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"× Expand Fibonacci Blue\n\nWanda Coker was rudely awakened to economic injustice during her pregnancy in 1995. ",
"Unable to secure government assistance, she says she was hospitalized seven times due to the overwork, poverty wages, and the resulting malnutrition that she endured as a fast-food worker.",
"\n\nBut the fifty-one-year-old, now an assistant manager at a Burger King in Durham, North Carolina, began fighting back a year and a half ago. ",
"That’s when her daughter, a McDonald’s employee at the time, recruited Coker to the Fight for $15 movement, which has sparked wage increases for millions across the country.",
"\n\nThe two are now looking to help kick Fight for $15 into higher gear. ",
"On February 12, they will participate in nationwide strikes and protests in partnership with a revived Poor People’s Campaign, originally organized by Dr. Martin Luther King. ",
"The event could offer a welcome boost to Fight for $15, while elevating the visibility of the the Poor People’s Campaign as it prepares to unleash a wave of mass civil disobedience this spring.",
"\n\nWanda Coker\n\n“We need everybody in America to be able to feed their families, afford to live, keep their lights on,” Coker tells The Progressive.",
"\n\nOn February 12, thousands of fast-food cooks and cashiers will walk off their jobs to demand higher wages and union rights, in a protest that commemorates the the fiftieth anniversary of a sanitation workers strike in Memphis, Tennessee—a historic struggle championed by King shortly before his assassination.",
"\n\nThe Poor People’s Campaign was launched in 1968 to “dramatize the plight of America’s poor of all races and make very clear that they are sick and tired of waiting for a better life,” the Reverend Ralph Abernathy said at the time. ",
"Abernathy led the campaign after King’s assassination.",
"\n\nThe rebooted movement—officially called the Poor People’s Campaign: A National Call for Moral Revival—will carry on this tradition, demanding solutions to a range of interlocking injustices, including systemic racism, economic inequality, voter suppression, and environmental destruction, says the Reverend Liz Theoharis, who co-chairs the Poor People’s Campaign with the Reverend William Barber II.",
"\n\nFight for $15, Theoharis explains in an interview, will provide “a real infusion of excitement and energy” into the Poor People’s Campaign. ",
"The collaboration could also provide a lift to Fight for $15.",
"\n\nSparked by New York City McDonald’s workers who staged a walkout in 2012, Fight for $15 has spurred dozens of cities and states to increase minimum wages, resulting in raises for roughly half of the forty-three million people who were reportedly earning poverty wages in 2013, estimates Stephanie Luce, a labor professor at the City University of New York. ",
"It’s put ten million of these workers on a path to $15 an hour, according to Fight for $15.",
"\n\nYet the movement has struggled to notch victories in states that prohibit localities from setting their own minimum wages, Luce said. ",
"It’s main underwriter, SEUI, is also thought to have scaled back funding, having reportedly planned on slashing its budget under a Trump administration. ",
"And the movement has had little success with unionizing low-wage workers, though it did spawn an innovative nonprofit in New York City.",
"\n\n“We need everybody in America to be able to feed their families, afford to live, keep their lights on.”",
"\n\nThe collaboration with the Poor People’s Campaign may breath new life into Fight for $15 by further emphasizing the link between economic and racial inequality, as well as by tying in other causes, Luce says.",
"\n\nThe movement has needed “to elevate the fight from issues to values” and articulate a “vision that challenges the very precepts and assumptions of capitalist society,” argues Jonathan Rosenblum, a long-time organizer who helped lead the first successful battle for a $15 minimum wage, in SeaTac, Washington,\n\n“The Poor People’s Campaign has the potential to provide this transformational lever, by elevating the fight from a number, 15, to a moral movement,” he said.",
"\n\nOn Monday, fast-food workers, historians, and community leaders from across the country will converge on Memphis for a forum on the legacy of the sanitation workers strike, followed by a march from Clayborn Temple to Memphis City Hall, the same path walked by the sanitation workers fifty years ago.",
"\n\nStrikers in more than two dozen other cities, including Los Angeles, Detroit, Atlanta, St. Louis, Chicago, Miami and Houston, will also hold marches and protests.",
"\n\n“We’re going to try to get some of the workers inside to come out and join us,” Coker says about a planned rally in front of a McDonald’s on Martin Luther King Parkway in Durham, Tennessee. ",
"Her Fight for $15 chapter helped put Durham city workers on a path to a minimum of $15 an hour, but she wants the wage expanded, along with stronger union rights.",
"\n\n“We can shift the conversation away from blaming people for problems they’re having.”",
"\n\nThe February 12 protest is a prelude to a forty-day offensive that the Poor People’s Campaign will launch on Mother’s Day, May 13. ",
"The nationwide campaign will feature six weeks of direct action, public education and civil disobedience, climaxing in a “massive mobilization,” in Washington, D.C. on June 23, Theoharis said.",
"\n\n“[We] will put ourselves and our bodies on the line to make sure that . . . ",
"we can shift the conversation away from blaming people for problems they’re having,” Theoharis says.",
"\n\nThe movement aligns a broad array of unions, community groups and other organizations, with coordinating committees in thirty-two states. ",
"It will be mutually “transformative” for participating organizations, not “transactional,” Theoharis says. ",
"And it will draw inspiration from a famous statement made by King during a lecture in 1967:\n\n“Disinherited people all over the world are bleeding to death from deep social and economic wounds. ",
"They need brigades of ambulance drivers who will have to ignore the red lights of the present system until the emergency is solved.”",
"\n\nTeke Wiggin is a freelance Brooklyn-based reporter who covers labor, technology and housing. ",
"Follow him at @tkwiggin."
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"Fans of Luke Danes, the rough-around-the-edges, yet surprisingly soft-hearted owner of Luke’s Diner in the hit drama Gilmore Girls, can check out the actor in a different capacity as Scott Patterson serves up not just coffee, but an acoustic set with this band Smithradio as well.",
"\n\nFox Coffee House will host Smithradio on Friday, July 21 at noon during their tour promoting the band as well as Patterson’s own coffee brand. ",
"Tickets are now available to participate in a contest, meet and greet and attend the acoustic set.",
"\n\nDuring the Atomic Love Coffee House US Tour, featuring intimate shows in coffee houses across the United States, Patterson is set to perform originals from his catalogue of nearly 600 songs.",
"\n\nTickets to the event can be purchased here.",
"\n\nFox Coffee House is located at 437 West Willow Street."
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"Last updated on .From the section Football\n\nArsenal are working on deals to sign Real Madrid attacking pair Karim Benzema and Angel Di Maria.",
"\n\nThe Gunners are prepared to pay £40m for 25-year-old France striker Benzema after missing out on Gonzalo Higuain and Liverpool's Luis Suarez.",
"\n\nArsenal boss Arsene Wenger also wants Argentina left-winger Di Maria, 25, and is understood to be chasing a keeper and a defender as well.",
"\n\nBenzema factfile Born: 19 December, 1987\n\nClub career: After excelling for hometown club Lyon, moved to Spanish giants Real Madrid for £35m in 2009\n\nInternational career: Continues to endure an infuriating time with France, with the 25-year-old currently suffering an international goal drought of 1,155 minutes\n\nThe Londoners won 3-0 at Fenerbahce in the Champions League on Wednesday.",
"\n\nIt means they are in control of the qualifying play-off tie heading into the second leg at Emirates Stadium on 27 August and should they reach the Champions League group stage for a 16th consecutive season, it could help attract transfer targets to the club.",
"\n\nWenger is a long-term admirer of Benzema, who joined Real from Lyon for an initial £30m in 2009, while Di Maria arrived at the Bernabeu from Benfica a year later.",
"\n\nArsenal's only summer signing to date is the 20-year-old French striker Yaya Sanogo on a free transfer from Auxerre, but it is thought they could spend close to £100m by the close of the transfer window at 23:00 BST on 2 September.",
"\n\nSpeaking after his side's win at Fenerbahce in their Champions League qualifying play-off first leg, Wenger admitted the pursuit of Suarez was over after Liverpool rejected two bids for their Uruguay forward and insisted he was not for sale.",
"\n\n\"Absolutely no chance of that,\" Wenger said about the chances of Suarez arriving at Emirates Stadium.",
"\n\nDi Maria factfile Born: 14 February, 1988\n\nClub career: After impressing at Benfica following his switch from Argentina's Rosario Central, has performed a key role at Real Madrid since his £20m move in 2010\n\nInternational career: Won Olympic gold with Argentina in 2008, and represented his country at the 2010 World Cup\n\nThe Gunners have also had a £10m offer for Newcastle midfielder Yohan Cabaye turned down, but Wenger suggested the final 12 days of the transfer window would be busy.",
"\n\nArsenal lost at home to Aston Villa on the opening day of the Premier League season and have suffered injuries to Mikel Arteta, Alex Oxlade-Chamberlain and Laurent Koscielny, while Abou Diaby remains sidelined and fellow midfielder Jack Wilshere is still returning to full match fitness.",
"\n\n\"Quality wise we do not need, but numbers wise we are short,\" Wenger continued.",
"\n\n\"We lost Arteta and Diaby. ",
"We are without three international midfielders. ",
"We will try and bring one in but we are working on that. ",
"What you have to understand is that there is still a long way to go.",
"\n\n\"The transfer market really starts now, a lot of activity will happen between now and 2 September. ",
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"Using the CSSTransition Component\n\nLet’s begin by creating a simple button that will display something when the user clicks on it.",
"\n\nInside the my-app ‘s src folder, open the index.js file and replace the code inside it with the one shown below:\n\nWe will also need to work a little bit on our CSS, but I don’t want to make this post unnecessarily long, so just go here and copy the code in to index.css file in your src folder. ",
"Don’t worry, we will take a look at it soon.",
"\n\nOpen your browser and you will get something like this:\n\nWhen the user clicks on the button, the onClick triggers the toggle method, which changes the state of the application. ",
"Based on this state, the list is either displayed or hidden from the view.",
"\n\nYou can see that the list is suddenly appearing on and disappearing from the screen. ",
"What if you want it to make this change a little smoother?",
"\n\nThe React Transition Group contains three main components:\n\nTransition\n\nCSSTransition\n\nTransitionGroup\n\nThe Transition and CSSTransition components can be use to handle transition of single components. ",
"Let’s start by taking a look at how we can us the CSSTransition component to make the above button and its function smoother.",
"\n\nLet’s start by importing the CSSTransition component from the react-transition-group library into the index.js file.",
"\n\nimport {CSSTransition} from 'react-transition-group';\n\nCSSTransition allows us to apply CSS transitions to DOM elements. ",
"In the render method, replace the this.state.display line with the CSSTransition component. ",
"This component will have an in prop which will check the boolean value of this.state.display . ",
"Also, the component will have a timeout prop which will describe the amount of milliseconds it will take for the element to enter or leave the DOM. ",
"We will also need to pass a classNames prop which will have a string as its value, and will tell our component which CSS properties to apply to the component’s transition. ",
"The unmountÒnExit prop is used to completely remove something from the DOM, instead of just hiding it away from the view.",
"\n\nSo wrap the <ul> and everything inside it in the <CSSTransition> as shown below:\n\n<CSSTransition\n\nin={this.state.display}\n\ntimeout={350}\n\nclassNames=\"display\"\n\nunmountOnExit\n\n>\n\n<div className=\"menu\">\n\n<ul className=\"list\">\n\n<li className=\"list-item\">Rajat</li>\n\n<li className=\"list-item\">Writes about React</li>\n\n<li className=\"list-item\">Loves Pizza</li>\n\n</ul>\n\n</div>\n\n</CSSTransition>\n\nLet’s take look at what we have in our browser now:\n\nHow did this happen? ",
"All we did was wrap the list inside the <CSSTransition> component. ",
"Let’s take a look at the CSS code inside index.css file to know more.",
"\n\nFirst, we have list of variables defined, that control the colors and measurements of the button and the list. ",
"We also have a timeout value set to 350ms, same as that of the timeout prop inside the CSSTransition component.",
"\n\nThen, we have set the style for the button and the list that is to be displayed. ",
"Nothing special here, we do this all the time.",
"\n\nAfter that, we have style code that controls the transition. ",
"This is where the CSSTransition component comes into play. ",
"The component gives us four class names to use in order to control the entrance and exit of an element from the DOM. ",
"These class names are:\n\ndisplay-enter\n\ndisplay-enter-active\n\ndisplay-exit\n\ndisplay-exit-active\n\nThe display-enter will be enacted immediately when the element enters the DOM. ",
"The display-enter-active will apply once the display-enter is done implementing. ",
"This is where we add our transition.",
"\n\ndisplay-exit will trigger when the display state turns false , followed by the display-exit-active , after which the list element will leave the DOM.",
"\n\nThe appear prop\n\nCurrently the app does not show the list when we initially load the app onto the browser. ",
"The user has to click on the button in order to make the list appear on the screen.",
"\n\nWhat if you want to show the list initially when the page loads? ",
"Well then you need to change the display state’s value to true in the code.",
"\n\nstate = {\n\ndisplay: true,\n\n};\n\nBut now when we take a look at the page in the browser, you will see that the list and the button are just there. ",
"Refresh the page, and you will notice that the list appear instantly, without any transition.",
"\n\nYou can implement an initial transition by adding the appear prop to the <CSSTransition> component as shown below:\n\n<CSSTransition\n\nin={this.state.display}\n\ntimeout={350}\n\nclassNames=\"display\"\n\nunmountOnExit\n\nappear\n\n>\n\nThen, go to the index.css file and add .display-appear to .display-enter and .display-appear-active to .display-enter-active as shown below:\n\n.display-enter, .display-appear {\n\ntop: var(--menu-starting-top);\n\nwidth: var(--toggler-width);\n\nmax-height: var(--toggler-height);\n\ncolor: var(--fade-from-color);\n\nbackground-color: var(--toggler-bg-color);\n\n} .display-enter-active, .display-appear-active {\n\ntop: var(--menu-ending-top);\n\nwidth: var(--menu-width);\n\nmax-height: var(--menu-max-height);\n\ncolor: var(--fade-to-color);\n\nbackground-color: var(--menu-bg-color);\n\ntransition: all var(--timeout);\n\n}\n\nIf you refresh the browser, you will get to see the initial transition like this:\n\nEnter and Exit\n\nIn order to disable a particular transition, we can use the enter and exit props.",
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"\n\nThis marks the third year in a row Milligan has won the NAIA Direct Qualifier event as the Buffaloes advance to the NAIA National Championship Tournament, which is set for May 23-26 at PGA National in Palm Beach Gardens, Fla.\n\nIn the top competition, St. Andrews finished second at 616 with SCAD Atlanta (640) taking third, Tennessee Wesleyan University (651) fourth, and Point University (653) fifth. ",
"Making up the rest of the field were: Truett McConnell University (676) sixth, Bryan College (687) seventh, Reinhardt University (716) eighth, Columbia College (726) ninth, Montreat College (763) 10th, and Union College did not finish.",
