\fontsize{5}{5}\\selectfont}] \\tikzset{baseline=0mm}\n\\draw(0,1) node[above]{$i$}--(0,0);\n\\draw(1,1) node[above]{$i$}--(1,0);\n\\draw(2,1) node[above]{$i$}--(2,0);\n\\draw(1,-1.3) node[above]{\\small $y_0$};\n\n\\draw [rounded corners,color=gray] (-0.2,0)--(2.2,0)--(2.2,-1)--(-0.2,-1)--cycle;\n\n\\end{tikzpicture}\n\n=\n \\begin{tikzpicture}[baseline=6mm,black,line width=1pt, scale=0.32,\n draw/.append style={rounded corners},\n every node/.append style={font=\\fontsize{5}{5}\\selectfont}] \\tikzset{baseline=0mm}\n\\draw(0,1) node[above]{$i$}--(0,-2);\n\\draw(1,1) node[above]{$i$}--(1,-2);\n\\draw(2,1) node[above]{$i$}--(2,-2);\n\\blackdot(1,-0.5);\n\\blackdot(2,0);\n\\blackdot(2,-1);\n\\end{tikzpicture}\n,\n\\quad\n1_{i^{(3)}}=\n \\begin{tikzpicture}[baseline=6mm,black,line width=1pt, scale=0.32,\n draw/.append style={rounded corners},\n every node/.append style={font=\\fontsize{5}{5}\\selectfont}] \\tikzset{baseline=0mm}\n\\draw(0,-0.7) node[above]{\\small $i$};\n\\draw(1,-0.7) node[above]{\\small $i$};\n\\draw(2,-0.7) node[above]{\\small $i$};\n\\draw [rounded corners,color=gray] (-0.4,0.7)--(2.4,0.7)--(2.4,-0.5)--(-0.4,-0.5)--cycle;\n\\end{tikzpicture}\n=\n \\begin{tikzpicture}[baseline=6mm,black,line width=1pt, scale=0.32,\n draw/.append style={rounded corners},\n every node/.append style={font=\\fontsize{5}{5}\\selectfont}] \\tikzset{baseline=0mm}\n\\draw(0,1) node[above]{$i$}--(2,-2);\n\\draw(1,1) node[above]{$i$}--(0,-0.5)--(1,-2);\n\\draw(2,1) node[above]{$i$}--(0,-2);\n\\blackdot(0.8,-1.7);\n\\blackdot(1.4,-1.1);\n\\blackdot(1.8,-1.7);\n\\end{tikzpicture}\n$$ More generally, we denote $$1_{i_1^{(d_1)}\\cdots\\, i_r^{(d_r)}}=:\n \\begin{tikzpicture}[baseline=6mm,black,line width=1pt, scale=0.32,\n draw/.append style={rounded corners},\n every node/.append style={font=\\fontsize{5}{5}\\selectfont}] \\tikzset{baseline=0mm}\n\\draw(1,-0.7) node[above]{\\small $i_1^{d_1}$};\n\\draw [rounded corners,color=gray] (-0.4,1.2)--(2.4,1.2)--(2.4,-0.5)--(-0.4,-0.5)--cycle;\n\\end{tikzpicture}\n\\cdots\n \\begin{tikzpicture}[baseline=6mm,black,line width=1pt, scale=0.32,\n draw/.append style={rounded corners},\n every node/.append style={font=\\fontsize{5}{5}\\selectfont}] \\tikzset{baseline=0mm}\n\\draw(1,-0.7) node[above]{\\small $i_r^{d_r}$};\n\\draw [rounded corners,color=gray] (-0.4,1.2)--(2.4,1.2)--(2.4,-0.5)--(-0.4,-0.5)--cycle;\n\\end{tikzpicture}\n$$\n\nFor any $1\\leq r< t\\leq d$, we denote the cycle $(t,t-1,\\dots,r)\\in\\Si_d$ by $(t\\to r)$. Note that $(t\\to r)=s_{t-1}s_{t-2}\\cdots s_{r}$ is a unique reduced decomposition. ", "So $$\\label{EPsiCycle}\n\\psi_{t\\to r}:=\\psi_{(t\\to r)}=\\psi_{t-1}\\psi_{t-2}\\dots\\psi_{r}\\in R_\\theta,$$ In terms of the diagrammatic notation we have $$1_\\bi\\psi_{t\\to r}= \\begin{tikzpicture}[baseline=6mm,black,line width=1pt, scale=0.32,\n draw/.append style={rounded corners},\n every node/.append style={font=\\fontsize{5}{5}\\selectfont}] \\tikzset{baseline=0mm}\n\n\\draw(0,1) node[above]{$i_1$}--(0,-1);\n\\draw(1,1.1) node[above]{$\\cdots$};\n\\draw(2.5,0.9) node[above]{$i_{r-1}$}--(2.5,-1);\n\\draw(4,1) node[above]{$i_{r}$}--(5.2,-1);\n\n\\draw(5.1,1.1) node[above]{$\\cdots$};\n\\draw(6.5,0.9) node[above]{$i_{t-1}$}--(7.7,-1);\n\n\\draw(7.7,1) node[above]{$i_{t}$}--(4,-1);\n\\draw(8.9,0.9) node[above]{$i_{t+1}$}--(8.9,-1);\n\n\\draw(10.4,1.1) node[above]{$\\cdots$};\n\\draw(11.4,1) node[above]{$i_{d}$}--(11.4,-1);\n\n\\end{tikzpicture}\n.$$\n\n\\[LDivPower\\] In the algebra $R_{d{\\alpha}_i}$, we have\n\n1. ", " \\[LDivPoweri\\] If $r_1+\\dots+r_t=d$ then $1_{i^{(r_1)} \\cdots i^{(r_t)}}\\psi_{w_{0,d}}=\\psi_{w_{0,d}}$ and $1_{i^{(r_1)} \\cdots i^{(r_t)}}1_{i^{(d)}}=1_{i^{(d)}}$.\n\n2. ", " \\[LDivPowerii\\] $1_{i^{(d)}}\\psi_{d\\to 1}1_{i\\,i^{(d-1)}}\n =\\psi_{d\\to 1}1_{i\\,i^{(d-1)}}$.\n\n\\(i) Write $\\psi_{w_{0,d}}=(\\psi_{w_{0,r_1}}\\circ\\dots\\circ \\psi_{w_{0,r_t}})\\psi_u$ for some $u\\in\\Si_d$ and use Lemma \\[LW0Y0\\].", "\n\n\\(ii) We have $$\\begin{aligned}\n1_{i^{(d)}}\\psi_{d-1}\\psi_{d-2}\\dots\\psi_11_{i\\,i^{(d-1)}}\n&=\n1_{i^{(d)}}\\psi_{d-1}\\psi_{d-2}\\dots\\psi_1(1_{{\\alpha}_i}\\circ \\psi_{w_{0,d-1}}y_{0,d-1})\n\\\\\n&=\n1_{i^{(d)}}\\psi_{w_{0,d}}(1_{{\\alpha}_i}\\circ y_{0,d-1})\n\\\\\n&=\n\\psi_{w_{0,d}}(1_{{\\alpha}_i}\\circ y_{0,d-1})\n\\\\\n&=\n\\psi_{d-1}\\psi_{d-2}\\dots\\psi_1(1_{{\\alpha}_i}\\circ \\psi_{w_{0,d-1}}y_{0,d-1})\n\\\\\n&=\n\\psi_{d\\to 1}1_{i\\,i^{(d-1)}},\\end{aligned}$$ where we have used Lemma \\[LW0Y0\\](\\[LW0Y0ii\\]) for the third equality.", "\n\nThe following lemma easily follows from the defining relations of $R_\\theta$:\n\n\\[LPull\\] Let $1\\leq r< s\\leq d$, $t\\in(r,s)$, $u\\in [r,s)$, and $\\bi\\in I^\\theta$. Then in $R_\\theta$ we have:\n\n1. ", " $1_\\bi\\psi_{s\\to r} \\psi_t=1_\\bi\\psi_{t-1}\\psi_{s\\to r}$ unless $i_s=i_{t-1}=i_t\\pm 1$.\n\n2. ", " $1_\\bi\\psi_{s\\to r} y_{u+1}=1_\\bi y_{u}\\psi_{s\\to r}$ unless $i_s=i_{u}$.\n\nModules over $R_\\theta$\n-----------------------\n\nLet $\\theta\\in Q_+$. We denote by $\\Mod{R_\\theta}$ the category of graded left $R_\\theta$-modules. ", "The morphisms in this category are all homogeneous degree zero $R_\\theta$-homomorphisms, which we denote $\\hom_{R_\\theta}(-,-)$. For $V\\in\\Mod{R_\\theta}$, let $q^d V$ denote its grading shift by $d$, so if $V_m$ is the degree $m$ component of $V$, then $(q^dV)_m= V_{m-d}.$ More generally, for a Laurent series $a=a(q)=\\sum_{n}a_nq^n\\in{\\mathbb{Z}}[q,q^{-1}]$ with non-negative coefficients, we set $a V:=\\bigoplus_n(q^n V)^{\\oplus a_n}$. For $U,V\\in \\Mod{R_\\theta}$, we set $\\HOM_{R_\\theta}(U, V):=\\bigoplus_{d \\in {\\mathbb{Z}}} \\HOM_{R_\\theta}(U, V)_d$, where $$\\HOM_{R_\\theta}(U, V)_d := \\hom_{R_\\theta}(q^d U, V) = \\hom_{R_\\theta}(U, q^{-d}V).$$ We define ${\\operatorname{Ext}}^m_{R_\\theta}(U,V)$ similarly in terms of $\\operatorname{ext}^m_{R_\\theta}(U,V)$.\n\nFor $\\theta_1,\\dots,\\theta_t\\in Q_+$ and $\\theta:=\\theta_1+\\dots+\\theta_t$, recalling (\\[EEmb\\]), we have a functor $${{\\mathrm {Ind}}}_{\\theta_1,\\dots,\\theta_t}=R_\\theta 1_{\\theta_1,\\dots,\\theta_t}\\otimes_{R_{\\theta_1}\\otimes\\dots\\otimes R_{\\theta_t}}-:\\Mod{(R_{\\theta_1}\\otimes\\dots\\otimes R_{\\theta_t})}\\to\\Mod{R_{\\theta}}.$$ For $V_1\\in\\Mod{R_{\\theta_1}}, \\dots, V_t\\in\\Mod{R_{\\theta_t}}$, we denote by $V_1\\boxtimes \\dots\\boxtimes V_t$ the $\\k$-module $V_1\\otimes \\dots\\otimes V_t$, considered naturally as an $(R_{\\theta_1}\\otimes\\dots\\otimes R_{\\theta_t})$-module, and set $$V_1\\circ\\dots\\circ V_t:={{\\mathrm {Ind}}}_{\\theta_1,\\dots,\\theta_t} V_1\\boxtimes \\dots\\boxtimes V_t.$$ For $v_1\\in V_1,\\dots, v_t\\in V_t$, we denote $$v_1\\circ \\dots\\circ v_t:= 1_{\\theta_1,\\dots,\\theta_t}\\otimes v_1\\otimes\\dots\\otimes v_t\\in V_1\\circ \\dots\\circ V_t.$$ Since $R_\\theta 1_{\\theta_1,\\dots,\\theta_t}$ is a free $R_{\\theta_1}\\otimes\\dots\\otimes R_{\\theta_t}$-module of finite rank by Theorem \\[TBasis\\], we get the following well-known properties:\n\n\\[circexact\\] The functor ${{\\mathrm {Ind}}}_{\\theta_1,\\dots,\\theta_t}$ is exact and sends finitely generated projectives to finitely generated projectives.", "\n\nThe following lemma is easy to check using the fact that $1_\\bk$ is an idempotent in $R_\\chi$ for $\\bk\\in I^\\chi_{{\\mathrm{div}}}$:\n\n\\[LIndIdemp\\] For $\\bi\\in I^{\\theta}_{{\\mathrm{div}}}$ and $\\bj\\in I^{\\eta}_{{\\mathrm{div}}}$, we have $R_\\theta1_{\\bi}\\circ R_\\eta 1_\\bj\\cong R_{\\theta+\\eta}1_{\\bi\\bj}$.\n\nStandard modules {#SSStdMod}\n----------------\n\nThe algebra $R_\\theta$ is affine quasihereditary in the sense of [@Kdonkin]. ", "In particular, it comes with an important class of [*standard modules*]{}, which we now describe explicitly, referring to [@BKM §3]. ", "We are going to work with the lexicographic convex order $\\preceq$ on $\\Phi_+$, i.e. for ${\\alpha}= \\alpha_r + \\cdots + \\alpha_s\\in \\Phi_+$ and ${\\alpha}' = \\alpha_{r'} + \\cdots + \\alpha_{s'}\\in \\Phi_+$, we have ${\\alpha}\\prec {\\alpha}'$ if and only if either $r < r'$ or $r = r'$ and $s < s'$.\n\nFix ${\\alpha}= \\alpha_r + \\cdots + \\alpha_{s} \\in \\Phi_+$ of height $l:=s-r+1$, and set $$\\bi_{\\alpha}:= r\\,(r+1)\\cdots s\\in I^{\\alpha}.$$ We define the $R_{\\alpha}$-module $\\Delta({\\alpha})$ to be the cyclic $R_{\\alpha}$-module generated by a vector $v_{\\alpha}$ of degree $0$ with defining relations\n\n- $1_\\bi v_{\\alpha}= \\delta_{\\bi,\\bi_{\\alpha}}v_{\\alpha}$ for all $\\bi\\in I^{\\alpha}$;\n\n- $\\psi_t v_{\\alpha}= 0$ for all $1\\leq t < l$;\n\n- $y_t v_{\\alpha}= y_u v_{\\alpha}$ for all $1\\leq t, u \\leq l$.\n\nBy [@BKM Corollary 3.5], ${\\Delta}({\\alpha})$ is indeed the standard module corresponding to ${\\alpha}$. In fact, if $\\k={\\mathbb{Z}}_p$, by [@KS (4.11)], ${\\Delta}({\\alpha})$ is a universal $\\k$-form of the standard module in the sense of [@KS §4.2].", "\n\nThe module $\\Delta({\\alpha})$ can be considered as an $(R_{\\alpha}, \\k[x])$-bimodule with the right action given by $v_{\\alpha}x := y_1 v_{\\alpha}.$ Then it is easy to check that there is an isomorphism of graded $\\k$-modules $\\k[x] \\to \\Delta({\\alpha}), \\ f\\mapsto v_{\\alpha}f.$\n\nFix an integer $m\\in {\\mathbb{Z}}_{>0}$. Let ${\\mathcal{NH}}_m$ be the rank $m$ nil-Hecke algebra with standard generators $x_1,\\dots,x_{m}$, $\\tau_1,\\dots,\\tau_{m-1}$. For any $i\\in I$, there is an isomorphism $\\phi: R_{m\\alpha_i}\\iso {\\mathcal{NH}}_m,\\ y_t\\mapsto x_t,\\ \\psi_u\\mapsto \\tau_u$, and we have the idempotent $$\\label{DeltaIdem}\ne_m := \\phi(1_{i^{(d)}}') \\in {\\mathcal{NH}}_m.$$\n\nThe $R_{m{\\alpha}}$-module $\\Delta({\\alpha})^{\\circ m}$ is cyclicly generated by $v_{\\alpha}^{\\circ m}$. As explained in [@BKM §3.2], ${\\mathcal{NH}}_m$ acts on $\\Delta({\\alpha})^{\\circ m}$ on the right so that $$\\begin{aligned}\nv_{\\alpha}^{\\circ m}x_t&=v_{\\alpha}^{\\circ (t-1)}\\circ (v_{\\alpha}x)\\circ v_{\\alpha}^{\\circ (m-t)}\\qquad(1\\leq t\\leq m),\n\\\\\nv_{\\alpha}^{\\circ m}\\tau_u&=v_{\\alpha}^{\\circ (u-1)}\\circ (\\psi_z (v_{\\alpha}\\circ v_{\\alpha}))\\circ v_{\\alpha}^{\\circ (m-u-1)}\\qquad(1\\leq u< m),\\end{aligned}$$ where $z$ is the longest element of ${{\\mathscr D}}^{(l,l)}$.\n\nDefine $$\\label{DeltaDef}\n\\Delta({\\alpha}^m) := q^{\\binom{m}{2}}\\Delta({\\alpha})^{\\circ m}e_m.$$ As in [@BKM Lemma 3.10], we have an isomorphism of $R_{m{\\alpha}}$-modules $$\\label{deltaiso}\n \\Delta({\\alpha})^{\\circ m} \\cong [m]^!\\Delta({\\alpha}^m).$$\n\nGiven $\\theta\\in Q_+$ and a Kostant partition $\\pi = (\\beta_1^{m_1}, \\ldots, \\beta_t^{m_t})\\in{\\operatorname{KP}}(\\theta)$ as in the Introduction, we define the corresponding [*standard module*]{} $$\\Delta(\\pi) := \\Delta(\\beta_1^{m_1}) \\circ \\cdots \\circ \\Delta(\\beta_t^{m_t}).$$ If $\\k$ is a field, the modules $\\{{\\Delta}(\\pi)\\mid \\pi\\in {\\operatorname{KP}}(\\theta)\\}$ are the standard modules for an affine quasihereditary structure on the algebra $R_\\theta$, see [@BKM; @Kdonkin]. ", "If $\\k={\\mathbb{Z}}$ or ${\\mathbb{Z}}_p$, they can be thought of as integral forms of the standard modules, see [@KS §4].", "\n\nSemicuspidal resolution {#SDPR}\n=======================\n\nThroughout the subsection, we fix $m\\in{\\mathbb{Z}}_{>0}$, $a,b\\in{\\mathbb{Z}}$ with $a\\leq b$, and set $$l:=b+2-a,\\quad d:=lm.$$ We denote $${\\alpha}:={\\alpha}_a+\\dots+{\\alpha}_{b+1}\\in \\Phi_+$$ and $\\theta:=m{\\alpha}$. Note that $l=\\height({\\alpha})$ and $d=\\height(\\theta)$. Our goal is to construct a resolution $P_\\bullet=P^{{\\alpha}^m}_{\\bullet}$ of the semicuspidal standard module ${\\Delta}({\\alpha}^m)$.\n\nCombinatorics {#SSComb}\n-------------\n\nWe consider the set of compositions $${\\Lambda}={\\Lambda}^{{\\alpha}^m}:=\\{{\\lambda}=({\\lambda}_a,\\dots,{\\lambda}_b)\\mid {\\lambda}_a,\\dots,{\\lambda}_b\\in [0,m]\\}.$$ For ${\\lambda}\\in{\\Lambda}$, we denote $|{\\lambda}|:={\\lambda}_a+\\dots+{\\lambda}_b$, and for $n\\in{\\mathbb{Z}}_{\\geq 0}$, we set $${\\Lambda}(n)={\\Lambda}^{{\\alpha}^m}(n):=\\{{\\lambda}\\in{\\Lambda}\\mid |{\\lambda}|=n\\}.$$ Let $a\\leq i\\leq b$. We set $$\\e_i:=(0,\\dots,0,1,0,\\dots,0)\\in{\\Lambda}(1),$$ with $1$ in the $i$th position. ", "Let ${\\lambda}\\in{\\Lambda}$. Set $$\\begin{aligned}\ns_{\\lambda}&:=-\\frac{lm(m-1)}{2}+(m+1)n-\\sum_{i=a}^b{\\lambda}_i^2\\in{\\mathbb{Z}},\\\\\n\\bj^{\\lambda}&:=a^{m-{\\lambda}_a}(a+1)^{m-{\\lambda}_{a+1}}\\cdots b^{m-{\\lambda}_b}(b+1)^{m}b^{{\\lambda}_b} (b-1)^{{\\lambda}_{b-1}}\\cdots a^{{\\lambda}_a}\\in I^\\theta,\n\\\\\n\\bi^{\\lambda}&:=a^{(m-{\\lambda}_a)}(a+1)^{(m-{\\lambda}_{a+1})}\\dots b^{(m-{\\lambda}_b)}(b+1)^{(m)}b^{({\\lambda}_b)} (b-1)^{({\\lambda}_{b-1})}\\dots a^{({\\lambda}_a)}\\in I^\\theta_{\\mathrm{div}}.\\end{aligned}$$ We also associate to ${\\lambda}$ a composition ${\\omega}_{\\lambda}$ of $d$ with $2n+1$ non-negative parts: $${\\omega}_{\\lambda}:=(m-{\\lambda}_a,m-{\\lambda}_{a+1},\\dots,m-{\\lambda}_b,m,{\\lambda}_b,{\\lambda}_{b-1},\\dots,{\\lambda}_a).$$ Let $i\\in[a,b]$. We denote $$\\begin{aligned}\nr_i^-({\\lambda})&:=\\sum_{s=a}^{i}(m-{\\lambda}_s),\\quad\n r_i^+({\\lambda}):=d-\\sum_{s=a}^{i-1}{\\lambda}_s, \\quad\nl_i^\\pm({\\lambda}):=r_{i\\pm1}^\\pm({\\lambda})+1,\\end{aligned}$$ where $r_{a-1}^-({\\lambda})$ is interpreted as $0$, and $r_{b+1}^+({\\lambda})$ is interpreted as $d-\\sum_{s=a}^{b}{\\lambda}_s$. Moreover, denote $$\\begin{aligned}\nr_{b+1}({\\lambda})&:=d-\\sum_{s=a}^{b}{\\lambda}_s,\\quad\nl_{b+1}({\\lambda}):=r_{b+1}({\\lambda})-m+1.\\end{aligned}$$ Define $$\\begin{aligned}\nU_i^\\pm({\\lambda})&:=[l_i^\\pm({\\lambda}),r_i^\\pm({\\lambda})],\\ U_i({\\lambda}):=U_i^-({\\lambda})\\sqcup U_i^+({\\lambda}), \\ U_{b+1}({\\lambda})&:=[l_{b+1}({\\lambda}),r_{b+1}({\\lambda})].\\end{aligned}$$ Observe that for all $j\\in[a,b+1]$, we have $$U_j({\\lambda})=\\{s\\in [1,d]\\mid \\bj^{\\lambda}_s=j\\}.$$\n\nWe also consider the sets of multicompositions $$\\begin{aligned}\n\\bLa&:=({\\Lambda}^{\\alpha})^m=\\{\\bde=({\\delta}^{(1)},\\dots,{\\delta}^{(m)})\\mid {\\delta}^{(1)},\\dots,{\\delta}^{(m)}\\in{\\Lambda}^{\\alpha}\\},\n\\\\\n\\bLa(n)&:=\\{\\bde=({\\delta}^{(1)},\\dots,{\\delta}^{(m)})\\in\\bLa\\mid |{\\delta}^{(1)}|+\\dots+|{\\delta}^{(m)}|=n\\}.\\end{aligned}$$ Note that by definition all ${\\delta}^{(r)}_i\\in\\{0,1\\}$. For $1\\leq r\\leq m$ and $a\\leq i\\leq b$, we define ${\\bolde}^{r}_i\\in\\bLa(1)$ to be the multicomposition whose $r$th component is $\\e_i$ and whose other components are zero. ", "For $\\bde\\in\\bLa$, denote $${\\lambda}^\\bde:={\\delta}^{(1)}+\\dots+{\\delta}^{(m)}\\in{\\Lambda}.$$\n\nFix $\\bde=({\\delta}^{(1)},\\dots,{\\delta}^{(m)})\\in\\bLa$. Define $$\\bj^\\bde:=\\bj^{{\\delta}^{(1)}}\\dots\\bj^{{\\delta}^{(m)}}\\in I^\\theta.$$ For $i\\in[a,b]$ we define $$\\begin{aligned}\nU_i^{(\\pm)}(\\bde)&:=\\{l(r-1)+u\\mid \\text{$r\\in[1,m]$, $u\\in U_i^{(\\pm)}({\\delta}^{(r)})$}\\},\\quad U_i(\\bde):=U_i^+(\\bde)\\sqcup U_i^-(\\bde),\\\\ U_{b+1}(\\bde)&:=\\{l(r-1)+u\\mid \\text{$r\\in[1,m]$, $u\\in U_{b+1}({\\delta}^{(r)})$}\\}.\\end{aligned}$$ Observe that for any $j\\in[a,b+1]$, we have $$U_j^{(\\bde)}=\\{s\\in[1,d]\\mid \\bj^\\bde_s=j\\} \\quad \\text{and}\\quad\n|U_j^{(\\pm)}({\\lambda}^\\bde)|=|U_j^{(\\pm)}(\\bde)|.$$\n\nFor ${\\lambda}\\in{\\Lambda}$, $\\bde\\in\\bLa$, and $i\\in[a,b]$, we define some signs: $$\\begin{aligned}\n\\sgn_{{\\lambda};i}&:=(-1)^{\\sum_{j=a}^{i-1}{\\lambda}_{j}},\n\\qquad\n\\sgn_{\\bde;r,i}:=(-1)^{\\sum_{s=1}^{r-1}|{\\delta}^{(s)}|+\\sum_{j=a}^{i-1}{\\delta}^{(r)}_j},\n\\\\\nt_\\bde&:= \\sum_{\\substack{1\\leq r<s\\leq m \\\\\na\\leq j<i\\leq b }}{\\delta}^{(r)}_i{\\delta}^{(s)}_j,\\qquad {\\sigma}_\\bde:=(-1)^{t_\\bde},\\\\\n\\tau_{\\lambda}&:=(-1)^{\\sum_{i=a}^b{\\lambda}_i({\\lambda}_i-1)/2},\\qquad \\tau_\\bde:={\\sigma}_\\bde\\tau_{{\\lambda}^\\bde}.\\end{aligned}$$ ($\\tau_{\\lambda},\\tau_\\bde$ are not to be confused with $\\tau_w\\in{\\mathcal{NH}}_d$ which will not be used again).", "\n\n\\[LSigns\\] Let $\\bde=({\\delta}^{(1)},\\dots,{\\delta}^{(m)})\\in\\bLa$, $i\\in[a,b]$ and $r\\in[1,m]$. If ${\\delta}_i^{(r)}=0$, then $$\\sgn_{{\\lambda}^\\bde;i}{\\sigma}_\\bde={\\sigma}_{\\bde+\\bolde_i^{r}} \\sgn_{\\bde;r,i}(-1)^{\\sum_{s=1}^{r-1}{\\delta}_i^{(s)}}.$$\n\nLet ${\\lambda}:={\\lambda}^\\bde$ and $\\bga:=\\bde+\\bolde_i^{r}$. Writing ‘$\\equiv$’ for ‘$\\equiv\\pmod{2}$’, we have to prove $$\\begin{aligned}\n\\sum_{j=a}^{i-1}{\\lambda}_j+\\sum_{t<s,\\ k>j}{\\delta}_k^{(t)}{\\delta}_j^{(s)}\\equiv\n\\sum_{t<s,\\ k>j}{\\gamma}_k^{(t)}{\\gamma}_j^{(s)}+\\sum_{s=1}^{r-1}|{\\delta}^{(s)}|+\\sum_{j=a}^{i-1}{\\delta}_j^{(r)}+\\sum_{s=1}^{r-1}{\\delta}_i^{(s)}.\\end{aligned}$$ Note that $$\\label{E170916}\n\\sum_{t<s,\\ k>j}{\\gamma}_k^{(t)}{\\gamma}_j^{(s)}=\\sum_{t<s,\\ k>j}{\\delta}_k^{(t)}{\\delta}_j^{(s)}+\\sum_{s>r,\\ j<i}{\\delta}_j^{(s)}+\\sum_{s<r,\\ j>i}{\\delta}_j^{(s)},$$ so the required comparison boils down to $$\\begin{aligned}\n\\sum_{j=a}^{i-1}{\\lambda}_j\\equiv\n\\sum_{s>r,\\ j<i}{\\delta}_j^{(s)}+\\sum_{s<r,\\ j>i}{\\delta}_j^{(s)}+\\sum_{s=1}^{r-1}|{\\delta}^{(s)}|+\\sum_{j=a}^{i-1}{\\delta}_j^{(r)}+\\sum_{s=1}^{r-1}{\\delta}_i^{(s)},\\end{aligned}$$ which is easy to see.", "\n\n\\[LSignsG\\] Let $\\bga=({\\gamma}^{(1)},\\dots,{\\gamma}^{(m)})\\in\\bLa$, $i\\in[a,b]$ and $r\\in[1,m]$. If ${\\gamma}_i^{(r)}=1$, then $$\\tau_\\bga \\sgn_{{\\lambda}^\\bga;i}=\\sgn_{\\bga-\\bolde_i^{r};r,i} \\tau_{\\bga-\\bolde_i^{r}}(-1)^{\\sum_{s=r+1}^m {\\gamma}_i^{(s)}\\}}.$$\n\nLet $\\mu:={\\lambda}^\\bga$, $\\bde:=\\bga-\\bolde_i^{r}$, and ${\\lambda}:={\\lambda}^\\bde$. Writing ‘$\\equiv$’ for ‘$\\equiv\\pmod{2}$’, we have to prove the comparison $$\\begin{aligned}\n&\\sum_{t<s,\\ k>j}{\\gamma}_k^{(t)}{\\gamma}_j^{(s)}+\\sum_{j=a}^b\\mu_j(\\mu_j-1)/2+\\sum_{j=a}^{i-1}\\mu_j\n\\\\\n\\equiv\n&\n\\sum_{s=1}^{r-1}|{\\delta}^{(s)}|+\\sum_{j=a}^{i-1}{\\delta}^{(r)}_j\n+\\sum_{t<s,\\ k>j}{\\delta}_k^{(t)}{\\delta}_j^{(s)}+\\sum_{j=a}^b{\\lambda}_j({\\lambda}_j-1)/2\n+\\sum_{s=r+1}^m {\\gamma}_i^{(s)}.\\end{aligned}$$ Note that $$\\sum_{j=a}^b\\mu_j(\\mu_j-1)/2-\\sum_{j=a}^b{\\lambda}_j({\\lambda}_j-1)/2={\\lambda}_i.$$ So, using also (\\[E170916\\]), the required comparison boils down to $$\\begin{aligned}\n\\sum_{s>r,\\ j<i}{\\delta}_j^{(s)}+\\sum_{s<r,\\ j>i}{\\delta}_j^{(s)}\n+\\sum_{j=a}^{i}{\\lambda}_j\\equiv\n\\sum_{s=1}^{r-1}|{\\delta}^{(s)}|+\\sum_{j=a}^{i-1}{\\delta}_j^{(r)}+\\sum_{s=r+1}^{m}{\\delta}_i^{(s)},\\end{aligned}$$ which is easy to see.", "\n\nThe resolutions $P_\\bullet^{{\\alpha}^m}$ and $P_\\bullet^{\\pi}$ {#SSRes}\n--------------------------------------------------------------\n\nLet ${\\lambda}\\in{\\Lambda}$. Recalling the divided power word $\\bi^{\\lambda}\\in I^\\theta_{\\mathrm{div}}$ and the integer $s_{\\lambda}$ from $\\S\\ref{SSComb}$, we set $$\\begin{aligned}\ne_{\\lambda}:=1_{\\bi^{\\lambda}}\\in R_\\theta \\qquad\\text{and}\\qquad\nP_{\\lambda}=P^{{\\alpha}^m}_{{\\lambda}}:=q^{s_{\\lambda}}R_\\theta e_{\\lambda}.\\end{aligned}$$ In particular, $P_{\\lambda}$ is a projective left $R_\\theta$-module. ", "Note that $1_{\\bj^{\\lambda}}e_{\\lambda}=e_{\\lambda}1_{\\bj^{\\lambda}}=e_{\\lambda}$. Further, set for any $n\\in{\\mathbb{Z}}_{\\geq 0}$: $$P_n=P^{{\\alpha}^m}_{n}:=\\bigoplus_{{\\lambda}\\in{\\Lambda}(n)} P_{\\lambda}.$$ Note that $P_n=0$ for $n>d-m$. The projective resolution $P_\\bullet=P^{{\\alpha}^m}_\\bullet$ of ${\\Delta}({\\alpha}^m)$ will be of the form $$\\dots \\longrightarrow P_{n+1}\\stackrel{d_n}{\\longrightarrow} P_n\\longrightarrow\\dots \\stackrel{d_0}{\\longrightarrow} P_0.", "\n$$\n\nTo describe the boundary maps $d_n$, we first consider a more general situation. ", "Suppose we are given two sets of idempotents $\\{e_a\\mid a\\in A\\}$ and $\\{f_b\\mid b\\in B\\}$ in an algebra $R$. An $A\\times B$ matrix $D:=(d^{a,b})_{a\\in A, b\\in B}$ with every $d^{a,b}\\in e_aR f_b$ then yields the homomorphism between the projective $R$-modules $$\\label{rightmult}\n\\rho_D:\\bigoplus_{a\\in A}Re_a\\to \\bigoplus_{b\\in B}Rf_b,\\ (r_ae_a)_{a\\in A}\\mapsto \\big(\\sum_{a\\in A}r_ad^{a,b}\\big)_{b\\in B},$$ which we refer to as the [*right multiplication with $D$.*]{}\n\nWe now define a ${\\Lambda}(n+1)\\times{\\Lambda}(n)$ matrix $D_n$ with entries $d_n^{\\mu,{\\lambda}}\\in e_\\mu R_\\theta e_{\\lambda}$. Let ${\\lambda}\\in{\\Lambda}(n)$ and $a\\leq i\\leq b$ be such that ${\\lambda}_i<m$. Recalling (\\[EPsiCycle\\]), define $$\\begin{aligned}\n\\psi_{{\\lambda};i}:=\\psi_{r_i^+({\\lambda}+\\e_i)\\to r_i^-({\\lambda})}.\\end{aligned}$$ Note that $\\psi_{{\\lambda};i}1_{\\bj^{\\lambda}}=1_{\\bj^{{\\lambda}+\\e_i}}\\psi_{{\\lambda};i}$. Recalling the sign $\\sgn_{{\\lambda};i}$ from §\\[SSComb\\], we now set $$d_n^{\\mu,{\\lambda}}:=\n\\left\\{\n\\begin{array}{ll}\n\\sgn_{{\\lambda};i}e_\\mu\\psi_{{\\lambda};i} e_{\\lambda}&\\hbox{if $\\mu={\\lambda}+\\e_i$ for some $a\\leq i\\leq b$,}\\\\\n0 &\\hbox{otherwise.}", "\n\\end{array}\n\\right.$$ Diagrammatically, for $\\mu={\\lambda}+\\e_i$ as above, we have $$d^{\\mu,{\\lambda}}_n=\\pm\n \\begin{tikzpicture}[baseline=6mm,black,line width=1pt, scale=0.32,\n draw/.append style={rounded corners},\n every node/.append style={font=\\fontsize{5}{5}\\selectfont}] \\tikzset{baseline=0mm}\n\\draw(1.05,2) node[above]{\\small $a^{m-{\\lambda}_a}$};\n\\draw [rounded corners,color=gray] (-0.6,3.6)--(2.6,3.6)--(2.6,2.2)--(-0.6,2.2)--cycle;\n\\draw(4,2) node[above]{\\small $\\cdots$};\n\\draw(7,2) node[above]{\\small $i^{m-{\\lambda}_i-1}$};\n\\draw [rounded corners,color=gray] (4.8,3.6)--(9,3.6)--(9,2.2)--(4.8,2.2)--cycle;\n\\draw(12,2) node[above]{\\small $(i+1)^{{\\lambda}_{i+1}}$};\n\\draw [rounded corners,color=gray] (9.3,3.6)--(14.5,3.6)--(14.5,2.2)--(9.3,2.2)--cycle;\n\\draw(16.6,2) node[above]{\\small $\\cdots$};\n\\draw(20,2) node[above]{\\small $i^{{\\lambda}_i+1}$};\n\\draw [rounded corners,color=gray] (18.2,3.6)--(21.9,3.6)--(21.9,2.2)--(18.2,2.2)--cycle;\n\\draw(25,2) node[above]{\\small $(i-1)^{{\\lambda}_{i-1}}$};\n\\draw [rounded corners,color=gray] (22.3,3.6)--(27.5,3.6)--(27.5,2.2)--(22.3,2.2)--cycle;\n\\draw(29,2) node[above]{\\small $\\cdots$};\n\\draw(31.4,2) node[above]{\\small $a^{{\\lambda}_a}$};\n\\draw [rounded corners,color=gray] (30,3.6)--(33,3.6)--(33,2.2)--(30,2.2)--cycle;\n\n\\draw(1.05,-3) node[above]{\\small $a^{m-{\\lambda}_a}$};\n\\draw [rounded corners,color=gray] (-0.6,-1.4)--(2.6,-1.4)--(2.6,-2.8)--(-0.6,-2.8)--cycle;\n\\draw(4,-3) node[above]{\\small $\\cdots$};\n\\draw(7.4,-3) node[above]{\\small $i^{m-{\\lambda}_i}$};\n\\draw [rounded corners,color=gray] (4.8,-1.4)--(9.4,-1.4)--(9.4,-2.8)--(4.8,-2.8)--cycle;\n\\draw(12.4,-3) node[above]{\\small $(i+1)^{{\\lambda}_{i+1}}$};\n\\draw [rounded corners,color=gray] (9.7,-1.4)--(14.9,-1.4)--(14.9,-2.8)--(9.7,-2.8)--cycle;\n\\draw(17,-3) node[above]{\\small $\\cdots$};\n\\draw(20.4,-3) node[above]{\\small $i^{{\\lambda}_i}$};\n\\draw [rounded corners,color=gray] (18.6,-1.4)--(21.8,-1.4)--(21.8,-2.8)--(18.6,-2.8)--cycle;\n\\draw(25,-3) node[above]{\\small $(i-1)^{{\\lambda}_{i-1}}$};\n\\draw [rounded corners,color=gray] (22.3,-1.4)--(27.5,-1.4)--(27.5,-2.8)--(22.3,-2.8)--cycle;\n\\draw(29,-3) node[above]{\\small $\\cdots$};\n\\draw(31.4,-3) node[above]{\\small $a^{{\\lambda}_a}$};\n\\draw [rounded corners,color=gray] (30,-1.4)--(33,-1.4)--(33,-2.8)--(30,-2.8)--cycle;\n\n\\draw(0,2.2)--(0,-1.4);\n\\draw(1,-0.3) node[above]{\\small $\\cdots$};\n\\draw(2,2.2)--(2,-1.4);\n\\draw(3.9,-0.3) node[above]{\\small $\\cdots$};\n\\draw(5.2,2.2)--(5.2,-1.4);\n\\draw(7,-0.3) node[above]{\\small $\\cdots$};\n\\draw(8.5,2.2)--(8.5,-1.4);\n\\draw(21.6,2.2)--(9,-1.4);\n\\draw(9.6,2.2)--(10,-1.4);\n\\draw(12.2,-0.3) node[above]{\\small $\\cdots$};\n\\draw(14,2.2)--(14.4,-1.4);\n\\draw(18.6,2.2)--(19,-1.4);\n\\draw(19.9,-0.3) node[above]{\\small $\\cdots$};\n\\draw(20.8,2.2)--(21.2,-1.4);\n\\draw(22.8,2.2)--(22.8,-1.4);\n\\draw(25,-0.3) node[above]{\\small $\\cdots$};\n\\draw(27,2.2)--(27,-1.4);\n\\draw(29,-0.3) node[above]{\\small $\\cdots$};\n\\draw(30.4,2.2)--(30.4,-1.4);\n\\draw(31.7,-0.3) node[above]{\\small $\\cdots$};\n\\draw(32.7,2.2)--(32.7,-1.4);\n\\end{tikzpicture}\n$$\n\nWe now set the boundary map $d_n$ to be the right multiplication with $D_n$: $$d_n:=\\rho_{D_n}.$$\n\n\\[ExP\\] [Let $a=b=1$ and $m=2$. Then the resolution $P_\\bullet$ is $$0\\to R_\\theta1_{2^{(2)}1^{(2)}}\\stackrel{d_1}{\\longrightarrow}\nR_\\theta1_{12^{(2)}1}\\stackrel{d_0}{\\longrightarrow}\nq^{-2} R_\\theta1_{1^{(2)}2^{(2)}}\\longrightarrow{\\Delta}(({\\alpha}_1+{\\alpha}_2)^2)\\longrightarrow 0,$$ where $d_1$ is a right multiplication with $$1_{2^{(2)}1^{(2)}} \\psi_3\\psi_2\\psi_1 1_{12^{(2)}1}= \\begin{tikzpicture}[baseline=6mm,black,line width=1pt, scale=0.32,\n draw/.append style={rounded corners},\n every node/.append style={font=\\fontsize{5}{5}\\selectfont}] \\tikzset{baseline=0mm}\n\\draw(1,2) node[above]{\\small $2\\ 2$};\n\\draw [rounded corners,color=gray] (-0.2,3.5)--(2.2,3.5)--(2.2,2.2)--(-0.2,2.2)--cycle;\n\\draw(3.55,2) node[above]{\\small $1\\ 1$};\n\\draw [rounded corners,color=gray] (2.4,3.5)--(4.8,3.5)--(4.8,2.2)--(2.4,2.2)--cycle;\n\n\\draw(0.4,-3) node[above]{\\small $1$};\n\\draw [rounded corners,color=gray] (1.2,-1.5)--(3.6,-1.5)--(3.6,-2.8)--(1.2,-2.8)--cycle;\n\\draw(1.8,-3) node[above]{\\small $2$};\n\\draw(2.9,-3) node[above]{\\small $2$};\n\\draw(4.2,-3) node[above]{\\small $1$};\n\n\\draw(0.5,2.2)--(1.7,-1.5);\n\\draw(1.5,2.2)--(2.7,-1.5);\n\\draw(3,2.2)--(4.2,-1.5);\n\\draw(4,2.2)--(0.5,-1.5);\n\\end{tikzpicture}\n$$ and $d_0$ is a right multiplication with $$1_{12^{(2)}1} \\psi_3\\psi_2 1_{1^{(2)}2^{(2)}}= \\begin{tikzpicture}[baseline=6mm,black,line width=1pt, scale=0.32,\n draw/.append style={rounded corners},\n every node/.append style={font=\\fontsize{5}{5}\\selectfont}] \\tikzset{baseline=0mm}\n\\draw(0.4,2) node[above]{\\small $1$};\n\\draw [rounded corners,color=gray] (1.2,3.5)--(3.6,3.5)--(3.6,2.2)--(1.2,2.2)--cycle;\n\\draw(1.8,2) node[above]{\\small $2$};\n\\draw(2.9,2) node[above]{\\small $2$};\n\\draw(4.2,2) node[above]{\\small $1$};\n\\draw(0.4,2) node[above]{\\small $1$};\n\n\\draw(1,-3) node[above]{\\small $1\\ 1$};\n\\draw [rounded corners,color=gray] (-0.2,-1.5)--(2.2,-1.5)--(2.2,-2.8)--(-0.2,-2.8)--cycle;\n\\draw(3.55,-3) node[above]{\\small $2\\ 2$};\n\\draw [rounded corners,color=gray] (2.4,-1.5)--(4.8,-1.5)--(4.8,-2.8)--(2.4,-2.8)--cycle;\n\n\n\\draw(0.5,2.2)--(0.5,-1.5);\n\\draw(1.7,2.2)--(2.9,-1.5);\n\\draw(2.9,2.2)--(4.1,-1.5);\n\\draw(4,2.2)--(1.5,-1.5);\n\\end{tikzpicture}\n$$ ]{}\n\nIt is far from clear that $\\ker d_n={\\operatorname{im}}d_{n+1}$ but at least the following is easy to see:\n\nThe homomorphisms $d_n$ are homogeneous of degree $0$ for all $n$.\n\nLet ${\\lambda}\\in{\\Lambda}(n)$ be such that ${\\lambda}_i<m$ for some $a\\leq i\\leq b$, so that $\\mu:={\\lambda}+\\e_i\\in {\\Lambda}(n+1)$. The homomorphism $d_n=\\rho_{D_n}$ is a right multiplication with the matrix $D_n$. Its $(\\mu,{\\lambda})$-component is a homomorphism $\nP_\\mu\\to P_{\\lambda}$ obtained by the right multiplication with $\\pm e_\\mu\\psi_{{\\lambda};i}e_{\\lambda}$. Recall that $P_\\mu=q^{s_\\mu}R_\\theta e_\\mu$ and $P_{\\lambda}=q^{s_{\\lambda}}R_\\theta e_{\\lambda}$. So we just need to show that $s_\\mu=s_{\\lambda}+\\deg(e_\\mu\\psi_{{\\lambda};i}e_{\\lambda})$. This is an easy computation using the fact that by definition we have $\n\\deg(e_\\mu\\psi_{{\\lambda};i}e_{\\lambda})=m-2{\\lambda}_i\n$.", "\n\nLet $\\eta\\in Q_+$ be arbitrary and $\\pi = (\\beta_1^{m_1}, \\dots, \\beta_t^{m_t})\\in {\\operatorname{KP}}(\\eta)$. We will define the resolution $P_\\bullet^\\pi$ of $\\Delta(\\pi) = \\Delta(\\beta_1^{m_1})\\circ\\cdots \\circ\\Delta(\\beta_t^{m_t})$ using the general notion of the induced product of chain complexes.", "\n\nLet $(C_\\bullet, d_C)$ and $(D_\\bullet, d_D)$ be chain complexes of left $R_{\\eta'}$-modules and $R_{\\eta''}$-modules, respectively. ", "We define a complex of $R_{\\eta'+\\eta''}$-modules $$\\label{ECircProdRes}\n(C_\\bullet\\circ D_\\bullet)_n := \\bigoplus_{p+q = n}C_p\\circ D_q$$ with differential given by $$d_{C\\circ D}: C_\\bullet\\circ D_\\bullet \\to C_\\bullet\\circ D_\\bullet, \\ x\\circ y \\mapsto x\\circ d_D(y) + (-1)^q d_C(x)\\circ y.$$\n\n\\[circresolution\\] If $C_\\bullet$ and $D_\\bullet$ are projective resolutions of modules $M$ and $N$, respectively, then $C_\\bullet\\circ D_\\bullet$ is a projective resolution of $M\\circ N$.\n\nThis follows from Lemma \\[circexact\\] and [@Weibel Lemma 2.7.3].", "\n\nWe now define $$\\label{fullresolution}\n P_\\bullet^\\pi := P_\\bullet^{\\beta_1^{m_1}}\\circ\\cdots\\circ P_\\bullet^{\\beta_t^{m_t}}$$ which, by Lemma \\[circresolution\\], will turn out to be a projective resolution of $\\Delta(\\pi)$ in view of Theorem \\[main theorem\\].", "\n\nThe resolution $Q_\\bullet$ {#SQdef}\n--------------------------\n\nIn order to check that $P_\\bullet$ is a resolution of ${\\Delta}({\\alpha}^m)$, we show that it is a direct summand of a known resolution $Q_\\bullet$ of $q^{m(m-1)/2}{\\Delta}({\\alpha})^{\\circ m}$. To describe the latter resolution, let us first consider the special case $m=1$.\n\n\\[L070417\\] We have that $P^{\\alpha}_{\\bullet}$ is a resolution of ${\\Delta}({\\alpha})$.\n\nThis is a special case of [@BKM Theorem 4.12], corresponding to the standard choice of $({\\alpha}_{i+1}+\\dots+{\\alpha}_j,{\\alpha}_i)$ as the minimal pair for an arbitrary positive root ${\\alpha}_i+\\dots+{\\alpha}_j$ in the definition of $\\bi_{{\\alpha},{\\sigma}}$, see [@BKM §4.5].", "\n\nLet $Q_\\bullet$ be the resolution $q^{m(m-1)/2} (P^{\\alpha}_{\\bullet})^{\\circ m}$, cf. (", "\\[ECircProdRes\\]). ", "To describe $Q_\\bullet$ more explicitly, let $n\\in{\\mathbb{Z}}_{\\geq 0}$ and $\\bde=({\\delta}^{(1)},\\dots,{\\delta}^{(m)})\\in\\bLa(n)$. Recalling the definitions of §\\[SSComb\\], we set $$\\begin{aligned}\ne_\\bde:=1_{\\bj^\\bde}\\in R_\\theta,\\quad\nQ_\\bde:=q^{n+m(m-1)/2}R_\\theta e_\\bde.\\end{aligned}$$ For example taking each ${\\delta}^{(r)}$ to be $0\\in{\\Lambda}(0)$, we get $$\\label{EBZero}\n\\bde={\\bzero}:=(0,\\dots,0)\\in\\bLa(0)$$ and $e_{\\bzero}=1_{(a\\,(a+1)\\cdots (b+1))^m}.$ Further for any $n\\in{\\mathbb{Z}}_{\\geq 0}$, we set $$Q_n:=\\bigoplus_{\\bde\\in\\bLa(n)}Q_\\bde.$$\n\nThe projective resolution $Q_\\bullet$ is $$\\dots \\longrightarrow Q_{n+1}\\stackrel{c_n}{\\longrightarrow} Q_n\\longrightarrow\\dots \\stackrel{c_0}{\\longrightarrow} Q_0\\stackrel{\\sf q}{\\longrightarrow} q^{m(m-1)/2}{\\Delta}({\\alpha})^{\\circ m}\\longrightarrow 0,$$ with the augmentation map $$\\label{EAugMap}\n{\\sf q}:Q_0\\to q^{m(m-1)/2}\\Delta(\\alpha)^{\\circ m},\\ xe_{\\bzero}\\mapsto xv_\\alpha^{\\circ m},$$ see §\\[SSStdMod\\], and $c_n$ being right multiplication with the $\\bLa(n+1)\\times\\bLa(n)$ matrix $C=(c_n^{\\bga,\\bde})$ defined as follows. ", "If $\\bde+\\bolde^{r}_i\\in\\bLa$ for some $r\\in [1, m]$ and $i\\in[a, b]$, i.e. ${\\delta}^{(r)}_i=0$, we set $$\\label{EQ123}\n\\psi_{\\bde;r,i}:=\\iota_{{\\alpha},\\dots,{\\alpha}}(1^{\\otimes (r-1)}\\otimes \\psi_{{\\delta}^{(r)};i}\\otimes 1^{\\otimes (m-r)})=1^{\\circ (r-1)}\\circ \\psi_{{\\delta}^{(r)};i}\\circ 1^{\\circ (m-r)}.", "\n$$ Recalling the signs defined in §\\[SSComb\\], for $\\bde\\in\\bLa(n)$ and $\\bga\\in\\bLa(n+1)$, we now define $$c_n^{\\bga,\\bde}=\n\\left\\{\n\\begin{array}{ll}\n\\sgn_{\\bde;r,i}e_\\bga\\psi_{\\bde;r,i}e_\\bde &\\hbox{if $\\bga=\\bde+\\bolde^{r}_i$ for some $1\\leq r\\leq m$ and $a\\leq i\\leq b$,}\\\\\n0 &\\hbox{otherwise.}", "\n\\end{array}\n\\right.$$\n\nThe fact that $Q_\\bullet$ is indeed isomorphic to the resolution $q^{m(m-1)/2} (P^{\\alpha}_{\\bullet})^{\\circ m}$ is easily checked using the isomorphism $R_\\theta e_\\bde\\cong R_\\theta 1_{\\bj^{{\\delta}^{(1)}}}\\circ\\dots\\circ R_\\theta1_{\\bj^{{\\delta}^{(m)}}}$, which comes from Lemma \\[LIndIdemp\\].", "\n\n\\[ExQ\\] [Let $a=b=1$ and $m=2$. Then the resolution $Q_\\bullet$ is $$0\\to q^3R_\\theta1_{2121}\\stackrel{c_1}{\\longrightarrow}\nq^2R_\\theta1_{2112}\\oplus q^2R_\\theta1_{1221}\\stackrel{c_0}{\\longrightarrow}\nq R_\\theta1_{1212}\\stackrel{\\sf q}{\\longrightarrow} q{\\Delta}({\\alpha}_1+{\\alpha}_2)^{\\circ 2}\\longrightarrow 0,$$ where $c_1$ is a right multiplication with the matrix $\n(-1_{2121} \\psi_3\\ \\ 1_{2121} \\psi_1)\n$, and $c_0$ is a right multiplication with the matrix $\n\\left(\n\\begin{matrix}\n 1_{2112} \\psi_1 \\\\\n 1_{1221} \\psi_3\n\\end{matrix}\n\\right).", "\n$ ]{}\n\nComparison maps {#SSComp}\n---------------\n\nWe now construct what will end up being a pair of chain maps $f:P_\\bullet\\to Q_\\bullet$ and $g:Q_\\bullet\\to P_\\bullet$ with $g\\circ f={\\operatorname{id}}$. As usual, $f_n$ and $g_n$ will be given as right multiplications with certain matrices $F_n$ and $G_n$, respectively.", "\n\nLet ${\\lambda}\\in{\\Lambda}$. Recall the definitions of §\\[SSComb\\]. ", "We denote by $w^{\\lambda}_0$ the longest element of the parabolic subgroup $\\Si_{{\\omega}_{\\lambda}}\\leq \\Si_d$. We also denote $$y^{\\lambda}:=1_{a^{m-{\\lambda}_a}\\cdots b^{m-{\\lambda}_b}}\\circ y_{0,m}\\circ 1_{b^{{\\lambda}_b}\\cdots a^{{\\lambda}_a}}.$$\n\nLet $\\bde=({\\delta}^{(1)},\\dots,{\\delta}^{(m)})\\in\\bLa$. We define $u(\\bde)\\in\\Si_d$ as follows: for all $i=a,\\dots,b$, the permutation $u(\\bde)$ maps:\n\n1. ", " the elements of $U^\\pm_i({\\lambda}^\\bde)$ increasingly to the elements of $U^\\pm_i(\\bde)$;\n\n2. ", " the elements of $U_{b+1}({\\lambda}^\\bde)$ increasingly to the elements of $U_{b+1}(\\bde)$.\n\nSet $w(\\bde):=u(\\bde)^{-1}$. Then $w(\\bde)$ can also be characterized as the element of $\\Si_d$ which for all $i=a,\\dots,b$, maps the elements of $U^{(\\pm)}_i(\\bde)$ increasingly to the elements of $U^{(\\pm)}_i({\\lambda}^\\bde)$ and the elements of $U_{b+1}(\\bde)$ increasingly to the elements of $U_{b+1}({\\lambda}^\\bde)$.\n\nRecall the signs ${\\sigma}_\\bde$ and $\\tau_{\\bde}$ defined in §\\[SSComb\\]. ", "We now define $F_n$ as the ${\\Lambda}(n)\\times \\bLa(n)$-matrix with the entries $f_n^{{\\lambda},\\bde}$ defined for any ${\\lambda}\\in{\\Lambda}(n),\\bde\\in\\bLa(n)$ as follows: $$f_n^{{\\lambda},\\bde}:=\n\\left\\{\n\\begin{array}{ll}\n{\\sigma}_{\\bde}e_{\\lambda}\\psi_{w_0^{\\lambda}}\\psi_{w(\\bde)}e_\\bde &\\hbox{if ${\\lambda}={\\lambda}^\\bde$,}\\\\\n0 &\\hbox{otherwise.}", "\n\\end{array}\n\\right.$$ We define $G_n$ as the $\\bLa(n)\\times {\\Lambda}(n)$-matrix with the entries $g_n^{\\bde,{\\lambda}}$ defined for any $\\bde\\in\\bLa(n), {\\lambda}\\in{\\Lambda}(n)$ as follows: $$g_n^{\\bde,{\\lambda}}:=\n\\left\\{\n\\begin{array}{ll}\n\\tau_\\bde e_\\bde\\psi_{u(\\bde)}y^{\\lambda}e_{\\lambda}&\\hbox{if ${\\lambda}={\\lambda}^\\bde$,}\\\\\n0 &\\hbox{otherwise.}", "\n\\end{array}\n\\right.$$\n\nLet $m=d=2$ as in Examples \\[ExP\\] and \\[ExQ\\]. ", "Then: $$\\begin{aligned}\nF_0\n&=\n\\left( \\begin{tikzpicture}[baseline=6mm,black,line width=1pt, scale=0.32,\n draw/.append style={rounded corners},\n every node/.append style={font=\\fontsize{5}{5}\\selectfont}] \\tikzset{baseline=0mm}\n\\draw(1,2) node[above]{\\small $1\\ 1$};\n\\draw [rounded corners,color=gray] (-0.2,3.5)--(2.2,3.5)--(2.2,2.2)--(-0.2,2.2)--cycle;\n\\draw(1,0) node[above]{\\small $w_0$};\n\\draw [rounded corners,color=gray] (-0.2,1.5)--(2.2,1.5)--(2.2,0.2)--(-0.2,0.2)--cycle;\n\\draw(0.5,2.2)--(0.5,1.5);\n\\draw(1.5,2.2)--(1.5,1.5);\n\\draw(3.55,2) node[above]{\\small $2\\ 2$};\n\\draw [rounded corners,color=gray] (2.4,3.5)--(4.8,3.5)--(4.8,2.2)--(2.4,2.2)--cycle;\n\\draw(3.9,0) node[above]{\\small $w_0$};\n\\draw [rounded corners,color=gray] (2.4,1.5)--(4.8,1.5)--(4.8,0.2)--(2.4,0.2)--cycle;\n\\draw(3.05,2.2)--(3.05,1.5);\n\\draw(4.05,2.2)--(4.05,1.5);\n\\draw(0.4,-3) node[above]{\\small $1$};\n\\draw(1.8,-3) node[above]{\\small $2$};\n\\draw(2.9,-3) node[above]{\\small $1$};\n\\draw(4.2,-3) node[above]{\\small $2$};\n\\draw(0.5,0.2)--(0.5,-1.5);\n\\draw(1.5,0.2)--(2.8,-1.5);\n\\draw(3,0.2)--(1.8,-1.5);\n\\draw(4,0.2)--(4,-1.5);\n\\end{tikzpicture}\n\\right)\n=\n\\left( \\begin{tikzpicture}[baseline=6mm,black,line width=1pt, scale=0.32,\n draw/.append style={rounded corners},\n every node/.append style={font=\\fontsize{5}{5}\\selectfont}] \\tikzset{baseline=0mm}\n\\draw(1,2) node[above]{\\small $1\\ 1$};\n\\draw [rounded corners,color=gray] (-0.2,3.5)--(2.2,3.5)--(2.2,2.2)--(-0.2,2.2)--cycle;\n\\draw(3.55,2) node[above]{\\small $2\\ 2$};\n\\draw [rounded corners,color=gray] (2.4,3.5)--(4.8,3.5)--(4.8,2.2)--(2.4,2.2)--cycle;\n\\draw(0.4,-3) node[above]{\\small $1$};\n\\draw(1.8,-3) node[above]{\\small $2$};\n\\draw(2.9,-3) node[above]{\\small $1$};\n\\draw(4.2,-3) node[above]{\\small $2$};\n\\draw(0.5,2.2)--(2.9,-1.5);\n\\draw(1.5,2.2)--(0.5,-1.5);\n\\draw(3,2.2)--(4.2,-1.5);\n\\draw(4,2.2)--(1.7,-1.5);\n\\end{tikzpicture}\n\\right),\n\\\\\nF_1&\n=\\left( \\begin{tikzpicture}[baseline=6mm,black,line width=1pt, scale=0.32,\n draw/.append style={rounded corners},\n every node/.append style={font=\\fontsize{5}{5}\\selectfont}] \\tikzset{baseline=0mm}\n\\draw(0.4,2) node[above]{\\small $1$};\n\\draw [rounded corners,color=gray] (1.2,3.5)--(3.6,3.5)--(3.6,2.2)--(1.2,2.2)--cycle;\n\\draw(1.8,2) node[above]{\\small $2$};\n\\draw(2.9,2) node[above]{\\small $2$};\n\\draw(2.4,0) node[above]{\\small $w_0$};\n\\draw [rounded corners,color=gray] (1.2,1.5)--(3.6,1.5)--(3.6,0.2)--(1.2,0.2)--cycle;\n\\draw(4.2,2) node[above]{\\small $1$};\n\\draw(0.4,-3) node[above]{\\small $1$};\n\\draw(1.8,-3) node[above]{\\small $2$};\n\\draw(2.9,-3) node[above]{\\small $2$};\n\\draw(4.2,-3) node[above]{\\small $1$};\n\\draw(0.5,2.2)--(0.5,-1.5);\n\\draw(1.75,2.2)--(1.75,1.5);\n\\draw(1.75,0.2)--(1.75,-1.5);\n\\draw(2.9,2.2)--(2.9,1.5);\n\\draw(2.9,0.2)--(2.9,-1.5);\n\\draw(4.2,2.2)--(4.2,-1.5);\n\\end{tikzpicture}\n\\quad\n \\begin{tikzpicture}[baseline=6mm,black,line width=1pt, scale=0.32,\n draw/.append style={rounded corners},\n every node/.append style={font=\\fontsize{5}{5}\\selectfont}] \\tikzset{baseline=0mm}\n\\draw(0.4,2) node[above]{\\small $1$};\n\\draw [rounded corners,color=gray] (1.2,3.5)--(3.6,3.5)--(3.6,2.2)--(1.2,2.2)--cycle;\n\\draw(1.8,2) node[above]{\\small $2$};\n\\draw(2.9,2) node[above]{\\small $2$};\n\\draw(2.4,0) node[above]{\\small $w_0$};\n\\draw [rounded corners,color=gray] (1.2,1.5)--(3.6,1.5)--(3.6,0.2)--(1.2,0.2)--cycle;\n\\draw(4.2,2) node[above]{\\small $1$};\n\\draw(0.4,-3) node[above]{\\small $2$};\n\\draw(1.8,-3) node[above]{\\small $1$};\n\\draw(2.9,-3) node[above]{\\small $1$};\n\\draw(4.2,-3) node[above]{\\small $2$};\n\\draw(0.5,2.2)--(1,0)--(2.9,-1.5);\n\\draw(1.75,2.2)--(1.75,1.5);\n\\draw(1.75,0.2)--(0.5,-1.5);\n\\draw(3,2.2)--(3,1.5);\n\\draw(3,0.2)--(4.2,-1.5);\n\\draw(4.2,2.2)--(3.8,0)--(1.7,-1.5);\n\\end{tikzpicture}\n\n\\right)\n=\n\\left( \\begin{tikzpicture}[baseline=6mm,black,line width=1pt, scale=0.32,\n draw/.append style={rounded corners},\n every node/.append style={font=\\fontsize{5}{5}\\selectfont}] \\tikzset{baseline=0mm}\n\\draw(0.4,2) node[above]{\\small $1$};\n\\draw [rounded corners,color=gray] (1.2,3.5)--(3.6,3.5)--(3.6,2.2)--(1.2,2.2)--cycle;\n\\draw(1.8,2) node[above]{\\small $2$};\n\\draw(2.9,2) node[above]{\\small $2$};\n\\draw(4.2,2) node[above]{\\small $1$};\n\\draw(0.4,-3) node[above]{\\small $1$};\n\\draw(1.8,-3) node[above]{\\small $2$};\n\\draw(2.9,-3) node[above]{\\small $2$};\n\\draw(4.2,-3) node[above]{\\small $1$};\n\\draw(0.5,2.2)--(0.5,-1.5);\n\\draw(1.75,2.2)--(2.9,-1.5);\n\\draw(2.95,2.2)--(1.7,-1.5);\n\\draw(4.2,2.2)--(4.2,-1.5);\n\\end{tikzpicture}\n\\quad\n \\begin{tikzpicture}[baseline=6mm,black,line width=1pt, scale=0.32,\n draw/.append style={rounded corners},\n every node/.append style={font=\\fontsize{5}{5}\\selectfont}] \\tikzset{baseline=0mm}\n\\draw(0.4,2) node[above]{\\small $1$};\n\\draw [rounded corners,color=gray] (1.2,3.5)--(3.6,3.5)--(3.6,2.2)--(1.2,2.2)--cycle;\n\\draw(1.8,2) node[above]{\\small $2$};\n\\draw(2.9,2) node[above]{\\small $2$};\n\\draw(4.2,2) node[above]{\\small $1$};\n\\draw(0.4,-3) node[above]{\\small $2$};\n\\draw(1.8,-3) node[above]{\\small $1$};\n\\draw(2.9,-3) node[above]{\\small $1$};\n\\draw(4.2,-3) node[above]{\\small $2$};\n\\draw(0.5,2.2)--(2.9,-1.5);\n\\draw(1.75,2.2)--(4.2,-1.5);\n\\draw(3,2.2)--(0.5,-1.5);\n\\draw(4.2,2.2)--(1.7,-1.5);\n\\end{tikzpicture}\n\n\\right),\n\\\\\nF_2&=\n\\left( \\begin{tikzpicture}[baseline=6mm,black,line width=1pt, scale=0.32,\n draw/.append style={rounded corners},\n every node/.append style={font=\\fontsize{5}{5}\\selectfont}] \\tikzset{baseline=0mm}\n\\draw(1,2) node[above]{\\small $2\\ 2$};\n\\draw [rounded corners,color=gray] (-0.2,3.5)--(2.2,3.5)--(2.2,2.2)--(-0.2,2.2)--cycle;\n\\draw(3.55,2) node[above]{\\small $1\\ 1$};\n\\draw [rounded corners,color=gray] (2.4,3.5)--(4.8,3.5)--(4.8,2.2)--(2.4,2.2)--cycle;\n\\draw(0.4,-3) node[above]{\\small $2$};\n\\draw(1.8,-3) node[above]{\\small $1$};\n\\draw(2.9,-3) node[above]{\\small $2$};\n\\draw(4.1,-3) node[above]{\\small $1$};\n\\draw(1,0) node[above]{\\small $w_0$};\n\\draw [rounded corners,color=gray] (-0.2,1.5)--(2.2,1.5)--(2.2,0.2)--(-0.2,0.2)--cycle;\n\\draw(3.9,0) node[above]{\\small $w_0$};\n\\draw [rounded corners,color=gray] (2.4,1.5)--(4.8,1.5)--(4.8,0.2)--(2.4,0.2)--cycle;\n\\draw(3.05,2.2)--(3.05,1.5);\n\\draw(4.05,2.2)--(4.05,1.5);\n\\draw(0.5,2.2)--(0.5,1.5);\n\\draw(1.5,2.2)--(1.5,1.5);\n\\draw(0.5,0.2)--(0.5,-1.5);\n\\draw(1.5,0.2)--(2.9,-1.5);\n\\draw(3,0.2)--(1.7,-1.5);\n\\draw(4,0.2)--(4,-1.5);\n\\end{tikzpicture}\n\\right)\n=\n\\left( \\begin{tikzpicture}[baseline=6mm,black,line width=1pt, scale=0.32,\n draw/.append style={rounded corners},\n every node/.append style={font=\\fontsize{5}{5}\\selectfont}] \\tikzset{baseline=0mm}\n\\draw(1,2) node[above]{\\small $2\\ 2$};\n\\draw [rounded corners,color=gray] (-0.2,3.5)--(2.2,3.5)--(2.2,2.2)--(-0.2,2.2)--cycle;\n\\draw(3.55,2) node[above]{\\small $1\\ 1$};\n\\draw [rounded corners,color=gray] (2.4,3.5)--(4.8,3.5)--(4.8,2.2)--(2.4,2.2)--cycle;\n\\draw(0.4,-3) node[above]{\\small $2$};\n\\draw(1.8,-3) node[above]{\\small $1$};\n\\draw(2.9,-3) node[above]{\\small $2$};\n\\draw(4.2,-3) node[above]{\\small $1$};\n\\draw(0.5,2.2)--(2.9,-1.5);\n\\draw(1.5,2.2)--(0.5,-1.5);\n\\draw(3,2.2)--(4.2,-1.5);\n\\draw(4,2.2)--(1.7,-1.5);\n\\end{tikzpicture}\n\\right),\n\\\\\nG_0&\n=\\left(\n \\begin{tikzpicture}[baseline=6mm,black,line width=1pt, scale=0.32,\n draw/.append style={rounded corners},\n every node/.append style={font=\\fontsize{5}{5}\\selectfont}] \\tikzset{baseline=0mm}\n\\draw(0.4,2) node[above]{\\small $1$};\n\\draw(1.6,2) node[above]{\\small $2$};\n\\draw(2.9,2) node[above]{\\small $1$};\n\\draw(4.2,2) node[above]{\\small $2$};\n\\draw(1,-3) node[above]{\\small $1\\ 1$};\n\\draw [rounded corners,color=gray] (-0.2,-2.8)--(2.2,-2.8)--(2.2,-1.5)--(-0.2,-1.5)--cycle;\n\\draw(3.55,-3) node[above]{\\small $2\\ 2$};\n\\draw [rounded corners,color=gray] (2.4,-2.8)--(4.8,-2.8)--(4.8,-1.5)--(2.4,-1.5)--cycle;\n\\draw(3.7,-1.1) node[above]{\\small $y_0$};\n\\draw [rounded corners,color=gray] (2.4,0.4)--(4.8,0.4)--(4.8,-1)--(2.4,-1)--cycle;\n\\draw(0.5,2.2)--(0.5,-1.5);\n\\draw(1.5,2.2)--(2.9,0.4);\n\\draw(2.9,-1)--(2.9,-1.5);\n\\draw(3,2.2)--(2.3,1.3)--(1.5,-1.5);\n\\draw(4.2,2.2)--(4.2,0.4);\n\\draw(4.2,-1)--(4.2,-1.5);\n\\end{tikzpicture}\n\\right)\n=\\left(\n \\begin{tikzpicture}[baseline=6mm,black,line width=1pt, scale=0.32,\n draw/.append style={rounded corners},\n every node/.append style={font=\\fontsize{5}{5}\\selectfont}] \\tikzset{baseline=0mm}\n\\draw(0.4,2) node[above]{\\small $1$};\n\\draw(1.6,2) node[above]{\\small $2$};\n\\draw(2.9,2) node[above]{\\small $1$};\n\\draw(4,2) node[above]{\\small $2$};\n\\draw(1,-3) node[above]{\\small $1\\ 1$};\n\\draw [rounded corners,color=gray] (-0.2,-2.8)--(2.2,-2.8)--(2.2,-1.5)--(-0.2,-1.5)--cycle;\n\\draw(3.55,-3) node[above]{\\small $2\\ 2$};\n\\draw [rounded