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"Generated by Doxygen 1.8.5 -->\n<script type=\"text/javascript\">\nvar searchBox = new SearchBox(\"searchBox\", \"search\",false,'Search');\n</script>\n <div id=\"navrow1\" class=\"tabs\">\n <ul class=\"tablist\">\n <li><a href=\"index.html\"><span>Main Page</span></a></li>\n <li><a href=\"namespaces.html\"><span>Namespaces</span></a></li>\n <li class=\"current\"><a href=\"annotated.html\"><span>Classes</span></a></li>\n <li><a href=\"files.html\"><span>Files</span></a></li>\n <li>\n <div id=\"MSearchBox\" class=\"MSearchBoxInactive\">\n <span class=\"left\">\n <img id=\"MSearchSelect\" src=\"search/mag_sel.png\"\n onmouseover=\"return searchBox.",
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"window showing the filter options -->\n<div id=\"MSearchSelectWindow\"\n onmouseover=\"return searchBox.",
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"OnSelectItem(4)\"><span class=\"SelectionMark\"> </span>Variables</a><a class=\"SelectItem\" href=\"javascript:void(0)\" onclick=\"searchBox.",
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"OnSelectItem(6)\"><span class=\"SelectionMark\"> </span>Enumerations</a><a class=\"SelectItem\" href=\"javascript:void(0)\" onclick=\"searchBox.",
"OnSelectItem(7)\"><span class=\"SelectionMark\"> </span>Enumerator</a><a class=\"SelectItem\" href=\"javascript:void(0)\" onclick=\"searchBox.",
"OnSelectItem(8)\"><span class=\"SelectionMark\"> </span>Friends</a></div>\n\n<!-- ",
"iframe showing the search results (closed by default) -->\n<div id=\"MSearchResultsWindow\">\n<iframe src=\"javascript:void(0)\" frameborder=\"0\" \n name=\"MSearchResults\" id=\"MSearchResults\">\n</iframe>\n</div>\n\n<div id=\"nav-path\" class=\"navpath\">\n <ul>\n<li class=\"navelem\"><a class=\"el\" href=\"namespacefaiss.html\">faiss</a></li><li class=\"navelem\"><a class=\"el\" href=\"structfaiss_1_1IndexFlatL2BaseShift.html\">IndexFlatL2BaseShift</a></li> </ul>\n</div>\n</div><!-- top -->\n<div class=\"header\">\n <div class=\"headertitle\">\n<div class=\"title\">faiss::IndexFlatL2BaseShift Member List</div> </div>\n</div><!--header-->\n<div class=\"contents\">\n\n<p>This is the complete list of members for <a class=\"el\" href=\"structfaiss_1_1IndexFlatL2BaseShift.html\">faiss::IndexFlatL2BaseShift</a>, including all inherited members.</p>\n<table class=\"directory\">\n <tr class=\"even\"><td class=\"entry\"><a class=\"el\" href=\"structfaiss_1_1IndexFlat.html#a406f028c702edec72477eacc5733f59c\">add</a>(idx_t n, const float *x) override</td><td class=\"entry\"><a class=\"el\" href=\"structfaiss_1_1IndexFlat.html\">faiss::IndexFlat</a></td><td class=\"entry\"><span class=\"mlabel\">virtual</span></td></tr>\n <tr><td class=\"entry\"><a class=\"el\" href=\"structfaiss_1_1Index.html#aa6931dfe054b33b02c842ff75f7a0c7f\">add_with_ids</a>(idx_t n, const float *x, const long *xids)</td><td class=\"entry\"><a class=\"el\" href=\"structfaiss_1_1Index.html\">faiss::Index</a></td><td class=\"entry\"><span class=\"mlabel\">virtual</span></td></tr>\n <tr class=\"even\"><td class=\"entry\"><a class=\"el\" href=\"structfaiss_1_1Index.html#a8bc5d8d1cd0dd7b34b3c98a9f76b4a9c\">assign</a>(idx_t n, const float *x, idx_t *labels, idx_t k=1)</td><td class=\"entry\"><a class=\"el\" href=\"structfaiss_1_1Index.html\">faiss::Index</a></td><td class=\"entry\"></td></tr>\n <tr bgcolor=\"#f0f0f0\"><td class=\"entry\"><b>component_t</b> typedef (defined in <a class=\"el\" href=\"structfaiss_1_1Index.html\">faiss::Index</a>)</td><td class=\"entry\"><a class=\"el\" href=\"structfaiss_1_1Index.html\">faiss::Index</a></td><td class=\"entry\"></td></tr>\n <tr class=\"even\"><td class=\"entry\"><a class=\"el\" href=\"structfaiss_1_1IndexFlat.html#a14b51786e7f98be1954eef35d02813a7\">compute_distance_subset</a>(idx_t n, const float *x, idx_t k, float *distances, const idx_t *labels) const </td><td class=\"entry\"><a class=\"el\" href=\"structfaiss_1_1IndexFlat.html\">faiss::IndexFlat</a></td><td class=\"entry\"></td></tr>\n <tr><td class=\"entry\"><a class=\"el\" href=\"structfaiss_1_1Index.html#aaae77608bbda70b1098897e9167a82f9\">compute_residual</a>(const float *x, float *residual, idx_t key) const </td><td class=\"entry\"><a class=\"el\" href=\"structfaiss_1_1Index.html\">faiss::Index</a></td><td class=\"entry\"></td></tr>\n <tr class=\"even\"><td class=\"entry\"><a class=\"el\" href=\"structfaiss_1_1Index.html#a2a002388d2c081c2dbab8508dcefe73d\">d</a></td><td class=\"entry\"><a class=\"el\" href=\"structfaiss_1_1Index.html\">faiss::Index</a></td><td class=\"entry\"></td></tr>\n <tr><td class=\"entry\"><a class=\"el\" href=\"structfaiss_1_1Index.html#a373c30e3d87d1d4e616f450d87152b1a\">display</a>() const </td><td class=\"entry\"><a class=\"el\" href=\"structfaiss_1_1Index.html\">faiss::Index</a></td><td class=\"entry\"></td></tr>\n <tr bgcolor=\"#f0f0f0\" class=\"even\"><td class=\"entry\"><b>distance_t</b> typedef (defined in <a class=\"el\" href=\"structfaiss_1_1Index.html\">faiss::Index</a>)</td><td class=\"entry\"><a class=\"el\" href=\"structfaiss_1_1Index.html\">faiss::Index</a></td><td class=\"entry\"></td></tr>\n <tr><td class=\"entry\"><a class=\"el\" href=\"structfaiss_1_1Index.html#ad3f0d3071f987baabbdd3da4500c87ea\">idx_t</a> typedef</td><td class=\"entry\"><a class=\"el\" href=\"structfaiss_1_1Index.html\">faiss::Index</a></td><td class=\"entry\"></td></tr>\n <tr bgcolor=\"#f0f0f0\" class=\"even\"><td class=\"entry\"><b>Index</b>(idx_t d=0, MetricType metric=METRIC_L2) (defined in <a class=\"el\" href=\"structfaiss_1_1Index.html\">faiss::Index</a>)</td><td class=\"entry\"><a class=\"el\" href=\"structfaiss_1_1Index.html\">faiss::Index</a></td><td class=\"entry\"><span class=\"mlabel\">inline</span><span class=\"mlabel\">explicit</span></td></tr>\n <tr bgcolor=\"#f0f0f0\"><td class=\"entry\"><b>IndexFlat</b>(idx_t d, MetricType metric=METRIC_L2) (defined in <a class=\"el\" href=\"structfaiss_1_1IndexFlat.html\">faiss::IndexFlat</a>)</td><td class=\"entry\"><a class=\"el\" href=\"structfaiss_1_1IndexFlat.html\">faiss::IndexFlat</a></td><td class=\"entry\"><span class=\"mlabel\">explicit</span></td></tr>\n <tr bgcolor=\"#f0f0f0\" class=\"even\"><td class=\"entry\"><b>IndexFlat</b>() (defined in <a class=\"el\" href=\"structfaiss_1_1IndexFlat.html\">faiss::IndexFlat</a>)</td><td class=\"entry\"><a class=\"el\" href=\"structfaiss_1_1IndexFlat.html\">faiss::IndexFlat</a></td><td class=\"entry\"><span class=\"mlabel\">inline</span></td></tr>\n <tr bgcolor=\"#f0f0f0\"><td class=\"entry\"><b>IndexFlatL2</b>(idx_t d) (defined in <a class=\"el\" href=\"structfaiss_1_1IndexFlatL2.html\">faiss::IndexFlatL2</a>)</td><td class=\"entry\"><a class=\"el\" href=\"structfaiss_1_1IndexFlatL2.html\">faiss::IndexFlatL2</a></td><td class=\"entry\"><span class=\"mlabel\">inline</span><span class=\"mlabel\">explicit</span></td></tr>\n <tr bgcolor=\"#f0f0f0\" class=\"even\"><td class=\"entry\"><b>IndexFlatL2</b>() (defined in <a class=\"el\" href=\"structfaiss_1_1IndexFlatL2.html\">faiss::IndexFlatL2</a>)</td><td class=\"entry\"><a class=\"el\" href=\"structfaiss_1_1IndexFlatL2.html\">faiss::IndexFlatL2</a></td><td class=\"entry\"><span class=\"mlabel\">inline</span></td></tr>\n <tr bgcolor=\"#f0f0f0\"><td class=\"entry\"><b>IndexFlatL2BaseShift</b>(idx_t d, size_t nshift, const float *shift) (defined in <a class=\"el\" href=\"structfaiss_1_1IndexFlatL2BaseShift.html\">faiss::IndexFlatL2BaseShift</a>)</td><td class=\"entry\"><a class=\"el\" href=\"structfaiss_1_1IndexFlatL2BaseShift.html\">faiss::IndexFlatL2BaseShift</a></td><td class=\"entry\"></td></tr>\n <tr class=\"even\"><td class=\"entry\"><a class=\"el\" href=\"structfaiss_1_1Index.html#a6e92732617c4dbe364e7678dd8773a7f\">is_trained</a></td><td class=\"entry\"><a class=\"el\" href=\"structfaiss_1_1Index.html\">faiss::Index</a></td><td class=\"entry\"></td></tr>\n <tr><td class=\"entry\"><a class=\"el\" href=\"structfaiss_1_1Index.html#a8e18f641854b2bde83ecff0a2f9a6f4e\">metric_type</a></td><td class=\"entry\"><a class=\"el\" href=\"structfaiss_1_1Index.html\">faiss::Index</a></td><td class=\"entry\"></td></tr>\n <tr class=\"even\"><td class=\"entry\"><a class=\"el\" href=\"structfaiss_1_1Index.html#a6970683faa021b7a6f1a0865c0d4eccd\">ntotal</a></td><td class=\"entry\"><a class=\"el\" href=\"structfaiss_1_1Index.html\">faiss::Index</a></td><td class=\"entry\"></td></tr>\n <tr><td class=\"entry\"><a class=\"el\" href=\"structfaiss_1_1IndexFlat.html#ac56b7ed90ab65fab9c586a1e56006d12\">range_search</a>(idx_t n, const float *x, float radius, RangeSearchResult *result) const override</td><td class=\"entry\"><a class=\"el\" href=\"structfaiss_1_1IndexFlat.html\">faiss::IndexFlat</a></td><td class=\"entry\"><span class=\"mlabel\">virtual</span></td></tr>\n <tr class=\"even\"><td class=\"entry\"><a class=\"el\" href=\"structfaiss_1_1IndexFlat.html#ae4b33315752b62cff1626f9f967167b1\">reconstruct</a>(idx_t key, float *recons) const override</td><td class=\"entry\"><a class=\"el\" href=\"structfaiss_1_1IndexFlat.html\">faiss::IndexFlat</a></td><td class=\"entry\"><span class=\"mlabel\">virtual</span></td></tr>\n <tr><td class=\"entry\"><a class=\"el\" href=\"structfaiss_1_1Index.html#a1936604fffe16b0ef2a3879305950738\">reconstruct_n</a>(idx_t i0, idx_t ni, float *recons) const </td><td class=\"entry\"><a class=\"el\" href=\"structfaiss_1_1Index.html\">faiss::Index</a></td><td class=\"entry\"><span class=\"mlabel\">virtual</span></td></tr>\n <tr class=\"even\"><td class=\"entry\"><a class=\"el\" href=\"structfaiss_1_1IndexFlat.html#a8d1ea1d28e80849f8b0f5493679d68c9\">remove_ids</a>(const IDSelector &sel) override</td><td class=\"entry\"><a class=\"el\" href=\"structfaiss_1_1IndexFlat.html\">faiss::IndexFlat</a></td><td class=\"entry\"><span class=\"mlabel\">virtual</span></td></tr>\n <tr><td class=\"entry\"><a class=\"el\" href=\"structfaiss_1_1IndexFlat.html#ab63dc34ef5d33f98f94aa0ade7c7324f\">reset</a>() override</td><td class=\"entry\"><a class=\"el\" href=\"structfaiss_1_1IndexFlat.html\">faiss::IndexFlat</a></td><td class=\"entry\"><span class=\"mlabel\">virtual</span></td></tr>\n <tr class=\"even\"><td class=\"entry\"><a class=\"el\" href=\"structfaiss_1_1IndexFlatL2BaseShift.html#a16e9bf1aec9d18b3ebbe78fea6bfecc0\">search</a>(idx_t n, const float *x, idx_t k, float *distances, idx_t *labels) const override</td><td class=\"entry\"><a class=\"el\" href=\"structfaiss_1_1IndexFlatL2BaseShift.html\">faiss::IndexFlatL2BaseShift</a></td><td class=\"entry\"><span class=\"mlabel\">virtual</span></td></tr>\n <tr><td class=\"entry\"><a class=\"el\" href=\"structfaiss_1_1Index.html#aa5b4e63e1064f9bf9c75625d114b353f\">search_and_reconstruct</a>(idx_t n, const float *x, idx_t k, float *distances, idx_t *labels, float *recons) const </td><td class=\"entry\"><a class=\"el\" href=\"structfaiss_1_1Index.html\">faiss::Index</a></td><td class=\"entry\"><span class=\"mlabel\">virtual</span></td></tr>\n <tr bgcolor=\"#f0f0f0\" class=\"even\"><td class=\"entry\"><b>shift</b> (defined in <a class=\"el\" href=\"structfaiss_1_1IndexFlatL2BaseShift.html\">faiss::IndexFlatL2BaseShift</a>)</td><td class=\"entry\"><a class=\"el\" href=\"structfaiss_1_1IndexFlatL2BaseShift.html\">faiss::IndexFlatL2BaseShift</a></td><td class=\"entry\"></td></tr>\n <tr><td class=\"entry\"><a class=\"el\" href=\"structfaiss_1_1Index.html#abf601502bdbfa02b9d7bcd7b3671b71d\">train</a>(idx_t n, const float *x)</td><td class=\"entry\"><a class=\"el\" href=\"structfaiss_1_1Index.html\">faiss::Index</a></td><td class=\"entry\"><span class=\"mlabel\">virtual</span></td></tr>\n <tr class=\"even\"><td class=\"entry\"><a class=\"el\" href=\"structfaiss_1_1Index.html#a5590d847c5c2b958affd2a05e58a6f23\">verbose</a></td><td class=\"entry\"><a class=\"el\" href=\"structfaiss_1_1Index.html\">faiss::Index</a></td><td class=\"entry\"></td></tr>\n <tr><td class=\"entry\"><a class=\"el\" href=\"structfaiss_1_1IndexFlat.html#a9001de47890fe5d2eced9551d3613d47\">xb</a></td><td class=\"entry\"><a class=\"el\" href=\"structfaiss_1_1IndexFlat.html\">faiss::IndexFlat</a></td><td class=\"entry\"></td></tr>\n <tr bgcolor=\"#f0f0f0\" class=\"even\"><td class=\"entry\"><b>~Index</b>() (defined in <a class=\"el\" href=\"structfaiss_1_1Index.html\">faiss::Index</a>)</td><td class=\"entry\"><a class=\"el\" href=\"structfaiss_1_1Index.html\">faiss::Index</a></td><td class=\"entry\"><span class=\"mlabel\">virtual</span></td></tr>\n</table></div><!-- contents -->\n<!-- ",
"start footer part -->\n<hr class=\"footer\"/><address class=\"footer\"><small>\nGenerated by  <a href=\"http://www.doxygen.org/index.html\">\n<img class=\"footer\" src=\"doxygen.png\" alt=\"doxygen\"/>\n</a> 1.8.5\n</small></address>\n</body>\n</html>\n"
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"Q:\n\nHow to have std::function or lambda as (optional) template parameter?",
"\n\nHi I was playing around with TMP and was thinking of generating of a class\nthat looks something like:\ntemplate<typename T, typename LogFunc>\nclass\n{\n\n(where LogFunc should be defaulted to \"nop\" function)\nIdea is to have a class that defines some functionality for instances of type T, for example checks if the number is even, and also has the option to log by calling \nvoid memberFunc(T& t)\n{\n LogFunc(t); \n}\n\nor maybe \nvoid memberFunc(T& t)\n{\n LogFunc lf;\n lf(t);\n}\n\nCan it be done? ",
"\nFrom reading A on SO, lambdas are kind of problematic as templ params. ",
"\nBTW if somebody cares this is what I tried but it prints out \n\n:(\n\nA:\n\nThe problem is that the type of a lambda is a compiler-enforced singleton; it has only one value, which is the lambda itself; furthermore, the type has a deleted constructor. ",
"So you can't pass lambdas as part of a template instantiation, even with decltype. ",
"But there's nothing stopping you from passing them as constructor arguments.",
"\nHowever, here we run into another problem: constructor arguments are not used to deduce a template instantiation (which is why the standard library provides utilities like make_pair and make_tuple). ",
"So we need a templatized factory function.",
"\nWith all that, the solution is pretty simple:\ntemplate<typename T, typename LogFunc>\nclass Foo {\n public:\n Foo(const T& t, LogFunc fn) : t_(t), lfn_(fn) {}\n //...\n\n private:\n T t_;\n LogFunc lfn_;\n};\n\nstruct Noop {\n template<typename...A>\n void operator()(A...) { };\n};\n\ntemplate<typename T, typename LogFunc=Noop>\nFoo<T, LogFunc> make_foo(const T& t, LogFunc func=LogFunc()) {\n return Foo<T, LogFunc>(t, func);\n}\n\n"
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"namespace hyperionnet;\n\n// A priority value of -1 clears all priorities\ntable Register {\n origin:string (required);\n priority:int;\n}\n\ntable RawImage {\n data:[ubyte];\n width:int = -1;\n height:int = -1;\n}\n\nunion ImageType {RawImage}\n\ntable Image {\n data:ImageType (required);\n duration:int = -1;\n}\n\ntable Clear {\n priority:int;\n}\n\ntable Color {\n data:int = -1;\n duration:int = -1;\n}\n\nunion Command {Color, Image, Clear, Register}\n\ntable Request {\n command:Command (required);\n}\n\nroot_type Request;\n"
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"Mocha Uson is not the problem Posted by The Society of Honor on January 5, 2017 · 265 Comments\n\nBy Joe America\n\nWe have sorted the Philippine population into three groups to help make sense of things:\n\nThe entitled, or class of impunity, that takes care of its own, is fundamentally amoral (lying is a tool, murder a campaign), and is not committed to the principles of democracy and human rights. ",
"Most legislators are in this group, and almost all of the Duterte cabinet. ",
"The educated elite who believe in the principles of democracy, laws, and human rights. ",
"A few legislators belong to this group, as does Vice President Robredo. ",
"Interestingly enough, so does arch-leftist Waldon Bello. ",
"The needful masses who may be poor or just stuck in traffic or otherwise angry that their lot in life is so small or troubled.",
"\n\nMocha Uson belongs to the class of impunity and speaks to the needful. ",
"She does not speak to the elite and only concerns herself with them if they pose a threat to the Duterte agenda. ",
"Vice President Robredo is viewed as a threat and is now in the spotlight to be diminished.",
"\n\nMocha Uson is highly skilled at what she does.",
"\n\nThe elite are busy mainly talking to themselves whilst trying to lecture or convert the entitled to better values by appealing to their conscience or reason. ",
"They have no organization and are basically ineffective at speaking to the needful. ",
"So they aren’t making a lot of progress at influencing policies or decisions. ",
"The international press probably have a greater impact.",
"\n\nThe idea that the elite could impose a conscience on Mocha Uson, or others of the entitled class, is rather futile I think. ",
"I don’t know why they spend so much time worrying about her, and others like her. ",
"They should be busy ignoring her to the best of their ability, and speaking to the needful.",
"\n\nThe needful are not a rational bunch, in the main, but an emotional bunch, and I suspect that endless appeals to conscience, to sense, and to principles miss the mark. ",
"The emotional foundation of the needful is not rational. ",
"I don’t know if it is mass insanity or mass need, but it is typical to see the needful get upset about dogs killed for a movie but not Filipinos killed for drugs. ",
"It is common to see the Duterte Administration given a free pass for bad traffic, its position on SS hikes and pork, giving away sea resources, being rude to the US, and other acts for which President Aquino would have been excoriated.",
"\n\nex·co·ri·ate, ikˈskôrēˌāt, ekˈskôrēˌāt, verb, censure or criticize severely, “the papers that had been excoriating him were now lauding him”\n\nThis is not an argument to be won on reason.",
"\n\nIt is an argument to be won on emotions and taking care of people who have tremendous needs and no easy way out of their condition.",
"\n\nI suspect Senator De Lima calling DOJ Secretary Aguirre a “lying bastard” is better communication than Vice President Robredo extolling the importance of human rights.",
"\n\nCome to think of it, the elite are confined by their good manners. ",
"Good manners don’t impress the needful. ",
"Good manners make the needful angry. ",
"Needful values are crab values . . . ",
"inside out. ",
"Upside down. ",
"Ambition is bad, it shows “us” up. ",
"Success is bad, it makes us feel bad. ",
"Goodie goodie is weak and pretending to have higher values is offensive.",
"\n\nThe needful need strength. ",
"They need tough. ",
"They need blood in the streets.",
"\n\nThey need things their emotions (not brains) can relate to.",
"\n\nAs long as the elite adhere to good manners, they will be ineffective. ",
"As long as they keep speaking to the deaf ears of the entitled, babbling amongst themselves, or lording it over the needful . . . ",
"they will be ineffective.",
"\n\nIf they are worrying about Mocha Uson, they are on the defensive.",
"\n\nIf they are trying to insult those of no conscience, they are beating dead horses.",
"\n\nIf they are talking about human rights, they have put their target audience to sleep.",
"\n\nIf they have no organization, they are just noise.",
"\n\nI was thinking about proposing how to avoid these pitfalls, but I am foreigner. ",
"Not my job.",
"\n\nYou can discuss it freely amongst yourselves, however, and I’d guess you would come up with something like:\n\nPut an organization in place (let Waldon Bello head it to get rid of the LP stigma).",
"\n\nDevelop a very simple set of goals. ",
"End EJKs and death culture, real sovereignty, more jobs, uplift the nation.",
"\n\nDecide on an overarching message (“Defend democracy and the honor of Filipinos”).",
"\n\nDevelop a troll army to disseminate content that resonates (De Lima’s “Aguirre is a lying bastard” or Bello’s recent comment that supporters of Duterte are either ignorant or crazy).",
"\n\nThose are not proposals, just idea starters. ",
"I leave the discussion to you at this point."
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"It’s situations like this that prompt blogger Thomas Peters (@AmericanPapist) to consider attempts to “silence and marginalize” conservatives and people of faith as the number one threat to the conservative movement.",
"\n\nA southern California native, Peters now resides in D.C. He grew up in a conservative Catholic household, and attended Ave Maria College in Michigan. ",
"He then earned his M.A. in Theology at Sacred Heart Seminary, where he began blogging.",
"\n\n“I found it a nice change of pace from my homework,” he said.",
"\n\nWhat began as commentary on the Catholic Church grew political as Peters moved to the nation’s capital and started his second Master’s at the Dominican House of Studies. ",
"Two years and 17,000 tweets later, he’s a seasoned blogger, writing on his American Papist blog at CatholicVote.org. ",
"He’s also a speaker and political activist, making a splash in the social conservative movement.",
"\n\n“Social media is essential for keeping a tight-knit online community of experts and activists,” Peters said, adding, “It’s a very immediate way to keep supporters informed.”",
"\n\nAs a dedicated social conservative, Peters closely follows Steve Ertelt (@StevenErtelt) of LifeNews.com, pro-life activist Jill Stanek (@JillStanek), and the Washington Examiner’s David Freddoso (@Freddoso) and Timothy Carney (@TPCarney) for all things newsworthy.",
"\n\n“I actually enjoy following a few left-wing activists because it’s important to know what both sides are thinking in real-time,” he added. ",
"Among them: Daily Kos (@DailyKos), The Advocate (@TheAdvocateMag) and Amanda Marcotte (@AmandaMarcotte).",
"\n\nSocial media is more than just a way to find news and self-promote, and Peters is one of a handful of conservatives who have successfully initiated and organized Twitter campaigns to get conservative issues trending. ",
"During the 2012 March for Life, followers retweeted him hundreds of times.",
"\n\nIn addition to blogging, Peters works at the National Organization for Marriage where he is overseeing a project to identify and encourage young activists who are pro-marriage.",
"\n\nMarriage could be a big issue this year, with a number of states – like Washington and Maryland – considering legislation to legalize gay marriage. ",
"Other states, including Minnesota and North Carolina, are trying to add traditional marriage to the state constitution.",
"\n\nAs part of his work for NOM, Peters travels the country speaking to young people, and teaching them how to defend their views.",
"\n\n“We have to work hard at understanding our own conservative principles so we are better equipped to defend and promote them,” He said.",
"\n\nAnd social media is key, he noted, “It contributes to a more robust and free democracy.”",
"\n\nComments\n\nComments\n\nIn their lengthy quest for public affirmation, for what they call marriage “equality” and for legitimization of their perverted and socially unacceptable lifestyle, homosexuals often ask, if not marriage, what should gay couples do when they love each other and want to enter into committed relationships, especially when marriage is the most widely used expression of love between two people? ",
"So far, apparently, traditional values advocates, the conservative wing of the Republican Party, and others who oppose their sordid agenda have no answer. ",
"It should first be pointed out, however, that pre-pubescent girls all over the country may idolize Justin Bieber, but we don’t hand out marriage licenses to children just because they are capable of emotional feelings. ",
"Another question homosexuals often ask is, “are we to be condemned for loving?” ",
"Neither society nor religious principles condemns them for loving. ",
"They, like everybody else, can love anybody they want. ",
"The condemnation, however, comes from engaging in sexual congress with people of their same gender. ",
"Albeit a tagline coined in the War on Drugs, society has simply lost the ability – or the spine – to “just say no”, especially in the socio-moral war against sexual perversion that is progressively corrupting our country and our most sacred traditions and whose strategy, sadly, includes targeting children.",
"\n\nHoping to condition a whole generation of people whose attitudes toward the practice of same sex relations, the pro-homosexual lobby wants school children to be brainwashed about homosexuals. ",
"In California, they have forced it into the education system just like they have forced their way into everything else; i.e., with lawyers, a lot of noise, the help of sympathetic, naive, spineless jurists, quoting inapplicable legal predicates, ultra rich supporters funding them, and by strategically placing gays into the body politic. ",
"If a subject, even a disgusting one, is tossed into the public eye long enough and often enough, LGBT seems to think it will become so commonplace it will ultimately be accepted as main stream. ",
"They are also intent on investing into the school systems curricula designed to put the most favorable spin on the contributions made to society by homosexuals as though that is a magic wand for normalizing the abnormal.",
"\n\nThere is no doubting that homosexuals are, first of all, people. ",
"But they are people with mental aberrations manifested in their choice of sexual partners and the sexual theater in which they find themselves most comfortable. ",
"People with a brain or a decent measure of skills are always able to make contributions to society, if they choose to do so. ",
"However, the nature of a person’s work and/or societal contributions has very little to do with their sex lives (unless they are sex workers). ",
"In other words, the contributions of people like Walt Whitman or Oscar Wilde resulted from their literary skills, not from their sexual practices, so their contributions to the literary world prove nothing and provide nothing more than a straw man argument about the value of homosexuals or homosexuality. ",
"As to contributions, though, Jeffrey Dahmer was at one time an army medic, a noble profession and one in which he must have made honorable contributions. ",
"But that doesn’t erase what he was beneath the surface.",
"\n\nIn the interest of fair and balanced reporting, if California educators are forced by homosexual legislators or lobbyists to teach gay history and the contributions to society made by mentally abnormal people, the list should also include those who have made contributions because of, not in spite of, their sexual perversions, the substance of which is their socially detrimental behavior; e.g., openly gay soldier, Bradley Manning, who gave hundreds of thousands of secret documents to Wikileaks, putting at serious risk his country’s security, national image, and diplomatic relations with allies, because he got upset over a break up with his homosexual lover. ",
"Then there is the case of Ottis Toole, a homosexual who decapitated six-year-old Adam Walsh. ",
"And, if homosexuals could manage to flaunt their role models without cherry picking their ranks, they might look to a gay business man who was a war veteran, a graduate of Northwestern Business University, who rubbed elbows with the likes of First Lady, Rosalynn Carter. ",
"He was financially well off, and worked tirelessly in community projects. ",
"On the surface, he sounds like a model citizen and one the gay lobbyists would be proud to offer up as a role model who made significant contributions to society, but it’s doubtful the rest of the story would be revealed about him in California schools if positive spin is the central goal, because this homosexual was serial killer, John Wayne Gacy.",
"\nSome research seems to indicate that, among serial killers, whose brains obviously do not function the way a normal brain does, homosexuals (whose brains likewise do not function the way a normal brain does) own a disproportionate share of such crimes compared to their representation within the total population. ",
"Considering the observations of forensic pathologists, Bernard Knight (professor of forensic psychology, University of Wales) and Pekka Saukko (head of forensic medicine, University of Turku, Finland), some of the most violent and gruesome murders happen among homosexual males, so there is no surprise at the statistics concerning serial killers. ",
"As another point of fact, according to the American College of Pediatricians, which cites several studies, violence among homosexual couples is two to three times more common than among married heterosexual couples. ",
"Sadly, though, homosexuality as a mental condition was removed from the Diagnostic and Statistical Manual of the American Psychiatric Association. ",
"Until 1973, homosexuality was at the top of the list of sexual deviations (paraphilias) under Section 302 of the DSM. ",
"Whether scientists removed homosexuals unilaterally or justifiably, or whether as some claim, it was a more political move that resulted from bullying, bribing, or defrauding and the APA yielded to political pressure, the net result is that the decision shot homosexuals in the foot. ",
"An appropriate code is not now available to practitioners of the healing arts to diagnose or report the condition, develop a therapeutic plan, or get insurance to pay for treatment of those who want to abandon this modern plague.",
"\n\nHomosexuals loathed the label medical science put on them, but then hell hates holy water. ",
"Regardless, they didn’t want to think of themselves as mentally abnormal. ",
"So, they decided to change the way society looked at them rather than try to abandon the practice. ",
"In reality, however, we could call a skunk a rose, but that wouldn’t make it smell any sweeter. ",
"Gay activists often claim that their sexual deviation is a matter of choice which can’t be treated. ",
"The gay community even does its best to sugar coat their behavior by toning down descriptive terms and euphemizing homosexuality as an “alternative lifestyle.” ",
"This certainly sounds less threatening and less offensive, especially considering their strategy of keeping same sex relationships in the public eye, whether through the educational system or the entertainment media. ",
"The light-hearted and funny characters on Will and Grace, though, are far afield from the Andrew Cunanans in their midst.",
"\n\nAnd now the 9th circuit court of appeals has ruled California’s law against same sex marriage is unconstitutional with the reasoning of the three judges seeming to be no more than judicial pandering to political correctness rather than legally sound justice. ",
"The first thing American courts should have to decide in the case of gay marriage is whether marriage is a right. ",
"If it is, gays might have standing to bring a case, but there would then have to be sweeping reform of marriage laws in all fifty states. ",
"If marriage is not a right, then gays have no claim that denying them a marriage license is unconstitutional. ",
"The gay marriage cases to date have all leaned on the 14th amendment’s equal protection clause. ",
"However, Cornell University School of Law says that the equal protection clause doesn’t guarantee individual liberties; it demands equal application of the law. ",
"Thus, in states in which same sex couples do not qualify for marriage licenses any more than deaf mutes qualify for pilot’s licenses, if homosexual and heterosexual same gender couples are denied marriage licenses for the same reason (that same gender couples may not marry), there is no discrimination against homosexuals. ",
"Moreover, parroting Judge Vaughn Walker’s statement, the court said Prop 8 enshrines in law that same sex couples are inferior to heterosexual couples, which is a matter of conjecture more than a matter of law. ",
"Nothing in California’s law said or implied anything about superiority or inferiority. ",
"A blind man may not qualify for a driver’s license, but that doesn’t mean the state is discriminating against the disabled or that the applicant is inferior. ",
"It is simply common sense and good judgment.",
"\n\nThere is no issue of equality in respect to homosexuals and marriage. ",
"Marriage is not a right. ",
"If marriage was a right, then brothers and sisters or other close relatives could marry, the idea of in-breeding wouldn’t be so socially explosive, so Jerry Springer might have to find another career. ",
"A fairly profitable industry could be set up for U.S. citizens to marry foreigners who had enough money to hire temporary spouses and, hence, get a leg up on immigration. ",
"If there were no marriage laws regulating the practice, Mormons and Muslims would be able to have as many wives as they could manage to feed. ",
"But, thankfully, marriage is regulated in many common sense ways that have nothing to do with homosexuals, sexual orientation, gender confusion, or abnormal people claiming they want to enter “committed, loving relationships” with marriage as the only avenue of approach they will accept. ",
"Clearly, nobody has to be married to engage in sexual congress or to enter into loving, committed relationships and live happily ever after. ",
"Free love made the pill necessary and, as it happens, made it possible. ",
"For many years, Brad Pitt and Angelina Jolie have quite publicly been living and breeding together without benefit of clergy. ",
"The notion that gays want a marriage license is not likely the real issue, though. ",
"What is printed on a piece of paper in a scrapbook at a very well-decorated home would more likely be a symbol of victory over morality, over the laws of God and over traditional values than a life affirming emblem. ",
"But, in the final analysis, a question begging for an answer is: who benefits most from the corruption of human morals and who has been engineering that corruption for thousands of years? ",
"Answer that and the roots of homosexuality may may be more transparent."