corners,color=gray] (2.4,-2.8)--(4.8,-2.8)--(4.8,-1.5)--(2.4,-1.5)--cycle;\n\\draw(0.5,2.2)--(0.5,-1.5);\n\\draw(1.5,2.2)--(3,-1.5);\n\\draw(2.95,2.2)--(1.5,-1.5);\n\\draw(4,2.2)--(4,-1.5);\n\\blackdot(4,-0.5);\n\\end{tikzpicture}\n\\right),\n\\\\\nG_1&\n=\\left(\\begin{array}c\n \\begin{tikzpicture}[baseline=6mm,black,line width=1pt, scale=0.32,\n draw/.append style={rounded corners},\n every node/.append style={font=\\fontsize{5}{5}\\selectfont}] \\tikzset{baseline=0mm}\n\\draw(0.4,2) node[above]{\\small $1$};\n\\draw(1.7,2) node[above]{\\small $2$};\n\\draw(2.9,2) node[above]{\\small $2$};\n\\draw(4.2,2) node[above]{\\small $1$};\n\\draw(0.4,-3) node[above]{\\small $1$};\n\\draw [rounded corners,color=gray] (1.2,-2.8)--(3.6,-2.8)--(3.6,-1.5)--(1.2,-1.5)--cycle;\n\\draw(1.8,-3) node[above]{\\small $2$};\n\\draw(2.9,-3) node[above]{\\small $2$};\n\\draw(4.2,-3) node[above]{\\small $1$};\n\\draw(2.4,-1.1) node[above]{\\small $y_0$};\n\\draw [rounded corners,color=gray] (1.2,0.4)--(3.6,0.4)--(3.6,-1)--(1.2,-1)--cycle;\n\\draw(0.5,2.2)--(0.5,-1.5);\n\\draw(1.7,2.2)--(1.7,0.4);\n\\draw(2.95,2.2)--(2.95,0.4);\n\\draw(1.7,-1)--(1.7,-1.5);\n\\draw(2.95,-1)--(2.95,-1.5);\n\\draw(4.2,2.2)--(4.2,-1.5);\n\\end{tikzpicture}\n\\\\\n \\begin{tikzpicture}[baseline=6mm,black,line width=1pt, scale=0.32,\n draw/.append style={rounded corners},\n every node/.append style={font=\\fontsize{5}{5}\\selectfont}] \\tikzset{baseline=0mm}\n\\draw(0.4,2) node[above]{\\small $2$};\n\\draw(1.6,2) node[above]{\\small $1$};\n\\draw(2.9,2) node[above]{\\small $1$};\n\\draw(4.2,2) node[above]{\\small $2$};\n\\draw(0.4,-3) node[above]{\\small $1$};\n\\draw [rounded corners,color=gray] (1.2,-2.8)--(3.6,-2.8)--(3.6,-1.5)--(1.2,-1.5)--cycle;\n\\draw(1.8,-3) node[above]{\\small $2$};\n\\draw(2.9,-3) node[above]{\\small $2$};\n\\draw(4.2,-3) node[above]{\\small $1$};\n\\draw(2.4,-1.1) node[above]{\\small $y_0$};\n\\draw [rounded corners,color=gray] (1.2,0.4)--(3.6,0.4)--(3.6,-1)--(1.2,-1)--cycle;\n\\draw(1.7,-1)--(1.7,-1.5);\n\\draw(2.95,-1)--(2.95,-1.5);\n\\draw(0.5,2.2)--(1.7,0.4);\n\\draw(1.5,2.2)--(3.8,1.2)--(4.2,-1.5);\n\\draw(2.95,2.2)--(1.1,1.2)--(0.5,-1.5);\n\\draw(4.2,2.2)--(2.95,0.4);\n\\end{tikzpicture}\n\n\\end{array}\\right)\n=\\left(\\begin{array}c\n \\begin{tikzpicture}[baseline=6mm,black,line width=1pt, scale=0.32,\n draw/.append style={rounded corners},\n every node/.append style={font=\\fontsize{5}{5}\\selectfont}] \\tikzset{baseline=0mm}\n\\draw(0.4,2) node[above]{\\small $1$};\n\\draw(1.7,2) node[above]{\\small $2$};\n\\draw(2.9,2) node[above]{\\small $2$};\n\\draw(4.2,2) node[above]{\\small $1$};\n\\draw(0.4,-3) node[above]{\\small $1$};\n\\draw [rounded corners,color=gray] (1.2,-2.8)--(3.6,-2.8)--(3.6,-1.5)--(1.2,-1.5)--cycle;\n\\draw(1.8,-3) node[above]{\\small $2$};\n\\draw(2.9,-3) node[above]{\\small $2$};\n\\draw(4.2,-3) node[above]{\\small $1$};\n\\draw(0.5,2.2)--(0.5,-1.5);\n\\draw(1.7,2.2)--(1.7,-1.5);\n\\draw(2.95,2.2)--(2.95,-1.5);\n\\draw(4.2,2.2)--(4.2,-1.5);\n\\blackdot(2.95,-0.5);\n\\end{tikzpicture}\n\\\\\n \\begin{tikzpicture}[baseline=6mm,black,line width=1pt, scale=0.32,\n draw/.append style={rounded corners},\n every node/.append style={font=\\fontsize{5}{5}\\selectfont}] \\tikzset{baseline=0mm}\n\\draw(0.4,2) node[above]{\\small $2$};\n\\draw(1.6,2) node[above]{\\small $1$};\n\\draw(2.9,2) node[above]{\\small $1$};\n\\draw(4.2,2) node[above]{\\small $2$};\n\\draw(0.4,-3) node[above]{\\small $1$};\n\\draw [rounded corners,color=gray] (1.2,-2.8)--(3.6,-2.8)--(3.6,-1.5)--(1.2,-1.5)--cycle;\n\\draw(1.8,-3) node[above]{\\small $2$};\n\\draw(2.9,-3) node[above]{\\small $2$};\n\\draw(4.2,-3) node[above]{\\small $1$};\n\\draw(0.5,2.2)--(1.7,-1.5);\n\\draw(1.5,2.2)--(4.2,-1.5);\n\\draw(3,2.2)--(0.5,-1.5);\n\\draw(4.2,2.2)--(2.95,-1.5);\n\\blackdot(3.15,-1);\n\\end{tikzpicture}\n\n\\end{array}\\right),\n\\\\\nG_2&\n=\\left(- \\begin{tikzpicture}[baseline=6mm,black,line width=1pt, scale=0.32,\n draw/.append style={rounded corners},\n every node/.append style={font=\\fontsize{5}{5}\\selectfont}] \\tikzset{baseline=0mm}\n\\draw(0.4,2) node[above]{\\small $2$};\n\\draw(1.6,2) node[above]{\\small $1$};\n\\draw(2.9,2) node[above]{\\small $2$};\n\\draw(4,2) node[above]{\\small $1$};\n\\draw(1,-3) node[above]{\\small $2\\ 2$};\n\\draw [rounded corners,color=gray] (-0.2,-2.8)--(2.2,-2.8)--(2.2,-1.5)--(-0.2,-1.5)--cycle;\n\\draw(3.55,-3) node[above]{\\small $1\\ 1$};\n\\draw [rounded corners,color=gray] (2.4,-2.8)--(4.8,-2.8)--(4.8,-1.5)--(2.4,-1.5)--cycle;\n\\draw(1,-1.1) node[above]{\\small $y_0$};\n\\draw [rounded corners,color=gray] (-0.2,0.4)--(2.2,0.4)--(2.2,-1)--(-0.2,-1)--cycle;\n\\draw(1.55,-1)--(1.55,-1.5);\n\\draw(0.5,-1)--(0.5,-1.5);\n\\draw(0.5,2.2)--(0.5,0.4);\n\\draw(1.65,2.2)--(3.1,-1.5);\n\\draw(3,2.2)--(1.5,0.4);\n\\draw(4,2.2)--(4,-1.5);\n\\end{tikzpicture}\n\\right)\n=\\left(- \\begin{tikzpicture}[baseline=6mm,black,line width=1pt, scale=0.32,\n draw/.append style={rounded corners},\n every node/.append style={font=\\fontsize{5}{5}\\selectfont}] \\tikzset{baseline=0mm}\n\\draw(0.4,2) node[above]{\\small $2$};\n\\draw(1.6,2) node[above]{\\small $1$};\n\\draw(2.9,2) node[above]{\\small $2$};\n\\draw(4,2) node[above]{\\small $1$};\n\\draw(1,-3) node[above]{\\small $2\\ 2$};\n\\draw [rounded corners,color=gray] (-0.2,-2.8)--(2.2,-2.8)--(2.2,-1.5)--(-0.2,-1.5)--cycle;\n\\draw(3.55,-3) node[above]{\\small $1\\ 1$};\n\\draw [rounded corners,color=gray] (2.4,-2.8)--(4.8,-2.8)--(4.8,-1.5)--(2.4,-1.5)--cycle;\n\\draw(0.5,2.2)--(0.5,-1.5);\n\\draw(1.6,2.2)--(3.05,-1.5);\n\\draw(3,2.2)--(1.5,-1.5);\n\\draw(4,2.2)--(4,-1.5);\n\\blackdot(1.73,-1);\n\\end{tikzpicture}\n\\right).\\end{aligned}$$\n\n\\[LDeg\\] Let $\\bde\\in\\bLa(n)$ and ${\\lambda}={\\lambda}^\\bde$. Then:\n\n1. ", " $\\deg(\\psi_{w(\\bde)}e_\\bde)=\\frac{m(m-1)(l-1)}{2}-mn+\\sum_{i=a}^b{\\lambda}_i^2$,\n\n2. ", " $\\deg(f_{n}^{{\\lambda},\\bde})=-\\frac{m(m-1)(l+1)}{2}+mn-\\sum_{i=a}^b{\\lambda}_i^2$,\n\n3. ", " $\\deg(g_{n}^{\\bde,{\\lambda}})=\\frac{m(m-1)(l+1)}{2}-mn+\\sum_{i=a}^b{\\lambda}_i^2$.\n\n\\(i) We prove this by induction on $m$. Denote the right hand side by $R(m)$ and the left hand side by $L(m)$. If $m=1$ then $w(\\bde)=1$, so $L(1)=0$. Moreover, $$R(1)=-n+ \\sum_{i=a}^b{\\lambda}_i^2=-n+\\sum_{i=a}^b({\\delta}^{(1)}_i)^2=-n+\\sum_{i=a}^b{\\delta}^{(1)}_i=0.$$\n\nLet $m>1$. It suffices to prove that $R(m)-R(m-1)=L(m)-L(m-1)$. Let ${\\delta}^{(m)}=(\\eps_a,\\dots,\\eps_b)$. Then, since all $\\eps_i$ are $0$ or $1$, we have $$\\begin{aligned}\nR(m)-R(m-1)&=\\frac{m(m-1)(l-1)}{2}-mn+\\sum_{i=a}^b{\\lambda}_i^2\n -\n\\frac{(m-1)(m-2)(l-1)}{2}\n\\\\\n&\\ \\ \\\n+(m-1)(n-\\sum_{i=a}^b\\eps_i)-\\sum_{i=a}^b({\\lambda}_i-\\eps_i)^2\n\\\\&=(m-1)(l-1) -n -m\\sum_{i=a}^b\\eps_i+2\\sum_{i=a}^b{\\lambda}_i\\eps_i.\\end{aligned}$$\n\nOn the other hand, consider the Khovanov-Lauda diagram of $\\psi_{w(\\bde)}e_\\bde$. The bottom positions of the diagram correspond to to the letters if the word $\\bj^\\bde$, and so the rightmost $l$ bottom positions of this diagram correspond to the letters of $\\bj^{{\\delta}^{(m)}}$. In other words, counting from the right, the sequence of colors of these positions is $a^{\\eps_a},\\dots,b^{\\eps_b},b+1,b^{1-\\eps_b},\\dots,a^{1-\\eps_a}$. Note that the strings which originate in these positions do not intersect each other, so $L(m)-L(m-1)$ equals the sum of the degrees of the intersections of these strings with the other strings of the diagram, i.e. $$\\begin{aligned}\nL(m)-L(m-1)&=\\sum_{i=a+1}^b\\eps_i({\\lambda}_{i-1}-\\eps_{i-1})+{\\lambda}_b-\\eps_b\n\\\\\n&\\ \\ \\ +\\sum_{i=a+1}^b(1-\\eps_i)(m-1-2({\\lambda}_i-\\eps_i)+{\\lambda}_{i-1}-\\eps_{i-1})\n\\\\\n&\\ \\ \\ + (1-\\eps_a)(m-1-2({\\lambda}_a-\\eps_a)),\\end{aligned}$$ which is easily seen to equal the expression for $R(m)-R(m-1)$ obtained above.", "\n\n\\(ii) This follows from (i) since $\\deg(f_{n}^{{\\lambda},\\bde})=\\deg(\\psi_{w(\\bde)}e_\\bd)+\\deg(e_{\\lambda}\\psi_{w_0^{\\lambda}})$ and $$\\begin{aligned}\n\\deg(e_{\\lambda}\\psi_{w_0^{\\lambda}})=-m(m-1)-\\sum_{i=a}^b({\\lambda}_i({\\lambda}_i-1)+(m-{\\lambda}_i)(m-{\\lambda}_i-1)).\\end{aligned}$$\n\n\\(iii) This follows from (i) since $$\\deg(g_{n}^{\\bde,{\\lambda}})=\\deg(e_\\bde\\psi_{u(\\bde)})+\\deg(y^{\\lambda})=\\deg(\\psi_{w(\\bde)}e_\\bde)+m(m-1).$$\n\nThe homomorphisms $f_n$ and $g_n$ are homogeneous of degree $0$ for all $n$.\n\nLet $\\bde\\in\\bLa(n)$ and ${\\lambda}={\\lambda}^\\bde$. The homomorphism $f_n$ is a right multiplication with the matrix $F_n$. Its $({\\lambda},\\bde)$-component is a homomorphism $\nP_{\\lambda}\\to Q_\\bde\n$ obtained by the right multiplication with $f_n^{{\\lambda},\\bde}$. Recall that $P_{\\lambda}=q^{s_{\\lambda}}R_\\theta e_{\\lambda}$ and $Q_\\bde=q^{n+m(m-1)/2}R_\\theta e_\\bde$. So we just need to show that $s_{\\lambda}=n+m(m-1)/2+\\deg(f_n^{{\\lambda},\\bde})$, which easily follows from Lemma \\[LDeg\\](ii).", "\n\nThe homomorphism $g_n$ is a right multiplication with the matrix $G_n$. Its $(\\bde,{\\lambda})$-component is a homomorphism $\nQ_\\bde\\to P_{\\lambda}$ obtained by the right multiplication with $g_n^{\\bde,{\\lambda}}$. So we just need to show that $n+m(m-1)/2=s_{\\lambda}+\\deg(g_n^{\\bde,{\\lambda}})$, which easily follows from Lemma \\[LDeg\\](iii).", "\n\n\\[Csamedegree\\] Suppose $\\bde, \\beps \\in \\bLa(n)$ are such that ${\\lambda}^{\\bde}={\\lambda}^{\\beps}$. Then $\\deg(\\psi_{w(\\bde)}e_\\bde) = \\deg(\\psi_{w(\\beps)}e_{\\beps})$.\n\nIndependence of reduced decompositions\n--------------------------------------\n\nThroughout this subsection we fix $\\bde\\in\\bLa(n)$ and set ${\\lambda}:={\\lambda}^\\bde$.\n\nRecall that in general the element $\\psi_w\\in R_\\theta$ depends on a choice of a reduced decomposition of $w\\in\\Si_d$. While it is clear from the form of the braid relations in the KLR algebra that $e_{\\lambda}\\psi_{w_0^{\\lambda}}$ does not depend on a choice of a reduced decomposition of $w_0^{\\lambda}$, it is not obvious that a similar statement is true for $\\psi_{w(\\bde)}e_\\bde$ and $e_\\bde\\psi_{u(\\bde)}$. So a priori the elements $f_n^{{\\lambda},\\bde}=\\pm e_{\\lambda}\\psi_{w_0^{\\lambda}}\\psi_{w(\\bde)}e_\\bde$ and $g_n^{\\bde,{\\lambda}}=\\pm e_\\bde\\psi_{u(\\bde)}y^{\\lambda}e_{\\lambda}$ might depend on choices of reduced decompositions of $w(\\bde)$ and $u(\\bde)$. In this subsection we will prove that this is not the case, and so in a sense the maps $f_n$ and $g_n$ are canonical.", "\n\nRecall the composition ${\\omega}_{\\lambda}$ and the words $\\bj^{\\lambda},\\bj^\\bde$ from §\\[SSComb\\].", "\n\n\\[Lunique\\] The element $w(\\bde)$ is the unique element of ${}^{{\\omega}_{\\lambda}}{{\\mathscr D}}^{(l^m)}$ with $w(\\bde) \\cdot \\bj^\\bde=\\bj^{\\lambda}$.\n\nThat $w(\\bde)\\in {}^{{\\omega}_{\\lambda}}{{\\mathscr D}}^{(l^m)}$ and $w(\\bde) \\cdot \\bj^\\bde=\\bj^{\\lambda}$ follows from the definitions. ", "To prove the uniqueness statement, let $w\\in {}^{{\\omega}_{\\lambda}}{{\\mathscr D}}^{(l^m)}$ and $w \\cdot \\bj^\\bde=\\bj^{\\lambda}$. Since $w\\in {}^{{\\omega}_{\\lambda}}{{\\mathscr D}}$, it maps the elements of $U_{b+1}(\\bde)$ increasingly to the elements of $U_{b+1}({\\lambda})$. By definition, $\\bj^{\\bde}=\\bj^{{\\delta}^{(1)}}\\dots\\bj^{{\\delta}^{(m)}}$. For every $r\\in [1,m]$, the entries of $\\bj^{{\\delta}^{(r)}}$ have the following properties: (1) each $i\\in[a,b+1]$ appears among them exactly once; (2) the entries that precede $b+1$ appear in the increasing order; (3) the entries that succeed $b+1$ appear in the decreasing order. ", "Since $w\\in {{\\mathscr D}}^{(l^m)}$, it maps the positions corresponding to the entries in (2) to the positions which are to the left of the positions occupied with $b+1$ in $\\bj^{\\lambda}$, and it maps the positions corresponding to the entries in (3) to the positions which are to the right of the positions occupied with $b+1$ in $\\bj^{\\lambda}$. In other words, for all $i\\in[a,b]$, the permutation $w$ maps the elements of $U_i^\\pm(\\bde)$ to the elements of $U_i^\\pm({\\lambda})$. As $w\\in {}^{{\\omega}_{\\lambda}}{{\\mathscr D}}$, it now follows that for every $i\\in[a,b]$, the permutation $w$ maps the elements of $U_i^\\pm(\\bde)$ to the elements of $U_i^\\pm({\\lambda})$ increasingly. ", "We have shown that $w=w(\\bde)$.\n\n\\[Lposdeg\\]Let $\\eps,{\\delta}\\in{\\Lambda}^{\\alpha}$, and $\\bj^\\eps=w\\cdot\\bj^{\\delta}$ for some $w\\in\\Si_l$. Then either $\\eps={\\delta}$ and $w=1$, or $\\deg(\\psi_w 1_{\\bj^{\\delta}})>0$.\n\nSince every $i\\in[a,b+1]$ appears in $\\bj^{\\delta}$ exactly once, $\\eps={\\delta}$ implies $w=1$. On the other hand, if $\\eps\\neq{\\delta}$, let $i$ be maximal with $\\eps_i\\neq {\\delta}_i$. Then the strings colored $i$ and $i+1$ in the Khovanov-Lauda diagram $D$ for $\\psi_w 1_{\\bj^{\\delta}}$ intersect (for any choice of a reduced decomposition of $w$), which contributes a degree $1$ crossing into $D$. On the other hand, since every $j\\in[a,b+1]$ appears in $\\bj^{\\delta}$ exactly once, $D$ has no same color crossings, which are the only possible crossings of negative degree. ", "The lemma follows.", "\n\n\\[L160316\\] Suppose that $w\\in {}^{(l^m)}{{\\mathscr D}}^{{\\omega}_{\\lambda}}$ and $w\\cdot \\bj^{\\lambda}$ is of the form $\\bi^{(1)}\\dots\\bi^{(m)}$ with $\\bi^{(1)},\\dots,\\bi^{(m)}\\in I^{\\alpha}$. Then $w\\cdot \\bj^{\\lambda}=\\bj^\\beps$ for some $\\beps\\in\\bLa$ with ${\\lambda}^\\beps={\\lambda}$.\n\nLer $r\\in[1,m]$. By assumption, the entries $i^{(r)}_1,\\dots,i^{(r)}_l$ of $\\bi^{(r)}$ have the following properties: (1) each $i\\in[a,b+1]$ appears among them exactly once; (2) the entries that precede $b+1$ appear in the increasing order; (3) the entries that succeed $b+1$ appear in the decreasing order. ", "The result follows.", "\n\n\\[deg1\\]Let $P=\\{w\\in {}^{{\\omega}_{\\lambda}}{{\\mathscr D}}\\mid w\\cdot\\bj^{\\bde}=\\bj^{\\lambda}\\}$. Then $w(\\bde)\\in P$ and $\\deg(\\psi_{w(\\bde)}e_\\bde)<\\deg (\\psi_{w}e_\\bde)$ for any $w\\in P\\setminus\\{w(\\bde)\\}$.\n\nIt is clear that $w(\\bde)\\in P$. On the other hand, by Lemma \\[LDJ\\], an arbitrary $w\\in P$ can be written uniquely in the form $w=xy$ with $x\\in {}^{{\\omega}_{\\lambda}}{{\\mathscr D}}^{(l^m)}$, $y\\in\\Si_{(l^m)}$ and $\\ell(xy)=\\ell(x)+\\ell(y)$.\n\nSince $xy\\cdot\\bj^\\bde=\\bj^{\\lambda}$, we have $y\\cdot\\bj^\\bde=x^{-1}\\cdot\\bj^{\\lambda}$. As $x^{-1}\\in {}^{(l^m)}{{\\mathscr D}}^{{\\omega}_{\\lambda}}$, it follows from Lemma \\[L160316\\], that $y\\cdot\\bj^\\bde=x^{-1}\\cdot\\bj^{\\lambda}$ is of the form $\\bj^\\beps$ for some $\\beps\\in\\bLa$ with ${\\lambda}^{\\beps}={\\lambda}$. By Lemma \\[Lunique\\], $x=w(\\beps)$. If $w \\neq w(\\bde)$, then $y \\neq 1$ and we have $$\\begin{aligned}\n\\deg(\\psi_{w}e_\\bde)=\\deg(\\psi_{w(\\beps)} e_\\beps)+\\deg(\\psi_{y}e_\\bde)=\\deg(\\psi_{w(\\bde)}e_\\bde)+\\deg(\\psi_y e_\\bde)>\\deg(\\psi_{w(\\bde)}e_\\bde),\\end{aligned}$$ where we have used Corollary \\[Csamedegree\\] for the second equality and Lemma \\[Lposdeg\\] for the inequality.", "\n\n\\[LFIndependent\\] The element $f_n^{{\\lambda},\\bde}=\\sigma_\\bde e_{\\lambda}\\psi_{w_0^{\\lambda}}\\psi_{w(\\bde)}e_\\bde$ is independent of the choice of reduced expressions for $w_0^{\\lambda}$ and $w(\\bde)$.\n\nIt is clear from the form of the braid relations in the KLR algebra that $e_{\\lambda}\\psi_{w_0^{\\lambda}}$ is independent of the choice of a reduced expression for $w_0^{\\lambda}$. On the other hand, if $\\psi_{w(\\bde)}e_\\bde$ and ${\\psi_{w(\\bde)}'}e_\\bde$ correspond to different reduced expressions of $w(\\bde)$, it follows from the defining relations of the KLR algebra and Theorem \\[TBasis\\] that $\\psi_{w(\\bde)}e_\\bde-{\\psi_{w(\\bde)}'}e_\\bde$ is a linear combination of elements of the form $\\psi_u ye_\\bde$ with $u\\in\\Si_d$, $y\\in \\k[y_1,\\dots,y_d]$ such that, $\\deg(\\psi_u ye_\\bde)=\\deg(\\psi_{w(\\bde)}e_\\bde)$ and $u\\bj^\\bde=\\bj^{\\lambda}$. We have to prove $e_{\\lambda}\\psi_{w_0^{\\lambda}}\\psi_uye_\\bde=0$. Suppose otherwise.", "\n\nSince we are using any preferred reduced decompositions for $u$, we may assume in addition that $u\\in{}^{{\\omega}_{\\lambda}}{{\\mathscr D}}$, since otherwise $e_{\\lambda}\\psi_{w_0^{\\lambda}}\\psi_u=0$. Now by Lemma \\[deg1\\], $\\deg(\\psi_ue_\\bde)>\\deg(\\psi_{w(\\bde)}e_\\bde)$, whence $\\deg(\\psi_u ye_\\bde)>\\deg(\\psi_{w(\\bde)}e_\\bde)$, giving a contradiction.", "\n\n\\[LGIndependent\\] The element $g_n^{\\bde,{\\lambda}}=\\tau_\\bde e_\\bde\\psi_{u(\\bde)}y^{\\lambda}e_{\\lambda}$ is independent of the choice of a reduced expression for $u(\\bde)$.\n\nThe argument is similar to that of the previous lemma. ", "If $e_\\bde\\psi_{u(\\bde)}$ and $e_\\bde\\psi_{u(\\bde)}'$ correspond to different reduced expressions of $u(\\bde)$, then $e_\\bde\\psi_{u(\\bde)}-e_\\bde\\psi_{u(\\bde)}'$ is a linear combination of elements of the form $e_\\bde y\\psi_w$ with $w\\in\\Si_d$, $y\\in \\k[y_1,\\dots,y_d]$ such that $\\deg(e_\\bde y\\psi_w)=\\deg(e_\\bde\\psi_{u(\\bde)})$ and $w^{-1}\\bj^\\bde=\\bj^{\\lambda}$. Moreover, in the KL dialgram of $\\psi_{w}1_{\\bj^{{\\lambda}}}$ the strings colored $b+1$ do not cross each other, since this was the case for the KL diagram of $\\psi_{u(\\bde)}1_{\\bj^{\\lambda}}$. Hence, if $e_\\bde y\\psi_w y^{\\lambda}e_{\\lambda}\\neq 0$, we may assume in addition that $w^{-1}\\in{}^{{\\omega}_{\\lambda}}{{\\mathscr D}}$. Now, using Lemma \\[deg1\\], we conclude that $\\deg(e_\\bde y\\psi_w)>\\deg(e_\\bde\\psi_{u(\\bde)})$, getting a contradiction.", "\n\nSplitting\n---------\n\nIn this subsection, we aim to show that $g\\circ f = {\\operatorname{id}}$. We fix ${\\lambda}\\in {\\Lambda}(n)$ throughout the subsection. ", "We need to prove $\\sum_{\\bde\\in\\bLa(n)}f_n^{{\\lambda},\\bde}g_n^{\\bde,{\\lambda}}=e_{\\lambda}$. Since $f_n^{{\\lambda},\\bde}=0$ unless ${\\lambda}^\\bde={\\lambda}$, this is equivalent to $$\\sum_{\\bde\\in\\bLa(n),\\ {\\lambda}^\\bde={\\lambda}}f_n^{{\\lambda},\\bde}g_n^{\\bde,{\\lambda}}=e_{\\lambda}.$$\n\nLet $\\bde\\in\\bLa(n)$ with ${\\lambda}^\\bde={\\lambda}$. We say that $\\bde$ is [*initial*]{} if $a$ preceeds $a+1$ in $\\bj^{{\\delta}^{(r)}}$ for $r\\in[1, m-{\\lambda}_a]$ and $a$ succeeds $a+1$ in $\\bj^{{\\delta}^{(r)}}$ for $r\\in(m-{\\lambda}_a, m]$. In other words, $\\bde$ is initial if ${\\delta}^{(r)}_a=0$ for $r\\in[1,m-{\\lambda}_a]$ and ${\\delta}^{(r)}_a=1$ for $r\\in(m-{\\lambda}_a,m]$.\n\nLet $w\\in\\Si_d$ and $1\\leq r,s\\leq d$. We say that $(r,s)$ is an [*inversion pair for $w$*]{} if $r<s$, $w(r)>w(s)$, and $\\bj^{\\lambda}_s-\\bj^{\\lambda}_r=\\pm1$.\n\n\\[LInd\\] Let $\\bde\\in \\bLa(n)$ be initial with ${\\lambda}^\\bde={\\lambda}$. Set $\\bar {\\alpha}={\\alpha}_{a+1}+\\dots+{\\alpha}_b$, $\\bar\\theta=m\\bar{\\alpha}$, $\\bar{\\lambda}=({\\lambda}_{a+1},\\dots,{\\lambda}_b)$, $\\bar n:={\\lambda}_{a+1}+\\dots+{\\lambda}_b$, and $\\bar \\bde=(\\bar{\\delta}^{(1)},\\dots,\\bar{\\delta}^{(m)})$, where $\\bar {\\delta}^{(r)}=({\\delta}^{(r)}_{a+1},\\dots,{\\delta}^{(r)}_b)$ for all $r\\in[1,m]$. Then $$\\label{E210916}\nf_n^{{\\lambda},\\bde} g_n^{\\bde,{\\lambda}}=1_{a^{(m-{\\lambda}_a)}}\\circ f_{\\bar n}^{\\bar{\\lambda},\\bar\\bde} g_{\\bar n}^{\\bar \\bde,\\bar {\\lambda}}\\circ 1_{a^{({\\lambda}_a)}}.$$\n\nBy definition, $$f_n^{{\\lambda},\\bde} g_n^{\\bde,{\\lambda}}=(-1)^{\\sum_{i=a}^b{\\lambda}_i({\\lambda}_i-1)/2}e_{\\lambda}\\psi_{w_0^{\\lambda}}\\psi_{w(\\bde)}\\psi_{u(\\bde)}y^{\\lambda}e_{\\lambda}.$$ Throughout the proof, ‘inversion pair’ means ‘inversion pair for $w(\\bde)$’. ", "Recall that $w(\\bde)=u(\\bde)^{-1}$. Since $\\bde$ is initial, in the Khovanov-Lauda diagram for $\\psi_{w(\\bde)}$ (for any choice of reduced expression) no strings of color $a$ cross each other. ", "We want to apply quadratic relations on pairs of strings one of which has color $a$ and the other has color $a+1$. These correspond to inversion pairs $(r,s)$ with $r\\in U^-_a({\\lambda}), s\\not \\in U^-_a({\\lambda})$ or $s\\in U^+_a({\\lambda}), r\\not\\in U^+_a({\\lambda})$.\n\nNote that there are exactly $r-1$ inversion pairs of the form $(r,s)$ when $r\\in U^-_a({\\lambda})$ and $d-s$ inversion pairs of the form $(r,s)$ when $s\\in U^+_a({\\lambda})$. Applying the corresponding quadratic relations, we see that $f_n^{{\\lambda},\\bde} g_n^{\\bde,{\\lambda}}$ equals $$\\label{E190316}\n(-1)^{{\\lambda}_a({\\lambda}_a-1)/2}\ne_{\\lambda}\\psi_{w_0^{\\lambda}}\n(y_{0,m-{\\lambda}_a}\\circ f_{\\bar n}^{\\bar{\\lambda},\\bar\\bde} g_{\\bar n}^{\\bar \\bde,\\bar {\\lambda}}\\circ y_{0,{\\lambda}_a}')\ny^{\\lambda}e_{\\lambda}+(*),$$ where $(*)$ a sum of elements of the form $$e_{\\lambda}\\psi_{w_0^{\\lambda}}\n\\iota_{(m-{\\lambda}_a){\\alpha}_a,\\bar \\theta,{\\lambda}_a{\\alpha}_a}(Y^-\\otimes X\\otimes Y'^+)\ny^{\\lambda}e_{\\lambda},$$ with $X\\in R_{\\bar\\theta}$, $Y^\\pm$ a polynomial in the variables $y_r$ with $r\\in U_a^\\pm({\\lambda})$, and $\\deg Y^-+\\deg Y^+<\\deg y_{0,m-{\\lambda}_a}+\\deg y_{0,{\\lambda}_a}'$. By Lemma \\[LW0Y0\\](\\[LW0Y0i\\]), we have $(*)=0$. So by Lemma \\[LW0Y0\\](\\[LW0Y0ii\\]), the expression (\\[E190316\\]) equals the right hand side of (\\[E210916\\]).", "\n\nDefine $\\bde_{\\lambda}=({\\delta}_{\\lambda}^{(1)}, \\cdots, {\\delta}_{\\lambda}^{(m)})$ to be the unique element of $\\bLa(n)$ such that for each $a \\leq i \\leq b$ we have:\n\n- $i$ precedes $b+1$ in $\\bj^{{\\delta}_{\\lambda}^{(r)}}$ for $1\\leq r\\leq m-{\\lambda}_i$;\n\n- $i$ succeeds $b+1$ in $\\bj^{{\\delta}_{\\lambda}^{(r)}}$ for $m-{\\lambda}_i<r\\leq m$.\n\nNote that ${\\lambda}^{\\bde_{\\lambda}}={\\lambda}$ but $\\bde_{{\\lambda}^\\bde}$ in general differs from $\\bde$.\n\nLet $\\bde\\in\\bLa$ satisfy ${\\lambda}^\\bde={\\lambda}$. Then $$f_n^{{\\lambda},\\bde} g_n^{\\bde,{\\lambda}}=\n\\left\\{\n\\begin{array}{ll}\ne_{\\lambda}&\\hbox{if $\\bde=\\bde_{\\lambda}$,}\\\\\n0 &\\hbox{otherwise.}", "\n\\end{array}\n\\right.$$\n\nIf $\\bde=\\bde_{\\lambda}$, the result follows by induction on $\\height({\\alpha})$ using from Lemma \\[LInd\\]. ", "If $\\bde\\neq \\bde_{\\lambda}$, we may assume using Lemma \\[LInd\\] that $\\bde$ is not initial. ", "This implies that for some $r\\in[1,m)$, we have ${\\delta}^{(r)}_a=1$ and ${\\delta}^{(r+1)}_a=0$, i.e. the last entry of the word $\\bj^{{\\delta}^{(r)}}$ and the first entry of the word $\\bj^{{\\delta}^{(r+1)}}$ are both equal to $a$. It follows that $\n \\begin{tikzpicture}[baseline=6mm,black,line width=1pt, scale=0.32,\n draw/.append style={rounded corners},\n every node/.append style={font=\\fontsize{5}{5}\\selectfont}] \\tikzset{baseline=0mm}\n\\draw(0,0.5) node[above]{$a$}--(1,0)--(0,-0.5);\n\\draw(1,0.5) node[above]{$a$}--(0,0)--(1,-0.5);\n\\end{tikzpicture}\n\n$ is a sub-diagram of a Khovanov-Lauda diagram for $\\psi_{w(\\bde)}\\psi_{u(\\bde)}y^{\\lambda}e_{\\lambda}$, so $\nf_n^{{\\lambda},\\bde} g_n^{\\bde,{\\lambda}}=\\pm e_{\\lambda}\\psi_{w_0^{\\lambda}}\\psi_{w(\\bde)}\\psi_{u(\\bde)}y^{\\lambda}e_{\\lambda}=0.", "\n$\n\n\\[CSplit\\] For any $n\\in{\\mathbb{Z}}_{\\geq 0}$, we have $g_n\\circ f_n={\\operatorname{id}}$.\n\nProof of Theorem \\[TA\\], assuming $f$ and $g$ are chain maps {#SSProof}\n------------------------------------------------------------\n\nIn Sections \\[SF\\] and \\[SG\\], we will prove that $f$ and $g$ constructed above are chain maps. ", "The goal of this subsection is to demonstrate that this is sufficient to establish our main result.", "\n\nLet $$Y_0 := \\prod_{k=1}^m y_{kl}^{k-1} \\in \\k[y_1, \\ldots, y_d].$$ We also define $W_0$ to be the longest element of ${{\\mathscr D}}^{(l^m)}$. For $1\\leq r<m$, we have a fully commutative element $$z_r:=\\prod_{k=1}^l((r-1)l+k,rl+k) \\in \\Si_d.$$ In fact, if $w_{0,m}=s_{r_1}\\dots s_{r_N}$ is a reduced decomposition in $\\Si_m$, then $W_0=z_{r_1}\\dots z_{r_N}$ in $\\Si_d$ with $\\ell(W_0)= \\ell(z_{r_1})+\\dots+\\ell( z_{r_N})$. Recalling (\\[EBZero\\]) we have $$\\bj^\\bzero=(a\\,(a+1)\\cdots (b+1))^m\\in I^d.$$ Then the following is easy to check:\n\n\\[thickcrossdegree\\] Let $P = \\{ w\\in {{\\mathscr D}}^{(l^m)} \\mid w\\cdot \\bj^\\bzero = \\bj^\\bzero\\}$. Then $W_0\\in P$ and $\\deg(\\psi_{W_0}e_\\bzero) < \\deg(\\psi_w e_\\bzero)$ for any $w\\in P\\setminus \\{ W_0\\}$\n\n\\[thickcrossindep\\] Let $\\psi_{W_0}$ and $\\psi_{W_0}'$ in $R_\\theta$ correspond to different reduced expressions of $W_0\\in\\Si_d$. Then $\\psi_{W_0}v_\\alpha^{\\circ m}=\\psi_{W_0}'v_\\alpha^{\\circ m}$ in $\\Delta(\\alpha)^{\\circ m}$.\n\nIt follows from the defining relations of the KLR algebra and Theorem \\[TBasis\\] that $\\psi_{W_0}e_\\bzero - \\psi_{W_0}'e_\\bzero$ is a linear combination of elements of the form $\\psi_w e_\\bzero$ where $w\\cdot \\bj^\\bzero = \\bj^\\bzero$, $w \\neq W_0$, and $\\deg(\\psi_w e_\\bzero) = \\deg(\\psi_{W_0}e_\\bzero)$. Moreover, for each such $w$, by Lemma \\[LDJ\\], there exist (unique) elements $x\\in {{\\mathscr D}}^{(l^m)}$ and $y\\in \\Si_{(l^m)}$ such that $w = xy$ and $\\ell(w) = \\ell(x)+\\ell(y)$. Since $\\psi_y v_\\alpha^{\\circ m} = 0$ if $y\\neq 1$, we may assume $w \\in {{\\mathscr D}}^{(l^m)}$. We now have $w\\in {{\\mathscr D}}^{(l^m)}$, $w\\cdot \\bj^\\bzero = \\bj^\\bzero$, and $w\\neq W_0$. By Lemma \\[thickcrossdegree\\], no such element $w$ can exist, so $(\\psi_{W_0}e_\\bzero - \\psi_{W_0}'e_\\bzero)v_\\alpha^{\\circ m} = 0$.\n\n\\[FafterG\\] There is a choice of reduced expression of $W_0$ for which $g_0^{\\bzero,0}f_0^{0,\\bzero} = e_{\\bzero} Y_0 \\psi_{W_0}e_{\\bzero}$.\n\nNote that $\\ell(u(\\bzero)w_0^0 w(\\bzero)) = \\ell(u(\\bzero))+\\ell(w_0^0)+\\ell(w(\\bzero))$ and $u(\\bzero)w_0^0 w(\\bzero) = W_0$. So for an appropriate choice of reduced expression for $W_0$, we have $\\psi_{u(\\bzero)}\\psi_{w_0^0}\\psi_{w(\\bzero)} = \\psi_{W_0}$. We now compute: $$\\begin{aligned}\n g_0^{\\bzero,0}f_0^{0,\\bzero} &= e_{\\bzero}\\psi_{u(\\bzero)}y^0 e_0 \\psi_{w_0^0}\\psi_{w(\\bzero)} e_\\bzero \\\\\n &= e_{\\bzero}\\psi_{u(\\bzero)}y^0 \\psi_{w_0^0}\\psi_{w(\\bzero)} e_\\bzero \\\\\n &= e_{\\bzero}Y_0\\psi_{u(\\bzero)}\\psi_{w_0^0}\\psi_{w(\\bzero)} e_\\bzero \\\\\n &= e_\\bzero Y_0 \\psi_{W_0}e_\\bzero,\n \\end{aligned}$$ where the first equality is by definition of $g_0^{\\bzero,0}$ and $f_0^{0,\\bzero}$, the second follows from Lemma \\[LW0Y0\\](\\[LW0Y0ii\\]), the third by the defining relations of $R_\\theta$ and the observation that $Y_0 = u(\\bzero)\\cdot y^0$, and the fourth from the remark at the beginning of the proof.", "\n\nNote that $$f_0^{0,\\bzero}={\\sigma}_{\\bzero}e_0\\psi_{w_0^0}\\psi_{w(\\bzero)}e_\\bzero=\\psi_g1_{\\bi_{\\alpha}^m},$$ where $g$ is the longest element of $\\Si_d$ with $g\\cdot(\\bi_{\\alpha}^m)=a^m(a+1)^m\\cdots (b+1)^m$. Let $$\\label{ESG}\nv_{{\\alpha}^m}:=f_0^{0,\\bzero}v_{\\alpha}^{\\circ m}e_m= \\psi_gv_{\\alpha}^{\\circ m}e_m\\in{\\Delta}({\\alpha}^m).$$ We refer to $v_{{\\alpha}^m}$ as the [*standard generator*]{} of ${\\Delta}({\\alpha}^m)$. It can be checked directly but also follows from Theorem \\[main theorem\\] that it does generate ${\\Delta}({\\alpha}^m)$. Note that $e_0 v_{{\\alpha}^m}=v_{{\\alpha}^m}$, so there is a homomorphism $${\\sf p}:P_0=q^{-lm(m-1)/2}R_\\theta e_0 \\longrightarrow {\\Delta}({\\alpha}^m),\\ xe_0\\mapsto xv_{{\\alpha}^m},$$ where $v_{{\\alpha}^m}$ is the standard generator of ${\\Delta}({\\alpha}^m)$, see (\\[ESG\\]).", "\n\n\\[main theorem\\]If $f$ and $g$ are chain maps then $P_\\bullet=P_\\bullet^{{\\alpha}^m}$ is a projective resolution of ${\\Delta}({\\alpha}^m)$, with the augmentation map ${\\sf p}$.\n\nThe modules $P_n$ are projective by construction. ", "By Corollary \\[CSplit\\], $P_\\bullet$ is a complex, isomorphic to a direct summand of the complex $Q_\\bullet$. Since $Q_\\bullet$ is a resolution of $q^{m(m-1)/2}{\\Delta}({\\alpha})^{\\circ m}$, it follows from the assumptions that $P_\\bullet$ is exact in degrees $>0$ and its $0$th cohomology is given by ${\\sf q} f_0 g_0(Q_0)$ where ${\\sf q}:Q_0\\to q^{m(m-1)/2}{\\Delta}({\\alpha})^{\\circ m}$ is the augmentation map (\\[EAugMap\\]).", "\n\nRecalling the $(R_\\theta, {\\mathcal{NH}}_m)$-bimodule structure of $q^{m(m-1)/2}{\\Delta}({\\alpha})^{\\circ m}$ from §\\[SSStdMod\\] and the idempotent $e_m\\in {\\mathcal{NH}}_m$ defined in (\\[DeltaIdem\\]), using Lemma \\[thickcrossindep\\], we have $$\\label{E221018}\n Y_0 \\psi_{W_0}v_\\alpha^{\\circ m} = Y_0 \\psi_{z_{r_1}}\\cdots \\psi_{z_{r_N}} v_{\\alpha}^{\\circ m} = v_\\alpha^{\\circ m}e_m,$$ where $w_{0,m}=s_{r_1}\\cdots s_{r_N}$ is a reduced decomposition in $\\Si_m$. We now have: $$\\begin{aligned}\n {\\sf q} f_0 g_0(Q_0) &= {\\sf q}(q^{m(m-1)/2}R_\\theta e_\\bzero Y_0\\psi_{W_0} e_\\bzero) \\\\\n &= q^{m(m-1)/2}R_\\theta Y_0\\psi_{W_0} v_\\alpha^{\\circ m} \\\\\n &= q^{m(m-1)/2}R_\\theta v_\\alpha^{\\circ m} e_m \\\\\n &= q^{m(m-1)/2}\\Delta(\\alpha)^{\\circ m}e_m \\\\\n &= \\Delta(\\alpha^m),\\end{aligned}$$ where the first equality follows from Lemma \\[FafterG\\], the second from the definition of ${\\sf q}$, the third from (\\[E221018\\]), and the last two from the definitions.", "\n\nIt remains to note that ${\\sf q}(f_0(e_0))=v_{{\\alpha}^m}$. For, note that ${\\sf q}(f_0(e_0))=f_0v_{\\alpha}^{\\circ m}$, and ${\\sf q}(f_0(e_0))\\in\n{\\sf q}(f_0(P_0))={\\sf q}(f_0(g_0(Q_0)))=\\Delta(\\alpha^m)$. So $f_0v_{\\alpha}^{\\circ m}=f_0v_{\\alpha}^{\\circ m}e_m=\nv_{{\\alpha}^m}$.\n\nVerification that $f$ is a chain map {#SF}\n====================================\n\nWe continue with the running assumptions of the previous section. ", "In addition, throughout the section we fix $$n\\in{\\mathbb{Z}}_{\\geq 0},\\quad \\mu=(\\mu_a,\\dots,\\mu_b)\\in{\\Lambda}(n+1)\\quad \\text{and}\\quad \\bde=({\\delta}^{(1)},\\dots,{\\delta}^{(m)})\\in \\bLa(n).$$\n\nSpecial reduced expressions\n---------------------------\n\nRecall the notation of §\\[SSComb\\]. ", "Let ${\\lambda}\\in{\\Lambda}^{{\\alpha}^m}$ and ${\\delta}\\in{\\Lambda}^{\\alpha}$ be such that $\\bar{\\lambda}:={\\lambda}-{\\delta}\\in{\\Lambda}^{{\\alpha}^{m-1}}$. For $i\\in[a,b+1]$, we denote by $p_i=p_i({\\delta})\\in[1,l]$ the position occupied by $i$ in $\\bj^{{\\delta}}$, and set $$\\label{EQI}\nq_i=q_i({\\lambda},{\\delta}):=\n\\left\\{\n\\begin{array}{ll}\nl_i^-({\\lambda}) &\\hbox{if $i\\neq b+1$ and ${\\delta}_i=0$,}\\\\\nl_i^+({\\lambda}) &\\hbox{if $i\\neq b+1$ and ${\\delta}_i=1$,}\\\\\nl_{b+1}({\\lambda}) &\\hbox{if $i= b+1$.}\n\\end{array}\n\\right.$$ Let $$Q:=\\{q_a,\\dots,q_{b+1}\\}\\subseteq [1,d].$$ Note that $\\{p_a,\\dots,p_{b+1}\\}=[1,l]$. Define $x_{\\delta}^{\\lambda}\\in\\Si_d$ to be the permutation which maps $p_i$ to $q_i$ for all $i\\in[a,b+1]$, and maps the elements of $[l+1,d]$ increasingly to the elements of $[1,d]\\setminus Q$. It is easy to see that $x_{\\delta}^{\\lambda}$ is fully commutative, so $\\psi_{x_{\\delta}^{\\lambda}}$ is well defined, and $1_{\\bj^{\\lambda}}\\psi_{x_{\\delta}^{\\lambda}}=\\psi_{x_{\\delta}^{\\lambda}}1_{\\bj^{\\delta}\\bj^{\\bar{\\lambda}}}$.\n\nNow let ${\\lambda}={\\lambda}^\\bde$, and $r\\in[1,m]$. Define $$\\bde^{\\geq r}:=({\\delta}^{(r)},\\dots,{\\delta}^{(m)})\\in({\\Lambda}^{\\alpha})^{m-r+1},\\quad\n{\\lambda}^{\\geq r}:={\\lambda}^{\\bde^{\\geq r}}\\in{\\Lambda}^{{\\alpha}^{m-r+1}}.$$ Define $x(\\bde,1):=x_{{\\delta}^{(1)}}^{\\lambda}\\in\\Si_d$. More generally, define for all $r=1,\\dots,m-1$, the permutations $x(\\bde,r)\\in\\Si_d$ so that $x(\\bde,r)$ is the image of $$(1_{\\Si_{(r-1)l}},x_{{\\delta}^{(r)}}^{{\\lambda}^{\\geq r}})\\in \\Si_{(r-1)l}\\times\\Si_{(m-r+1)l}$$ under the natural embedding $\\Si_{(r-1)l}\\times\\Si_{(m-r+1)l}\\into \\Si_d$. Recall the element $w(\\bde)\\in\\Si_d$ defined in §\\[SSComp\\]. ", "The following lemma follows from definitions:\n\n\\[LWX\\] We have $w(\\bde)=x(\\bde,1)\\cdots x(\\bde,m-1)$ and $\\ell(w(\\bde))=\\ell(x(\\bde,1))+\\dots +\\ell(x(\\bde,m-1))$.\n\nIn view of the lemma, when convenient, we will always choose reduced decompositions so that $$\\label{WPsiW}\n\\psi_{w(\\bde)}=\\psi_{x(\\bde,1)}\\dots \\psi_{x(\\bde,m-1)}.$$ By Lemma \\[LFIndependent\\], we then have $$\\label{CWX}\nf_n^{{\\lambda},\\bde}={\\sigma}_\\bde e_{\\lambda}\\psi_{w_0^{\\lambda}}\\psi_{x(\\bde,1)}\\dots \\psi_{x(\\bde,m-1)}.$$\n\n[Let $a=1$, $b=2$, ${\\lambda}=(2,2)$, and $\\bde=\\big((1,0),(1,1),(0,1),(0,0)\\big)$, so that $m=4$ and $n=4$. Then $f_n^{{\\lambda},\\bde}$ is $$ \\begin{tikzpicture}[baseline=6mm,black,line width=1pt, scale=0.32,\n draw/.append style={rounded corners},\n every node/.append style={font=\\fontsize{5}{5}\\selectfont}] \\tikzset{baseline=0mm}\n\\draw(1,9) node[above]{\\small $1$};\n\\draw(2,9) node[above]{\\small $1$};\n\\draw(3,9) node[above]{\\small $2$};\n\\draw(4,9) node[above]{\\small $2$};\n\\draw(5,9) node[above]{\\small $3$};\n\\draw(6,9) node[above]{\\small $3$};\n\\draw(7,9) node[above]{\\small $3$};\n\\draw(8,9) node[above]{\\small $3$};\n\\draw(9,9) node[above]{\\small $2$};\n\\draw(10,9) node[above]{\\small $2$};\n\\draw(11,9) node[above]{\\small $1$};\n\\draw(12,9) node[above]{\\small $1$};\n\\draw [rounded corners,color=gray] (0.6,10.5)--(2.4,10.5)--(2.4,9.1)--(0.6,9.1)--cycle;\n\\draw [rounded corners,color=gray] (2.6,10.5)--(4.4,10.5)--(4.4,9.1)--(2.6,9.1)--cycle;\n\\draw [rounded corners,color=gray] (4.6,10.5)--(8.4,10.5)--(8.4,9.1)--(4.6,9.1)--cycle;\n\\draw [rounded corners,color=gray] (8.6,10.5)--(10.4,10.5)--(10.4,9.1)--(8.6,9.1)--cycle;\n\\draw [rounded corners,color=gray] (10.6,10.5)--(12.4,10.5)--(12.4,9.1)--(10.6,9.1)--cycle;\n\\draw(1,9.1)--(1,8.5);\n\\draw(2,9.1)--(2,8.5);\n\\draw(3,9.1)--(3,8.5);\n\\draw(4,9.1)--(4,8.5);\n\\draw(5,9.1)--(5,8.5);\n\\draw(6,9.1)--(6,8.5);\n\\draw(7,9.1)--(7,8.5);\n\\draw(8,9.1)--(8,8.5);\n\\draw(9,9.1)--(9,8.5);\n\\draw(10,9.1)--(10,8.5);\n\\draw(11,9.1)--(11,8.5);\n\\draw(12,9.1)--(12,8.5);\n\\draw [rounded corners,color=gray] (0.6,8.5)--(2.4,8.5)--(2.4,7.1)--(0.6,7.1)--cycle;\n\\draw [rounded corners,color=gray] (2.6,8.5)--(4.4,8.5)--(4.4,7.1)--(2.6,7.1)--cycle;\n\\draw [rounded corners,color=gray] (4.6,8.5)--(8.4,8.5)--(8.4,7.1)--(4.6,7.1)--cycle;\n\\draw [rounded corners,color=gray] (8.6,8.5)--(10.4,8.5)--(10.4,7.1)--(8.6,7.1)--cycle;\n\\draw [rounded corners,color=gray] (10.6,8.5)--(12.4,8.5)--(12.4,7.1)--(10.6,7.1)--cycle;\n\\draw(1.5,7) node[above]{\\small $w_0$};\n\\draw(3.5,7) node[above]{\\small $w_0$};\n\\draw(6.5,7) node[above]{\\small $w_0$};\n\\draw(9.5,7) node[above]{\\small $w_0$};\n\\draw(11.5,7) node[above]{\\small $w_0$};\n\\draw(1,7.1)--(4,4)--(7,1)--(7,-2);\n\\draw(2,7.1)--(5,4)--(8,1)--(10,-2);\n\\draw(3,7.1)--(1,4)--(1,1)--(1,-2);\n\\draw(4,7.1)--(6,4)--(9,1)--(11,-2);\n\\draw(5,7.1)--(2,4)--(2,1)--(2,-2);\n\\draw(6,7.1)--(7,4)--(4,1)--(4,-2);\n\\draw(7,7.1)--(8,4)--(10,1)--(8,-2);\n\\draw(8,7.1)--(9,4)--(11,1)--(12,-2);\n\\draw(9,7.1)--(10,4)--(5,1)--(5,-2);\n\\draw(10,7.1)--(11,4)--(12,1)--(9,-2);\n\\draw(11,7.1)--(3,4)--(3,1)--(3,-2);\n\\draw(12,7.1)--(12,4)--(6,1)--(6,-2);\n\\draw(14,5.5) node{$\\left.{", "\n\\begin{matrix}\n \\\\\n \\\\\n \\\\\n \\\\\n \\\\\n\\end{matrix}\n}\\right\\}$};\n\\draw(14,2.5) node{$\\left.{", "\n\\begin{matrix}\n \\\\\n \\\\\n \\\\\n \\\\\n \\\\\n\\end{matrix}\n}\\right\\}$};\n\\draw(14,-0.5) node{$\\left.{", "\n\\begin{matrix}\n \\\\\n \\\\\n \\\\\n \\\\\n \\\\\n\\end{matrix}\n}\\right\\}$};\n\\draw(16.2,5.5) node{\\small $\\psi_{x(\\bde,1)}$};\n\\draw(16.2,2.5) node{\\small $\\psi_{x(\\bde,2)}$};\n\\draw(16.2,-0.5) node{\\small $\\psi_{x(\\bde,3)}$};\n\\draw(1,-2.8) node{\\small $2$};\n\\draw(2,-2.8) node{\\small $3$};\n\\draw(3,-2.8) node{\\small $1$};\n\\draw(4,-2.8) node{\\small $3$};\n\\draw(5,-2.8) node{\\small $2$};\n\\draw(6,-2.8) node{\\small $1$};\n\\draw(7,-2.8) node{\\small $1$};\n\\draw(8,-2.8) node{\\small $3$};\n\\draw(9,-2.8) node{\\small $2$};\n\\draw(10,-2.8) node{\\small $1$};\n\\draw(11,-2.8) node{\\small $2$};\n\\draw(12,-2.8) node{\\small $3$};\n\\end{tikzpicture}\n$$ ]{}\n\nA commutation lemma {#SSCommL}\n-------------------\n\nIt will be convenient to use the following notation. ", "Let ${\\lambda}\\in{\\Lambda}(n)$. Consider the parabolic (non-unital) subalgebra $$R^{\\lambda}:=R_{(m-{\\lambda}_a){\\alpha}_a,\\dots,(m-{\\lambda}_b){\\alpha}_b,m{\\alpha}_{b+1},{\\lambda}_b{\\alpha}_b,\\dots,{\\lambda}_a{\\alpha}_a}\\subseteq R_\\theta.$$ We have $$R^{\\lambda}\\cong R_{(m-{\\lambda}_a){\\alpha}_a}\\otimes \\dots\\otimes R_{(m-{\\lambda}_b){\\alpha}_b}\\otimes R_{m{\\alpha}_{b+1}}\\otimes R_{{\\lambda}_b{\\alpha}_b}\\otimes \\dots\\otimes R_{{\\lambda}_a{\\alpha}_a}.$$ The natural (unital) embeddings of the algebras $$R_{(m-{\\lambda}_a){\\alpha}_a},\\dots,R_{(m-{\\lambda}_b){\\alpha}_b},R_{m{\\alpha}_{b+1}},R_{{\\lambda}_b{\\alpha}_b},\\dots,R_{{\\lambda}_a{\\alpha}_a}$$ into $R^{\\lambda}$, allow us to consider them as (non-unital) subalgebras of $R_\\theta$. We denote the corresponding (non-unital) algebra embeddings by $$\\iota^{\\lambda}_{a;-},\\dots,\\iota^{\\lambda}_{b;-},\\iota^{\\lambda}_{b+1},\\iota^{\\lambda}_{b;+},\\dots,\\iota^{\\lambda}_{a;+}.$$ For example, setting $$\\psi_{w_0}^{\\lambda}(i;-):=\\iota^{\\lambda}_{i;-}(\\psi_{w_{0,m-{\\lambda}_i}}),\\ \\psi_{w_0}^{\\lambda}(i;+):=\\iota^{\\lambda}_{i;+}(\\psi_{w_{0,{\\lambda}_i}}),\\\n\\psi_{w_0}^{\\lambda}(b+1):=\\iota^{\\lambda}_{b+1}(\\psi_{w_{0,m}}),$$ for all $i\\in [a,b]$, can write $\\psi_{w_0^{\\lambda}}\\in R_\\theta$ as a commuting product $$\\label{E130416}\n\\psi_{w_0^{\\lambda}}=\\psi_{w_0}^{\\lambda}(a;-) \\dots \\psi_{w_0}^{\\lambda}(b;-) \\psi_{w_0}^{\\lambda}(b+1) \\psi_{w_0}^{\\lambda}(b;+)\\dots \\psi_{w_0}^{\\lambda}(a;+).$$\n\n\\[L290316\\] Let $i\\in[a,b]$ with $\\mu_i>0$, and ${\\lambda}:=\\mu-\\e_i$. Then $$1_{\\bj^\\mu}\\psi_{{\\lambda};i} \\psi_{w_0^{\\lambda}}=1_{\\bj^\\mu} \\psi_{w_0^\\mu}\\psi_{l_i^+(\\mu)\\to l_i^-({\\lambda})}.$$\n\nWe have $$\\begin{aligned}\n1_{\\bj^\\mu}\\psi_{{\\lambda};i} \\psi_{w_0^{\\lambda}}&=\n1_{\\bj^\\mu}\\psi_{{\\lambda};i}1_{\\bj^{\\lambda}} \\psi_{w_0^{\\lambda}}\n\\\\\n&=1_{\\bj^\\mu}\\psi_{{\\lambda};i} \\psi_{w_0}^{\\lambda}(b+1) \\prod_{j\\in [a,b]}\\psi_{w_0}^{\\lambda}(j;-)\\psi_{w_0}^{\\lambda}(j;+)\n\\\\\n&=1_{\\bj^\\mu}\\psi_{w_0}^\\mu(b+1) \\Big[\\prod_{j\\in [a,b]\\setminus\\{i\\}}\\psi_{w_0}^\\mu(j;-)\\psi_{w_0}^\\mu(j;+)\\Big]\n\\psi_{{\\lambda};i} \\psi_{w_0}^{\\lambda}(i;-)\\psi_{w_0}^{\\lambda}(i;+)\n\\\\\n&=1_{\\bj^\\mu} \\psi_{w_0}^\\mu(b+1) \\Big[\\prod_{j\\in [a,b]}\\psi_{w_0}^\\mu(j;-)\\psi_{w_0}^\\mu(j;+)\\Big]\\psi_{l_i^+(\\mu)\\to l_i^-({\\lambda})}\n\\\\\n&=1_{\\bj^\\mu} \\psi_{w_0^\\mu}\\psi_{l_i^+(\\mu)\\to l_i^-({\\lambda})},\\end{aligned}$$ where we have used (\\[E130416\\]) for the second equality, Lemma \\[LPull\\](i) for the third equality, and the definition of $\\psi_{{\\lambda},i}$ as an explicit cycle element for the fourth equality.", "\n\nWe illustrate Lemma \\[L290316\\] diagramatically. ", "Let $a=1$, $b=2$, $m=4$ and $\\mu = (2,3)$. Then, Lemma \\[L290316\\] claims the following equality: $$ \\begin{tikzpicture}[baseline=6mm,black,line width=1pt, scale=0.32,\n draw/.append style={rounded corners},\n every node/.append style={font=\\fontsize{5}{5}\\selectfont}] \\tikzset{baseline=15mm}\n\\draw(-0.5,7.7) node[above]{\\small $1_{\\bj^\\mu}\\{$};\n\\draw(0.2,6.3) node{$\\left.{", "\n\\begin{matrix}\n\\\\\n\\\\\n\\\\\n\\\\\n\\\\\n\\\\\n\\\\\n\\end{matrix}\n}\\right\\{$};\n\\draw(0.2,3) node{$\\left.{", "\n\\begin{matrix}\n \\\\\n \\\\\n \\\\\n\\\\\n\\\\\n\\end{matrix}\n}\\right\\{$};\n\\draw(-0.9,6.4) node{\\small $\\psi_{{\\lambda};1}$};\n\\draw(-0.9,3) node{\\small $\\psi_{w_0^{\\lambda}}$};\n\\draw(1,8) node[above]{\\small $1$};\n\\draw(2,8) node[above]{\\small $1$};\n\\draw(3,8) node[above]{\\small $2$};\n\\draw(4,8) node[above]{\\small $3$};\n\\draw(5,8) node[above]{\\small $3$};\n\\draw(6,8) node[above]{\\small $3$};\n\\draw(7,8) node[above]{\\small $3$};\n\\draw(8,8) node[above]{\\small $2$};\n\\draw(9,8) node[above]{\\small $2$};\n\\draw(10,8) node[above]{\\small $2$};\n\\draw(11,8) node[above]{\\small $1$};\n\\draw(12,8) node[above]{\\small $1$};\n\\draw [rounded corners,color=gray] (0.6,4.5)--(3.4,4.5)--(3.4,3.1)--(0.6,3.1)--cycle;\n\\draw [rounded corners,color=gray] (4.6,4.5)--(8.4,4.5)--(8.4,3.1)--(4.6,3.1)--cycle;\n\\draw [rounded corners,color=gray] (8.6,4.5)--(11.4,4.5)--(11.4,3.1)--(8.6,3.1)--cycle;\n\\draw(1,8.1)--(1,4.5);\n\\draw(2,8.1)--(2,4.5);\n\\draw(3,8.1)--(4,4.5)--(4,2.5);\n\\draw(4,8.1)--(5,4.5);\n\\draw(5,8.1)--(6,4.5);\n\\draw(6,8.1)--(7,4.5);\n\\draw(7,8.1)--(8,4.5);\n\\draw(8,8.1)--(9,4.5);\n\\draw(9,8.1)--(10,4.5);\n\\draw(10,8.1)--(11,4.5);\n\\draw(11,8.1)--(12,4.5)--(12,2.5);\n\\draw(12,8.1)--(3,4.5);\n\\draw(1,3.1)--(1,2.5);\n\\draw(2,3.1)--(2,2.5);\n\\draw(3,3.1)--(3,2.5);\n\\draw(5,3.1)--(5,2.5);\n\\draw(6,3.1)--(6,2.5);\n\\draw(7,3.1)--(7,2.5);\n\\draw(8,3.1)--(8,2.5);\n\\draw(9,3.1)--(9,2.5);\n\\draw(10,3.1)--(10,2.5);\n\\draw(11,3.1)--(11,2.5);\n\\draw(2,3) node[above]{\\small $w_0$};\n\\draw(6.5,3) node[above]{\\small $w_0$};\n\\draw(6.5,3) node[above]{\\small $w_0$};\n\\draw(10,3) node[above]{\\small $w_0$};\n\\draw(1,1) node[above]{\\small $1$};\n\\draw(2,1) node[above]{\\small $1$};\n\\draw(3,1) node[above]{\\small $1$};\n\\draw(4,1) node[above]{\\small $2$};\n\\draw(5,1) node[above]{\\small $3$};\n\\draw(6,1) node[above]{\\small $3$};\n\\draw(7,1) node[above]{\\small $3$};\n\\draw(8,1) node[above]{\\small $3$};\n\\draw(9,1) node[above]{\\small $2$};\n\\draw(10,1) node[above]{\\small $2$};\n\\draw(11,1) node[above]{\\small $2$};\n\\draw(12,1) node[above]{\\small $1$};\n\\end{tikzpicture}\n\n=\n \\begin{tikzpicture}[baseline=6mm,black,line width=1pt, scale=0.32,\n draw/.append style={rounded corners},\n every node/.append style={font=\\fontsize{5}{5}\\selectfont}] \\tikzset{baseline=15mm}\n\\draw(13.9,7.7) node[above]{\\small $\\} 1_{\\bj^\\mu}$};\n\\draw(13,7) node{$\\left.{", "\n\\begin{matrix}\n\\\\\n\\\\\n\\\\\n\\\\\n\\end{matrix}\n}\\right\\}$};\n\\draw(13,3.7) node{$\\left.{", "\n\\begin{matrix}\n\\\\\n\\\\\n\\\\\n\\\\\n\\\\\n\\\\\n\\\\\n\\\\\n\\end{matrix}\n}\\right\\}$};\n\\draw(14.5,7) node{\\small $\\psi_{w_0^\\mu}$};\n\\draw(16.5,3.7) node{\\small $\\psi_{l_1^+(\\mu) \\to l_1^-({\\lambda})}$};\n\\draw(1,8) node[above]{\\small $1$};\n\\draw(2,8) node[above]{\\small $1$};\n\\draw(3,8) node[above]{\\small $2$};\n\\draw(4,8) node[above]{\\small $3$};\n\\draw(5,8) node[above]{\\small $3$};\n\\draw(6,8) node[above]{\\small $3$};\n\\draw(7,8) node[above]{\\small $3$};\n\\draw(8,8) node[above]{\\small $2$};\n\\draw(9,8) node[above]{\\small $2$};\n\\draw(10,8) node[above]{\\small $2$};\n\\draw(11,8) node[above]{\\small $1$};\n\\draw(12,8) node[above]{\\small $1$};\n\\draw [rounded corners,color=gray] (0.6,7.5)--(2.4,7.5)--(2.4,6.1)--(0.6,6.1)--cycle;\n\\draw [rounded corners,color=gray] (3.6,7.5)--(7.4,7.5)--(7.4,6.1)--(3.6,6.1)--cycle;\n\\draw [rounded corners,color=gray] (7.6,7.5)--(10.4,7.5)--(10.4,6.1)--(7.6,6.1)--cycle;\n\\draw [rounded corners,color=gray] (10.6,7.5)--(12.4,7.5)--(12.4,6.1)--(10.6,6.1)--cycle;\n\\draw(1,8.1)--(1,7.5);\n\\draw(2,8.1)--(2,7.5);\n\\draw(3,8.1)--(3,6.1)--(4,2.5);\n\\draw(4,8.1)--(4,7.5);\n\\draw(5,8.1)--(5,7.5);\n\\draw(6,8.1)--(6,7.5);\n\\draw(7,8.1)--(7,7.5);\n\\draw(8,8.1)--(8,7.5);\n\\draw(9,8.1)--(9,7.5);\n\\draw(10,8.1)--(10,7.5);\n\\draw(11,8.1)--(11,7.5);\n\\draw(12,8.1)--(12,7.5);\n\\draw(1,6.1)--(2,2.5);\n\\draw(2,6.1)--(3,2.5);\n\\draw(4,6.1)--(5,2.5);\n\\draw(5,6.1)--(6,2.5);\n\\draw(6,6.1)--(7,2.5);\n\\draw(7,6.1)--(8,2.5);\n\\draw(8,6.1)--(9,2.5);\n\\draw(9,6.1)--(10,2.5);\n\\draw(10,6.1)--(11,2.5);\n\\draw(11,6.1)--(1,2.5);\n\\draw(12,6.1)--(12,2.5);\n\\draw(1.5,6) node[above]{\\small $w_0$};\n\\draw(5.5,6) node[above]{\\small $w_0$};\n\\draw(9,6) node[above]{\\small $w_0$};\n\\draw(11.5,6) node[above]{\\small $w_0$};\n\\draw(1,1) node[above]{\\small $1$};\n\\draw(2,1) node[above]{\\small $1$};\n\\draw(3,1) node[above]{\\small $1$};\n\\draw(4,1) node[above]{\\small $2$};\n\\draw(5,1) node[above]{\\small $3$};\n\\draw(6,1) node[above]{\\small $3$};\n\\draw(7,1) node[above]{\\small $3$};\n\\draw(8,1) node[above]{\\small $3$};\n\\draw(9,1) node[above]{\\small $2$};\n\\draw(10,1) node[above]{\\small $2$};\n\\draw(11,1) node[above]{\\small $2$};\n\\draw(12,1) node[above]{\\small $1$};\n\\end{tikzpicture}\n$$\n\n$f$ is a chain map\n------------------\n\nLet ${\\lambda}={\\lambda}^\\bde$. For $i\\in[a,b+1]$, let $q_i=q_i({\\lambda},{\\delta}^{(1)})$ be defined as in (\\[EQI\\]), and consider the cycle $$c_i=\\left\\{\n\\begin{array}{ll}\nr_i^-(\\mu)\\to l_i^-(\\mu) &\\hbox{if $i\\neq b+1$ and ${\\delta}^{(1)}_i=0$,}\\\\\nr_i^+(\\mu)\\to l_i^+(\\mu) &\\hbox{if $i\\neq b+1$ and ${\\delta}^{(1)}_i=1$,}\\\\\nr_{b+1}(\\mu)\\to l_{b+1}(\\mu) &\\hbox{if $i= b+1$.