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"Q:\n\nAndroid get current date and show it in TextView\n\nI do not know what is wrong with code below -\npublic void onCreate(Bundle savedInstanceState) {\n super.onCreate(savedInstanceState);\n setContentView(R.layout.activity_main);\n TextView tv = (TextView) findViewById(R.id.textView1);\n\n String dt;\n Date cal = (Date) Calendar.getInstance().getTime();\n dt = cal.toLocaleString();\n tv.setText(dt.toString());\n\n}\n\nA:\n\nI suggest: \nlong date = System.currentTimeMillis(); \n\nSimpleDateFormat sdf = new SimpleDateFormat(\"MMM MM dd, yyyy h:mm a\");\nString dateString = sdf.format(date); \ntvDisplayDate.setText(dateString);\n\nwhich displays in the following example format\nMon Jan 5, 2009 4:55 PM\nYou can use whatever format you want - options can be found at Oracle\n\nA:\n\nuse this code:\ntvDisplayDate = (TextView) findViewById(R.id.tvDate);\n\n final Calendar c = Calendar.getInstance();\n yy = c.get(Calendar.",
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"Eswatini Democracy Campaign\n\nThe Eswatini Democracy Campaign consists of organisations from Eswatini and South Africa that advocate democracy in Eswatini. ",
"The campaign supports the democratic initiatives of trade unions, NGOs, student organisations and other organisations that further the cause of democratization in Eswatini. ",
"The campaign calls upon the South African government and those of other SADC countries to acknowledge that they are in effect protecting the undemocratic and repressive Eswatini regime. ",
"The campaign seeks the removal of restrictions on political parties, the news media and political gatherings, and calls for free, multi-party elections.",
"\n\nReferences\n\nExternal links\n Official website \n Launch of the Eswatini Democracy Campaign\n Eswatini Democracy Campaign at Eswatini Media Commentary\n The Swazi Observer\n\nCategory:Political organisations based in Eswatini"
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"Q:\n\nScraping: Logging in headers are encrypted: how to send credentials?",
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"\n1 A.3d 970 (2010)\nRichard L. GESCHWINDT and Maureen T. Geschwindt, Appellants\nv.\nDennis G. WAGNER, Melissa M. Wagner, h/w and R.D. Contracting, Inc.\nNo. ",
"1972 C.D. 2009\nCommonwealth Court of Pennsylvania.",
"\nArgued May 18, 2010.",
"\nDecided July 16, 2010.",
"\n*972 Byron M. Yatron, Reading, for appellant.",
"\nKatherine Rightmyer O'Brien, Hamburg, for appellee.",
"\nBEFORE: PELLEGRINI, Judge, and LEAVITT, Judge, and FLAHERTY, Senior Judge.",
"\nOPINION BY Senior Judge FLAHERTY.",
"\nAppellants, Richard L. Geschwindt (Husband) and Maureen T. Geschwindt (Wife) appeal from an order of the Court of Common Pleas of Berks County (trial court) which denied Appellants' motion for post trial relief taken from the order granting the motion for directed verdict filed by Dennis G. Wagner and Melissa M. Wagner, collectively (Wagner) and R.D. Contracting, Inc. (R.D.). ",
"We affirm.",
"\nAppellants own a home located at the corner of Noble Avenue and Reber Street in Shoemakersville Borough. ",
"Appellants' property is divided into a residence with a front door on Reber Street and a law office, which has an entrance on Noble Avenue.[1] The property is zoned R-1 Low Density Residential.",
"\nThe Wagner home is also located in Shoemakersville Borough at 212 7th Avenue. ",
"The distance from the Wagner residence to Appellants' residence is seventy feet. ",
"Both residences back into the same alley, Sixth Lane.",
"\nIn January of 2005, Wagner obtained a zoning permit to erect a 720 square foot accessory building (garage). ",
"Thereafter, in June of 2005, a zoning enforcement notice was issued to Wagner regarding the location of the garage being within 15 feet of the western property sideline and indicating that such was in violation of the Zoning Ordinance. ",
"Wagner appealed the enforcement notice and, in the alternative, requested a variance. ",
"The first two hearings were continued. ",
"At the next hearing, which was scheduled for September 29, 2005, the zoning officer failed to appear and the Board granted Wagner's appeal and determined that Wagner's request for a variance was moot, inasmuch as the zoning action had been dismissed. ",
"The Board later issued an opinion in support of its decision and no appeal was taken therefrom.",
"\nIn June of 2006, Appellants filed the complaint at issue with the trial court alleging a private enforcement action pursuant to Section 617 of the Pennsylvania Municipalities Planning Code (MPC), Act of July 31, 1968, P.L. 805, as amended, 53 P.S. § 10617. ",
"Section 617 of the MPC provides in pertinent part:\nIn case any building, structure ... is, or is proposed to be, erected, constructed. . . ",
"or used in violation of any ordinance. . . ",
"any aggrieved owner or tenant *973 of real property who shows that his property or person will be substantially affected by the alleged violation . . . ",
"may institute any appropriate action or proceeding to . . . ",
"correct or abate such building, structure. . . .",
"\n(Emphasis added.)",
"\nAppellants alleged that Wagner's garage violates setback requirements and sought to have it removed. ",
"Appellants also alleged that Wagner was operating R.D. from his home in violation of the Ordinance, as such does not qualify as a home occupation. ",
"Appellants requested that Wagner be ordered to cease and desist from operating R.D. at the home and to cease parking R.D. vehicles in the vicinity of the home. ",
"Appellants later filed an amended complaint and Wagner filed an answer with counterclaims, to which Appellants replied with new matter. ",
"Wagner, thereafter, filed a motion for summary judgment, which the trial court denied.",
"\nAfter a non-jury trial, Wagner filed a motion for directed verdict. ",
"The trial court granted the motion, concluding that Appellants did not meet their burden of proving that they were substantially affected by Wagner's garage and business. ",
"As to the garage, the trial court found that Appellants objected to it based on aesthetic reasons. ",
"Concerning the operation of R.D. from Wagner's home, the trial court determined that Appellants failed to prove that the business functions had any impact on the neighborhood. ",
"Additionally, there was no evidence that R.D. vehicles were at the Wagner home other than for short periods of time. ",
"This appeal followed.[2]\nInitially, Appellants allege that the trial court erred in granting Wagner's motion for directed verdict on the basis that Appellants lacked standing, inasmuch as Wagner waived the issue of standing because it was not pled as new matter.",
"\nPa. R.C.P. No. ",
"1030, entitled \"New Matter\" provides in pertinent part:\n(a) Except as provided in subdivision (b), all affirmative defenses including but not limited to the defenses of accord and satisfaction, arbitration and award, consent, discharge in bankruptcy, duress, estoppel, failure of consideration, fair comment, fraud, illegality, immunity from suit, impossibility of performance, justification, laches, license, payment, privilege, release, res judicata, statute of limitations, truth and waiver shall be pleaded in a responsive pleading under the heading \"New Matter.\"",
"\nPa. R.C.P. No. ",
"1032 provides that \"[a] party waives all defenses and objections which are not presented either by preliminary objection, answer or reply, except a defense under Rule 1030(b) ....\"\nAppellants argue that standing is a waivable defense and the failure to plead standing in new matter precluded Wagner from obtaining a directed verdict because such defense was not asserted and preserved.",
"\nWe note that standing is not specifically addressed in either Pa. R.C.P. Nos. ",
"1030 or 1032. ",
"More importantly, we agree with the trial court that the issue of standing is an element of the cause of action under Section 617 of the MPC, inasmuch as an aggrieved owner of property must show that his property or person will be substantially affected by the illegal act. ",
"The fact remains that this was an element of Appellant's burden of proof and, therefore, cannot be waived.",
"\n*974 Next, Appellants claim that the trial court erred in granting the motion for directed verdict because it disregarded the uncontradicted testimony of Appellants' witnesses.",
"\nA motion for directed verdict may be granted only where the facts are clear and there is no room for doubt. ",
"Lear, Inc. v. Eddy, 749 A.2d 971 (Pa.Super.2000). ",
"In ruling on a motion for directed verdict, the trial court must consider the facts in the light most favorable to the non-moving party and must accept as true all evidence which supports that party's contention and reject all adverse testimony. ",
"Id.\nAppellants allege that the trial court, rather than accepting as true the evidence presented by Appellants, disregarded all of such evidence and based the directed verdict on its finding that all of the testimony from Appellants' witnesses was not credible. ",
"Specifically, the trial court stated that Appellants \"claim that they were substantially affected by the Defendants had no credibility.\" (",
"Trial court opinion at 7). ",
"Appellants point to numerous instances throughout the trial court opinion where the trial court concludes that Appellants' testimony was not credible. ",
"Appellants maintain that the trial court failed to consider the testimony according to the standard enunciated in Lear.",
"\nAs correctly observed by the trial court, however, and later addressed by this court, it was not enough for Appellants to merely state that they were \"aggrieved\" and \"substantially affected.\" ",
"Section 617 of the MPC requires that an aggrieved owner must show that his property or person will be substantially affected. (",
"Emphasis added.) ",
"Because Appellants must show that their persons or property would be substantially affected, the trial court did not err in discrediting Appellants' bald assertion that they were substantially affected. ",
"The allegata must be supported by the probata.",
"\nAppellants next argue that the trial court erred in failing to apply Appeal of Hoover, 147 Pa.Cmwlth. ",
"475, 608 A.2d 607 (1992), in determining whether Appellants had standing.",
"\nAppellants claim that it is undisputed that their property is within 70 feet of the Wagner's and that Appellants can see the Wagner property from their patio. ",
"According to Appellants, because of their close proximity, such makes them aggrieved. ",
"Specifically, in Hoover, this court stated that persons who own property within 150 to 200 yards are within \"close proximity\" and are \"aggrieved\" by the grant of a zoning permit and therefore have standing to challenge same. \"",
"A property owner need not establish pecuniary or financial loss if his property is located in close proximity to the subject property because the zoning decision is presumed to have an effect on the property owner's property.\" ",
"Laughman v. Zoning Hearing Board, 964 A.2d 19, 22 (Pa. Cmwlth.2009).",
"\nWe agree with the trial court, however, which determined that Hoover is not applicable, inasmuch as that case involved Section 913.3 of the MPC, 53 P.S. § 10913.3, added by the Act of December 21, 1988, P.L. 1329, not Section 617 of the MPC, 53 P.S. § 10617, which is applicable here. ",
"Specifically, Section 913.3 provides that appeals under Section 909.1 of the MPC may be filed with the board by the \"landowner affected\" or \"any person aggrieved.\" ",
"Section 617 of the MPC, applicable here, states that when any building has been erected in violation of an ordinance, any \"aggrieved owner or tenant of real property who has shown that his property or person will be substantially affected\" by *975 the alleged violation, may institute an appropriate action. ",
"Thus, Appellants, under Section 617 of the MPC, were required to show that they were not only \"aggrieved\" but \"substantially affected.\"",
"\nFinally, Appellants claim that viewing the facts in the light most favorable to them that they established a claim for a private enforcement action.",
"\nIn considering a motion for directed verdict, the trial court is to consider facts in the light most favorable to the non-moving party and accept as true all evidence which supports that party's contentions. ",
"Lear.",
"\nAs a neighboring property owner, Appellants claim that they have standing. ",
"Appellants claim that the trial court erred in requiring that Appellants show that they were somehow \"inconvenienced.\" ",
"Appellants maintain that Siegmond v. Duschak, 714 A.2d 489 (Pa.Cmwlth.1998), which was relied on by the trial court, states that Section 617 of the MPC, \"contains no language requiring that the property owner establish that the violation of the ordinance resulted in an injury special and peculiar to his or her property.\" ",
"Id. at 491. ",
"Rather, Section 617 of the MPC \"requires only that a property owner be substantially affected by the ordinance violation to have a cause of action.\" ",
"Id.\nIn Siegmond, the Duschaks applied for and received a building permit to repair the roof of their garage and to add a deck to the garage. ",
"The Duschaks then proceeded to construct a second floor above the garage. ",
"The Siegmonds filed a complaint in equity seeking enforcement of the ordinance against the Duschaks. ",
"This court determined that the Siegmonds had a cause of action under Section 617 of the MPC because \"[t]he Duschaks' ordinance violation resulted in increased noise and activity, as well as a loss of privacy to the Siegmonds. ",
"Such effects are sufficient to establish that the Siegmonds were substantially affected by the ordinance violation.\" ",
"Id.\nHere, considering the evidence in the light most favorable to Appellants, Appellants argue that they established standing. ",
"Husband testified that he was \"substantially affected\" and that there was \"no home occupation business . . . ",
"in the neighborhood when we purchased it. ",
"And moreover, we are 70 feet away, and we see this when we come out of our patio . . . .\" (",
"R.R. at 423a.) ",
"Husband also testified that the garage is too big for the lot and that there is no required side yard. ",
"Wife testified \"[t]he garage itself is too big for the homes that are on this alley.\" (",
"R.R. at 433a.) ",
"Wife also testified that she did not like living next to a commercial parking lot and that R.D. trucks park in front of the Wagner home.[3]\nAs previously stated, however, it is not enough for Appellants to state that they were substantially affected, they must show how they were so affected. ",
"Although Appellants object to the garage, Wagner had a permit for its construction. ",
"Moreover, Appellants' objections focus on the aesthetics and the materials that were used to construct the garage, including its color, and the \"new\" look of the structure. ",
"Here, Wagner had the right to construct and paint the garage with materials and colors of his choice and Appellants have failed to cite to any Ordinance which dictates what material and colors are to be used. ",
"When proceeding under Section 617 of the MPC, it is not sufficient to simply *976 allege that one is aggrieved by the fact that a zoning regulation has not been enforced, one must show that the alleged violation has damaged Appellants' property to the point that the party is `substantially affected.' ",
"Phillips v. Griffiths, 366 Pa. 468, 77 A.2d 375 (1951). ",
"We agree with the trial court that Appellants failed to meet their burden of proving how they were substantially affected by the garage.",
"\nAs to R.D., Wagner concedes that R.D. operates at least administratively from the home. ",
"Home occupations are governed by Section 621 of the Ordinance. ",
"Upon complaint by Appellants, the zoning officer investigated the issue of whether R.D. was operating illegally from the Wagner residence. ",
"The zoning officer testified that she determined that operation of R.D. was a \"no impact home based business\" and did not issue a violation. (",
"R.R. at 418a.) ",
"As determined by the trial court, Appellants failed to prove that the business functions occurring at the home had any impact on the neighborhood and there was no evidence the R.D. vehicles were at Wagner's home other than for short periods of time.",
"\nIn accordance with the above, the decision of the trial court is affirmed.",
"\n\nORDER\nNow, July 16, 2010, the order of the Court of Common Pleas of Berks County, in the above-captioned matter, is affirmed.",
"\nNOTES\n[1] Appellants obtained a zoning permit for the law office when the building was purchased in 1990.",