}\n\\end{array}\n\\right.$$ Let $c$ be the commuting product of cycles: $$c:=c_ac_{a+1}\\dots c_{b+1}.$$ Recall also the elements defined in (\\[EQ123\\]).", "\n\n\\[L140416\\] Suppose $i\\in [a,b]$ is such that $\\mu_i>0$ and ${\\lambda}:=\\mu-\\e_i={\\lambda}^\\bde$. Set $\\bar\\theta=(m-1){\\alpha}$, $\\bar\\mu:=\\mu-{\\delta}^{(1)}$, and $\\bar{\\lambda}:={\\lambda}-{\\delta}^{(1)}$. Then $1_{\\bj^\\mu}\\psi_{{\\lambda};i}e_{\\lambda}\\psi_{w_0^{\\lambda}}\\psi_{x(\\bde,1)}$ equals $$\\left\\{\n\\begin{array}{ll}\n1_{\\bj^\\mu} \\psi_{w_0^\\mu}\\psi_{x(\\bde+\\bolde_i^{1},1)}\\psi_{\\bde;1,i}\n+1_{\\bj^\\mu}\\psi_c \\psi_{x_{{\\delta}^{(1)}}^\\mu}\n(1_{\\alpha}\\circ 1_{\\bj^{\\bar\\mu}}\\psi_{\\bar{\\lambda};i}e_{\\bar {\\lambda}}\\psi_{w_0^{\\bar{\\lambda}}})\n &\\hbox{if ${\\delta}^{(1)}_i=0$,}\\\\\n-1_{\\bj^\\mu}\\psi_c \\psi_{x_{{\\delta}^{(1)}}^\\mu}\n(1_{\\alpha}\\circ 1_{\\bj^{\\bar\\mu}}\\psi_{\\bar{\\lambda};i}e_{\\bar {\\lambda}}\\psi_{w_0^{\\bar{\\lambda}}}) &\\hbox{if ${\\delta}^{(1)}_i=1$.}\n\\end{array}\n\\right.$$\n\nBy Lemma \\[LW0Y0\\](\\[LW0Y0ii\\]), we have $e_{\\lambda}\\psi_{w_0^{\\lambda}}=1_{\\bj^{\\lambda}}\\psi_{w_0^{\\lambda}}$. So using also Lemma \\[L290316\\], we get $$1_{\\bj^\\mu}\\psi_{{\\lambda};i}e_{\\lambda}\\psi_{w_0^{\\lambda}}\\psi_{x(\\bde,1)}=\n 1_{\\bj^\\mu}\\psi_{{\\lambda};i}1_{\\bj^{\\lambda}}\\psi_{w_0^{\\lambda}}\\psi_{x(\\bde,1)}\n=1_{\\bj^\\mu} \\psi_{w_0^\\mu}\\psi_{l_i^+(\\mu)\\to l_i^-({\\lambda})}\\psi_{x(\\bde,1)}.$$\n\nAs usual, we denote by $p_j$ the position occupied by $j$ in ${\\delta}^{(1)}$ and $q_j$ be defined as in (\\[EQI\\]). ", "By Lemma \\[LWX\\], the permutation $x(\\bde,1)$ maps $p_j$ to $q_j$ for all $j\\in[a,b+1]$, and the elements of $[l+1,d]$ increasingly to the elements of $[1,d]\\setminus Q$.\n\n[*Case 1: ${\\delta}^{(1)}_i=0$*]{}. ", "In this case we have $q_i=l_i^-({\\lambda})$. So the KLR diagram $D$ of $1_{\\bj^\\mu}\\psi_{l_i^+(\\mu)\\to l_i^-({\\lambda})}\\psi_{x(\\bde,1)}$ has an $i$-string $S$ from the position $p_i$ in the bottom to the position $l_i^+(\\mu)$ in the top, and the only $(i,i)$-crossings in $D$ will be the crossings of the string $S$ with the $m-\\mu_i$ strings which originate in the positions $L_i^-(\\mu)$ in the top. ", "The $(i+1)$-string $T$ in $D$ originating in position $p_{i+1}$ in the bottom is to the right of all $(i,i)$ crossings. ", "Pulling $T$ to the left produces error terms, which arise from opening $(i,i)$-crossings, but all of them, except the last one, amount to zero, when multiplied on the left by $1_{\\bj^\\mu} \\psi_{w_0^\\mu}$. The last error term is equal to $\\psi_{x_{{\\delta}^{(1)}}^\\mu}\n\\iota_{{\\alpha},\\bar\\theta}(1_{\\alpha}\\otimes \\psi_{l_i^+(\\bar\\mu)\\to l_i^-(\\bar{\\lambda})}))$, and the result of pulling $T$ past all $(i,i)$-crossings gives $\\psi_{x(\\bde+\\bolde_i^{1},1)}\\psi_{\\bde;1,i}$. Multiplying on the left by $1_{\\bj^\\mu} \\psi_{w_0^\\mu}$, gives $$1_{\\bj^\\mu} \\psi_{w_0^\\mu}\\psi_{x(\\bde+\\bolde_i^{1},1)}\\psi_{\\bde;1,i}+1_{\\bj^\\mu} \\psi_{w_0^\\mu}\\psi_{x_{{\\delta}^{(1)}}^\\mu}\n\\iota_{{\\alpha},\\bar\\theta}(1_{\\alpha}\\otimes \\psi_{l_i^+(\\bar\\mu)\\to l_i^i(\\bar{\\lambda})}),$$ and it remains to observe using Lemma \\[LPull\\] that $$\\psi_{w_0^\\mu}\\psi_{x_{{\\delta}^{(1)}}^\\mu}\n\\iota_{{\\alpha},\\bar\\theta}(1_{\\alpha}\\otimes \\psi_{l_i^+(\\bar\\mu)\\to l_i^i(\\bar{\\lambda})})=1_{\\bj^\\mu}\\psi_c \\psi_{x_{{\\delta}^{(1)}}^\\mu}\n(1_{\\alpha}\\circ 1_{\\bj^{\\bar\\mu}}\\psi_{\\bar{\\lambda};i}e_{\\bar {\\lambda}}\\psi_{w_0^{\\bar{\\lambda}}}).$$\n\n[*Case 2: ${\\delta}^{(1)}_i=1$.*]{} Let $D$ be the KLR diagram of $1_{\\bj^\\mu}\\psi_{l_i^+(\\mu)\\to l_i^-({\\lambda})}\\psi_{x(\\bde,1)}$. Let $S$ be the $i$-string originating in the position $l^+_{i}(\\mu)$ in the top row of $D$, and $T$ be the $(i+1)$-string originating in the position $p_{i+1}$ in the bottom row of $D$. The quadratic relation on these strings produces a difference of two terms, one with a dot on $S$ and the other with a dot on $T$. The term with a dot on $T$ equals $0$ after multiplying on the left by $1_{\\bj^\\mu} \\psi_{w_0^\\mu}$. The term with a dot on $S$, when multiplied on the left by $1_{\\bj^\\mu} \\psi_{w_0^\\mu}$, yields $$-1_{\\bj^\\mu} \\psi_{w_0^\\mu}\\psi_{x_{{\\delta}^{(1)}}^\\mu}\n\\iota_{{\\alpha},\\bar\\theta}(1_{\\alpha}\\otimes \\psi_{l_i^+(\\bar\\mu)\\to l_i^-(\\bar{\\lambda})})=-1_{\\bj^\\mu}\\psi_c \\psi_{x_{{\\delta}^{(1)}}^\\mu}\n(1_{\\alpha}\\circ 1_{\\bj^{\\bar\\mu}}\\psi_{\\bar{\\lambda};i}e_{\\bar {\\lambda}}\\psi_{w_0^{\\bar{\\lambda}}}),$$ where we have used Lemma \\[LPull\\] for the last equality.", "\n\nWe illustrate Lemma \\[L140416\\] diagramatically. ", "Let $a=1$, $b=2$, $m=4$, $\\mu=(2,3)$ and $\\bde=((1,0),(0,1),(1,1),(0,1))$.\n\nFirst, take $i=2$. Then ${\\delta}_1^{(2)}=0$ and Lemma \\[L140416\\] claims the following: $$ \\begin{tikzpicture}[baseline=6mm,black,line width=1pt, scale=0.32,\n draw/.append style={rounded corners},\n every node/.append style={font=\\fontsize{5}{5}\\selectfont}] \\tikzset{baseline=8mm}\n\\draw(1,8) node[above]{\\small $1$};\n\\draw(2,8) node[above]{\\small $1$};\n\\draw(3,8) node[above]{\\small $2$};\n\\draw(4,8) node[above]{\\small $3$};\n\\draw(5,8) node[above]{\\small $3$};\n\\draw(6,8) node[above]{\\small $3$};\n\\draw(7,8) node[above]{\\small $3$};\n\\draw(8,8) node[above]{\\small $2$};\n\\draw(9,8) node[above]{\\small $2$};\n\\draw(10,8) node[above]{\\small $2$};\n\\draw(11,8) node[above]{\\small $1$};\n\\draw(12,8) node[above]{\\small $1$};\n\\draw [rounded corners,color=gray] (0.6,4.5)--(2.4,4.5)--(2.4,3.1)--(0.6,3.1)--cycle;\n\\draw [rounded corners,color=gray] (2.6,4.5)--(4.4,4.5)--(4.4,3.1)--(2.6,3.1)--cycle;\n\\draw [rounded corners,color=gray] (4.6,4.5)--(8.4,4.5)--(8.4,3.1)--(4.6,3.1)--cycle;\n\\draw [rounded corners,color=gray] (8.6,4.5)--(10.4,4.5)--(10.4,3.1)--(8.6,3.1)--cycle;\n\\draw [rounded corners,color=gray] (10.6,4.5)--(12.4,4.5)--(12.4,3.1)--(10.6,3.1)--cycle;\n\\draw(1,8.1)--(1,4.5);\n\\draw(2,8.1)--(2,4.5);\n\\draw(3,8.1)--(3,4.5);\n\\draw(4,8.1)--(5,4.5);\n\\draw(5,8.1)--(6,4.5);\n\\draw(6,8.1)--(7,4.5);\n\\draw(7,8.1)--(8,4.5);\n\\draw(8,8.1)--(9,4.5);\n\\draw(9,8.1)--(10,4.5);\n\\draw(10,8.1)--(4,4.5);\n\\draw(11,8.1)--(11,4.5);\n\\draw(12,8.1)--(12,4.5);\n\\draw(1,3.1)--(1,2.5);\n\\draw(2,3.1)--(2,2.5);\n\\draw(3,3.1)--(3,2.5);\n\\draw(4,3.1)--(4,2.5);\n\\draw(5,3.1)--(5,2.5);\n\\draw(6,3.1)--(6,2.5);\n\\draw(7,3.1)--(7,2.5);\n\\draw(8,3.1)--(8,2.5);\n\\draw(9,3.1)--(9,2.5);\n\\draw(10,3.1)--(10,2.5);\n\\draw(11,3.1)--(11,2.5);\n\\draw(12,3.1)--(12,2.5);\n\\draw [rounded corners,color=gray] (0.6,2.5)--(2.4,2.5)--(2.4,1.1)--(0.6,1.1)--cycle;\n\\draw [rounded corners,color=gray] (2.6,2.5)--(4.4,2.5)--(4.4,1.1)--(2.6,1.1)--cycle;\n\\draw [rounded corners,color=gray] (4.6,2.5)--(8.4,2.5)--(8.4,1.1)--(4.6,1.1)--cycle;\n\\draw [rounded corners,color=gray] (8.6,2.5)--(10.4,2.5)--(10.4,1.1)--(8.6,1.1)--cycle;\n\\draw [rounded corners,color=gray] (10.6,2.5)--(12.4,2.5)--(12.4,1.1)--(10.6,1.1)--cycle;\n\\draw(1.5,1) node[above]{\\small $w_0$};\n\\draw(3.5,1) node[above]{\\small $w_0$};\n\\draw(6.5,1) node[above]{\\small $w_0$};\n\\draw(9.5,1) node[above]{\\small $w_0$};\n\\draw(11.5,1) node[above]{\\small $w_0$};\n\\draw(1,3) node[above]{\\small $1$};\n\\draw(2,3) node[above]{\\small $1$};\n\\draw(3,3) node[above]{\\small $2$};\n\\draw(4,3) node[above]{\\small $2$};\n\\draw(5,3) node[above]{\\small $3$};\n\\draw(6,3) node[above]{\\small $3$};\n\\draw(7,3) node[above]{\\small $3$};\n\\draw(8,3) node[above]{\\small $3$};\n\\draw(9,3) node[above]{\\small $2$};\n\\draw(10,3) node[above]{\\small $2$};\n\\draw(11,3) node[above]{\\small $1$};\n\\draw(12,3) node[above]{\\small $1$};\n\\draw(1,1.1)--(4,-2);\n\\draw(2,1.1)--(5,-2);\n\\draw(3,1.1)--(1,-2);\n\\draw(4,1.1)--(6,-2);\n\\draw(5,1.1)--(2,-2);\n\\draw(6,1.1)--(7,-2);\n\\draw(7,1.1)--(8,-2);\n\\draw(8,1.1)--(9,-2);\n\\draw(9,1.1)--(10,-2);\n\\draw(10,1.1)--(11,-2);\n\\draw(11,1.1)--(3,-2);\n\\draw(12,1.1)--(12,-2);\n\n\\draw(1,-2.8) node{\\small $2$};\n\\draw(2,-2.8) node{\\small $3$};\n\\draw(3,-2.8) node{\\small $1$};\n\\draw(4,-2.8) node{\\small $1$};\n\\draw(5,-2.8) node{\\small $1$};\n\\draw(6,-2.8) node{\\small $2$};\n\\draw(7,-2.8) node{\\small $3$};\n\\draw(8,-2.8) node{\\small $3$};\n\\draw(9,-2.8) node{\\small $3$};\n\\draw(10,-2.8) node{\\small $2$};\n\\draw(11,-2.8) node{\\small $2$};\n\\draw(12,-2.8) node{\\small $1$};\n\\end{tikzpicture}\n\n=\n \\begin{tikzpicture}[baseline=6mm,black,line width=1pt, scale=0.32,\n draw/.append style={rounded corners},\n every node/.append style={font=\\fontsize{5}{5}\\selectfont}] \\tikzset{baseline=8mm}\n\\draw(1,8) node[above]{\\small $1$};\n\\draw(2,8) node[above]{\\small $1$};\n\\draw(3,8) node[above]{\\small $2$};\n\\draw(4,8) node[above]{\\small $3$};\n\\draw(5,8) node[above]{\\small $3$};\n\\draw(6,8) node[above]{\\small $3$};\n\\draw(7,8) node[above]{\\small $3$};\n\\draw(8,8) node[above]{\\small $2$};\n\\draw(9,8) node[above]{\\small $2$};\n\\draw(10,8) node[above]{\\small $2$};\n\\draw(11,8) node[above]{\\small $1$};\n\\draw(12,8) node[above]{\\small $1$};\n\\draw(1,8.1)--(1,7.5);\n\\draw(2,8.1)--(2,7.5);\n\\draw(3,8.1)--(3,6)--(6,2.5);\n\\draw(4,8.1)--(4,7.5);\n\\draw(5,8.1)--(5,7.5);\n\\draw(6,8.1)--(6,7.5);\n\\draw(7,8.1)--(7,7.5);\n\\draw(8,8.1)--(8,7.5);\n\\draw(9,8.1)--(9,7.5);\n\\draw(10,8.1)--(10,7.5);\n\\draw(11,8.1)--(11,7.5);\n\\draw(12,8.1)--(12,7.5);\n\\draw(1,1) node[above]{\\small $3$};\n\\draw(2,1) node[above]{\\small $2$};\n\\draw(3,1) node[above]{\\small $1$};\n\\draw(4,1) node[above]{\\small $1$};\n\\draw(5,1) node[above]{\\small $1$};\n\\draw(6,1) node[above]{\\small $2$};\n\\draw(7,1) node[above]{\\small $3$};\n\\draw(8,1) node[above]{\\small $3$};\n\\draw(9,1) node[above]{\\small $3$};\n\\draw(10,1) node[above]{\\small $2$};\n\\draw(11,1) node[above]{\\small $2$};\n\\draw(12,1) node[above]{\\small $1$};\n\\draw(1,1.1)--(2,-2.0);\n\\draw(2,1.1)--(1,-2.0);\n\\draw(3,1.1)--(3,-2.0);\n\\draw(4,1.1)--(4,-2.0);\n\\draw(5,1.1)--(5,-2.0);\n\\draw(6,1.1)--(6,-2.0);\n\\draw(7,1.1)--(7,-2.0);\n\\draw(8,1.1)--(8,-2.0);\n\\draw(9,1.1)--(9,-2.0);\n\\draw(10,1.1)--(10,-2.0);\n\\draw(11,1.1)--(11,-2.0);\n\\draw(12,1.1)--(12,-2.0);\n\\draw(1,6.1)--(4,2.5);\n\\draw(2,6.1)--(5,2.5);\n\\draw(4,6.1)--(1,2.5);\n\\draw(5,6.1)--(7,2.5);\n\\draw(6,6.1)--(8,2.5);\n\\draw(7,6.1)--(9,2.5);\n\\draw(8,6.1)--(2,2.5);\n\\draw(9,6.1)--(10,2.5);\n\\draw(10,6.1)--(11,2.5);\n\\draw(11,6.1)--(3,2.5);\n\\draw(12,6.1)--(12,2.5);\n\\draw [rounded corners,color=gray] (0.6,7.5)--(2.4,7.5)--(2.4,6.1)--(0.6,6.1)--cycle;\n\\draw [rounded corners,color=gray] (3.6,7.5)--(7.4,7.5)--(7.4,6.1)--(3.6,6.1)--cycle;\n\\draw [rounded corners,color=gray] (7.6,7.5)--(10.4,7.5)--(10.4,6.1)--(7.6,6.1)--cycle;\n\\draw [rounded corners,color=gray] (10.6,7.5)--(12.4,7.5)--(12.4,6.1)--(10.6,6.1)--cycle;\n\\draw(1.5,6) node[above]{\\small $w_0$};\n\\draw(5.5,6) node[above]{\\small $w_0$};\n\\draw(9,6) node[above]{\\small $w_0$};\n\\draw(11.5,6) node[above]{\\small $w_0$};\n\\draw(1,-2.8) node{\\small $2$};\n\\draw(2,-2.8) node{\\small $3$};\n\\draw(3,-2.8) node{\\small $1$};\n\\draw(4,-2.8) node{\\small $1$};\n\\draw(5,-2.8) node{\\small $1$};\n\\draw(6,-2.8) node{\\small $2$};\n\\draw(7,-2.8) node{\\small $3$};\n\\draw(8,-2.8) node{\\small $3$};\n\\draw(9,-2.8) node{\\small $3$};\n\\draw(10,-2.8) node{\\small $2$};\n\\draw(11,-2.8) node{\\small $2$};\n\\draw(12,-2.8) node{\\small $1$};\n\\end{tikzpicture}\n\n+\n \\begin{tikzpicture}[baseline=6mm,black,line width=1pt, scale=0.32,\n draw/.append style={rounded corners},\n every node/.append style={font=\\fontsize{5}{5}\\selectfont}] \\tikzset{baseline=8mm}\n\\draw(1,8) node[above]{\\small $1$};\n\\draw(2,8) node[above]{\\small $1$};\n\\draw(3,8) node[above]{\\small $2$};\n\\draw(4,8) node[above]{\\small $3$};\n\\draw(5,8) node[above]{\\small $3$};\n\\draw(6,8) node[above]{\\small $3$};\n\\draw(7,8) node[above]{\\small $3$};\n\\draw(8,8) node[above]{\\small $2$};\n\\draw(9,8) node[above]{\\small $2$};\n\\draw(10,8) node[above]{\\small $2$};\n\\draw(11,8) node[above]{\\small $1$};\n\\draw(12,8) node[above]{\\small $1$};\n\\draw(1,8.1)--(4,4.5);\n\\draw(2,8.1)--(5,4.5);\n\\draw(3,8.1)--(1,4.5);\n\\draw(4,8.1)--(6,4.5);\n\\draw(5,8.1)--(7,4.5);\n\\draw(6,8.1)--(8,4.5);\n\\draw(7,8.1)--(2,4.5);\n\\draw(8,8.1)--(9,4.5);\n\\draw(9,8.1)--(10,4.5);\n\\draw(10,8.1)--(11,4.5);\n\\draw(11,8.1)--(12,4.5);\n\\draw(12,8.1)--(3,4.5);\n\\draw(1,3) node[above]{\\small $2$};\n\\draw(2,3) node[above]{\\small $3$};\n\\draw(3,3) node[above]{\\small $1$};\n\\draw(4,3) node[above]{\\small $1$};\n\\draw(5,3) node[above]{\\small $1$};\n\\draw(6,3) node[above]{\\small $3$};\n\\draw(7,3) node[above]{\\small $3$};\n\\draw(8,3) node[above]{\\small $3$};\n\\draw(9,3) node[above]{\\small $2$};\n\\draw(10,3) node[above]{\\small $2$};\n\\draw(11,3) node[above]{\\small $2$};\n\\draw(12,3) node[above]{\\small $1$};\n\\draw(1,3.1)--(1,-1.9);\n\\draw(2,3.1)--(2,-1.9);\n\\draw(3,3.1)--(3,-1.9);\n\\draw(4,3.1)--(4,0.7);\n\\draw(5,3.1)--(5,0.7);\n\\draw(6,3.1)--(7,0.7);\n\\draw(7,3.1)--(8,0.7);\n\\draw(8,3.1)--(9,0.7);\n\\draw(9,3.1)--(10,0.7);\n\\draw(10,3.1)--(11,0.7);\n\\draw(11,3.1)--(6,0.7);\n\\draw(12,3.1)--(12,0.7);\n\\draw(4,-0.7)--(4,-1.9);\n\\draw(5,-0.7)--(5,-1.9);\n\\draw(6,-0.7)--(6,-3.1);\n\\draw(7,-0.7)--(7,-1.9);\n\\draw(8,-0.7)--(8,-1.9);\n\\draw(9,-0.7)--(9,-1.9);\n\\draw(10,-0.7)--(10,-1.9);\n\\draw(11,-0.7)--(11,-1.9);\n\\draw(12,-0.7)--(12,-3.1);\n\\draw [rounded corners,color=gray] (3.6,0.7)--(5.4,0.7)--(5.4,-0.7)--(3.6,-0.7)--cycle;\n\\draw [rounded corners,color=gray] (6.6,0.7)--(9.4,0.7)--(9.4,-0.7)--(6.6,-0.7)--cycle;\n\\draw [rounded corners,color=gray] (9.6,0.7)--(11.4,0.7)--(11.4,-0.7)--(9.6,-0.7)--cycle;\n\\draw [rounded corners,color=gray] (3.6,-1.9)--(5.4,-1.9)--(5.4,-3.3)--(3.6,-3.3)--cycle;\n\\draw [rounded corners,color=gray] (6.6,-1.9)--(9.4,-1.9)--(9.4,-3.3)--(6.6,-3.3)--cycle;\n\\draw [rounded corners,color=gray] (9.6,-1.9)--(11.4,-1.9)--(11.4,-3.3)--(9.6,-3.3)--cycle;\n\\draw(4.5,-2.6) node{\\small $w_0$};\n\\draw(8,-2.6) node{\\small $w_0$};\n\\draw(10.5,-2.6) node{\\small $w_0$};\n\\draw(1,-2.8) node{\\small $2$};\n\\draw(2,-2.8) node{\\small $3$};\n\\draw(3,-2.8) node{\\small $1$};\n\\draw(4,-0.8) node[above]{\\small $1$};\n\\draw(5,-0.8) node[above]{\\small $1$};\n\\draw(6,-0.8) node[above]{\\small $2$};\n\\draw(7,-0.8) node[above]{\\small $3$};\n\\draw(8,-0.8) node[above]{\\small $3$};\n\\draw(9,-0.8) node[above]{\\small $3$};\n\\draw(10,-0.8) node[above]{\\small $2$};\n\\draw(11,-0.8) node[above]{\\small $2$};\n\\draw(12,-0.8) node[above]{\\small $1$};\n\\end{tikzpicture}\n$$\n\nOn the other hand, if $i=1$, we have ${\\delta}_1^{(1)}=1$, and Lemma \\[L140416\\] posits the following equality. ", "$$ \\begin{tikzpicture}[baseline=6mm,black,line width=1pt, scale=0.32,\n draw/.append style={rounded corners},\n every node/.append style={font=\\fontsize{5}{5}\\selectfont}] \\tikzset{baseline=8mm}\n\\draw(1,8) node[above]{\\small $1$};\n\\draw(2,8) node[above]{\\small $1$};\n\\draw(3,8) node[above]{\\small $2$};\n\\draw(4,8) node[above]{\\small $3$};\n\\draw(5,8) node[above]{\\small $3$};\n\\draw(6,8) node[above]{\\small $3$};\n\\draw(7,8) node[above]{\\small $3$};\n\\draw(8,8) node[above]{\\small $2$};\n\\draw(9,8) node[above]{\\small $2$};\n\\draw(10,8) node[above]{\\small $2$};\n\\draw(11,8) node[above]{\\small $1$};\n\\draw(12,8) node[above]{\\small $1$};\n\\draw [rounded corners,color=gray] (0.6,4.5)--(3.4,4.5)--(3.4,3.1)--(0.6,3.1)--cycle;\n\\draw [rounded corners,color=gray] (4.6,4.5)--(8.4,4.5)--(8.4,3.1)--(4.6,3.1)--cycle;\n\\draw [rounded corners,color=gray] (8.6,4.5)--(11.4,4.5)--(11.4,3.1)--(8.6,3.1)--cycle;\n\\draw(1,8.1)--(1,4.5);\n\\draw(2,8.1)--(2,4.5);\n\\draw(3,8.1)--(4,4.5);\n\\draw(4,8.1)--(5,4.5);\n\\draw(5,8.1)--(6,4.5);\n\\draw(6,8.1)--(7,4.5);\n\\draw(7,8.1)--(8,4.5);\n\\draw(8,8.1)--(9,4.5);\n\\draw(9,8.1)--(10,4.5);\n\\draw(10,8.1)--(11,4.5);\n\\draw(11,8.1)--(12,4.5);\n\\draw(12,8.1)--(3,4.5);\n\\draw(1,3.1)--(1,2.5);\n\\draw(2,3.1)--(2,2.5);\n\\draw(3,3.1)--(3,2.5);\n\\draw(4,3.1)--(4,1.1)--(1,-2);\n\\draw(5,3.1)--(5,2.5);\n\\draw(6,3.1)--(6,2.5);\n\\draw(7,3.1)--(7,2.5);\n\\draw(8,3.1)--(8,2.5);\n\\draw(9,3.1)--(9,2.5);\n\\draw(10,3.1)--(10,2.5);\n\\draw(11,3.1)--(11,2.5);\n\\draw(12,3.1)--(12,1.1)--(3,-2);\n\\draw [rounded corners,color=gray] (0.6,2.5)--(3.4,2.5)--(3.4,1.1)--(0.6,1.1)--cycle;\n\\draw [rounded corners,color=gray] (4.6,2.5)--(8.4,2.5)--(8.4,1.1)--(4.6,1.1)--cycle;\n\\draw [rounded corners,color=gray] (8.6,2.5)--(11.4,2.5)--(11.4,1.1)--(8.6,1.1)--cycle;\n\\draw(2,1) node[above]{\\small $w_0$};\n\\draw(6.5,1) node[above]{\\small $w_0$};\n\\draw(6.5,1) node[above]{\\small $w_0$};\n\\draw(10,1) node[above]{\\small $w_0$};\n\\draw(1,3) node[above]{\\small $1$};\n\\draw(2,3) node[above]{\\small $1$};\n\\draw(3,3) node[above]{\\small $1$};\n\\draw(4,3) node[above]{\\small $2$};\n\\draw(5,3) node[above]{\\small $3$};\n\\draw(6,3) node[above]{\\small $3$};\n\\draw(7,3) node[above]{\\small $3$};\n\\draw(8,3) node[above]{\\small $3$};\n\\draw(9,3) node[above]{\\small $2$};\n\\draw(10,3) node[above]{\\small $2$};\n\\draw(11,3) node[above]{\\small $2$};\n\\draw(12,3) node[above]{\\small $1$};\n\\draw(1,1.1)--(4,-2);\n\\draw(2,1.1)--(5,-2);\n\\draw(3,1.1)--(6,-2);\n\\draw(5,1.1)--(2,-2);\n\\draw(6,1.1)--(7,-2);\n\\draw(7,1.1)--(8,-2);\n\\draw(8,1.1)--(9,-2);\n\\draw(9,1.1)--(10,-2);\n\\draw(10,1.1)--(11,-2);\n\\draw(11,1.1)--(12,-2);\n\n\\draw(1,-2.8) node{\\small $2$};\n\\draw(2,-2.8) node{\\small $3$};\n\\draw(3,-2.8) node{\\small $1$};\n\\draw(4,-2.8) node{\\small $1$};\n\\draw(5,-2.8) node{\\small $1$};\n\\draw(6,-2.8) node{\\small $1$};\n\\draw(7,-2.8) node{\\small $3$};\n\\draw(8,-2.8) node{\\small $3$};\n\\draw(9,-2.8) node{\\small $3$};\n\\draw(10,-2.8) node{\\small $2$};\n\\draw(11,-2.8) node{\\small $2$};\n\\draw(12,-2.8) node{\\small $2$};\n\\end{tikzpicture}\n\n=\n \\begin{tikzpicture}[baseline=6mm,black,line width=1pt, scale=0.32,\n draw/.append style={rounded corners},\n every node/.append style={font=\\fontsize{5}{5}\\selectfont}] \\tikzset{baseline=8mm}\n\\draw(1,8) node[above]{\\small $1$};\n\\draw(2,8) node[above]{\\small $1$};\n\\draw(3,8) node[above]{\\small $2$};\n\\draw(4,8) node[above]{\\small $3$};\n\\draw(5,8) node[above]{\\small $3$};\n\\draw(6,8) node[above]{\\small $3$};\n\\draw(7,8) node[above]{\\small $3$};\n\\draw(8,8) node[above]{\\small $2$};\n\\draw(9,8) node[above]{\\small $2$};\n\\draw(10,8) node[above]{\\small $2$};\n\\draw(11,8) node[above]{\\small $1$};\n\\draw(12,8) node[above]{\\small $1$};\n\\draw(1,3) node[above]{\\small $2$};\n\\draw(2,3) node[above]{\\small $3$};\n\\draw(3,3) node[above]{\\small $1$};\n\\draw(4,3) node[above]{\\small $1$};\n\\draw(5,3) node[above]{\\small $1$};\n\\draw(6,3) node[above]{\\small $3$};\n\\draw(7,3) node[above]{\\small $3$};\n\\draw(8,3) node[above]{\\small $3$};\n\\draw(9,3) node[above]{\\small $2$};\n\\draw(10,3) node[above]{\\small $2$};\n\\draw(11,3) node[above]{\\small $2$};\n\\draw(12,3) node[above]{\\small $1$};\n\\draw(1,3.1)--(1,-2);\n\\draw(2,3.1)--(2,-2);\n\\draw(3,3.1)--(3,-2);\n\\draw(4,3.1)--(4,-0.1);\n\\draw(5,3.1)--(5,-0.1);\n\\draw(6,3.1)--(7,-0.1);\n\\draw(7,3.1)--(8,-0.1);\n\\draw(8,3.1)--(9,-0.1);\n\\draw(9,3.1)--(10,-0.1);\n\\draw(10,3.1)--(11,-0.1);\n\\draw(11,3.1)--(12,-0.1);\n\\draw(12,3.1)--(6,-0.1);\n\\draw(4,-1.5)--(4,-1.7);\n\\draw(5,-1.5)--(5,-1.7);\n\\draw(6,-1.5)--(6,-1.7);\n\\draw(7,-1.5)--(7,-1.7);\n\\draw(8,-1.5)--(8,-1.7);\n\\draw(9,-1.5)--(9,-1.7);\n\\draw(10,-1.5)--(10,-1.7);\n\\draw(11,-1.5)--(11,-1.7);\n\\draw(12,-1.5)--(12,-1.7);\n\\draw(1,8.1)--(1,6.3)--(4,4.5);\n\\draw(2,8.1)--(2,6.3)--(5,4.5);\n\\draw(3,8.1)--(3,6.3)--(1,4.5);\n\\draw(4,8.1)--(5,6.3)--(6,4.5);\n\\draw(5,8.1)--(6,6.3)--(7,4.5);\n\\draw(6,8.1)--(7,6.3)--(8,4.5);\n\\draw(7,8.1)--(4,6.3)--(2,4.5);\n\\draw(8,8.1)--(8,6.3)--(9,4.5);\n\\draw(9,8.1)--(9,6.3)--(10,4.5);\n\\draw(10,8.1)--(10,6.3)--(11,4.5);\n\\draw(11,8.1)--(12,6.3)--(12,4.5);\n\\draw(12,8.1)--(11,6.3)--(3,4.5);\n\\draw [rounded corners,color=gray] (3.6,-0.1)--(6.4,-0.1)--(6.4,-1.5)--(3.6,-1.5)--cycle;\n\\draw [rounded corners,color=gray] (6.6,-0.1)--(9.4,-0.1)--(9.4,-1.5)--(6.6,-1.5)--cycle;\n\\draw [rounded corners,color=gray] (9.6,-0.1)--(12.4,-0.1)--(12.4,-1.5)--(9.6,-1.5)--cycle;\n\\draw [rounded corners,color=gray] (3.6,-1.7)--(6.4,-1.7)--(6.4,-3.1)--(3.6,-3.1)--cycle;\n\\draw [rounded corners,color=gray] (6.6,-1.7)--(9.4,-1.7)--(9.4,-3.1)--(6.6,-3.1)--cycle;\n\\draw [rounded corners,color=gray] (9.6,-1.7)--(12.4,-1.7)--(12.4,-3.1)--(9.6,-3.1)--cycle;\n\\draw(5,-3.3) node[above]{\\small $w_0$};\n\\draw(8,-3.3) node[above]{\\small $w_0$};\n\\draw(11,-3.3) node[above]{\\small $w_0$};\n\\draw(0,2) node[above]{\\small $-$};\n\\draw(1,-2.8) node{\\small $2$};\n\\draw(2,-2.8) node{\\small $3$};\n\\draw(3,-2.8) node{\\small $1$};\n\\draw(4,-0.8) node{\\small $1$};\n\\draw(5,-0.8) node{\\small $1$};\n\\draw(6,-0.8) node{\\small $1$};\n\\draw(7,-0.8) node{\\small $3$};\n\\draw(8,-0.8) node{\\small $3$};\n\\draw(9,-0.8) node{\\small $3$};\n\\draw(10,-0.8) node{\\small $2$};\n\\draw(11,-0.8) node{\\small $2$};\n\\draw(12,-0.8) node{\\small $2$};\n\\end{tikzpicture}\n$$\n\n\\[C160416\\] If $\\mu_i>0$ for some $i\\in[a,b]$ and ${\\lambda}:=\\mu-\\e_i={\\lambda}^\\bde$, then $$\\label{E150416}\n1_{\\bj^\\mu}\\psi_{{\\lambda};i}e_{\\lambda}\\psi_{w_0^{\\lambda}}\\psi_{w(\\bde)}\n=\\sum_{r\\in[1,m]:\\ {\\delta}_i^{(r)}=0} (-1)^{\\sum_{s=1}^{r-1} {\\delta}_i^{(s)}}1_{\\bj^\\mu} \\psi_{w_0^\\mu}\\psi_{w(\\bde+\\bolde_i^{r})}\\psi_{\\bde;r,i}.$$\n\nThe proof is by induction on $m$, the induction base $m=1$ being obvious. ", "Let $\\bar\\bde:=({\\delta}^{(2)},\\dots,{\\delta}^{(m)})$, $\\bar\\theta=(m-1){\\alpha}$, $\\bar\\mu:=\\mu-{\\delta}^{(1)}$, and $\\bar{\\lambda}:={\\lambda}-{\\delta}^{(1)}$. By (\\[WPsiW\\]), we have $$\\label{E200416}\n1_{\\bj^\\mu}\\psi_{{\\lambda};i}e_{\\lambda}\\psi_{w_0^{\\lambda}}\\psi_{w(\\bde)}=1_{\\bj^\\mu}\\psi_{{\\lambda};i}e_{\\lambda}\\psi_{w_0^{\\lambda}}\\psi_{x(\\bde,1)}\\psi_{x(\\bde,2)}\\dots \\psi_{x(\\bde,m-1)}.$$ Now we apply Lemma \\[L140416\\]. ", "We consider the case ${\\delta}_i^{(1)}=0$, the case ${\\delta}_i^{(1)}=1$ being similar. ", "Then we get the following expression for the right hand side of (\\[E200416\\]): $$\\big(1_{\\bj^\\mu} \\psi_{w_0^\\mu}\\psi_{x(\\bde+\\bolde_i^{1},1)}\\psi_{\\bde;1,i}\n+1_{\\bj^\\mu}\\psi_c \\psi_{x_{{\\delta}^{(1)}}^\\mu}\n(1_{\\alpha}\\circ 1_{\\bj^{\\bar\\mu}}\\psi_{\\bar{\\lambda};i}e_{\\bar {\\lambda}}\\psi_{w_0^{\\bar{\\lambda}}})\\big)\n\\psi_{x(\\bde,2)}\\dots \\psi_{x(\\bde,m-1)}.$$ Opening parentheses, we get two summands $S_1+S_2$. Note that $$\\begin{aligned}\nS_1&=1_{\\bj^\\mu} \\psi_{w_0^\\mu}\\psi_{x(\\bde+\\bolde_i^{1},1)}\\psi_{\\bde;1,i}\\psi_{x(\\bde,2)}\\dots \\psi_{x(\\bde,m-1)}\n\\\\\n&= 1_{\\bj^\\mu} \\psi_{w_0^\\mu}\\psi_{x(\\bde+\\bolde_i^{1},1)}\\psi_{x(\\bde,2)}\\dots \\psi_{x(\\bde,m-1)}\\psi_{\\bde;1,i}\n\\\\\n&= 1_{\\bj^\\mu} \\psi_{w_0^\\mu}\\psi_{w(\\bde+\\bolde_i^{1})}\\psi_{\\bde;1,i}.\\end{aligned}$$ Moreover, using the inductive assumption for the third equality below, we get that $S_2$ equals $$\\begin{aligned}\n&1_{\\bj^\\mu}\\psi_c \\psi_{x_{{\\delta}^{(1)}}^\\mu}\n(1_{\\alpha}\\circ 1_{\\bj^{\\bar\\mu}}\\psi_{\\bar{\\lambda};i}e_{\\bar {\\lambda}}\\psi_{w_0^{\\bar{\\lambda}}})\\psi_{x(\\bde,2)}\\dots \\psi_{x(\\bde,m-1)}\n\\\\\n=& 1_{\\bj^\\mu}\\psi_c \\psi_{x_{{\\delta}^{(1)}}^\\mu}\n(1_{\\alpha}\\circ 1_{\\bj^{\\bar\\mu}}\\psi_{\\bar{\\lambda};i}e_{\\bar {\\lambda}}\\psi_{w_0^{\\bar{\\lambda}}}\\psi_{x(\\bar\\bde,1)}\\dots \\psi_{x(\\bar \\bde,m-2)})\n\\\\\n=& 1_{\\bj^\\mu}\\psi_c \\psi_{x_{{\\delta}^{(1)}}^\\mu}\n(1_{\\alpha}\\circ 1_{\\bj^{\\bar\\mu}}\\psi_{\\bar{\\lambda};i}e_{\\bar {\\lambda}}\\psi_{w_0^{\\bar{\\lambda}}}\\psi_{w(\\bar\\bde)})\n\\\\\n=& 1_{\\bj^\\mu}\\psi_c \\psi_{x_{{\\delta}^{(1)}}^\\mu}\n\\big(1_{\\alpha}\\circ \\sum_{r\\in[2,m]:\\ {\\delta}_i^{(r)}=0} (-1)^{\\sum_{s=2}^{r-1} {\\delta}_i^{(s)}}1_{\\bj^{\\bar\\mu}} \\psi_{w_0^{\\bar \\mu}}\\psi_{w(\\bar \\bde+\\bolde_i^{r-1})}\\psi_{\\bar\\bde;r-1,i}\\big).\\end{aligned}$$ As ${\\delta}_i^{(1)}=0$, we have $\\sum_{s=2}^{r-1} {\\delta}_i^{(s)}=\\sum_{s=1}^{r-1} {\\delta}_i^{(s)}$. So $$\\begin{aligned}\n&\\iota_{{\\alpha},\\bar\\theta}\\big(1_{\\alpha}\\otimes \\sum_{r\\in[2,m]:\\ {\\delta}_i^{(r)}=0} (-1)^{\\sum_{s=2}^{r-1} {\\delta}_i^{(s)}}1_{\\bj^{\\bar\\mu}} \\psi_{w_0^{\\bar \\mu}}\\psi_{w(\\bar \\bde+\\bolde_i^{r-1})}\\psi_{\\bar\\bde;r-1,i}\\big)\n\\\\\n=&\\sum_{r\\in[2,m]:\\ {\\delta}_i^{(r)}=0} (-1)^{\\sum_{s=1}^{r-1} {\\delta}_i^{(s)}}\\iota_{{\\alpha},\\bar\\theta}\\big(1_{\\alpha}\\otimes 1_{\\bj^{\\bar\\mu}} \\psi_{w_0^{\\bar \\mu}}\\bigg(\\prod_{t=1}^{m-2}\\psi_{x(\\bar \\bde+\\bolde_i^{r-1},t)}\\bigg)\\psi_{\\bar\\bde;r-1,i}\\big)\n\\\\\n=&\\sum_{r\\in[2,m]:\\ {\\delta}_i^{(r)}=0} (-1)^{\\sum_{s=1}^{r-1} {\\delta}_i^{(s)}}\\iota_{{\\alpha},\\bar\\theta}\\big(1_{\\alpha}\\otimes 1_{\\bj^{\\bar\\mu}} \\psi_{w_0^{\\bar \\mu}}\\big)\\bigg(\\prod_{t=2}^{m-1}\\psi_{x(\\bde+\\bolde_i^{r},t)}\\bigg)\\psi_{\\bde;r,i}.\\end{aligned}$$ Moreover, $$\\psi_{x_{{\\delta}^{(1)}}^\\mu}\\prod_{t=2}^{m-1}\\psi_{x(\\bde+\\bolde_i^{r},t)}\n=\\psi_{x(\\bde+\\bolde_i^{r},1)}\\prod_{t=2}^{m-1}\\psi_{x(\\bde+\\bolde_i^{r},t)}=\\psi_{w(\\bde+\\bolde_i^{r})}.$$ So $S_2$ equals $$\\begin{aligned}\n& \\sum_{r\\in[2,m]:\\ {\\delta}_i^{(r)}=0} (-1)^{\\sum_{s=1}^{r-1} {\\delta}_i^{(s)}} 1_{\\bj^\\mu}\\psi_c \\psi_{x_{{\\delta}^{(1)}}^\\mu}\n\\iota_{{\\alpha},\\bar\\theta}(1_{\\alpha}\\otimes 1_{\\bj^{\\bar\\mu}} \\psi_{w_0^{\\bar \\mu}})\\bigg(\\prod_{t=2}^{m-1}\\psi_{x(\\bde+\\bolde_i^{r},t)}\\bigg)\\psi_{\\bde;r,i}\n\\\\\n=& \\sum_{r\\in[2,m]:\\ {\\delta}_i^{(r)}=0} (-1)^{\\sum_{s=1}^{r-1} {\\delta}_i^{(s)}} 1_{\\bj^\\mu}\\psi_{w_0^\\mu} \\psi_{x_{{\\delta}^{(1)}}^\\mu}\n\\bigg(\\prod_{t=2}^{m-1}\\psi_{x(\\bde+\\bolde_i^{r},t)}\\bigg)\\psi_{\\bde;r,i}\n\\\\\n=& \\sum_{r\\in[2,m]:\\ {\\delta}_i^{(r)}=0} (-1)^{\\sum_{s=1}^{r-1} {\\delta}_i^{(s)}} 1_{\\bj^\\mu}\\psi_{w_0^\\mu} \\psi_{w(\\bde+\\bolde_i^{r})}\\psi_{\\bde;r,i},\\end{aligned}$$ where we have used Lemma \\[LPull\\](i) to see the first equality. ", "Thus $S_1+S_2$ equals the right hand side of (\\[E150416\\]).", "\n\nThe following statement means that $f$ is chain map:\n\n\\[fchain\\]Let $\\mu\\in{\\Lambda}(n+1)$ and $\\bde\\in\\bLa(n)$. Then $$\\sum_{{\\lambda}\\in{\\Lambda}(n)} d_n^{\\mu,{\\lambda}}f^{{\\lambda},\\bde}_{n}=\\sum_{\\bga\\in\\bLa(n+1)} f^{\\mu,\\bga}_{n+1}c_n^{\\bga,\\bde}.$$\n\nBy definition, $d_n^{\\mu,{\\lambda}}=0$ unless ${\\lambda}=\\mu-\\e_i$ for some $i\\in [a,b]$, and $f_n^{{\\lambda},\\bde}=0$ unless ${\\lambda}={\\lambda}^\\bde$. On the other hand, $f_n^{\\mu,\\bga}=0$ unless $\\mu={\\lambda}^\\bga$, and $c_n^{\\bga,\\bde}=0$, unless $\\bde=\\bga-\\bolde_i^{r}$ for some $i\\in [a,b]$ and $r\\in[1,m]$. So we may assume that $\\mu={\\lambda}^{\\bde+\\bolde_i^{r}}$ for some $i\\in [a,b]$ and $r\\in[1,m]$ such that ${\\delta}_i^{(r)}=0$. In this case, letting ${\\lambda}:={\\lambda}^{\\bde}$, we have to prove $$d_n^{\\mu,{\\lambda}}f^{{\\lambda},\\bde}_{n}=\\sum_{r\\in [1,m]:\\ {\\delta}_i^{(r)}=0} f^{\\mu,\\bde+\\bolde_i^{r}}_{n+1}c_n^{\\bde+\\bolde_i^{r},\\bde}.$$ By definition of the elements involved, this means $$\\begin{aligned}\n&(\\sgn_{{\\lambda};i}e_\\mu\\psi_{{\\lambda};i}e_{\\lambda})\n({\\sigma}_\\bde e_{\\lambda}\\psi_{w_0^{\\lambda}}\\psi_{w(\\bde)}e_\\bde)\n\\\\\n=\n&\\sum_{r\\in [1,m]:\\ {\\delta}_i^{(r)}=0}\n({\\sigma}_{\\bde+\\bolde_i^{r}} e_\\mu\\psi_{w_0^\\mu}\\psi_{w(\\bde+\\bolde_i^{r})}e_{\\bde+\\bolde_i^{r}})\n(\\sgn_{\\bde;r,i}e_{\\bde+\\bolde_i^{r}}\\psi_{\\bde;r,i}e_\\bde).\\end{aligned}$$ Equivalently, we need to prove $$\\begin{aligned}\n\\sgn_{{\\lambda};i}{\\sigma}_\\bde e_\\mu\\psi_{{\\lambda};i}e_{\\lambda}\\psi_{w_0^{\\lambda}}\\psi_{w(\\bde)}\n=\n\\sum_{r\\in [1,m]:\\ {\\delta}_i^{(r)}=0}\n{\\sigma}_{\\bde+\\bolde_i^{r}} \\sgn_{\\bde;r,i}\ne_\\mu\\psi_{w_0^\\mu}\\psi_{w(\\bde+\\bolde_i^{r})}\n\\psi_{\\bde;r,i},\\end{aligned}$$ which, in view of Corollary \\[C160416\\], is equivalent to the statement that $$\\sgn_{{\\lambda}^;i}{\\sigma}_\\bde={\\sigma}_{\\bde+\\bolde_i^{r}} \\sgn_{\\bde;r,i}(-1)^{\\sum_{s=1}^{r-1} {\\delta}_i^{(s)}}$$ for all $r\\in [1,m]$ such that ${\\delta}_i^{(r)}=0$. But this is Lemma \\[LSigns\\].", "\n\nVerification that $g$ is a chain map {#SG}\n====================================\n\nWe continue with the running assumptions of Section \\[SDPR\\]. ", "In addition, throughout the section we fix $n\\in{\\mathbb{Z}}_{\\geq 0}$, ${\\lambda}\\in{\\Lambda}(n)$ and $\\bga=({\\gamma}^{(1)},\\dots,{\\gamma}^{(m)})\\in \\bLa(n+1)$.\n\nSpecial reduced expressions and a commutation lemma {#SSSpecialG}\n---------------------------------------------------\n\nRecall the notation of §\\[SSComb\\]. ", "Let $\\mu\\in{\\Lambda}^{{\\alpha}^m}$ and ${\\gamma}\\in{\\Lambda}^{\\alpha}$ be such that $\\bar\\mu:=\\mu-{\\gamma}\\in{\\Lambda}^{{\\alpha}^{m-1}}$. For $i\\in[a,b+1]$, we denote $$\\begin{aligned}\np^i&:=&(m-1)l+(\\text{the position occupied by $i$ in $\\bj^{\\gamma}$}),\n\\label{EQIG'}\n\\\\\n\\label{EQIG}\nq^i&:=&\n\\left\\{\n\\begin{array}{ll}\nr_i^-(\\mu) &\\hbox{if $i\\neq b+1$ and ${\\gamma}^{(m)}_i=0$,}\\\\\nr_i^+(\\mu) &\\hbox{if $i\\neq b+1$ and ${\\gamma}^{(m)}_i=1$,}\\\\\nr_{b+1}(\\mu) &\\hbox{if $i= b+1$.}\n\\end{array}\n\\right.\\end{aligned}$$ Let $Q:=\\{q^a,\\dots,q^{b+1}\\}$. Note that $\\{p^a,\\dots,p^{b+1}\\}=(d-l,d]$.\n\nDefine $z_\\mu^{\\gamma}\\in\\Si_d$ to be the permutation which maps $q^i$ to $p^i$ for all $i\\in[a,b+1]$, and maps the elements of $[1,d]\\setminus Q$ increasingly to the elements of $[1,d-l]$. It is easy to see that $z_\\mu^{\\gamma}$ is fully commutative, so $\\psi_{z_\\mu^{\\gamma}}$ is well defined, and $\\psi_{z_\\mu^{\\gamma}}1_{\\bj^\\mu}=1_{\\bj^{\\bar\\mu}\\bj^{\\gamma}}\\psi_{z_\\mu^{\\gamma}}$.\n\nNow let $\\mu:={\\lambda}^\\bga$, and $r\\in[1,m]$. Define $$\\bga^{\\leq r}:=({\\gamma}^{(1)},\\dots,{\\gamma}^{(r)})\\in\\bLa^{{\\alpha}^{r}},\\quad\n\\mu^{\\leq r}:={\\lambda}^{\\bga^{\\leq r}}\\in{\\Lambda}^{{\\alpha}^{r}}.$$ Define $z(\\bga,m):=z_\\mu^{{\\gamma}^{(m)}}\\in\\Si_d$. More generally, define for all $r=2,\\dots,m$, the permutations $$z(\\bga,r):=(x_{\\mu^{\\leq r}}^{{\\gamma}^{(r)}}, 1_{\\Si_{(m-r)l}})\\in \\Si_{rl}\\times \\Si_{(m-r)l} \\leq \\Si_d.$$\n\nRecall the element $u(\\bga)\\in\\Si_d$ defined in §\\[SSComp\\]. ", "The following lemma follows from definitions:\n\n\\[LWXG\\] We have $u(\\bga)=z(\\bga,2)\\cdots z(\\bga,m)$ and $\\ell(u(\\bga))=\\ell(z(\\bga,1))+\\dots +\\ell(z(\\bga,m))$.\n\nIn view of the lemma, when convenient, we will always choose reduced decompositions so that $$\\label{WPsiWG}\n\\psi_{u(\\bga)}=\\psi_{z(\\bga,2)}\\dots \\psi_{z(\\bga,m)}.$$\n\nIn view of Lemma \\[LFIndependent\\], we have $$\\label{CWX2}\ng_{n+1}^{\\bga,\\mu}= \\tau_\\bga \\psi_{z(\\bga,2)}\\dots \\psi_{z(\\bga,m)}y^\\mu e_\\mu.$$\n\n[Let $a=1$, $b=2$, $\\mu=(2,2)$, and $\\bga=\\big((1,0),(1,1),(0,1),(0,0)\\big)$, so that $m=4$ and $n=4$. Then $g_n^{{\\lambda},\\bga}$ is $$ \\begin{tikzpicture}[baseline=6mm,black,line width=1pt, scale=0.32,\n draw/.append style={rounded corners},\n every node/.append style={font=\\fontsize{5}{5}\\selectfont}] \\tikzset{baseline=0mm}\n\\draw(1,9) node[above]{\\small $2$};\n\\draw(2,9) node[above]{\\small $3$};\n\\draw(3,9) node[above]{\\small $1$};\n\\draw(4,9) node[above]{\\small $3$};\n\\draw(5,9) node[above]{\\small $2$};\n\\draw(6,9) node[above]{\\small $1$};\n\\draw(7,9) node[above]{\\small $1$};\n\\draw(8,9) node[above]{\\small $3$};\n\\draw(9,9) node[above]{\\small $2$};\n\\draw(10,9) node[above]{\\small $1$};\n\\draw(11,9) node[above]{\\small $2$};\n\\draw(12,9) node[above]{\\small $3$};\n\\draw [rounded corners,color=gray] (0.6,-2.7)--(2.4,-2.7)--(2.4,-4.1)--(0.6,-4.1)--cycle;\n\\draw [rounded corners,color=gray] (2.6,-2.7)--(4.4,-2.7)--(4.4,-4.1)--(2.6,-4.1)--cycle;\n\\draw [rounded corners,color=gray] (4.6,-2.7)--(8.4,-2.7)--(8.4,-4.1)--(4.6,-4.1)--cycle;\n\\draw [rounded corners,color=gray] (8.6,-2.7)--(10.4,-2.7)--(10.4,-4.1)--(8.6,-4.1)--cycle;\n\\draw [rounded corners,color=gray] (10.6,-2.7)--(12.4,-2.7)--(12.4,-4.1)--(10.6,-4.1)--cycle;\n\\draw [rounded corners,color=gray] (4.6,-1.1)--(8.4,-1.1)--(8.4,-2.3)--(4.6,-2.3)--cycle;\n\n\\draw(6.5,-2.6) node[above]{\\small $y_0$};\n\\draw(1,9.1)--(1,5.6)--(2,2.6)--(3,-0.4)--(3,-2.7);\n\\draw(2,9.1)--(2,5.6)--(3,2.6)--(5,-0.4)--(5,-1.1);\n\\draw(3,9.1)--(5,5.6)--(8,2.6)--(11,-0.4)--(11,-2.7);\n\\draw(4,9.1)--(3,5.6)--(4,2.6)--(6,-0.4)--(6,-1.1);\n\\draw(5,9.1)--(4,5.6)--(6,2.6)--(9,-0.4)--(9,-2.7);\n\\draw(6,9.1)--(6,5.6)--(9,2.6)--(12,-0.4)--(12,-2.7);\n\\draw(7,9.1)--(7,5.6)--(1,2.6)--(1,-0.4)--(1,-2.7);\n\\draw(8,9.1)--(8,5.6)--(5,2.6)--(7,-0.4)--(7,-1.1);\n\\draw(9,9.1)--(9,5.6)--(7,2.6)--(10,-0.4)--(10,-2.7);\n\\draw(10,9.1)--(10,5.6)--(10,2.6)--(2,-0.4)--(2,-2.7);\n\\draw(11,9.1)--(11,5.6)--(11,2.6)--(4,-0.4)--(4,-2.7);\n\\draw(12,9.1)--(12,5.6)--(12,2.6)--(8,-0.4)--(8,-1.1);\n\\draw(5,-2.3)--(5,-2.7);\n\\draw(6,-2.3)--(6,-2.7);\n\\draw(7,-2.3)--(7,-2.7);\n\\draw(8,-2.3)--(8,-2.7);\n\\draw(14,7.35) node{$\\left.{", "\n\\begin{matrix}\n \\\\\n \\\\\n \\\\\n \\\\\n \\\\\n \\\\\n\\end{matrix}\n}\\right\\}$};\n\\draw(14,4.05) node{$\\left.{", "\n\\begin{matrix}\n \\\\\n \\\\\n \\\\\n \\\\\n \\\\\n\\end{matrix}\n}\\right\\}$};\n\\draw(14,1.0) node{$\\left.{", "\n\\begin{matrix}\n \\\\\n \\\\\n \\\\\n \\\\\n \\\\\n \\\\\n\\end{matrix}\n}\\right\\}$};\n\\draw(16.2,7.35) node{\\small $\\psi_{z(\\bga,2)}$};\n\\draw(16.2,4.05) node{\\small $\\psi_{z(\\bga,3)}$};\n\\draw(16.2,1.0) node{\\small $\\psi_{z(\\bga,4)}$};\n\\draw(1,-3.4) node{\\small $1$};\n\\draw(2,-3.4) node{\\small $1$};\n\\draw(3,-3.4) node{\\small $2$};\n\\draw(4,-3.4) node{\\small $2$};\n\\draw(5,-3.4) node{\\small $3$};\n\\draw(6,-3.4) node{\\small $3$};\n\\draw(7,-3.4) node{\\small $3$};\n\\draw(8,-3.4) node{\\small $3$};\n\\draw(9,-3.4) node{\\small $2$};\n\\draw(10,-3.4) node{\\small $2$};\n\\draw(11,-3.4) node{\\small $1$};\n\\draw(12,-3.4) node{\\small $1$};\n\\end{tikzpicture}\n$$ ]{}\n\n\\[L290316G\\] Let $i\\in[a,b]$ with ${\\lambda}_i<m$, and $\\mu:={\\lambda}+\\e_i$. Then $$y^\\mu e_\\mu\\psi_{{\\lambda};i} e_{\\lambda}=\\psi_{{\\lambda};i} y^{\\lambda}e_{\\lambda}.$$\n\nRecall the notation of §\\[SSCommL\\], we have that $y^\\mu e_\\mu\\psi_{{\\lambda};i} e_{\\lambda}$ equals $$\\begin{aligned}\n&\n\\Big[\\prod_{j\\in[a,b]} \\iota^\\mu_{j,-}(1_{j^{(m-\\mu_j)}})\n\\iota^\\mu_{j,+}(1_{j^{(\\mu_j)}})\\Big]\n\\iota_{b+1}^\\mu(y_{0,m}1_{(b+1)^{(m)}})\n\\psi_{{\\lambda};i} e_{\\lambda}\\\\\n=& \\iota^\\mu_{i,-}(1_{i^{(m-\\mu_i)}})\n\\iota^\\mu_{i,+}(1_{i^{(\\mu_i)}})\n\\Big[\\prod_{j\\in[a,b]\\setminus\\{i\\}} \\iota^\\mu_{j,-}(1_{j^{(m-\\mu_j)}})\n\\iota^\\mu_{j,+}(1_{j^{(\\mu_j)}})\\Big]\n\\\\\n&\\times \\iota_{b+1}^\\mu(y_{0,m}1_{(b+1)^{(m)}})\n\\psi_{{\\lambda};i} e_{\\lambda}\\\\\n=& \\iota^\\mu_{i,-}(1_{i^{(m-\\mu_i)}})\n\\iota^\\mu_{i,+}(1_{i^{(\\mu_i)}})\n\\psi_{{\\lambda};i}\n\\Big[\\prod_{j\\in[a,b]\\setminus\\{i\\}} \\iota^{\\lambda}_{j,-}(1_{j^{(m-{\\lambda}_j)}})\n\\iota^{\\lambda}_{j,+}(1_{j^{({\\lambda}_j)}})\\Big]\n\\\\\n&\\times \\iota_{b+1}^{\\lambda}(y_{0,m})\\iota_{b+1}^{\\lambda}(1_{(b+1)^{(m)}})\n e_{\\lambda}\\\\\n=& \\iota^\\mu_{i,-}(1_{i^{(m-\\mu_i)}})\n\\iota^\\mu_{j,+}(1_{j^{(\\mu_j)}})\n\\psi_{{\\lambda};i}\ny^{\\lambda}e_{\\lambda}=\\psi_{{\\lambda};i} y^{\\lambda}e_{\\lambda},\\end{aligned}$$ where we have used Lemma \\[LPull\\] for the second equality and Lemma \\[LDivPower\\] for the last equality.", "\n\nWe illustrate Lemma \\[L290316G\\] diagramatically. ", "Let $a=1$, $b=2$, $m=4$, $\\mu=(2,3)$ and ${\\lambda}=(1,3)$ so that $i=1$ using the notation of Lemma \\[L290316G\\]. ", "Then, the lemma claims the following equality. ", "$$ \\begin{tikzpicture}[baseline=6mm,black,line width=1pt, scale=0.32,\n draw/.append style={rounded corners},\n every node/.append style={font=\\fontsize{5}{5}\\selectfont}] \\tikzset{baseline=0mm}\n\\draw(-0.5,2.8) node{$\\left.{", "\n\\begin{matrix}\n\\\\\n\\\\\n\\\\\n\\\\\n\\\\\n\\\\\n\\end{matrix}\n}\\right\\{$};\n\\draw(-0.5,-1.3) node{$\\left.{", "\n\\begin{matrix}\n\\\\\n\\\\\n\\\\\n\\\\\n\\\\\n\\\\\n\\\\\n\\\\\n\\end{matrix}\n}\\right\\{$};\n\\draw(-2,2.8) node{\\small $y^\\mu e_\\mu$};\n\\draw(-2.2,-1.3) node{\\small $\\psi_{{\\lambda};1}e_{\\lambda}$};\n\\draw(1,1) node[above]{\\small $1$};\n\\draw(2,1) node[above]{\\small $1$};\n\\draw(3,1) node[above]{\\small $2$};\n\\draw(4,1) node[above]{\\small $3$};\n\\draw(5,1) node[above]{\\small $3$};\n\\draw(6,1) node[above]{\\small $3$};\n\\draw(7,1) node[above]{\\small $3$};\n\\draw(8,1) node[above]{\\small $2$};\n\\draw(9,1) node[above]{\\small $2$};\n\\draw(10,1) node[above]{\\small $2$};\n\\draw(11,1) node[above]{\\small $1$};\n\\draw(12,1) node[above]{\\small $1$};\n\\draw [rounded corners,color=gray] (0.6,2.5)--(2.4,2.5)--(2.4,1.1)--(0.6,1.1)--cycle;\n\\draw [rounded corners,color=gray] (3.6,4.5)--(7.4,4.5)--(7.4,3.1)--(3.6,3.1)--cycle;\n\\draw [rounded corners,color=gray] (3.6,2.5)--(7.4,2.5)--(7.4,1.1)--(3.6,1.1)--cycle;\n\\draw [rounded corners,color=gray] (7.6,2.5)--(10.4,2.5)--(10.4,1.1)--(7.6,1.1)--cycle;\n\\draw [rounded corners,color=gray] (10.6,2.5)--(12.4,2.5)--(12.4,1.1)--(10.6,1.1)--cycle;\n\\draw [rounded corners,color=gray] (0.6,-2.5)--(3.4,-2.5)--(3.4,-3.9)--(0.6,-3.9)--cycle;\n\\draw [rounded corners,color=gray] (4.6,-2.5)--(8.4,-2.5)--(8.4,-3.9)--(4.6,-3.9)--cycle;\n\\draw [rounded corners,color=gray] (8.6,-2.5)--(11.4,-2.5)--(11.4,-3.9)--(8.6,-3.9)--cycle;\n\\draw(1,1.1)--(1,-2.5);\n\\draw(2,1.1)--(2,-2.5);\n\\draw(3,1.1)--(4,-2.5);\n\\draw(4,1.1)--(5,-2.5);\n\\draw(5,1.1)--(6,-2.5);\n\\draw(6,1.1)--(7,-2.5);\n\\draw(7,1.1)--(8,-2.5);\n\\draw(8,1.1)--(9,-2.5);\n\\draw(9,1.1)--(10,-2.5);\n\\draw(10,1.1)--(11,-2.5);\n\\draw(11,1.1)--(12,-2.5);\n\\draw(12,1.1)--(3,-2.5);\n\\draw(1,4.5)--(1,2.5);\n\\draw(2,4.5)--(2,2.5);\n\\draw(3,4.5)--(3,2.5);\n\\draw(4,3.1)--(4,2.5);\n\\draw(5,3.1)--(5,2.5);\n\\draw(6,3.1)--(6,2.5);\n\\draw(7,3.1)--(7,2.5);\n\\draw(8,4.5)--(8,2.5);\n\\draw(9,4.5)--(9,2.5);\n\\draw(10,4.5)--(10,2.5);\n\\draw(11,4.5)--(11,2.5);\n\\draw(12,4.5)--(12,2.5);\n\\draw(5.5,3) node[above]{\\small $y_0$};\n\\draw(1,-4) node[above]{\\small $1$};\n\\draw(2,-4) node[above]{\\small $1$};\n\\draw(3,-4) node[above]{\\small $1$};\n\\draw(4,-4) node[above]{\\small $2$};\n\\draw(5,-4) node[above]{\\small $3$};\n\\draw(6,-4) node[above]{\\small $3$};\n\\draw(7,-4) node[above]{\\small $3$};\n\\draw(8,-4) node[above]{\\small $3$};\n\\draw(9,-4) node[above]{\\small $2$};\n\\draw(10,-4) node[above]{\\small $2$};\n\\draw(11,-4) node[above]{\\small $2$};\n\\draw(12,-4) node[above]{\\small $1$};\n\\end{tikzpicture}\n\n=\n \\begin{tikzpicture}[baseline=6mm,black,line width=1pt, scale=0.32,\n draw/.append style={rounded corners},\n every node/.append style={font=\\fontsize{5}{5}\\selectfont}] \\tikzset{baseline=0mm}\n\\draw(13.5,1.7) node{$\\left.{", "\n\\begin{matrix}\n\\\\\n\\\\\n\\\\\n\\\\\n\\\\\n\\\\\n\\\\\n\\\\\n\\end{matrix}\n}\\right\\}$};\n\\draw(13.5,-2) node{$\\left.{", "\n\\begin{matrix}\n\\\\\n\\\\\n\\\\\n\\\\\n\\\\\n\\end{matrix}\n}\\right\\}$};\n\\draw(15.2,1.7) node{\\small $\\psi_{{\\lambda};1}$};\n\\draw(15.2,-2) node{\\small $y^{\\lambda}e_{\\lambda}$};\n\\draw(1,3) node[above]{\\small $1$};\n\\draw(2,3) node[above]{\\small $1$};\n\\draw(3,3) node[above]{\\small $2$};\n\\draw(4,3) node[above]{\\small $3$};\n\\draw(5,3) node[above]{\\small $3$};\n\\draw(6,3) node[above]{\\small $3$};\n\\draw(7,3) node[above]{\\small $3$};\n\\draw(8,3) node[above]{\\small $2$};\n\\draw(9,3) node[above]{\\small $2$};\n\\draw(10,3) node[above]{\\small $2$};\n\\draw(11,3) node[above]{\\small $1$};\n\\draw(12,3) node[above]{\\small $1$};\n\\draw [rounded corners,color=gray] (4.6,-0.5)--(8.4,-0.5)--(8.4,-1.9)--(4.6,-1.9)--cycle;\n\\draw [rounded corners,color=gray] (0.6,-2.5)--(3.4,-2.5)--(3.4,-3.9)--(0.6,-3.9)--cycle;\n\\draw [rounded corners,color=gray] (4.6,-2.5)--(8.4,-2.5)--(8.4,-3.9)--(4.6,-3.9)--cycle;\n\\draw [rounded corners,color=gray] (8.6,-2.5)--(11.4,-2.5)--(11.4,-3.9)--(8.6,-3.9)--cycle;\n\\draw(5,-1.9)--(5,-2.5);\n\\draw(6,-1.9)--(6,-2.5);\n\\draw(7,-1.9)--(7,-2.5);\n\\draw(8,-1.9)--(8,-2.5);\n\\draw(1,3.1)--(1,-0.5)--(1,-2.5);\n\\draw(2,3.1)--(2,-0.5)--(2,-2.5);\n\\draw(3,3.1)--(4,-0.5)--(4,-2.5);\n\\draw(4,3.1)--(5,-0.5);\n\\draw(5,3.1)--(6,-0.5);\n\\draw(6,3.1)--(7,-0.5);\n\\draw(7,3.1)--(8,-0.5);\n\\draw(8,3.1)--(9,-0.5)--(9,-2.5);\n\\draw(9,3.1)--(10,-0.5)--(10,-2.5);\n\\draw(10,3.1)--(11,-0.5)--(11,-2.5);\n\\draw(11,3.1)--(12,-0.5)--(12,-2.5);\n\\draw(12,3.1)--(3,-0.5)--(3,-2.5);\n\\draw(6.5,-2) node[above]{\\small $y_0$};\n\\draw(1,-4) node[above]{\\small $1$};\n\\draw(2,-4) node[above]{\\small $1$};\n\\draw(3,-4) node[above]{\\small $1$};\n\\draw(4,-4) node[above]{\\small $2$};\n\\draw(5,-4) node[above]{\\small $3$};\n\\draw(6,-4) node[above]{\\small $3$};\n\\draw(7,-4) node[above]{\\small $3$};\n\\draw(8,-4) node[above]{\\small $3$};\n\\draw(9,-4) node[above]{\\small $2$};\n\\draw(10,-4) node[above]{\\small $2$};\n\\draw(11,-4) node[above]{\\small $2$};\n\\draw(12,-4) node[above]{\\small $1$};\n\\end{tikzpicture}\n$$\n\n$g$ is a chain map\n------------------\n\nRecall that we have fixed ${\\lambda}\\in{\\Lambda}(n)$ and $\\bga\\in \\bLa(n+1)$.\n\n\\[L140416G\\] Suppose that $i\\in [a,b]$ is such that ${\\lambda}_i<m$ and $\\mu:={\\lambda}+\\e_i={\\lambda}^\\bga$. Set $\\bar\\theta=(m-1){\\alpha}$, $\\bar\\mu:=\\mu-{\\gamma}^{(m)}$, and $\\bar{\\lambda}:={\\lambda}-{\\gamma}^{(m)}$. Then $\\psi_{z(\\bga,m)}y^\\mu e_\\mu\\psi_{{\\lambda};i}e_{\\lambda}$ equals $$\\left\\{\n\\begin{array}{ll}\n\\begin{array}{ll}\n\\psi_{\\bga-\\bolde_i^{m};m,i}\\psi_{z(\\bga-\\bolde_i^{m},m)}y^{\\lambda}e_{\\lambda}\\\\\n-(y^{\\bar\\mu}e_{\\bar\\mu}\\psi_{\\bar{\\lambda};i}e_{\\bar{\\lambda}} \\circ 1_{\\alpha})\\psi_{z^{{\\gamma}^{(m)}}_{\\lambda}}y_{r_{b+1}({\\lambda})}^{m-1}e_{\\lambda}\\end{array}\n &\\hbox{if ${\\gamma}^{(m)}_i=1$,}\\\\\n(y^{\\bar\\mu}e_{\\bar\\mu}\\psi_{\\bar{\\lambda};i}e_{\\bar{\\lambda}} \\circ 1_{\\alpha})\\psi_{z^{{\\gamma}^{(m)}}_{\\lambda}}y_{r_{b+1}({\\lambda})}^{m-1}e_{\\lambda}&\\hbox{if ${\\gamma}^{(m)}_i=0$.}\n\\end{array}\n\\right.$$\n\nUsing Lemma \\[L290316G\\], we get $$\\psi_{z(\\bga,m)}y^\\mu e_\\mu\\psi_{{\\lambda};i}e_{\\lambda}=\n\\psi_{z(\\bga,m)}\\psi_{{\\lambda};i}y^{\\lambda}e_{\\lambda}$$ Recalling (\\[EQIG’\\]),(\\[EQIG\\]), the permutation $z(\\bga,m)$ maps $q^j$ to $p^j$ for all $j\\in[a,b+1]$, and the elements of $[1,d]\\setminus Q$ increasingly to the elements of $[1,d-l]$.