"\n[2] When reviewing a motion for directed verdict, this court's review is limited to determining whether the trial court abused its discretion or committed an error of law. ",
"Perkins v. Desipio, 736 A.2d 608 (Pa.Super.1999).",
"\n[3] Appellants claim that they are entitled to standing because Wagner deliberately violated Ordinance requirements when he constructed the garage is waived, inasmuch as Appellants did not raise this issue in their post-trial motion. ",
"In re Estate of Hall, 517 Pa. 115, 535 A.2d 47 (1987).",
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"Wednesday, April 2, 2014\n\nOn Peace Talks and Prisoner Releases\n\nOn Peace Talks and Prisoner ReleasesTom WilsonWe have come a long way from the days when Israeli Prime Minister Netanyahu used to call for negotiations without preconditions. ",
"Now it has simply become expected that Israel must demonstrate “good will” by purchasing the presence of the Palestinians at the negotiating table with round after round of painful concessions. ",
"And few things must be more painful for Israelis than having to see those who murdered their loved ones walk free. ",
"It flies in the face of the most basic notions about justice and, of course, it’s tactically suicidal: those well-schooled in terror go free to resume their activities; those contemplating the path of terrorism know that in the event they are captured they will likely be released in a prisoner exchange eventually. ",
"Yet, the Israeli government has set a dangerous precedent and throwing on the breaks now may prove easier said than done.",
"The Palestinians have recently issued a new demand. ",
"Either Israel lets 1,000 Palestinian prisoners walk free or Palestinian negotiators will walk from the current round of peace talks. ",
"The previous nine months of fruitless negotiations were paid for by the Israelis agreeing to release 104 Palestinian security prisoners. ",
"These were to be released in stages so as to ensure that the Palestinians wouldn’t simply take the prisoners and run. ",
"At each stage the Palestinians would be obliged to continue with the negotiations and the next batch of terrorists would be released. ",
"But the deadline for the final installment of convicted criminals came and went this weekend. ",
"With Palestinian Authority head Mahmoud Abbas refusing to carry on with the talks, Israel announced that this last prisoner release would not be made.",
"This was hardly an unfair decision. ",
"With the Palestinians insisting the talks were over and that they were going back to the United Nations to pursue statehood there, the Israelis had nothing to gain from setting more terrorists loose. ",
"Yet, not releasing the prisoners was only ever going to invite more condemnation, despite the fact that threatening not to do so is arguably Israel’s way of attempting to keep talks open.",
"Indeed, it has been reported that the State Department was not at all pleased about the prospect of Israel backing out on the prisoner release. ",
"By all accounts U.S. officials have warned Israel that if the Palestinians leave talks then America will not be able to stop them from going to the UN. ",
"In reality there is much that the U.S. could do to keep Abbas from leaving the talks in the first place, if only it chose to. ",
"The Palestinian Authority is in a dire financial mess; the threat of withholding the large amounts of U.S. funding the PA relies on to function would be one way of tying the Palestinians to the peace table.",
"Yet remarkably, it seems that the Israeli government has actually come forward with still more concessions of its own. ",
"This time the Israelis are offering 400 Palestinian terrorists in return for six more months of negotiations. ",
"That’s quite an inflation from the 104 terrorists agreed upon for nine months of talks. ",
"No doubt sensing that he is gaining the upper hand in all of this, Abbas has now done what tyrants always do when they sense they’re being appeased: he has demanded more. ",
"This time, says Abbas, Israel will have to release 1,000 prisoners to renew Palestinian participation in peace talks.",
"That last demand should be a signal to America and the world that the Palestinians are not remotely serious about the negotiation process. ",
"Not that any such signal should be needed by now. ",
"Perhaps the international community would be forced to note this if the Israelis weren’t sending out their own signal, one that only serves to undermine their ability to hold out against such unreasonableness on the part of the Palestinians. ",
"By upping the offer to 400, Israel is indicating that it is perfectly reasonable that large numbers of murderers should be released in return for halfhearted Palestinian participation in talks. ",
"All that has to be haggled over now is how many.",
"But this is a disastrous message to send to the world. ",
"It gives the impression that a negotiated peace is not in the Palestinians’ interest–that they would indeed be better off taking unilateral moves, and that all these talks are primarily for Israel’s benefit. ",
"That last point is the line that Obama pushes too.",
"Oh, but there is just one other small thing that Abbas is asking for along with that minor matter of the 1,000 terrorists going free. ",
"Abbas is now saying that Israel must agree to transfer parts of Israeli controlled Area C of the West Bank into PA control. ",
"But this demand may give a clue about where Abbas is weak and what he most fears from Israel. ",
"He has been threatening that the Palestinians will go back to the UN to continue pushing for unilateral recognition there. ",
"Israeli Economy Minister Naftali Bennett has suggested that Israel should simply let Abbas go. ",
"But Bennett and his party, along with much of the Likud, have also been calling for the annexation of Area C to Israel. ",
"It is possible that Abbas is demanding a reduction in the size of Area C precisely because he fears an Israeli annexation. ",
"That should tell Israel something about where it has some leverage."
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"Huawei has unveiled its new Mate 9 flagship smartphone and while there’s a lot to like about it, it is also the first handset to run the company’s new EMUI 5 interface. ",
"Back at IFA, Huawei teased to us that EMUI 5 would be its most refreshed interface ever and with the Mate 9 now official, let’s take a look at what’s new (and what’s the same) in EMUI 5.",
"\n\nLaunch breakdown:\n\nA refreshed interface?",
"\n\nWithout doubt, EMUI has proven to be a very polarizing interface, with Huawei often adding its own flourishes to Android that many users weren’t overly keen on. ",
"In EMUI 5, this is mostly no longer the case and while it looks visually similar to previous versions, there are some fundamental differences.",
"\n\nThe biggest of these is the presence of an app drawer and while it’s disabled by default, enabling it is as simple as flipping a switch in the settings menu. ",
"With that being said, even the default homescreen (where all the apps are present in a similar way to the iPhone) seems more polished than on previous devices and there is definitely less lag than previous versions as well.",
"\n\nOf course, there are parts of the interface that are similar to previous iterations and a customisable homescreen including transitions and settings is still present. ",
"Yet, all of Huawei’s apps seem to have undergone the same ideological transformation, with a focus on nature and the azure with white and blue interfaces interspersed with gentle, organic animations. ",
"Unlike previous years where the animations would be overly apparent, they have been tweaked in EMUI 5 to only show when time is not of the essence; for example, a cute lockscreen animation might look good at first but after you unlock your phone 20 times in a day, it’ll quickly grow irritating.",
"\n\nEMUI 5 also brings a new miss-touch feature that is somewhat indicative of things to come from the Chinese OEM. ",
"Huawei’s message is clear; sometimes a touch on your screen isn’t necessarily intentional and the miss-touch feature seems to mostly be able to distinguish real interactions from accidental taps. ",
"The curved nature of the Porsche Design Mate 9 is definitely likely to be a key factor behind developing this and from first impressions with the regular Mate 9 at least, it seems to be a well thought-out feature that does what it says on the tin.",
"\n\nNougat, Nougat, Nougat\n\nBased on Android Nougat, EMUI 5 also brings a lot of the native Android features relatively untouched, with multi-window, quick app switching and Google Now on tap all present. ",
"Multi-window has been ‘tweaked’ with the addition of Knock Knock support allowing you to swipe across the screen using your finger to launch multi-window, but like the rest of the Knock Knock feature set, this isn’t the most reliable way to do so.",
"\n\nAlongside this, Huawei has also kept the quick settings shortcuts from Nougat, essentially allowing you to access any of the deeper menus behind the quick settings by pressing and holding. ",
"This is one of their key examples of where they’ve used the features present in core Android natively – rather than re-engineer them – to deliver on their philosophy of a simplified interface where you can accomplish over 50% of core tasks in 2 clicks and 92% within 3 clicks.",
"\n\nUnder the hood changes\n\nVisually there’s not a lot different but EMUI 5 does bring with it several changes under the hood that Huawei hopes will allow it to transcend being merely an Android interface. ",
"Using on-device machine learning, EMUI 5 monitors resource usage in a bid to ensure the out-of-the-box fast experience continues regardless of how much you’ve used your phone.",
"\n\nThe algorithm learns from the way you use your phone (in this case, the Mate 9) in a bid to ensure there’s always enough of the right hardware resources for each app you want to use. ",
"It achieves this using a combination of smart CPU management based on most recently used apps, storage defragmentation – Huawei has replaced the native Android file system with F2FS which has a much smaller fail rate – memory compression and GPU acceleration thanks to native Vulkan support.",
"\n\nWhat else can we say about EMUI 5?",
"\n\nThrough several sessions in China, one thing became apparent and it’s that EMUI 5 is the first interface from Huawei where the company’s various divisions have actually liaised together. ",
"In previous years, the interface was developed mostly in China and then rolled out to other markets with little concern for local preferences but this seems to be a thing of the past.",
"\n\nThis year’s EMUI has had input from teams across the globe, including teams at design and research centres in San Francisco, London, India, Paris and Moscow. ",
"Furthermore, Huawei’s implementation of an interface goes beyond the visual elements of Android with roughly 1000 people dedicated to Linux-based development and a global workforce where roughly 10% have some understanding of kernel levels.",
"\n\nFor those wondering, EMUI 5 will be coming to other devices with the update planned for the Mate 8, P9 and P9 Plus early next year followed by the honor 8 and other Honor branded devices in Q2 2017. ",
"Hardware limitations aside – such as a dual lens camera etc – most devices getting EMUI 5 should get the full feature set and for those not set to get the update, there will be an updated version of EMUI 4.1 that will bring some of these changes. ",
"The P8 and P8 Lite are likely to be two devices that aren’t updated to EMUI 5 but instead get a tweaked version of EMUI 4.1, with some of the functionality from the latest version.",
"\n\nEMUI 5 – our initial verdict\n\nHuawei has gone to great lengths to explain that while they do use Android as a reference point, they have found areas they believe that need to be improved on and this philosophy is one of the less obvious changes. ",
"In previous years, we’ve seen the company attempt to redesign (and redefine even) what Android is with its interface but, whether it’s working with Google on the Nexus 6P last year, or understanding what customers want, EMUI 5 seems to be a break away from this tradition.",
"\n\nInstead, Huawei seems to have taken the core Android experience and merely tweaked elements (while also adding its own flourishes) while also adding its own design flourishes. ",
"The result is an experience that although visually similar to previous versions, marks a big shift for the company. ",
"The chances of a Huawei handset running stock Android may be minimal but the direction that EMUI is headed in suggests that maybe, the call for this is a thing of the past.",
"\n\nWe’ll have a full review of the Huawei Mate 9 in the coming days so stay tuned on more from Huawei’s latest flagship and its new-yet-same User Interface. ",
"In the meantime, what do you think of EMUI 5? ",
"Let us know your views in the comments below!"
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"A study from the Journal of Adolescence has been making the rounds on the internet. ",
"This study found that participation in policy debate (boo LD) contributed to academic achievement.",
"\n\nHere is the abstract\n\nThis study investigates the relationship between participating in a high school debate program on college-readiness in the Chicago Public School district over a 10-year period. ",
"At-risk school students were identified using an index including 8th grade achievement, poverty status, and enrollment in special education. ",
"Regression analyses were used to assess the association between debate participation and graduation and ACT performance. ",
"Overall, debaters were 3.1 times more likely to graduate from high school (95% confidence interval: 2.7-3.5) than non-debaters, and more likely to reach the college-readiness benchmarks on the English, Reading, and Science portions of the ACT. ",
"This association was similar for both low-risk and at-risk students. ",
"Debate intensity was positively related to higher scores on all sections of the ACT. ",
"Findings indicate that debate participation is associated with improved academic performance for at-risk adolescents. (",
"Contains 4 tables and 3 figures.)",
"\n\nIn addition to the obvious school administration propaganda function this article has, I would not be surprised to see it creep into framework debates. ",
"This is because these researches did something pretty cool- they made level of participation (amount of tournaments attended, I think they called it intensity which is awesome) and competitive success variables that they looked at."
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"CNET\n\nIt appears not only people in the tech world believe Bitcoin is the currency of the future -- one of the US' biggest banks also sees legitimacy in the virtual currency.",
"\n\nBank of America published its first research report (PDF) on Bitcoin on Thursday saying that the digital currency could become a major contender to other types of online money-transfer providers.",
"\n\n\"We believe Bitcoin could become a major means of payment for e-commerce and may emerge as a serious competitor to traditional money-transfer providers,\" Bank of America wrote in its report. \"",
"As a medium of exchange, Bitcoin has clear potential for growth, in our view.\"",
"\n\nWhile there are other digital currencies, Bitcoin is probably the most well known. ",
"It's been around since 2009, but didn't really get going until 2011 when it was worth $2 per coin. ",
"By 2013, the currency had climbed to $20 per coin, and then jumped to $266 in April. ",
"Within the past few weeks, it had another price jump and is now hovering around $1,000.",
"\n\nVirtual currencies aren't regulated, which has caused governments some concern. ",
"The digital money can be manipulated or used to launder other types of money. ",
"It is also susceptible to hacking and allows people to evade currency controls with ease.",
"\n\nBank of America echoed some of these same concerns in its report. ",
"The bank also said that the currency's volatility, which is based on speculation, could limit people's acceptance for it as method of payment; and its skyrocketing prices might cause it to get ahead of itself and create a bubble.",
"\n\nNevertheless, Bank of America still appears to believe that Bitcoin could one day become widely used. ",
"The bank did some data crunching in its report and concluded that the total Bitcoin economy could ultimately be worth $15 billion, with each coin being valued at $1,300."