\n\n[*Case 1: ${\\gamma}^{(m)}_i=1$*]{}. ", "In this case we have $q^i=r_i^+({\\lambda})$. So the KLR diagram $D$ of $\\psi_{z(\\bga,m)}\\psi_{{\\lambda};i}1^{\\bj^{\\lambda}}$ has an $i$-string $S$ from the position $r_i^-({\\lambda})$ in the bottom to the position $p^i$ in the top, and the only $(i,i)$-crossings in $D$ will be the crossings of the string $S$ with the ${\\lambda}_i$ strings which originate in the positions $R_i^+({\\lambda})$ in the bottom. ", "The $(i+1)$-string $T$ in $D$ originating in the position $p_{i+1}$ in the top is to the left of all $(i,i)$ crossings. ", "Pulling $T$ to the right produces error terms, which arise from opening $(i,i)$-crossings, but all of them, except the last one, amount to zero, when multiplied on the right by $y^{\\lambda}e_{\\lambda}$. The last error term is equal to $\n-\\iota_{\\bar\\theta,{\\alpha}}(\\psi_{\\bar{\\lambda};i} \\otimes 1_{\\alpha})\n\\psi_{z^{{\\gamma}^{(m)}}_{\\lambda}},\n$ and the result of pulling $T$ past all $(i,i)$-crossings gives $\\psi_{\\bga-\\bolde_i^{m};m,i}\\psi_{z(\\bga-\\bolde_i^{m},m)}$. Multiplying on the left by $y^{\\lambda}e_{\\lambda}$, gives $$-\\iota_{\\bar\\theta,{\\alpha}}(\\psi_{\\bar{\\lambda};i} \\otimes 1_{\\alpha})\n\\psi_{z^{{\\gamma}^{(m)}}_{\\lambda}}y^{\\lambda}e_{\\lambda}+\n\\psi_{\\bga-\\bolde_i^{m};m,i}\\psi_{z(\\bga-\\bolde_i^{m},m)}y^{\\lambda}e_{\\lambda},$$ and it remains to observe using Lemma \\[LPull\\] that $$-\\iota_{\\bar\\theta,{\\alpha}}(\\psi_{\\bar{\\lambda};i} \\otimes 1_{\\alpha})\n\\psi_{z^{{\\gamma}^{(m)}}_{\\lambda}}y^{\\lambda}e_{\\lambda}=\n-(y^{\\bar\\mu}e_{\\bar\\mu}\\psi_{\\bar{\\lambda};i}e_{\\bar{\\lambda}} \\circ 1_{\\alpha})\\psi_{z^{{\\gamma}^{(m)}}_{\\lambda}}y_{r_{b+1}({\\lambda})}^{m-1}e_{\\lambda}.$$\n\n[*Case 2: ${\\gamma}^{(m)}_i=0$.*]{} Let $D$ be the KLR diagram of $\\psi_{z(\\bga,m)}\\psi_{{\\lambda};i}1_{\\bj^{\\lambda}}$. Let $S$ be the $i$-string originating in the position $r^-_{i}({\\lambda})$ in the bottom row of $D$, and $T$ be the $(i+1)$-string originating in the position $p^{i+1}$ in the top row of $D$. The quadratic relation on these strings produces a linear combination of two diagrams, one with a dot on $S$ and the other with a dot on $T$. The term containing a dot on $T$ produces a term which is zero after multiplying on the right by $y^{\\lambda}e^{\\lambda}$. The term containing a dot on $S$, when multiplied on the right by $y^{\\lambda}e^{\\lambda}$, yields $$\\iota_{\\bar\\theta,{\\alpha}}(\\psi_{\\bar{\\lambda};i} \\otimes 1_{\\alpha})\\psi_{z^{{\\gamma}^{(m)}}_{\\lambda}} y^{\\lambda}e_{\\lambda}=(y^{\\bar\\mu}e_{\\bar\\mu}\\psi_{\\bar{\\lambda};i}e_{\\bar{\\lambda}} \\circ 1_{\\alpha})\\psi_{z^{{\\gamma}^{(m)}}_{\\lambda}} y_{r_{b+1}({\\lambda})}^{m-1}e_{\\lambda},$$ where we have used Lemmas \\[LPull\\] and \\[LDivPower\\] to deduce the last equality.", "\n\nWe illustrate Lemma \\[L140416G\\] diagramatically. ", "Using the notation of the lemma, let $a=1$, $b=2$, $\\mu=(2,2)$, ${\\lambda}=(1,2)$, $m=4$ and $i=1$. Then, if $\\bga =\\big((1,0),(1,1),(0,1),(0,0)\\big)$, we are in the $\\gamma_i^{(m)}=0$ case and the lemma claims the following equality. ", "$$ \\begin{tikzpicture}[baseline=6mm,black,line width=1pt, scale=0.32,\n draw/.append style={rounded corners},\n every node/.append style={font=\\fontsize{5}{5}\\selectfont}] \\tikzset{baseline=-7mm}\n\\draw(1,2.5) node[above]{\\small $1$};\n\\draw(2,2.5) node[above]{\\small $2$};\n\\draw(3,2.5) node[above]{\\small $3$};\n\\draw(4,2.5) node[above]{\\small $3$};\n\\draw(5,2.5) node[above]{\\small $3$};\n\\draw(6,2.5) node[above]{\\small $2$};\n\\draw(7,2.5) node[above]{\\small $2$};\n\\draw(8,2.5) node[above]{\\small $1$};\n\\draw(9,2.5) node[above]{\\small $1$};\n\\draw(10,2.5) node[above]{\\small $1$};\n\\draw(11,2.5) node[above]{\\small $2$};\n\\draw(12,2.5) node[above]{\\small $3$};\n\\draw [rounded corners,color=gray] (0.6,-2.7)--(2.4,-2.7)--(2.4,-4.1)--(0.6,-4.1)--cycle;\n\\draw [rounded corners,color=gray] (2.6,-2.7)--(4.4,-2.7)--(4.4,-4.1)--(2.6,-4.1)--cycle;\n\\draw [rounded corners,color=gray] (4.6,-2.7)--(8.4,-2.7)--(8.4,-4.1)--(4.6,-4.1)--cycle;\n\\draw [rounded corners,color=gray] (8.6,-2.7)--(10.4,-2.7)--(10.4,-4.1)--(8.6,-4.1)--cycle;\n\\draw [rounded corners,color=gray] (10.6,-2.7)--(12.4,-2.7)--(12.4,-4.1)--(10.6,-4.1)--cycle;\n\\draw [rounded corners,color=gray] (4.6,-1.1)--(8.4,-1.1)--(8.4,-2.3)--(4.6,-2.3)--cycle;\n\\draw(6.5,-2.6) node[above]{\\small $y_0$};\n\\draw(2,2.6)--(3,-0.4)--(3,-2.7);\n\\draw(3,2.6)--(5,-0.4)--(5,-1.1);\n\\draw(8,2.6)--(11,-0.4)--(11,-2.7);\n\\draw(4,2.6)--(6,-0.4)--(6,-1.1);\n\\draw(6,2.6)--(9,-0.4)--(9,-2.7);\n\\draw(9,2.6)--(12,-0.4)--(12,-2.7);\n\\draw(1,2.6)--(1,-0.4)--(1,-2.7);\n\\draw(5,2.6)--(7,-0.4)--(7,-1.1);\n\\draw(7,2.6)--(10,-0.4)--(10,-2.7);\n\\draw(10,2.6)--(2,-0.4)--(2,-2.7);\n\\draw(11,2.6)--(4,-0.4)--(4,-2.7);\n\\draw(12,2.6)--(8,-0.4)--(8,-1.1);\n\\draw(5,-2.3)--(5,-2.7);\n\\draw(6,-2.3)--(6,-2.7);\n\\draw(7,-2.3)--(7,-2.7);\n\\draw(8,-2.3)--(8,-2.7);\n\\draw(1,-3.4) node{\\small $1$};\n\\draw(2,-3.4) node{\\small $1$};\n\\draw(3,-3.4) node{\\small $2$};\n\\draw(4,-3.4) node{\\small $2$};\n\\draw(5,-3.4) node{\\small $3$};\n\\draw(6,-3.4) node{\\small $3$};\n\\draw(7,-3.4) node{\\small $3$};\n\\draw(8,-3.4) node{\\small $3$};\n\\draw(9,-3.4) node{\\small $2$};\n\\draw(10,-3.4) node{\\small $2$};\n\\draw(11,-3.4) node{\\small $1$};\n\\draw(12,-3.4) node{\\small $1$};\n\\draw(1,-9) node[above]{\\small $1$};\n\\draw(2,-9) node[above]{\\small $1$};\n\\draw(3,-9) node[above]{\\small $1$};\n\\draw(4,-9) node[above]{\\small $2$};\n\\draw(5,-9) node[above]{\\small $2$};\n\\draw(6,-9) node[above]{\\small $3$};\n\\draw(7,-9) node[above]{\\small $3$};\n\\draw(8,-9) node[above]{\\small $3$};\n\\draw(9,-9) node[above]{\\small $3$};\n\\draw(10,-9) node[above]{\\small $2$};\n\\draw(11,-9) node[above]{\\small $2$};\n\\draw(12,-9) node[above]{\\small $1$};\n\\draw [rounded corners,color=gray] (0.6,-8.9)--(3.4,-8.9)--(3.4,-7.4)--(0.6,-7.4)--cycle;\n\\draw [rounded corners,color=gray] (3.6,-8.9)--(5.4,-8.9)--(5.4,-7.4)--(3.6,-7.4)--cycle;\n\\draw [rounded corners,color=gray] (5.6,-8.9)--(9.4,-8.9)--(9.4,-7.4)--(5.6,-7.4)--cycle;\n\\draw [rounded corners,color=gray] (9.6,-8.9)--(11.4,-8.9)--(11.4,-7.4)--(9.6,-7.4)--cycle;\n\\draw(1,-4.1)--(1,-7.4);\n\\draw(2,-4.1)--(2,-7.4);\n\\draw(3,-4.1)--(4,-7.4);\n\\draw(4,-4.1)--(5,-7.4);\n\\draw(5,-4.1)--(6,-7.4);\n\\draw(6,-4.1)--(7,-7.4);\n\\draw(7,-4.1)--(8,-7.4);\n\\draw(8,-4.1)--(9,-7.4);\n\\draw(9,-4.1)--(10,-7.4);\n\\draw(10,-4.1)--(11,-7.4);\n\\draw(11,-4.1)--(12,-7.4);\n\\draw(12,-4.1)--(3,-7.4);\n\\end{tikzpicture}\n\n=\n \\begin{tikzpicture}[baseline=6mm,black,line width=1pt, scale=0.32,\n draw/.append style={rounded corners},\n every node/.append style={font=\\fontsize{5}{5}\\selectfont}] \\tikzset{baseline=-7mm}\n\\draw(1,1) node[above]{\\small $1$};\n\\draw(2,1) node[above]{\\small $2$};\n\\draw(3,1) node[above]{\\small $3$};\n\\draw(4,1) node[above]{\\small $3$};\n\\draw(5,1) node[above]{\\small $3$};\n\\draw(6,1) node[above]{\\small $2$};\n\\draw(7,1) node[above]{\\small $2$};\n\\draw(8,1) node[above]{\\small $1$};\n\\draw(9,1) node[above]{\\small $1$};\n\\draw(10,1) node[above]{\\small $1$};\n\\draw(11,1) node[above]{\\small $2$};\n\\draw(12,1) node[above]{\\small $3$};\n\\draw [rounded corners,color=gray] (0.6,-2.7)--(2.4,-2.7)--(2.4,-4.1)--(0.6,-4.1)--cycle;\n\\draw [rounded corners,color=gray] (3.6,-2.7)--(6.4,-2.7)--(6.4,-4.1)--(3.6,-4.1)--cycle;\n\\draw [rounded corners,color=gray] (6.6,-2.7)--(8.4,-2.7)--(8.4,-4.1)--(6.6,-4.1)--cycle;\n\\draw [rounded corners,color=gray] (2.6,4.1)--(5.4,4.1)--(5.4,2.8)--(2.6,2.8)--cycle;\n\\draw(4,2.5) node[above]{\\small $y_0$};\n\\draw [rounded corners,color=gray] (2.6,1.1)--(5.4,1.1)--(5.4,2.5)--(2.6,2.5)--cycle;\n\\draw [rounded corners,color=gray] (5.6,1.1)--(7.4,1.1)--(7.4,2.5)--(5.6,2.5)--cycle;\n\\draw [rounded corners,color=gray] (7.6,1.1)--(9.4,1.1)--(9.4,2.5)--(7.6,2.5)--cycle;\n\\draw(1,4.1)--(1,2.5);\n\\draw(2,4.1)--(2,2.5);\n\\draw(3,2.8)--(3,2.5);\n\\draw(4,2.8)--(4,2.5);\n\\draw(5,2.8)--(5,2.5);\n\\draw(6,4.1)--(6,2.5);\n\\draw(7,4.1)--(7,2.5);\n\\draw(8,4.1)--(8,2.5);\n\\draw(9,4.1)--(9,2.5);\n\\draw(10,4.1)--(10,2.5);\n\\draw(11,4.1)--(11,2.5);\n\\draw(12,4.1)--(12,2.5);\n\\draw(1,1.1)--(1,-2.7);\n\\draw(2,1.1)--(3,-2.7);\n\\draw(3,1.1)--(4,-2.7);\n\\draw(4,1.1)--(5,-2.7);\n\\draw(5,1.1)--(6,-2.7);\n\\draw(6,1.1)--(7,-2.7);\n\\draw(7,1.1)--(8,-2.7);\n\\draw(8,1.1)--(9,-2.7);\n\\draw(9,1.1)--(2,-2.7);\n\\draw(10,1.1)--(10,-2.7);\n\\draw(11,1.1)--(11,-2.7);\n\\draw(12,1.1)--(12,-2.7);\n\\draw(1,-3.4) node{\\small $1$};\n\\draw(2,-3.4) node{\\small $1$};\n\\draw(3,-3.4) node{\\small $2$};\n\\draw(4,-3.4) node{\\small $3$};\n\\draw(5,-3.4) node{\\small $3$};\n\\draw(6,-3.4) node{\\small $3$};\n\\draw(7,-3.4) node{\\small $2$};\n\\draw(8,-3.4) node{\\small $2$};\n\\draw(9,-3.4) node{\\small $1$};\n\\draw(10,-3.4) node{\\small $1$};\n\\draw(11,-3.4) node{\\small $2$};\n\\draw(12,-3.4) node{\\small $3$};\n\\draw(1,-9) node[above]{\\small $1$};\n\\draw(2,-9) node[above]{\\small $1$};\n\\draw(3,-9) node[above]{\\small $1$};\n\\draw(4,-9) node[above]{\\small $2$};\n\\draw(5,-9) node[above]{\\small $2$};\n\\draw(6,-9) node[above]{\\small $3$};\n\\draw(7,-9) node[above]{\\small $3$};\n\\draw(8,-9) node[above]{\\small $3$};\n\\draw(9,-9) node[above]{\\small $3$};\n\\draw(10,-9) node[above]{\\small $2$};\n\\draw(11,-9) node[above]{\\small $2$};\n\\draw(12,-9) node[above]{\\small $1$};\n\\draw [rounded corners,color=gray] (0.6,-8.9)--(3.4,-8.9)--(3.4,-7.4)--(0.6,-7.4)--cycle;\n\\draw [rounded corners,color=gray] (3.6,-8.9)--(5.4,-8.9)--(5.4,-7.4)--(3.6,-7.4)--cycle;\n\\draw [rounded corners,color=gray] (5.6,-8.9)--(9.4,-8.9)--(9.4,-7.4)--(5.6,-7.4)--cycle;\n\\draw [rounded corners,color=gray] (9.6,-8.9)--(11.4,-8.9)--(11.4,-7.4)--(9.6,-7.4)--cycle;\n\\draw(1,-4.1)--(1,-7.4);\n\\draw(2,-4.1)--(3,-7.4);\n\\draw(3,-4.1)--(4,-7.4);\n\\draw(4,-4.1)--(6,-7.4);\n\\draw(5,-4.1)--(7,-7.4);\n\\draw(6,-4.1)--(8,-7.4);\n\\draw(7,-4.1)--(10,-6.2)--(10,-7.4);\n\\draw(8,-4.1)--(11,-6.2)--(11,-7.4);\n\\draw(9,-4.1)--(12,-6.2)--(12,-7.4);\n\\draw(10,-4.1)--(2,-7.4);\n\\draw(11,-4.1)--(5,-7.4);\n\\draw(12,-4.1)--(9,-6.2)--(9,-7.4);\n\\blackdot(9,-7.1);\n\\blackdot(9,-6.6);\n\\blackdot(9.2,-6.1);\n\\end{tikzpicture}\n$$ If instead we let $\\bga =\\big((0,0),(1,1),(0,1),(1,0)\\big)$, we are in the $\\gamma_i^{(m)}=1$ case and the lemma claims the following equality. ", "$$ \\begin{tikzpicture}[baseline=6mm,black,line width=1pt, scale=0.32,\n draw/.append style={rounded corners},\n every node/.append style={font=\\fontsize{5}{5}\\selectfont}] \\tikzset{baseline=-7mm}\n\\draw(1,2.5) node[above]{\\small $1$};\n\\draw(2,2.5) node[above]{\\small $1$};\n\\draw(3,2.5) node[above]{\\small $2$};\n\\draw(4,2.5) node[above]{\\small $3$};\n\\draw(5,2.5) node[above]{\\small $3$};\n\\draw(6,2.5) node[above]{\\small $3$};\n\\draw(7,2.5) node[above]{\\small $2$};\n\\draw(8,2.5) node[above]{\\small $2$};\n\\draw(9,2.5) node[above]{\\small $1$};\n\\draw(10,2.5) node[above]{\\small $2$};\n\\draw(11,2.5) node[above]{\\small $3$};\n\\draw(12,2.5) node[above]{\\small $1$};\n\\draw [rounded corners,color=gray] (0.6,-2.7)--(2.4,-2.7)--(2.4,-4.1)--(0.6,-4.1)--cycle;\n\\draw [rounded corners,color=gray] (2.6,-2.7)--(4.4,-2.7)--(4.4,-4.1)--(2.6,-4.1)--cycle;\n\\draw [rounded corners,color=gray] (4.6,-2.7)--(8.4,-2.7)--(8.4,-4.1)--(4.6,-4.1)--cycle;\n\\draw [rounded corners,color=gray] (8.6,-2.7)--(10.4,-2.7)--(10.4,-4.1)--(8.6,-4.1)--cycle;\n\\draw [rounded corners,color=gray] (10.6,-2.7)--(12.4,-2.7)--(12.4,-4.1)--(10.6,-4.1)--cycle;\n\\draw [rounded corners,color=gray] (4.6,-1.1)--(8.4,-1.1)--(8.4,-2.3)--(4.6,-2.3)--cycle;\n\\draw(6.5,-2.6) node[above]{\\small $y_0$};\n\\draw(2,2.6)--(2,-0.4)--(2,-2.7);\n\\draw(3,2.6)--(3,-0.4)--(3,-2.7);\n\\draw(8,2.6)--(10,-0.4)--(10,-2.7);\n\\draw(4,2.6)--(5,-0.4)--(5,-1.1);\n\\draw(6,2.6)--(7,-0.4)--(7,-1.1);\n\\draw(9,2.6)--(11,-0.4)--(11,-2.7);\n\\draw(1,2.6)--(1,-0.4)--(1,-2.7);\n\\draw(5,2.6)--(6,-0.4)--(6,-1.1);\n\\draw(7,2.6)--(9,-0.4)--(9,-2.7);\n\\draw(10,2.6)--(4,-0.4)--(4,-2.7);\n\\draw(11,2.6)--(8,-0.4)--(8,-1.1);\n\\draw(12,2.6)--(12,-0.4)--(12,-2.7);\n\\draw(5,-2.3)--(5,-2.7);\n\\draw(6,-2.3)--(6,-2.7);\n\\draw(7,-2.3)--(7,-2.7);\n\\draw(8,-2.3)--(8,-2.7);\n\\draw(1,-3.4) node{\\small $1$};\n\\draw(2,-3.4) node{\\small $1$};\n\\draw(3,-3.4) node{\\small $2$};\n\\draw(4,-3.4) node{\\small $2$};\n\\draw(5,-3.4) node{\\small $3$};\n\\draw(6,-3.4) node{\\small $3$};\n\\draw(7,-3.4) node{\\small $3$};\n\\draw(8,-3.4) node{\\small $3$};\n\\draw(9,-3.4) node{\\small $2$};\n\\draw(10,-3.4) node{\\small $2$};\n\\draw(11,-3.4) node{\\small $1$};\n\\draw(12,-3.4) node{\\small $1$};\n\\draw(1,-9) node[above]{\\small $1$};\n\\draw(2,-9) node[above]{\\small $1$};\n\\draw(3,-9) node[above]{\\small $1$};\n\\draw(4,-9) node[above]{\\small $2$};\n\\draw(5,-9) node[above]{\\small $2$};\n\\draw(6,-9) node[above]{\\small $3$};\n\\draw(7,-9) node[above]{\\small $3$};\n\\draw(8,-9) node[above]{\\small $3$};\n\\draw(9,-9) node[above]{\\small $3$};\n\\draw(10,-9) node[above]{\\small $2$};\n\\draw(11,-9) node[above]{\\small $2$};\n\\draw(12,-9) node[above]{\\small $1$};\n\\draw [rounded corners,color=gray] (0.6,-8.9)--(3.4,-8.9)--(3.4,-7.4)--(0.6,-7.4)--cycle;\n\\draw [rounded corners,color=gray] (3.6,-8.9)--(5.4,-8.9)--(5.4,-7.4)--(3.6,-7.4)--cycle;\n\\draw [rounded corners,color=gray] (5.6,-8.9)--(9.4,-8.9)--(9.4,-7.4)--(5.6,-7.4)--cycle;\n\\draw [rounded corners,color=gray] (9.6,-8.9)--(11.4,-8.9)--(11.4,-7.4)--(9.6,-7.4)--cycle;\n\\draw(1,-4.1)--(1,-7.4);\n\\draw(2,-4.1)--(2,-7.4);\n\\draw(3,-4.1)--(4,-7.4);\n\\draw(4,-4.1)--(5,-7.4);\n\\draw(5,-4.1)--(6,-7.4);\n\\draw(6,-4.1)--(7,-7.4);\n\\draw(7,-4.1)--(8,-7.4);\n\\draw(8,-4.1)--(9,-7.4);\n\\draw(9,-4.1)--(10,-7.4);\n\\draw(10,-4.1)--(11,-7.4);\n\\draw(11,-4.1)--(12,-7.4);\n\\draw(12,-4.1)--(3,-7.4);\n\\end{tikzpicture}\n\n=\n \\begin{tikzpicture}[baseline=6mm,black,line width=1pt, scale=0.32,\n draw/.append style={rounded corners},\n every node/.append style={font=\\fontsize{5}{5}\\selectfont}] \\tikzset{baseline=-7mm}\n\\draw(1,2.5) node[above]{\\small $1$};\n\\draw(2,2.5) node[above]{\\small $1$};\n\\draw(3,2.5) node[above]{\\small $2$};\n\\draw(4,2.5) node[above]{\\small $3$};\n\\draw(5,2.5) node[above]{\\small $3$};\n\\draw(6,2.5) node[above]{\\small $3$};\n\\draw(7,2.5) node[above]{\\small $2$};\n\\draw(8,2.5) node[above]{\\small $2$};\n\\draw(9,2.5) node[above]{\\small $1$};\n\\draw(10,2.5) node[above]{\\small $2$};\n\\draw(11,2.5) node[above]{\\small $3$};\n\\draw(12,2.5) node[above]{\\small $1$};\n\\draw(1,2.5)--(1,-2.7);\n\\draw(2,2.5)--(2,-2.7);\n\\draw(3,2.5)--(3,-2.7);\n\\draw(4,2.5)--(4,-2.7);\n\\draw(5,2.5)--(5,-2.7);\n\\draw(6,2.5)--(6,-2.7);\n\\draw(7,2.5)--(7,-2.7);\n\\draw(8,2.5)--(8,-2.7);\n\\draw(9,2.5)--(9,-2.7);\n\\draw(10,2.5)--(11,-2.7);\n\\draw(11,2.5)--(12,-2.7);\n\\draw(12,2.5)--(10,-2.7);\n\\draw(1,-3.4) node{\\small $1$};\n\\draw(2,-3.4) node{\\small $1$};\n\\draw(3,-3.4) node{\\small $2$};\n\\draw(4,-3.4) node{\\small $3$};\n\\draw(5,-3.4) node{\\small $3$};\n\\draw(6,-3.4) node{\\small $3$};\n\\draw(7,-3.4) node{\\small $2$};\n\\draw(8,-3.4) node{\\small $2$};\n\\draw(9,-3.4) node{\\small $1$};\n\\draw(10,-3.4) node{\\small $1$};\n\\draw(11,-3.4) node{\\small $2$};\n\\draw(12,-3.4) node{\\small $3$};\n\\draw [rounded corners,color=gray] (5.6,-6)--(9.4,-6)--(9.4,-7.2)--(5.6,-7.2)--cycle;\n\\draw(7.5,-7.5) node[above]{\\small $y_0$};\n\\draw(1,-9) node[above]{\\small $1$};\n\\draw(2,-9) node[above]{\\small $1$};\n\\draw(3,-9) node[above]{\\small $1$};\n\\draw(4,-9) node[above]{\\small $2$};\n\\draw(5,-9) node[above]{\\small $2$};\n\\draw(6,-9) node[above]{\\small $3$};\n\\draw(7,-9) node[above]{\\small $3$};\n\\draw(8,-9) node[above]{\\small $3$};\n\\draw(9,-9) node[above]{\\small $3$};\n\\draw(10,-9) node[above]{\\small $2$};\n\\draw(11,-9) node[above]{\\small $2$};\n\\draw(12,-9) node[above]{\\small $1$};\n\\draw [rounded corners,color=gray] (0.6,-8.9)--(3.4,-8.9)--(3.4,-7.4)--(0.6,-7.4)--cycle;\n\\draw [rounded corners,color=gray] (3.6,-8.9)--(5.4,-8.9)--(5.4,-7.4)--(3.6,-7.4)--cycle;\n\\draw [rounded corners,color=gray] (5.6,-8.9)--(9.4,-8.9)--(9.4,-7.4)--(5.6,-7.4)--cycle;\n\\draw [rounded corners,color=gray] (9.6,-8.9)--(11.4,-8.9)--(11.4,-7.4)--(9.6,-7.4)--cycle;\n\\draw(1,-4.1)--(1,-7.4);\n\\draw(2,-4.1)--(3,-7.4);\n\\draw(3,-4.1)--(4,-7.4);\n\\draw(4,-4.1)--(6,-6);\n\\draw(5,-4.1)--(7,-6);\n\\draw(6,-4.1)--(8,-6);\n\\draw(7,-4.1)--(10,-6.2)--(10,-7.4);\n\\draw(8,-4.1)--(11,-6.2)--(11,-7.4);\n\\draw(9,-4.1)--(12,-6.2)--(12,-7.4);\n\\draw(10,-4.1)--(2,-6)--(2,-7.4);\n\\draw(11,-4.1)--(5,-6)--(5,-7.4);\n\\draw(12,-4.1)--(9,-6);\n\\draw(6,-7.2)--(6,-7.4);\n\\draw(7,-7.2)--(7,-7.4);\n\\draw(8,-7.2)--(8,-7.4);\n\\draw(9,-7.2)--(9,-7.4);\n\\end{tikzpicture}\n\n-\n \\begin{tikzpicture}[baseline=6mm,black,line width=1pt, scale=0.32,\n draw/.append style={rounded corners},\n every node/.append style={font=\\fontsize{5}{5}\\selectfont}] \\tikzset{baseline=-7mm}\n\\draw(1,1) node[above]{\\small $1$};\n\\draw(2,1) node[above]{\\small $1$};\n\\draw(3,1) node[above]{\\small $2$};\n\\draw(4,1) node[above]{\\small $3$};\n\\draw(5,1) node[above]{\\small $3$};\n\\draw(6,1) node[above]{\\small $3$};\n\\draw(7,1) node[above]{\\small $2$};\n\\draw(8,1) node[above]{\\small $2$};\n\\draw(9,1) node[above]{\\small $1$};\n\\draw(10,1) node[above]{\\small $2$};\n\\draw(11,1) node[above]{\\small $3$};\n\\draw(12,1) node[above]{\\small $1$};\n\\draw [rounded corners,color=gray] (3.6,4.1)--(6.4,4.1)--(6.4,2.8)--(3.6,2.8)--cycle;\n\\draw(5,2.5) node[above]{\\small $y_0$};\n\\draw(1,4.1)--(1,2.5);\n\\draw(2,4.1)--(2,2.5);\n\\draw(3,4.1)--(3,2.5);\n\\draw(4,2.8)--(4,2.5);\n\\draw(5,2.8)--(5,2.5);\n\\draw(6,2.8)--(6,2.5);\n\\draw(7,4.1)--(7,2.5);\n\\draw(8,4.1)--(8,2.5);\n\\draw(9,4.1)--(9,2.5);\n\\draw(10,4.1)--(10,2.5);\n\\draw(11,4.1)--(11,2.5);\n\\draw(12,4.1)--(12,2.5);\n\\draw(1,1.1)--(1,-2.7);\n\\draw(2,1.1)--(2,-2.7);\n\\draw(3,1.1)--(4,-2.7);\n\\draw(4,1.1)--(5,-2.7);\n\\draw(5,1.1)--(6,-2.7);\n\\draw(6,1.1)--(7,-2.7);\n\\draw(7,1.1)--(8,-2.7);\n\\draw(8,1.1)--(9,-2.7);\n\\draw(9,1.1)--(3,-2.7);\n\\draw(10,1.1)--(10,-2.7);\n\\draw(11,1.1)--(11,-2.7);\n\\draw(12,1.1)--(12,-2.7);\n\\draw(1,-3.4) node{\\small $1$};\n\\draw(2,-3.4) node{\\small $1$};\n\\draw(3,-3.4) node{\\small $1$};\n\\draw(4,-3.4) node{\\small $2$};\n\\draw(5,-3.4) node{\\small $3$};\n\\draw(6,-3.4) node{\\small $3$};\n\\draw(7,-3.4) node{\\small $3$};\n\\draw(8,-3.4) node{\\small $2$};\n\\draw(9,-3.4) node{\\small $2$};\n\\draw(10,-3.4) node{\\small $2$};\n\\draw(11,-3.4) node{\\small $3$};\n\\draw(12,-3.4) node{\\small $1$};\n\\draw [rounded corners,color=gray] (0.6,-4.1)--(3.4,-4.1)--(3.4,-2.7)--(0.6,-2.7)--cycle;\n\\draw [rounded corners,color=gray] (4.6,-4.1)--(7.4,-4.1)--(7.4,-2.7)--(4.6,-2.7)--cycle;\n\\draw [rounded corners,color=gray] (7.6,-4.1)--(9.4,-4.1)--(9.4,-2.7)--(7.6,-2.7)--cycle;\n\\draw(1,-9) node[above]{\\small $1$};\n\\draw(2,-9) node[above]{\\small $1$};\n\\draw(3,-9) node[above]{\\small $1$};\n\\draw(4,-9) node[above]{\\small $2$};\n\\draw(5,-9) node[above]{\\small $2$};\n\\draw(6,-9) node[above]{\\small $3$};\n\\draw(7,-9) node[above]{\\small $3$};\n\\draw(8,-9) node[above]{\\small $3$};\n\\draw(9,-9) node[above]{\\small $3$};\n\\draw(10,-9) node[above]{\\small $2$};\n\\draw(11,-9) node[above]{\\small $2$};\n\\draw(12,-9) node[above]{\\small $1$};\n\\draw [rounded corners,color=gray] (0.6,1.1)--(2.4,1.1)--(2.4,2.5)--(0.6,2.5)--cycle;\n\\draw [rounded corners,color=gray] (3.6,1.1)--(6.4,1.1)--(6.4,2.5)--(3.6,2.5)--cycle;\n\\draw [rounded corners,color=gray] (6.6,1.1)--(8.4,1.1)--(8.4,2.5)--(6.6,2.5)--cycle;\n\\draw [rounded corners,color=gray] (0.6,-8.9)--(3.4,-8.9)--(3.4,-7.4)--(0.6,-7.4)--cycle;\n\\draw [rounded corners,color=gray] (3.6,-8.9)--(5.4,-8.9)--(5.4,-7.4)--(3.6,-7.4)--cycle;\n\\draw [rounded corners,color=gray] (5.6,-8.9)--(9.4,-8.9)--(9.4,-7.4)--(5.6,-7.4)--cycle;\n\\draw [rounded corners,color=gray] (9.6,-8.9)--(11.4,-8.9)--(11.4,-7.4)--(9.6,-7.4)--cycle;\n\\draw(1,-4.1)--(1,-7.4);\n\\draw(2,-4.1)--(2,-7.4);\n\\draw(3,-4.1)--(3,-7.4);\n\\draw(4,-4.1)--(4,-7.4);\n\\draw(5,-4.1)--(6,-7.4);\n\\draw(6,-4.1)--(7,-7.4);\n\\draw(7,-4.1)--(8,-7.4);\n\\draw(8,-4.1)--(10,-6.2)--(10,-7.4);\n\\draw(9,-4.1)--(11,-6.2)--(11,-7.4);\n\\draw(10,-4.1)--(5,-7.4);\n\\draw(12,-4.1)--(12,-7.4);\n\\draw(11,-4.1)--(9,-6.2)--(9,-7.4);\n\\blackdot(9,-7.1);\n\\blackdot(9,-6.6);\n\\blackdot(9.2,-6.1);\n\\end{tikzpicture}\n$$\n\n\\[C160416G\\] Suppose that $i\\in [a,b]$ is such that ${\\lambda}_i<m$ and $\\mu:={\\lambda}+\\e_i={\\lambda}^\\bga$. Then $$\\psi_{u(\\bga)}y^\\mu e_\\mu\\psi_{{\\lambda};i}e_{\\lambda}=\\sum_{r\\in[1,m]:\\ {\\gamma}_i^{(r)}=1} (-1)^{\\sum_{s=r+1}^{m}{\\gamma}_i^{(s)}}\\psi_{\\bga-\\bolde_i^{r};r,i}\\psi_{u(\\bga-\\bolde_i^{r})}y^{\\lambda}e_{\\lambda}.$$\n\nThe proof is by induction on $m$, the induction base $m=1$ being obvious. ", "Let $\\bar{\\gamma}:=({\\gamma}^{(1)},\\dots,{\\gamma}^{(m-1)})$, $\\bar\\theta=(m-1){\\alpha}$, $\\bar\\mu:=\\mu-{\\gamma}^{(m)}$, and $\\bar{\\lambda}:={\\lambda}-{\\gamma}^{(m)}$. By (\\[WPsiWG\\]), we have $$\\label{E200416G}\n\\psi_{u(\\bga)}y^\\mu e_\\mu\\psi_{{\\lambda};i}e_{\\lambda}=\\psi_{z(\\bga,2)}\\dots \\psi_{z(\\bga,m)}\ny^\\mu e_\\mu\\psi_{{\\lambda};i}e_{\\lambda}.$$ Now we apply Lemma \\[L140416G\\]. ", "We consider the case ${\\gamma}_i^{(m)}=1$, the case ${\\gamma}_i^{(m)}=0$ being similar. ", "Then we get the following expression for the right hand side of (\\[E200416G\\]): $$\\begin{aligned}\n&\\psi_{z(\\bga,2)}\\dots \\psi_{z(\\bga,m-1)}\\big(\\psi_{\\bga-\\bolde_i^{m};m,i}\\psi_{z(\\bga-\\bolde_i^{m},m)}y^{\\lambda}e_{\\lambda}\\\\\n-&(y^{\\bar\\mu}e_{\\bar\\mu}\n\\psi_{\\bar{\\lambda};i}e_{\\bar{\\lambda}} \\circ 1_{\\alpha})\\psi_{z^{{\\gamma}^{(m)}}_{\\lambda}} y_{r_{b+1}({\\lambda})}^{m-1}e_{\\lambda}\\big)\n.\\end{aligned}$$ Opening parentheses, we get two summands $S_1+S_2$. Note that $$\\begin{aligned}\nS_1&=\\psi_{z(\\bga,2)}\\dots \\psi_{z(\\bga,m-1)}\n\\psi_{\\bga-\\bolde_i^{m};m,i}\\psi_{z(\\bga-\\bolde_i^{m},m)}y^{\\lambda}e_{\\lambda}\\\\\n&= \\psi_{\\bga-\\bolde_i^{m};m,i}\\psi_{z(\\bga,2)}\\dots \\psi_{z(\\bga,m-1)}\n\\psi_{z(\\bga-\\bolde_i^{m},m)}y^{\\lambda}e_{\\lambda}\\\\\n&= \\psi_{\\bga-\\bolde_i^{m};m,i}\\psi_{u(\\bga-\\bolde_i^{m})}y^{\\lambda}e_{\\lambda}.