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"While attempts are being made to increase cashless payment options, how feasible is it to get out and about without cash as it is? ",
"Channel NewsAsia’s Lianne Chia tries it out for a weekend and lives to tell the tale.",
"\n\nSINGAPORE: ‘Girl ah, you have no cash ah?’",
"\n\nIt was late morning at a crowded hawker centre in Toa Payoh, and I was holding up a line of people as I struggled to pay for my breakfast with a mobile phone that stubbornly refused to recognise my thumbprint.",
"\n\n\n\nI sighed in frustration. ",
"My breakfast choices had already been narrowed down significantly by the lack of stalls at this hawker centre that offered me the option to go cashless. ",
"And after finally locating a stall with the distinctive QR code sign on its front, queuing up and placing my order, my phone’s thumbprint scanner decided to fail me.",
"\n\nI began to panic, my mind running through the various options available to me in lieu of cash. ",
"Could I ask the hawker for grace and return another day with cash? ",
"Borrow money from someone else in line?",
"\n\nBut thankfully, there was another option.",
"\n\n“Uncle, FlashPay can?” ",
"I asked, as I extracted my card from where I had stashed it under my phone’s casing. ",
"With a grunt and nod, he assented, and with a reassuring beep from the reader, I was on my way.",
"\n\n\n\nTEETHING ISSUES\n\nIt seemed like it would be a tall order to survive without any cash for a weekend, and live to tell the tale. ",
"But after researching and writing a previous story on the availability of cashless payment options in hawker centres, I was encouraged to see how doable it could be. ",
"To sweeten the deal, I had also found out that some cashless payment modes like Liquid Pay offered discounts and incentives for customers who pay through their app.",
"\n\nLiquid Pay currently offers a voucher through its mobile app for 20 per cent off food at selected hawker stalls. (",
"Photo: Lianne Chia)\n\nSo I optimistically left my wallet at home, and walked out to the hawker centre with just my iPhone and credit card, which also has NETS FlashPay capabilities.",
"\n\nBut I had not expected to run into problems right from the get-go. ",
"With my phone’s thumbprint scanner out of order, I could no longer make payment via my banking app’s QR code function or Apple Pay, both of which required me to scan my thumbprint before payments could go through.",
"\n\nSlightly demoralised, I found a table, sat down and tried to enjoy my breakfast while looking up solutions to my thumbprint scanner woes. ",
"But I was soon distracted by the tapping of a cane next to me.",
"\n\nAn elderly lady had approached my table, proffering three packets of tissue paper. ",
"I smiled at her, but shook my head, indicating with hand gestures that I had no cash to spare – in fact, no cash at all. ",
"Feeling a twinge of guilt at her pleas, I waved her away, telling her that I would buy from her next time.",
"\n\nAll in all, not a very auspicious start to the weekend.",
"\n\nTAP AND GO\n\nIt had been a frustrating morning, but there was a silver lining: I had finally discovered how to fix the thumbprint scanner issue after deleting and re-adding all my saved fingerprints from my iPhone. ",
"And trying out Apple Pay for the first time restored my faith in the convenience of cashless payments.",
"\n\nIt was fast approaching lunch time, and I had agreed to meet a friend at a restaurant downtown. ",
"Having been duly warned of my cashless status, he suggested that he pay for lunch first, and I transfer my share of the meal to him via PayNow, a funds transfer service made available in July that allows customers to transfer money with just the recipient’s mobile number or NRIC.",
"\n\nThe interface of a banking app when transferring money to a recipient registered with PayNow. ",
"Customers must also key in a one-time password before the transaction will go through.",
"\n\nI had initially decided to go with that option. ",
"But when we were queuing up to pay at the cashier, my curiosity was piqued by the customer in front of me, who was holding her mobile phone to the card scanner and placing her finger on her phone’s home button.",
"\n\nI decided to give it a shot too.",
"\n\nWhen I reached the cashier, I said confidently, “I’d like to pay by Apple Pay, please,” hoping my tone would mask my inexperience with the system. ",
"He smiled and nodded. “",
"Please place your phone on the scanner.”",
"\n\nPaying for food again via Apple Pay.",
"\n\nIt sounded like he had done this many times before, and it must be a popular method of payment, I thought to myself. ",
"And no wonder: Just a few seconds after I opened my Wallet app and placed my finger on my phone’s home button, I was rewarded with a check mark appearing on my phone screen, indicating that the payment had gone through.",
"\n\nHaving settled payment with the restaurant, it was now time for my friend to pay me back. ",
"Thankfully, he had already registered with PayNow, and with a few taps on his phone, it was all sorted.",
"\n\nA HIT-AND-MISS SITUATION – EVEN IN SHOPPING MALLS\n\nOn the whole, it seemed easy enough to live without cash, as long as I stayed in areas like shopping malls or upmarket cafes. ",
"Getting around was also a breeze, thanks to ride-hailing apps like Grab and Uber, which utilise credit cards as a primary option for payment. ",
"And I discovered a bonus: By opting to go cashless with Grab, I was rewarded with additional rewards points, which I could redeem for more discounted rides.",
"\n\nBut going about my daily life without the reassuring comfort of cash made me realise that for now, it is unlikely people in Singapore will be comfortable going out without their wallets and using their mobile phones for all transactions.",
"\n\nTake, for example, the night I tried to buy a parking coupon from a stranger after realising I had run out of coupons after parking. ",
"After offering to pay him the 60 cents via PayNow, he declined and instead told me to just take the coupon for free.",
"\n\nOr my experience looking for a place to buy a lunch and a drink after a Sunday exercise class in the deserted CBD. ",
"Most stores and restaurants in the area were closed on weekends, and a walk to two nearby hawker centres yielded sparse results.",
"\n\nMost stalls in both centres were closing, and when I approached those that were still open, stallholders said apologetically that they only accepted cash. ",
"When I asked them why, the answers were generally the same: They felt it was too much trouble to get the systems up and running, and lack of demand for cashless payment from customers.",
"\n\nA hawker centre in the CBD on a Sunday afternoon. ",
"Most of the stalls were closing, and those that were still open for business did not accept cashless payment. (",
"Photo: Lianne Chia)\n\nAnd indeed, why would customers make the switch, when there were so many ATMs located prominently within the hawker centres? ",
"Ignoring my growing hunger pangs, I forced myself to walk away.",
"\n\nEven in shopping malls, it was a hit-and-miss situation. ",
"After giving up and walking towards a shopping mall in Tanjong Pagar, I made a beeline for my favourite bubble tea shop. ",
"But I went away disappointed – and still in need of a cold drink – when I was told in no uncertain terms that it was “cash only” for them.",
"\n\nBy the time I got my food and drink, it was 3pm, an hour and a half after I had begun my search, and my patience with the cashless experiment was wearing thin. ",
"All I wanted to do was grab a train back home and stay there for the rest of the weekend.",
"\n\nBut first, there was one more transaction I had to make: My ride home. ",
"As I arrived at the train station, I saw a middle-aged woman fumbling with her wallet at one of the cash top-up machines. ",
"As I walked past she dropped her wallet, and coins went rolling everywhere.",
"\n\nAs I bent to help her retrieve the coins, I realised this was a situation that could have happened to me any other day.",
"\n\nBut as I used my card to tap my way seamlessly past the train gantries, I smiled to myself. ",
"It would not happen today."
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"Vancouver Waldorf School\n\nThe Vancouver Waldorf School offers an experiential, age appropriate approach to education that integrates arts and academics to ignite a genuine passion for learning. ",
"Our unique curriculum inspires students to evolve into confident, creative thinkers with a strong sense of social and environmental responsibility."
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"In the specific assay methods based on bioaffinity the analytes are usually measured at very small concentrations, which require the use of labelling agents that are detectable by a very sensitive method. ",
"Such bioaffinity assays include inter alia immunochemical assays, nucleic acid hybridizations, lectin reactions as well as receptor assays. ",
"Various labelling agent methods are usually used in the analytical applications of all these reactions. ",
"The radioisotopes are conventional labelling agents used for example in radio immunological (RIA) and immonoradiometric (IRMA) assays, which are the most sensitive specific analytical methods used in the practice. ",
"The detection sensitivity of the RIA assays is ca. ",
"10.sup.-14 M and the corresponding sensitivity limit of the IRMA assays is ca. ",
"10.sup.-16 M. Despite the common usage, the radioisotopes as labelling agents present some drawbacks such as a limited lifetime as well as handling problems. ",
"For this reason, active research has been directed to possibilities to replace the radio active labelling agents with other alternatives.",
"\nThe fluorescence methods are more and more widely used in chemical, biochemical and medicinal analytics. ",
"Fluoroimmunological and immunofluorometric assays that are based on time-resolved fluorometrics and on lanthanide chelates as labelling agents give at least the same or even better sensitivity compared with RIA and IRMA assays."
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"Do you export to Spain? ",
"How can the catalonian conflict affect your business in Spain\n\nThe independence declaration of Catalonia is going to affect seriously the businesses in Spain.",
"\n\nThis conflict has already generated a strong division among the Spanish population. ",
"Many products made and sold by companies located in Catalonia are already been rejected by the Spanish buyers, which do not agree with their wish of declaring unilaterally the independence.",
"\n\nFrom the 1st of October around 100 companies per day have moved their head office to other regions in Spain caused by the legal uncertainty and many experts consider that this figure has just begun. ",
"Because of the independence declaration of today, it will be numerous the companies which will have to emigrate to other areas of Spain.",
"\n\nCatalonian companies have been already suffering a boycott for longer, especially the commodity products have seen their sales decrease in the last times. ",
"But this boycott has strongly increased during the last month, which has even arrived at the industry.",
"\n\nThe current situation is worrying for many companies located in Spain but also for other ones which have businesses with Catalonian Companies.",
"\n\nAfter the Independence Declaration, the reject to the Catalonian made and sold products will be surely supreme, not only because of politic reasons but also due to the insecurity related to delivery, guarantee, legal effects, etc.",
"\n\nIf you are selling in Spain through a CatalonianDistributor or any other representative, you should consider how can this conflict affect your business in the Spanish market and how is your partner or collaborator going to confront it, if this company could move their company to another region in Spain or you could need another partner to attend the rest of the Spanish market formed by another 16 regions.",
"\n\nWe really hope that this so dramatic situation come soon to an end and the waters turn its way because many people in Catalonia could see how they lose their job or have to move to another area."
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[
"igit of v?",
"\n0\nLet f be (-8)/10*(-340)/8. ",
"Suppose 37*z + 18 = f*z. ",
"What is the tens digit of (-3)/((-63)/z) - 4206/(-21)?",
"\n0\nSuppose 2520 = 4*c - 10*c. ",
"What is the units digit of (-527)/(-7) - 15/(c/(-8))?",
"\n5\nLet o(a) = -3*a**3 - 27*a**2 + 2*a + 3422. ",
"What is the hundreds digit of o(0)?",
"\n4\nSuppose -4*m = -31*a + 29*a - 13112, 0 = -2*m - 4*a + 6536. ",
"What is the tens digit of m?",
"\n7\nLet d = 4 + -7. ",
"Let t be (0 - 1) + (3 + -1)*d. ",
"What is the hundreds digit of 0 - 1 - (-113 + t)?",
"\n1\nSuppose 492 = -3*t + 2*s, -2*s = 5*t + s + 839. ",
"Let i = 120 - t. What is the hundreds digit of i?",
"\n2\nLet p = 37395 + -55830. ",
"What is the units digit of 72/(-84) + p/(-21)?",
"\n7\nLet o(d) = -1000*d + 8148. ",
"What is the hundreds digit of o(-27)?",
"\n1\nSuppose 0 = -0*g - 9*g - 126. ",
"Let a = 103 - g. What is the units digit of a?",
"\n7\nLet h be (-1)/5 - 7*112/(-20). ",
"Suppose 36*k - 297 = h*k. ",
"Let d = k + 267. ",
"What is the units digit of d?",
"\n8\nLet v(s) = s**3 + 6*s**2 - 3*s - 20. ",
"Let k be v(-5). ",
"What is the hundreds digit of (4*7165/k)/(3/3)?",
"\n4\nWhat is the units digit of (10*65273/910)/((-1)/(-7))?",
"\n1\nSuppose -4*d + 944 = 7348. ",
"Let v = d + 3109. ",
"What is the hundreds digit of 18/63 - v/(-14)?",
"\n1\nLet j(w) = -26*w**2 - 7*w + 18. ",
"Let x be j(7). ",
"Let l = x - -2153. ",
"What is the units digit of l?",
"\n8\nSuppose 9*d + 20*d = -5*d + 612136. ",
"What is the thousands digit of d?",
"\n8\nLet x = 43676 + -23893. ",
"What is the thousands digit of x?",
"\n9\nSuppose 93*p - 43526 = -87*p + 17494. ",
"What is the tens digit of p?",
"\n3\nLet s(t) = 23*t - 4*t + t**2 + 9*t + 63 + t. What is the units digit of s(-34)?",
"\n3\nSuppose 3*i = -12, 4*i - 8190 = -2*m + m. What is the units digit of m?",