\\end{aligned}$$ Moreover, using the inductive assumption, for the third equality below, $S_2$ equals $$\\begin{aligned}\n&-\\psi_{z(\\bga,2)}\\dots \\psi_{z(\\bga,m-1)}\n(y^{\\bar\\mu}e_{\\bar\\mu}\\psi_{\\bar{\\lambda};i}e_{\\bar{\\lambda}} \\circ 1_{\\alpha})\\psi_{z^{{\\gamma}^{(m)}}_{\\lambda}}y_{r_{b+1}({\\lambda})}^{m-1}e_{\\lambda}\\\\\n=& -\n\\big(\\psi_{z(\\bar\\bga,2)}\\dots \\psi_{z(\\bar\\bga,m-1)}y^{\\bar\\mu}e_{\\bar\\mu}\\psi_{\\bar{\\lambda};i}e_{\\bar{\\lambda}} \\circ 1_{\\alpha}\\big)\\psi_{z^{{\\gamma}^{(m)}}_{\\lambda}}y_{r_{b+1}({\\lambda})}^{m-1}e_{\\lambda}\\\\\n=& -\n(\\psi_{u(\\bar\\bga)}y^{\\bar\\mu}e_{\\bar\\mu}\\psi_{\\bar{\\lambda};i}e_{\\bar{\\lambda}} \\circ 1_{\\alpha})\\psi_{z^{{\\gamma}^{(m)}}_{\\lambda}}y_{r_{b+1}({\\lambda})}^{m-1}e_{\\lambda}\\\\\n=& -\n\\Big[\\sum_{r\\in[1,m-1]:\\ {\\gamma}_i^{(r)}=1} \\hspace{-7mm}(-1)^{\\sum_{s=r+1}^{m-1}{\\gamma}_i^{(s)}}\\psi_{\\bar\\bga-\\bolde_i^{r};r,i}\\psi_{u(\\bar\\bga-\\bolde_i^{r})}y^{\\bar {\\lambda}} e_{\\bar {\\lambda}} \\circ 1_{\\alpha}\\Big]\n \\psi_{z^{{\\gamma}^{(m)}}_{\\lambda}} y_{r_{b+1}({\\lambda})}^{m-1}e_{\\lambda}\\\\\n=& \\sum_{r\\in[1,m-1]:\\ {\\gamma}_i^{(r)}=1} (-1)^{\\sum_{s=r+1}^m {\\gamma}_i^{(s)}}\\psi_{\\bga-\\bolde_i^{r};r,i}\n\\psi_{z(\\bga-\\bolde_i^{r},2)}\\dots \\psi_{z(\\bga-\\bolde_i^{r},m-1)}\n\\\\\n&\\times \\Big[y^{\\bar {\\lambda}} e_{\\bar {\\lambda}} \\circ 1_{\\alpha}\\Big]\\psi_{z(\\bga-\\bolde_i^{r},m)}y_{r_{b+1}({\\lambda})}^{m-1}e_{\\lambda}\\\\\n=& \\sum_{r\\in[1,m-1]:\\ {\\gamma}_i^{(r)}=1} (-1)^{\\sum_{s=r+1}^m {\\gamma}_i^{(s)}}\\psi_{\\bga-\\bolde_i^{r};r,i}\n\\psi_{z(\\bga-\\bolde_i^{r},2)}\\dots \\psi_{z(\\bga-\\bolde_i^{r},m)}\n\\\\\n&\\times \\Big[y^{\\bar {\\lambda}} e_{\\bar {\\lambda}} \\circ 1_{\\alpha}\\Big]y_{r_{b+1}({\\lambda})}^{m-1}e_{\\lambda}\\\\\n=& \\sum_{r\\in[1,m-1]:\\ {\\gamma}_i^{(r)}=1} (-1)^{\\sum_{s=r+1}^m {\\gamma}_i^{(s)}}\\psi_{\\bga-\\bolde_i^{r};r,i}\n\\psi_{u(\\bga-\\bolde_i^{r})} y^{\\lambda}e_{\\lambda}.\\end{aligned}$$ Thus $S_1+S_2$ equals the right hand side of the expression in the corollary.", "\n\nThe following statement means that $g$ is chain map:\n\n\\[gchain\\]Let ${\\lambda}\\in{\\Lambda}(n)$ and $\\bga\\in\\bLa(n+1)$. Then $$\\sum_{\\mu\\in{\\Lambda}(n+1)} g^{\\bga,\\mu}_{n+1}d_n^{\\mu,{\\lambda}}=\\sum_{\\bde\\in\\bLa(n)} c_n^{\\bga,\\bde}g^{\\bde,{\\lambda}}_{n}.$$\n\nBy definition, $d_n^{\\mu,{\\lambda}}=0$ unless $\\mu={\\lambda}+\\e_i$ for some $i\\in [a,b]$, and $g^{\\bga,\\mu}_{n+1}=0$ unless $\\mu={\\lambda}^\\bga$. On the other hand, $g^{\\bde,{\\lambda}}_{n}=0$ unless ${\\lambda}={\\lambda}^\\bde$, and $c_n^{\\bga,\\bde}=0$, unless $\\bde=\\bga-\\bolde_i^{r}$ for some $i\\in [a,b]$ and $r\\in[1,m]$. So we may assume that there exists $i\\in [a,b]$ such that ${\\lambda}^\\bga={\\lambda}+\\e_i$, in which case, setting $\\mu:={\\lambda}^\\bga$, we have to prove $$g^{\\bga,\\mu}_{n+1}d_n^{\\mu,{\\lambda}}=\\sum_{r\\in [1,m]:\\ {\\gamma}_i^{(r)}=1}\nc_n^{\\bga,\\bga-\\bolde_i^{r}}g^{\\bga-\\bolde_i^{r},{\\lambda}}_{n}.$$ By definition of the elements involved, this means $$\\begin{aligned}\n&(\\tau_\\bga e_\\bga\\psi_{u(\\bga)}y^\\mu e_\\mu)\n(\\sgn_{{\\lambda};i}e_\\mu\\psi_{{\\lambda};i}e_{\\lambda})\n\\\\\n=\n&\\sum_{r\\in [1,m]:\\ {\\gamma}_i^{(r)}=1}\n(\\sgn_{\\bga-\\bolde_i^{r};r,i}e_{\\bga}\\psi_{\\bga-\\bolde_i^{r};r,i}e_{\\bga-\\bolde_i^{r}})\n(\\tau_{\\bga-\\bolde_i^{r}} e_{\\bga-\\bolde_i^{r}}\\psi_{u(\\bga-\\bolde_i^{r})}y^{\\lambda}e_{\\lambda}).\\end{aligned}$$ Equivalently, we need to prove $$\\begin{aligned}\n\\tau_\\bga \\sgn_{{\\lambda};i} \\psi_{u(\\bga)}y^\\mu e_\\mu\\psi_{{\\lambda};i}e_{\\lambda}=\n\\sum_{r\\in [1,m]:\\ {\\gamma}_i^{(r)}=1}\n\\sgn_{\\bga-\\bolde_i^{r};r,i} \\tau_{\\bga-\\bolde_i^{r}}\n\\psi_{\\bga-\\bolde_i^{r};r,i}\\psi_{u(\\bga-\\bolde_i^{r})}y^{\\lambda}e_{\\lambda},\\end{aligned}$$ which, in view of Corollary \\[C160416G\\], is equivalent to the statement that $$\\tau_\\bga \\sgn_{{\\lambda};i}=\\sgn_{\\bga-\\bolde_i^{r};r,i} \\tau_{\\bga-\\bolde_i^{r}}(-1)^{\\sum_{s=r+1}^m {\\gamma}_i^{(s)}}$$ for all $r\\in [1,m]$ such that ${\\gamma}_i^{(r)}=1$. But this is Lemma \\[LSignsG\\].", "\n\n[BKW]{}\n\n[BKM]{} J. Brundan, A. Kleshchev and P.J. McNamara, Homological properties of finite type Khovanov-Lauda-Rouquier algebras, [*Duke Math. ", "J.*]{} [**163**]{} (2014), 1353–1404.", "\n\n[BKSTwo]{} D. Buursma, A. Kleshchev and D.J. Steinberg, Some Ext algebras for standard modules over KLR algebras of type $A$, [*preprint*]{}, University of Oregon, 2018.", "\n\n[DJ]{} R. Dipper and G.D. James, Representations of Hecke algebras and general linear groups, [*Proc. ", "Lord. ", "Math. ", "Soc. (", "3)*]{} [**52**]{} (1986), 20–52.", "\n\n[Kato]{} S. Kato, Poincaré-Birkhoff-Witt bases and Khovanov-Lauda-Rouquier algebras, [*Duke Math. ", "J.*]{} [**163**]{} (2014), 619–663.", "\n\n[KL1]{} M. Khovanov and A. Lauda, A diagrammatic approach to categorification of quantum groups I, [*Represent. ", "Theory*]{} [**13**]{} (2009), 309–347.", "\n\n[KLMS]{} M. Khovanov, A. Lauda, M. Mackaay and M. Stošić, Extended graphical calculus for categorified quantum $sl(2)$, [*Mem. ", "Amer. ", "Math. ", "Soc.*]{} [**", "219**]{}, No. ", "1029 (2012).", "\n\n[Kdonkin]{} A. Kleshchev, Affine highest weight categories and affine quasihereditary algebras, [*Proc. ", "Lond. ", "Math. ", "Soc. (", "3)*]{} [**110**]{} (2015), 841–882.", "\n\n[KlL]{} A. Kleshchev and J. Loubert, Affine cellularity of Khovanov-Lauda-Rouquier algebras of finite types, [*Int. ", "Math. ", "Res. ", "Not. ", "IMRN*]{} [**14**]{} (2015), 5659–5709.", "\n\n[KS]{} A. Kleshchev and D.J. Steinberg, Homomorphisms between standard modules over finite-type KLR algebras, [*Compos. ", "Math.*]{} [**", "153**]{} (2017), 621–646.", "\n\n[Ro]{} R. Rouquier, $2$-Kac-Moody algebras; [arXiv:0812.5023]{}.", "\n\n[Weibel]{} C. Weibel, [*An Introduction to Homological Algebra*]{}, Cambridge University Press, 1994\n\n[^1]: The second author was supported by the NSF grants DMS-1161094, DMS-1700905, the Max-Planck-Institut, the Fulbright Foundation, and the DFG Mercator program through the University of Stuttgart.", "\n" ]

{ "pile_set_name": "ArXiv" }

[ 0.008884501480750246, 0, 0, 0.00267379679144385, 0.005509641873278237, 0.002, 0, 0, 0, 0, 0.005698005698005698, 0, 0.002173913043478261, 0, 0, 0, 0.0019880715705765406, 0.037037037037037035, 0.002105263157894737, 0, 0, 0.007936507936507936, 0, 0, 0, 0, 0, 0, 0, 0, 0.002369668246445498, 0, 0, 0.008849557522123894, 0, 0, 0.008375209380234505, 0.010526315789473684, 0.004888647474198805, 0.008866075594960336, 0.0048449612403100775, 0.0044994375703037125, 0, 0, 0, 0.006472491909385114, 0, 0.0038707756438886407, 0.006486486486486486, 0, 0.004405286343612335, 0.003929273084479371, 0, 0, 0, 0.004075394803871625, 0.002320185614849188, 0.007518796992481203, 0.006616257088846881, 0.008020050125313283, 0.008264462809917356, 0, 0.0014038371548900327, 0.0015048908954100827, 0.0026455026455026454, 0.002540220152413209, 0.0018248175182481751, 0, 0, 0.0017167381974248926, 0.0018990346573824971, 0, 0, 0.014519056261343012, 0.007547169811320755, 0.0028089887640449437, 0, 0, 0.004533091568449683, 0.003215434083601286, 0.0033444816053511705, 0.00625, 0.003616636528028933, 0, 0, 0, 0, 0, 0.002840909090909091, 0.0028011204481792717, 0.013888888888888888, 0.0020479213598197828, 0, 0, 0.002826455624646693, 0.0009823182711198428, 0.005813953488372093, 0.0026619343389529724, 0.00980392156862745, 0, 0, 0, 0.0025031289111389237, 0, 0.0016638935108153079, 0, 0.0034542314335060447, 0.003194888178913738, 0, 0, 0.0024479804161566705, 0.006289308176100629, 0.0023296447291788003, 0.0051813471502590676, 0.002253944402704733, 0.006042296072507553, 0.015151515151515152, 0.021505376344086023, 0.002380952380952381, 0, 0, 0.005222841225626741, 0.0012106537530266344, 0, 0.00468384074941452, 0.013360739979445015, 0, 0, 0.0023584905660377358, 0.002861685214626391, 0.010869565217391304, 0.010752688172043012, 0.0013679890560875513, 0.001968503937007874, 0.0196078431372549, 0.004796163069544364, 0.011235955056179775, 0.005596211795092553, 0.024691358024691357, 0.004825538233110616, 0.0030464584920030465, 0, 0.0024875621890547263, 0, 0.0023584905660377358, 0.0196078431372549, 0.0025041736227045075, 0.0027522935779816515, 0.004651162790697674, 0, 0.002800336040324839, 0, 0.002074688796680498, 0.013793103448275862, 0, 0.0047489823609226595, 0.0011389521640091116, 0.010309278350515464, 0.021739130434782608, 0.0040941658137154556, 0.019230769230769232, 0.008695652173913044, 0, 0.0037593984962406013, 0.022222222222222223, 0.002253944402704733, 0.010638297872340425, 0.0012224938875305623, 0.004901960784313725, 0, 0.0009337068160597573, 0, 0.00851063829787234, 0.0018582046883933677, 0.0020939276099311995, 0, 0, 0.005522827687776142, 0.0010498687664041995, 0.02702702702702703, 0, 0.029239766081871343, 0.009615384615384616, 0, 0, 0, 0, 0.03, 0, 0.008771929824561403, 0, 0.007751937984496124, 0, 0, 0, 0, 0, 0.02830188679245283, 0, 0, 0, 0, 0.025423728813559324, 0, 0, 0, 0.02631578947368421, 0.01639344262295082, 0, 0, 0.030303030303030304, 0.019867549668874173, 0 ]

[ "As I sit in front of my air conditioner, looking up weather forecasts of extreme heat for most of the United States, I started to wonder about how computers keep themselves cool. ", "Let’s look at desktops. ", "Why would anyone need more than a simple fan exhaust? ", "If you are just checking your e-mails and reading articles on Wikipedia, you will not need to worry about anything more than that. ", "Increased power consumption equates to more" ]

{ "pile_set_name": "Pile-CC" }

[ 0, 0.041666666666666664, 0, 0.007633587786259542, 0 ]

[ "How to Build a Barn Owl Box\n\nPurpose: To construct and install a fully functioning Barn Owl nest box that can be used for nesting broods.", "\n\nWhy build a Barn Owl box? ", "Barn Owls are one of the most widespread owl species in the world, but in many parts of their range across the United States, populations have been declining because of habitat loss. ", "These birds prey upon small mammals, particularly rodents, which makes them beneficial in many habitats. ", "Many farmers are major advocates of owl nest boxes for this reason alone. ", "These birds require nests that are roomy enough to support a brood size up to 18 nestlings, yet small enough to deter larger birds like the Great Horned Owl from entering the nests. ", "Barn Owls are cavity nesters and therefore, do not build their own nests. ", "This reason is why it is highly important to encourage people to create nest boxes. ", "By constructing nest boxes, Barn Owls are encouraged to inhabit them and rear their young in them.", "\n\nFor Safety:Wear goggles for eye protection when using the saw\n\nBe aware when using the saw\n\nWhen not in use, keep saw out of reach of children\n\nKeep track of tools at all times\n\nWear closed-toe shoes\n\nEquipment Checklist:\n\n4’ x 8’ x ½” plywood sheet\n\nHammer\n\n56 (minimum) common nails, size 8d\n\nSafety goggles\n\nRuler or yard stick\n\n# 2 pencil or preferred marking utensil\n\nDrill\n\n12 amp 7 1/2\" electric circular saw\n\n1 lb of wood shavings\n\nOverview of Steps:\n\n1. ", "Measuring and cutting plywood boards\n\n2. ", "Drilling holes in bottom board for drainage\n\n3. ", "Assembling the pieces for a finished product\n\n4. ", "Bedding installation\n\nSupplies:\n\nStep 1: Measuring and Cutting Plywood Boards\n\n1. ", "Using your ruler, measure out two sections that are 22” x 23” and make a mark using your pencil. ", "These two pieces will be designated as the top and the bottom of the nest box.", "\n\n2. ", "Using the same plywood board, measure four sections that are 18” x 22” and mark them with your pencil. ", "These pieces will be used for the two sides, the front, and the back.", "\n\n3. ", "Now, you are going to want to put your goggles on and grab the saw. ", "Cut out each section from the plywood that you have traced. ", "Take your time on this part and make sure to follow along the lines.", "\n\n4. ", "Take one of the 18” x 22” pieces you have cut and designate it as the front board that will have the entrance. ", "Measure 5.5” from both edges on the longer side and then draw a line from to this point towards the opposite of the board that is 10” long.. This should give you a space in between those two points that is 10” long. ", "Finally, connect the two 10” lines all the way across to make a square.", "\n\n5. ", "Once you have completed step 4, use your saw to carefully cut out the 10” x 10”entrance square.", "\n\n6. ", "With the leftover plywood, measure one section 16” x 3’ and make a mark using your pencil. ", "Measure another section of 3” x 3” and mark it with your pencil.", "\n\n7. ", "Carefully use your saw to cut the marked areas. ", "These are the pieces for the platform that will be nailed under the entrance square. ", "You now all the pieces you need to start constructing the nest box.", "\n\nStep 2: Drilling Holes in Bottom of Board for Drainage\n\n1. ", "Before assembling the nest box, take the bottom 23” x 22” piece of plywood and, using the drill, drill a generous number of holes approximately ¼” to ½” in diameter, 1\"-2\" apart.", "\n\nStep 3: Assembling the Pieces to Create a Finished Product\n\n1. ", "Put one 22” x 18” side panel and the front panel together so that they meet at a 90 degree angle. ", "Make sure the front panel is facing the correct way, with the entrance at the top. ", "The side panel should overlap the front panel for easy assembly. ", "Hammer at least 4 nails into the side panel where they come together, spaced apart as needed.", "\n\n2. ", "With another 22” x 18” side panel, attach it to the opposite side of the front panel at a 90 degree angle, overlapping the side panel on top. ", "Hammer in at least 4 nails the same way as the first side panel.", "\n\n3. ", "Now attach the last 22” x 18” side panel (the back) at a 90 degree angle to the two attached sides. ", "Hammer at least 4 nails into each edge through the back panel the same way you attached the others in step 1 & 2.", "\n\n4. ", "Flip the box over and lay the bottom 22” x 23” panel on top. ", "Try to line up the sides of the box with the edge of the panel as precisely as possible. ", "Hammer in at least 4 nails on each edge similar to the previous steps.", "\n\n5. ", "Flip the box back over, so that the bottom is on the bottom. ", "From the inside, use at least 2 nails to hammer in the 3\" x 3\" base of the platform.", "\n\nStep 4: Bedding Installation\n\n1. ", "Cover the bottom of the nest box evenly with 1”-2” of wood shavings." ]

{ "pile_set_name": "Pile-CC" }

[ 0, 0, 0, 0, 0, 0, 0, 0, 0.01020408163265306, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.04918032786885246, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]

[ "Thursday, March 20, 2008\n\nAdmiral Fallon Goes Down With His Ship\n\nEver since the invasion of Iraq, my opinion of US flag officers in all services is one of disgust; these officers, in the main, put their careers above their integrity. ", "One exception was Army General Shenseki who told Congress that the battle plan for Iraq was seriously flawed; afterwards, his career was quickly ended. ", "Admiral Fallon's recent abrupt resignation was a loss to America, but it restored hope that US military leadership still has elements that prefer integrity to career promotion and survival.", "\n\nTop US Military leadership is mainly composed of graduates from the national military academy system. ", "Patriotism is imbued into the graduates with a strong allegiance to a chain of command that emanates from the president as commander and chief. ", "It is apparent that during their education process a normal synapse between judgment, duty and loyalty is severed. ", "Otherwise, how can you explain the failure of this leadership corps to raise serious objections to the military fiasco in Iraq as it proceeded. ", "Even an eighth-grade student playing battle checkers knew better. (", "Failure to prevent widespread looting and secure Saddam's ammo dumps – duh.)", "\n\nThis appalling failure of flag officer professionalism was compounded as many took lucrative work on retirement on the cable and network news shows as military experts. ", "Their main task seemed to justify the military disasters. ", "You do not see them on TV much anymore. ", "The military experts who mainly survived this time are below flag rank and were less politicized.", "\n\nThese talking head generals and admirals were followed by another wave of more flag officers saying mea culpa for following stupid orders blindly. ", "The publishing of two books on the Iraq war, COBRA TWO and FIASCO, no doubt prompted their epiphany. ", "You can find some of them now bobbing their heads on stage with Hillary Clinton at campaign rallies. ", "All blame Rumsfeld for their failures. ", "While on active duty, they conducted themselves as Chihuahuas, but transformed themselves into Doberman Pinchers on retirement.", "\n\nOn March 11th of this year the USS Admiral Fallon hit a political reef and subsequently sank. ", "The admiral went down with his ship. ", "Fallon had consented to interviews in ESQUIRE MAGAZINE that were published on that date. ", "The article was titled MAN BETWEEN WAR AND PEACE; it portrayed Fallon as a man who believed in political engagement as opposed to neocon saber rattling. ", "The article was written by T.P.M. Barnett whose giddy, almost immature piece projected Fallon as the bulwark against more wars promoted by GW Bush's neocons. ", "It further demonstrated that Fallon was a pragmatic, strategic thinker who had no time for the neocon political voodoo, and democratic messianism. ", "This clash of ideology was enough for the White House to have SECDEF Gates fire Fallon. ", "The admiral and his staff bear some responsibility for letting the story get away from them.", "\n\nWith his resignation, Fallon,apparently wanting to salute pro forma, claimed that there were no policy differences between him and the White house; this is nonsense. ", "It is clear that Fallon wanted troop draw downs in Iraq soonest and to be circumspect on Iran; the admiral sat on the Administration's darling General Save US Petraeus who has been muzzled until a few days ago when he popped up in the news after Fallon no longer was his boss at CENTCOM.", "\n\nAdmiral Fallon is a special breed of flag officer seldom found today. ", "He combines moral and physical courage, intellect with sense for action found only in high class leaders. ", "His problem was that he was smarter than the loony tunes leadership in the White House; with the unintended help of the ESQUIRE article, he let GW Bush know it. ", "See you in Valhalla, Admiral – DAMN THE TORPEDOES; FULL SPEED AHEAD. ", "Thank you for your outstanding service. ", "Hope there are more like you wandering around the Pentagon and unified commands. ", "Colonel Robert E Bartos USA Ret.", "\n\nFYI: Admiral Fallon is a graduate of Villanova University and not a graduate of a service academy. ", "This probably explains his different national sense of duty with the ability to think for himself. ", "He has 1300 carrier-assisted landings and 4800 flight hours. ", "Unlike Bomb Bomb McCain, he has not crashed three aircraft and was not shot down. ", "Also, his father was not an Admiral.", "\n\n1 Comments:\n\nAnonymous said...\n\nIt is hard to believe ADM Fallon made it this far. ", "The Navy likes to promote \"head nodders\", people who agree and do not think.", "\n\nI think the failure in Iraq, would be a good reason to consider abolishing or restructuring the academies. ", "Why waste all the money to learn, then loose another war, because the Academies train people to \"go along and get along\". ", "Do not try and create waves or make improvement.", "\n\nLinks to this post:\n\nAbout Me\n\nColonel Robert E Bartos Ret US Army-served as Military Attache to Moscow and Belgrade-Chief of Foreign Intelligence on Army Dept Army Staff-commanded battalion in Vietman-member of President Reagan's transition team-advisor to Strategic Arms Delegation in Geneva--now spends time between Washington, DC and the Caribbean" ]

{ "pile_set_name": "Pile-CC" }

[ 0, 0.019736842105263157, 0, 0.009615384615384616, 0, 0, 0, 0, 0.013157894736842105, 0, 0, 0, 0, 0, 0, 0.009900990099009901, 0.02564102564102564, 0.015748031496062992, 0, 0, 0, 0, 0.012658227848101266, 0, 0.011363636363636364, 0, 0.005952380952380952, 0.010452961672473868, 0, 0, 0.012422360248447204, 0.014492753623188406, 0, 0.012345679012345678, 0.03125, 0.009900990099009901, 0, 0, 0.012195121951219513, 0.027777777777777776, 0.011764705882352941, 0.013157894736842105, 0, 0, 0, 0.0113314447592068 ]

[ "Workers facing redundancy at Scottish factories Pinneys and 2 Sisters should be offered the chance to buy out the companies to save their jobs, says Scottish Labour leader Richard Leonard.", "\n\nMr Leonard, MSP for Central Scotland, told delegates from the Scottish TUC of his plans for a version of Italy’s Marcora Law, which allows redundant workers to use their unemployment benefit to buy their companies.", "\n\nHe made the remarks after Young’s Seafood announced plans to shut its Pinneys plant at Annan, Dumfries, and move production south, threatening 450 jobs.", "\n\nAnd another 450 jobs are at stake at food manufacturer 2 Sisters, which is consulting on the closure of its plant at Cambuslang, Lanarkshire.", "\n\nHe said: “We need forward planning, economic planning and also environmental planning to tackle humanity’s greatest challenge – climate change.", "\n\n“We need democracy in our economy, not just when things go wrong, but to help things go right in the first place.”", "\n\nHe added: “We need to look afresh at who owns the Scottish economy and why we are so vulnerable to external shocks – and why so much wealth leaks out from our country.”", "\n\nThe Marcora Law, brought in by Italy’s trade and industry minister Giovanni Marcora in 1985, provides state backing for two funds to support co-­operatives, including one for new co­-ops set up by employees who have been laid off when companies close or downsize.", "\n\nIt has seen the creation of more than 250 worker-owned firms, saving more than 9,000 jobs." ]

{ "pile_set_name": "OpenWebText2" }

[ 0.005319148936170213, 0.009259259259259259, 0.012987012987012988, 0.006993006993006993, 0, 0, 0, 0.0037735849056603774, 0 ]