"\n6\nLet i(z) = 3*z**2 - 1. ",
"Let a(r) = 53*r**2 - 2*r - 4. ",
"Let q(g) = 2*a(g) - 6*i(g). ",
"Suppose 0 = -d - 3*p + 8, d - 2 = 2*p - 3*p. ",
"What is the units digit of q(d)?",
"\n0\nLet h = 605 - 491. ",
"Let n = h + 133. ",
"What is the tens digit of n?",
"\n4\nLet s = -11 + 11. ",
"Let o be 3*(3 + -2 + s). ",
"Suppose -57 = o*k - 6*k. ",
"What is the tens digit of k?",
"\n1\nSuppose 0 = -6*r + 67*w - 72*w + 51288, 2*r + w = 17096. ",
"What is the thousands digit of r?",
"\n8\nLet f = 14 + -12. ",
"Suppose f*w = -12 + 30. ",
"What is the units digit of 3*(240/w + 1)?",
"\n3\nLet v(l) = -l - 16. ",
"Let n be v(-18). ",
"Suppose 0 = 2*c - 0*c - n. What is the tens digit of 12*c - 0/8?",
"\n1\nLet n(b) = -20*b - 14. ",
"Let k be n(-4). ",
"Let u be ((-1628)/k)/(2/12 - 0). ",
"Let t = 249 + u. What is the units digit of t?",
"\n1\nLet h(b) = -283*b - 2572. ",
"What is the ten thousands digit of h(-56)?",
"\n1\nLet q(z) be the second derivative of z**3/3 - 9*z**2 - 16*z. ",
"Let s be q(12). ",
"Suppose s*h - 3*h = -2*d + 194, 4*d = 16. ",
"What is the tens digit of h?",
"\n6\nLet s(o) = -442*o**3 - 2*o**2 + 5*o + 3. ",
"Let v be s(-2). ",
"Let i = -2103 + v. What is the thousands digit of i?",
"\n1\nLet q(w) be the third derivative of -w**6/120 + 13*w**5/60 + 17*w**4/24 + 10*w**3/3 - 17*w**2. ",
"Let u be q(14). ",
"Let l = 68 - u. What is the units digit of l?",
"\n6\nLet n(k) = 33710*k**3 - 4*k**2 - 3*k + 5. ",
"What is the ten thousands digit of n(1)?",
"\n3\nSuppose 0 = z - 3*j + 39 + 18, -5*z = j + 285. ",
"Let v = 122 + z. What is the units digit of (-13)/v - 26/(-5)?",
"\n5\nSuppose 0 = s + 5*h - 20, s + h - 4 = 5*s. ",
"Suppose s = 5*n - 2*l - 31, -2*l = 3*n - 2*n + 1. ",
"Suppose -6*r = -n*r - 25. ",
"What is the units digit of r?",
"\n5\nSuppose -22*h = -163*h - 49*h + 8598450. ",
"What is the tens digit of h?",
"\n5\nWhat is the tens digit of 2 + 7830 - (24 + -12)?",
"\n2\nSuppose -8*m + m = -217. ",
"Let k = -29 + m. Suppose k*p - 5*z - 306 = 0, 2*p + 4*z = 407 - 65. ",
"What is the units digit of p?",
"\n3\nSuppose 3*y = 5*m - 64, 5*m - 2*y - 30 = 36. ",
"Suppose -60*p + 58*p + m = 0. ",
"Suppose -d - p = -2*v + 11, 46 = 5*v - 3*d. ",
"What is the units digit of v?",
"\n8\nLet x(c) be the first derivative of 2*c**3/3 - 11*c**2/2 + 6*c + 60. ",
"What is the hundreds digit of x(-11)?",
"\n3\nLet w(a) = -432*a - 1921. ",
"What is the thousands digit of w(-9)?",
"\n1\nSuppose 4*i = 1625 - 1609, -3*s + 4*i = -17993. ",
"What is the hundreds digit of s?",
"\n0\nLet z = 225 - 221. ",
"Suppose -t + 2*x + 2*x = -378, 8 = z*x. ",
"What is the units digit of t?",
"\n6\nSuppose 4*q - 3*k - 3 - 4 = 0, -4*k + 12 = 0. ",
"Suppose -q*v - 4*i = i - 1553, -4*i = 3*v - 1164. ",
"What is the units digit of v?",
"\n2\nLet c be (-408)/(-108) + 4/18. ",
"Suppose j + c = -1, -5*s = -j - 130. ",
"What is the units digit of s?",
"\n5\nSuppose 2*c + 163 = -111. ",
"Suppose 556 = 4*w - 268. ",
"Let q = w + c. What is the tens digit of q?",
"\n6\nLet g(h) = 6*h - 194. ",
"Let p be g(33). ",
"Suppose d - 263 = -p*i, 4*d - 386 = -4*i + 714. ",
"What is the hundreds digit of d?",
"\n2\nLet f = 25 - 22. ",
"Suppose j + j - f*b = 20, -b = -3*j + 30. ",
"Suppose -11*i = -6*i - j. What is the units digit of i?",
"\n2\nLet j be 34/51 + (-8)/(-6). ",
"Suppose 0 = j*v + 318 - 1058. ",
"Let f = v + -242. ",
"What is the hundreds digit of f?",
"\n1\nLet j = -17579 - -25072. ",
"What is the tens digit of j?",
"\n9\nLet l be ((-6)/(-18))/(2/(-6)). ",
"What is the units digit of (-1375)/l + (2 - (-8 + 11))?",
"\n4\nLet j = 107 - 87. ",
"Suppose 0 = 5*v - 5*t + 37 + 13, v + 5*t - j = 0. ",
"Let d(w) = -w**3 - 5*w - 3. ",
"What is the tens digit of d(v)?",
"\n4\nSuppose -2*b = -4*z - 43660, -43652 = 44*b - 46*b + 2*z. ",
"What is the ten thousands digit of b?",
"\n2\nSuppose 32 = -4*s, i - 29626 + 10994 = -5*s. ",
"What is the ten thousands digit of i?",
"\n1\nSuppose -32*d + 15*d = -696660. ",
"What is the tens digit of d?",
"\n8\nLet w = -1001 + 1783. ",
"What is the hundreds digit of w?",
"\n7\nSuppose -2484 = -4*r - 4*j, 2*r - 6*j - 1239 = -5*j. ",
"Let q = r - 390. ",
"What is the units digit of q?",
"\n0\nSuppose 30*k = -2*u + 24*k + 63820, 5*u = -4*k + 159528. ",
"What is the thousands digit of u?",
"\n1\nLet n(h) = 11*h**3 - 38*h**2 + 11*h + 29. ",
"What is the hundreds digit of n(11)?",
"\n1\nLet f = 447 - 227. ",
"Let g(q) = -2*q**2 + 4*q - 1. ",
"Let x be g(-6). ",
"Let h = f + x. What is the tens digit of h?",
"\n2\nSuppose -58 = -7*d + 110. ",
"Suppose -d*w = -26*w. ",
"Suppose -3*h = 3*f - 126, -4*f + 2*h = -w*h - 150. ",
"What is the units digit of f?",
"\n9\nLet j = 1619 - 1136. ",
"Let i = 730 - j. What is the tens digit of i?",
"\n4\nWhat is the thousands digit of (10294/(-4))/(7/(-154)*11)?",
"\n5\nWhat is the thousands digit of (173 + -203)/((-2)/807)?",
"\n2\nLet f be (11 - 3) + -3 + 0. ",
"Suppose -2*o + f*o = 4*b - 668, -3*b = -4*o - 494. ",
"Suppose -4*v + 209 = 5*s + 39, 0 = 5*s - 3*v - b. What is the tens digit of s?",
"\n3\nSuppose 2160*m = 2138*m + 69168. ",
"What is the tens digit of m?",
"\n4\nSuppose 71 + 1949 = 10*w. ",
"Let j = 303 - w. What is the units digit of j?",
"\n1\nSuppose -3*u = -3*h - 106 + 316, -160 = -2*h - 2*u. ",
"Let a = 31 + h. What is the units digit of a?",
"\n6\nLet h(o) = -19*o + 8. ",
"Let y be h(1). ",
"Let j(v) = -v**3 - 7*v**2 + 10*v - 30. ",
"What is the units digit of j(y)?",
"\n4\nLet i(n) = 38*n**2 - 4*n + 2. ",
"Let r(s) = s**3 + s**2 - 5*s - 7. ",
"Let a be r(-3). ",
"Let f be (-1 + a/(-4))*(-4)/(-6). ",
"What is the units digit of i(f)?",
"\n6\nSuppose -81*c + 62*c = -90877. ",
"What is the tens digit of c?",
"\n8\nLet l = 1578 + -63. ",
"What is the thousands digit of l + (5 - 1) + 2?",
"\n1\nLet i be 4 + 25/(-5) - 31. ",
"Let s = i - -40. ",
"Suppose s*k + 1374 = 14*k. ",
"What is the units digit of k?",
"\n9\nLet n = 7 + 141. ",
"Suppose -2*y - 8*y = y. Suppose y = -7*j + 5*j + n. What is the units digit of j?",
"\n4\nLet b be ((-76)/(-16))/((-1)/(-4)). ",
"Let x = b - 9. ",
"What is the units digit of (-10)/(-25) + 966/x?",
"\n7\nLet x(p) = -9821*p + 386. ",
"What is the tens digit of x(-1)?",
"\n0\nLet y = 2537 + -2034. ",
"What is the tens digit of y?",
"\n0\nLet b = 123 - 81. ",
"Let k(p) = 27 + 21 - 33*p - b. What is the tens digit of k(-7)?",
"\n3\nSuppose 1234 = -8*d + 1458. ",
"Suppose 0 = 18*l - d*l + 12050. ",
"What is the hundreds digit of l?",
"\n2\nSuppose -64*m + 3960 = -40*m. ",
"Suppose -3*z = -5*p - m - 303, -3*z = p - 468. ",
"What is the hundreds digit of z?",
"\n1\nSuppose -8*q + 6 = -5*q. ",
"Suppose 2*u = -5*r + 13, 7 = 3*u + q*r - 7. ",
"Suppose 0 = -0*x + u*x - 300. ",
"What is the units digit of x?",
"\n5\nLet s(i) = 131*i + 3. ",
"Let n be s(-3). ",
"Let g be (n/(-24))/((-4)/(-64)). ",
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"/*\n * {{{ header & license\n * Copyright (c) 2007 Patrick Wright\n *\n * This program is free software; you can redistribute it and/or\n * modify it under the terms of the GNU Lesser General Public License\n * as published by the Free Software Foundation; either version 2.1\n * of the License, or (at your option) any later version.",
"\n *\n * This program is distributed in the hope that it will be useful,\n * but WITHOUT ANY WARRANTY; without even the implied warranty of\n * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. ",
"See the\n * GNU Lesser General Public License for more details.",
"\n *\n * You should have received a copy of the GNU Lesser General Public License\n * along with this program; if not, write to the Free Software\n * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.",
"\n * }}}\n */\npackage org.xhtmlrenderer.util;\n\nimport java.util.",
"Map;\nimport java.util.",
"HashMap;\n\n\n/**\n * Simple enumerated constants for downscaling (scaling to smaller image size)--since we have various options\n * for what algorithm to use. ",
"Not general-purpose, applies only to methods used in ImageUtil. ",
"Types constants\n * can be looked up using {@link #forString(String, DownscaleQuality)} and the corresponding string\n * for the quality\n*/\n// made a separate class only to reduce size of ImageUtil\npublic class DownscaleQuality {\n\t/** Internal map string type to DQ instance */\n\tprivate static Map constList;\n\n\t/**\n\t * Highest-quality downscaling; probably slowest as well.",
"\n\t */\n\tpublic static final DownscaleQuality HIGH_QUALITY = addConstant(\"HIGH\");\n\n\t/** Low-quality, but not worst quality */\n\tpublic static final DownscaleQuality LOW_QUALITY = addConstant(\"MED\");\n\n\t/** Low quality, but very fast. */",
"\n\tpublic static final DownscaleQuality FAST = addConstant(\"LOW\");\n\n\t/** One step, fast, but should be better than low-quality. */",
"\n\tpublic static final DownscaleQuality AREA = addConstant(\"AREA\");\n\n\tprivate final String type;\n\n\t/**\n\t * Create and add constant instance\n\t * @param type Unique string for the instance\n\t * @return The constant for that type\n\t */\n\tprivate static DownscaleQuality addConstant(String type) {\n\t\tinit();\n\t\tif ( constList.containsKey(type)) {\n\t\t\tthrow new RuntimeException(\"Type strings for DownscaleQuality should be unique; \" + type +\n\t\t\t\" is declared twice\");\n\t\t}\n\t\tDownscaleQuality q = new DownscaleQuality(type);\n\t\tconstList.put(type, q);\n\t\treturn q;\n\t}\n\n\tprivate static void init() {\n\t\tif ( constList == null ) constList = new HashMap();\n\t}\n\n\tprivate DownscaleQuality(String type) {\n\t\tthis.type = type;\n\t}\n\n\tpublic String asString() {\n\t\treturn type;\n\t}\n\n\t/**\n\t * Retrieves the DownscaleQuality instance for the corresponding string.",
"\n\t *\n\t * @param type The string describing the quality, e.g. HIGH\n\t * @param dflt Default value to use if not found\n\t * @return The constant quality instance for the type, or the default if not found.",
"\n\t */\n\tpublic static DownscaleQuality forString(String type, DownscaleQuality dflt) {\n\t\tDownscaleQuality q = (DownscaleQuality) constList.get(type);\n\n\t\treturn q == null ? ",
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"/*\n * drivers/net/ibm_newemac/phy.h\n *\n * Driver for PowerPC 4xx on-chip ethernet controller, PHY support\n *\n * Copyright 2007 Benjamin Herrenschmidt, IBM Corp.\n * <benh@kernel.crashing.org>\n *\n * Based on the arch/ppc version of the driver:\n *\n * Benjamin Herrenschmidt <benh@kernel.crashing.org>\n * February 2003\n *\n * Minor additions by Eugene Surovegin <ebs@ebshome.net>, 2004\n *\n * This program is free software; you can redistribute it and/or modify it\n * under the terms of the GNU General Public License as published by the\n * Free Software Foundation; either version 2 of the License, or (at your\n * option) any later version.",
"\n *\n * This file basically duplicates sungem_phy.{c,h} with different PHYs\n * supported. ",
"I'm looking into merging that in a single mii layer more\n * flexible than mii.c\n */\n\n#ifndef __IBM_NEWEMAC_PHY_H\n#define __IBM_NEWEMAC_PHY_H\n\nstruct mii_phy;\n\n/* Operations supported by any kind of PHY */\nstruct mii_phy_ops {\n\tint (*init) (struct mii_phy * phy);\n\tint (*suspend) (struct mii_phy * phy, int wol_options);\n\tint (*setup_aneg) (struct mii_phy * phy, u32 advertise);\n\tint (*setup_forced) (struct mii_phy * phy, int speed, int fd);\n\tint (*poll_link) (struct mii_phy * phy);\n\tint (*read_link) (struct mii_phy * phy);\n};\n\n/* Structure used to statically define an mii/gii based PHY */\nstruct mii_phy_def {\n\tu32 phy_id;\t\t/* Concatenated ID1 << 16 | ID2 */\n\tu32 phy_id_mask;\t/* Significant bits */\n\tu32 features;\t\t/* Ethtool SUPPORTED_* defines or\n\t\t\t\t 0 for autodetect */\n\tint magic_aneg;\t\t/* Autoneg does all speed test for us */\n\tconst char *name;\n\tconst struct mii_phy_ops *ops;\n};\n\n/* An instance of a PHY, partially borrowed from mii_if_info */\nstruct mii_phy {\n\tstruct mii_phy_def *def;\n\tu32 advertising;\t/* Ethtool ADVERTISED_* defines */\n\tu32 features;\t\t/* Copied from mii_phy_def.features\n\t\t\t\t or determined automaticaly */\n\tint address;\t\t/* PHY address */\n\tint mode;\t\t/* PHY mode */\n\tint gpcs_address;\t/* GPCS PHY address */\n\n\t/* 1: autoneg enabled, 0: disabled */\n\tint autoneg;\n\n\t/* forced speed & duplex (no autoneg)\n\t * partner speed & duplex & pause (autoneg)\n\t */\n\tint speed;\n\tint duplex;\n\tint pause;\n\tint asym_pause;\n\n\t/* Provided by host chip */\n\tstruct net_device *dev;\n\tint (*mdio_read) (struct net_device * dev, int addr, int reg);\n\tvoid (*mdio_write) (struct net_device * dev, int addr, int reg,\n\t\t\t int val);\n};\n\n/* Pass in a struct mii_phy with dev, mdio_read and mdio_write\n * filled, the remaining fields will be filled on return\n */\nint emac_mii_phy_probe(struct mii_phy *phy, int address);\nint emac_mii_reset_phy(struct mii_phy *phy);\nint emac_mii_reset_gpcs(struct mii_phy *phy);\n\n#endif /* __IBM_NEWEMAC_PHY_H */\n"
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"The widow of a man who tried to save the life of murdered MP Jo Cox has collected the George Medal on his behalf.",
"\n\nDoreen Kenny received the honour from the Queen at Buckingham Palace in place of her late husband, Bernard Kenny, who was stabbed as he intervened when Thomas Mair attacked Mrs Cox in his home village of Birstall, West Yorkshire, in June 2016.",
"\n\nThe former miner died in August, aged 79, following a battle with cancer, before he could collect the medal for his bravery.",
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"I saw the blood and I thought ‘Oh my God’.”",
"\n\nMr Kenny described Mair’s actions as a “pure act of evil”.",
"\n\nAfter the attack, more than 80,000 people signed an online petition calling for Mr Kenny to be awarded the George Cross for his bravery.",
"\n\nMr Kenny, who shared a birthday with Mrs Cox, worked as a miner for 40 years and was a former member of the Gomersal Mines Rescue team, which tried to save victims of the Lofthouse Colliery disaster in 1973.",
"\n\nNeo-Nazi Mair was given a whole life sentence for the murder of Mrs Cox, and was also found guilty of causing grievous bodily harm to Mr Kenny and possession of a gun and dagger."
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"In the previous round of sanctions, which ended with the 2015 nuclear agreement, officially known as the Joint Comprehensive Plan of Action (JCPOA), the United States made an exception for medicine and medical equipment. ",
"But then and now, Iranian officials attribute the country’s medicine shortage to the sanctions. ",
"On July 29, Dr. Hassan Ghazizadeh Hashemi, President Rouhani’s minister of health, said claims that medicine supplies had not been affected by the sanctions were untrue [Persian link].",
"\n\nAnd yet the US State Department has denied this claim. ",
"The American Treasury Department had announced that Iran would be able to buy medicine and medical equipment as long as it was done in a financially transparent way and that the transactions did not go through Iran’s Central Bank and other Iranian banks that appeared on the sanctions list. ",
"The treasury made it possible for Iranian currency to be transferred for the purpose of buying medicine as long as it didn’t do it via these proscribed banks, not least because the Iranian banking system does not operate under international rules for financial transparency, including those of the Financial Action Task Force on Money Laundering (FATF). ",
"These measures made it more difficult and dangerous for international banks to work with Iran.",
"\n\nSome US officials, such as David Cohen, the former undersecretary of the US Treasury under President Obama, have said that the effect of sanctions on medicine was manageable and Iran had exaggerated the problem, but Iranian officials repeatedly insisted this was a lie. [",
"Persian link].",
"\n\nIn his book, The Art of Sanctions: A View from the Field, Richard Nephew — responsible for the development and execution of US sanctions strategy for Iran for the American National Security Council (NSC) from 2011 to 2013 — writes that one of the secrets to the success of sanctions under President Obama was the “propaganda” that accompanied them. ",
"According to him, the exemption of medicine and food from sanctions was part of this, since the US could argue that the measures were not inhumane. ",
"At the same time, it the US Treasury sought to remove any chance of money laundering.",
"\n\nFront for the Revolutionary Guards\n\nSo international banks had no appetite to deal with Iranian banks because the sources of funds were not transparent. ",
"Also, it was possible that Iranian pharmaceutical companies or importers were providing a front for the Revolutionary Guards and the real identities of the banks could not be ascertained. ",
"Some so-called “private” banks were actually owned by the Revolutionary Guards or the Paramilitary Basij Organization. ",
"Any country, business, or individual dealing with these banks could be forced to pay heavy fines, so Iran became synonymous with these dangers.",
"\n\nThe purchase of radiation therapy equipment and radiopharmaceuticals was next to impossible because of their connections to the nuclear industry. ",
"According to Kamran Bagheri Lankarani, President Ahmadinejad’s minister of health during his first term, in the winter of 2008 Iranians “were told as we woke up that they would no longer give us radiopharmaceuticals … Some governments that claimed to be our friends called us and offered to sell us radiopharmaceuticals that [should] cost around $200 for $2,000.”",
"\n\nIranian healthcare providers were caught off-guard by the shortage of medicine and medical equipment. ",
"In 2011, with the intensification of sanctions and the near exhaustion of Iran’s medicine reserves, the shortage turned into a crisis. ",
"At the time, imports of medicine fell by one third.",
"\n\nBut was it only the sanctions that caused this crisis?",
"\n\nAccording to official reports, fully 40 percent of the raw material used by Iranian pharmaceutical companies is imported. ",
"Before the first round of sanctions, most of the materials were imported from Europe, the United States and Canada. ",
"But when sanctions began, China and India replaced these countries as the major suppliers of medical raw material.",
"\n\nIran imports more than 300 types of medicine, including special drugs for hard-to-cure illnesses. ",
"The emerging situation led to tragedies that would have been otherwise preventable. ",
"For instance, in 2012, Iranian media reported that a 15-year old teenager, Manouchehr Esmaili, had died from hemophilia in Khuzestan because his doctors did not have access to the necessary medicine.",
"\n\nLuxury Cars instead of Medicine\n\nHowever, the crisis did not come about simply because of the sanctions. ",
"Pervasive corruption and the government’s mismanagement actually posed a bigger problem for those trying to procure medicine and medical equipment. ",
"When Marzieh Vahid Dastjerdi, President Ahmadinejad’s second-term health minister and Iran’s first female cabinet minister, publicly criticized the mismanagement and misappropriation of funds that had been earmarked for importing vital medicine, she was summarily dismissed by Ahmadinejad. “",
"I have heard that luxury cars have been imported with subsidized dollars but I don't know what happened to the dollars that were supposed to be allocated for importing medicine,\" she said on state television.",
"\n\nHer dismissal did not stop her from talking about it. “",
"At the height of sanctions [in 2012] when I joined the government’s Special Measures Headquarters, I saw that the foreign currency situation was very dire,” Kharab Online quoted Dastjerdi as saying [Persian link]. “",
"I told my colleagues that they must do their best to find currency to acquire medicine. ",
"We needed around $2.5 billion to buy medicine and medical equipment for treating heart illnesses and the like, but they gave the Health Ministry only $41 million. ",
"This made my blood boil…Our medical needs were the eighth priority. ",
"Dog food and horse saddles were the fourth and fifth priority.”",
"\n\nAnd the mismanagement did not stop here. ",
"The government consistently delayed the release of supplies to pharmaceutical companies, and medicine patients desperately needed remained inaccessible in customs warehouses. ",
"There were many reports about medical teams using out-of-date anesthetics — a direct threat to the lives of Iranian patients.",
"\n\n“We are under sanctions but we ourselves have put sanctions on medicine imports,” said Mohammad Reza Naderi, the deputy head of Iran’s Department of Customs. ",
"But Mahmoud Bahmani, then the governor of Iran’s Central Bank, denied accusations that the government had failed to supply the foreign currency needed to import medicine; he in turn accused the importers of medicine of using the currency to bring in luxury cars [Persian link]. ",
"In one case, the Central Bank announced that there had been plans to use the government’s foreign currency to import dozens of luxury cars.",
"\n\nThe government had found ways to bypass sanctions, but those people who had access to the Central Banks’ dollars at the official price preferred to import non-essential goods because they were more profitable.",
"\n\nFeel the Pain\n\nAccording to Richard Nephew, when the United States was getting ready to impose sanctions on Iran, it removed luxury items from the sanctions list so that, first of all, the Islamic Republic’s currency reserve would be exhausted faster and, secondly, “the feeling of pain due to sanctions” would intensify among Iranians.",
"\n\nSo both medicine and luxury items were exempted from the sanctions regime by design, but mismanagement and the corruption within the Iranian financial environment assured the success of the two goals of the US sanctions as defined by Richard Nephew — exhaustion of currency reserves and deepening the class divide — by awarding priority to luxury cars that were more profitable than the medicine needed by Iranian health providers.",
"\n\nStarting on August 6, some US sanctions were reimposed on Iran’s access to US currency, gold and precious metals, and the full sanctions regime will resume in three months’ time. ",
"But Iranian officials have said that they are fully prepared to take on the approaching storm and provide Iranians with the medicine and medical supplies they need [Persian link]. ",
"One such measure was an agreement that was signed during President Rouhani’s state visit to Switzerland in July to counter the effects of US sanctions in the areas of medicine and health. ",
"And Iran’s Food and Drug Administration has announced that it has identified what is necessary to supply medicine to Iran under sanctions. ",
"At the same time, the extent of corruption and mismanagement in Iran is so vast that even a humanitarian concern like medicine becomes overshadowed by them.",
"\n\nAs the return of sanctions drove up the price of the dollar in the open market to 12,000 tomans [120,000 rials] the government reported that some Iranian pharmaceutical companies, having received dollars at an official price of 3,8000 tomans in early August, chose to import vacuum cleaners and steam irons instead of drugs and medical supplies because they will attract a greater profit.",
"\n\nWhen Iranians lived under re-JCPOA sanctions, life became increasingly difficult, with basic necessities and medicine unavailable or unaffordable. ",
"But in reality, the corruption and mismanagement so rife in Iran during that time played a more important role in these shortfalls than the sanctions themselves. ",
"Today, and in the light of fresh sanctions, it looks as if this cycle is once again taking hold.",
"\n\nMore on the aftermath of Trump’s withdrawal from the nuclear treaty with Iran:\n\nIran’s Revolutionary Guards Commander Threatens Trump, July 26, 2018\n\nDecoding Iran’s Politics: The 12-Point US Ultimatum, July 6, 2018\n\nGuards Sell Missile Program to the Iranian Public, June 22, 2018\n\nIran and its Fleeting Dream of New Airplanes, June 13, 2018\n\nKhamenei Calls for Immediate Action on Nuclear Enrichment, June 6, 2018\n\nPresident Rouhani's Plane on the US Sanctions List, June 1, 2018\n\nDecoding Iranian Politics: Ayatollah Khamenei’s Stance on the JCPOA, June 1, 2018\n\nThe Nuclear Deal: Will Khamenei Get What he Wants?, ",
"May 29, 2018\n\nKhamenei’s Eight Conditions for Talks with Europe, May 25, 2018\n\nRevolutionary Guards Respond to Pompeo’s “Empty Bluff”, May 23, 2018\n\nThe 12 Demands of Pompeo's New Iran Strategy, May 21, 2018\n\nWhen Will US Sanctions Hit Iranian Oil Sales?, ",
"May 18, 2018\n\nThe JCPOA: A Missed Opportunity, May 17, 2018\n\nThe Future of Iran’s Economy as the US Bows Out of the Deal, May 10, 2018\n\nWhat are Iran’s Choices as US Abandons the Nuclear Deal?, ",
"May 9, 2018"
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[
"Q:\n\nPython Regex -Parse a string and split it by comma & dollar\n\nI have a sentence like this-\nstmt =\"Is abc service accessible to sd, rc & odd in XYZ?\"",
"\n\nAnd I have entities in string like this -\nstr_entities= \"abc service$Service,sd,rc & odd$Processes, XYZ$Name\"\n\nI want to convert these entities in the spacy json format eg. ",
"which contains the word indexes for each entity and the label for that entity\n(stmt, {\"entities\": [(3,14, 'Service'),(30, 41, 'Processes'), (46, 48, 'Name')]})\n\nI tried below regex but it works for only one case, i want a generic one which can extract any no. ",
"of entities.",
"\nre.findall(\"(.*.?)\\$(\\S+),(.*.?)\\$(\\S+)\", str_entities)\n\nI hv 10000s of such rows in many files, want to generate that format so that i can train a custom spacy model. ",
"I am not able to generate entities as the commas are splitting the entities multiple times and I am loosing the word to find the indexes from the stmt.",
"\n\nA:\n\nI'm not sure if I understood you correctly, but I would split the str_entities with \n[^ ^,]+[^\\$]*\\$[^\\$^,]+\n\nso that you get both, the string and the entity still combined with the $ sign. ",
"After that you can go through the elements with a for statement and get the index values.",
"\nenentity_list=[]\nfor e in re.findall(\"[^ ^,]+[^\\$]*\\$[^\\$^,]+\", str_entities):\n entity_list.append((stmt.index(e.split('$')[0]),stmt.index(e.split('$')[0])+len(e.split('$')[0]),e.split('$')[1]))\njson=(stmt,{\"entities\":entity_list})\n\nYou can try it on https://rextester.com/LRKTPL77140\n\n"
] | {
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"---\nabstract: 'In this paper we present a general tool to handle the presence of zero dynamics which are asymptotically but not locally exponentially stable in problems of robust nonlinear stabilization by output feedback. ",
"We show how it is possible to design [*locally Lipschitz*]{} stabilizers under conditions which only rely upon a partial detectability assumption on the controlled plant, by obtaining a robust stabilizing paradigm which is not based on design of observers and separation principles. ",
"The main design idea comes from recent achievements in the field of output regulation and specifically in the design of nonlinear internal models.'",
"\nauthor:\n- |\n L. Marconi$^{\\circ}$, L. Praly$^\\ast$, A. Isidori$^{\\circ\\dag}$\\\n $^{\\circ}$ C.A.SY. – ",
"DEIS, University of Bologna, Bologna, Italy.\\\n $^{\\ast}$ École des Mines de Paris, Fontainebleau, France.\\\n $^{\\dag}$DIS, Università di Roma “La Sapienza”, Rome, Italy.",
"\ntitle: |\n Robust Asymptotic Stabilization of Nonlinear Systems\\\n with Non-Hyperbolic Zero Dynamics\n---\n\nIntroduction\n============\n\nThe problem of output feedback stabilization in the large for nonlinear systems has been the subject of a remarkable research attempt in the last twenty years or so (see [@IsBook2]). ",
"The attempt has been initially turned to identify systematic design procedures for [*state-feedback*]{} stabilization of specific classes of nonlinear systems. ",
"To this respect it is worth mentioning the research current focused on back-stepping design procedures for lower triangular nonlinear systems with [@KoKo] for the global case and [@TP] for the semiglobal case. ",
"Then, the attention of the researchers shifted to the identification of partial-state and [*output feedback*]{} stabilization algorithms mainly addressed in a semi-global sense due to intrinsic limitations characterizing this class of problems (see [@Daya]). ",
"Within the number of research directions undertaken in this field, a special role has been played by [*nonlinear separation principles*]{} based on the design of an explicit full state observer (see [@TPSCL]). ",
"The main limitation of this approach is, thought, the lack of a guaranteed level of robustness of the resulting controller mainly due to the absence of a well-established theory of robust nonlinear state observers. ",
"Furthermore, full state observability of the controlled plant is not, in principle, a necessary condition for output feedback stabilization. ",
"A step forward to overcome these limitations has been taken in [@TP] with the definition of Uniform Completely Observable (UCO) state-feedback control law, namely a stabilizing state dependent law which can be expressed as nonlinear function of the control input and output and their time derivatives. ",
"In this case the issue is not to estimate the full-state but rather to reproduce directly the stabilizing law through the estimation of the input-output derivatives. ",
"This, in [@TP], has been achieved by a mix of back-stepping and partial-state observation techniques yielding an output feedback stabilizer which is [*robust*]{} in the measure in which the UCO function does not depend on the uncertainties and the UCO control law is [*vanishing*]{} on the desired asymptotic attractor. ",
"Furthermore the [*asymptotic*]{} features of the resulting closed-loop system are subjected to the requirement that the initial state-feedback UCO-based closed-loop system is locally exponential stable. ",
"Practical stability must be accepted otherwise (see also [@Celani] at this regard). ",
"The latter limitation may be overtaken with the design of a local nonlinear observer in the spirit of [@TPSCL] by resuming again nonlinear separation principles. ",
"However, so-doing, the same limitations outlined before come out.\\\nExponential stability assumptions are recurrent in several contexts of nonlinear control literature while studying asymptotic behaviors of nonlinear systems. ",
"Backstepping ([@Freeman], [@TP]), in which the backstepped control law is usually required to exponentially stabilize the controlled dynamics, singular perturbation ([@OReilly], [@TeMoNe03]), in which the so-called boundary layer system is required to posses an exponentially stable attractor, averaging ([@Khalil], [@TeMoNe03]), in which exponential stability of the so-called averaged system is needed, stabilization by output feedback ([@IsBook2], [@TP]), in which hyperbolic minimum-phase assumptions are usually required, are just a few contexts, involving problems of both synthesis and analysis of nonlinear systems, where the possibility of concluding asymptotic (and not only practical) results relies upon requirements that certain dynamics fulfill exponential stability assumptions. ",
"A particular mention must be done for the design of output feedback stabilizers for nonlinear systems which can be written in so-called normal form (see [@IsBook2]). ",
"In this context exponential stability of the so-called zero dynamics (that is, hyperbolic zero dynamics) is very often a crucial pre-requisite if one is willing to address robust output feedback stabilization by means of [*locally Lipschitz*]{} regulators.\\\nIn this paper we present a tool to handle the presence of not necessarily hyperbolic zero dynamics in the stabilization of nonlinear systems by output feedback. ",
"As particular application, the tool is then used to extend the main “UCO” results presented in [@TP] by, so doing, overtaking the obstacle of exponential stability in the backstepping procedure and output derivatives observer design. ",
"More specifically, by means of the mathematical tools which have been developed in a context of nonlinear output regulation (see [@SICON]), [@BI03]), we show how the design of a dynamic output feedback control law which [*asymptotically*]{} stabilizes a compact attractor can be obtained by starting from a UCO state-feedback control law which does not necessarily stabilize in exponential way the desired asymptotic attractor and which is not necessarily vanishing on it. ",
"We will show that these limitations can be removed by means of design techniques aiming to robustly get rid of interconnections terms between nonlinear dynamics arising in the stability analysis which are not vanishing on the desired asymptotic attractor and which, as a consequence, can not be dominated only by means of high-gain. ",
"This will lead to identify a dynamic back-stepping and an extended partial-state observer algorithms which embed solution techniques typical of internal model-based design.\\\nThis work is organized as follows. ",
"In the next section the framework and the general result is given. ",
"Then, Section 3 discusses the proposed framework and solution by properly framing the result in the existing literature. ",
"Section 4, articulated in three subsections, is focused on the application of the proposed tool in the UCO context presented in [@TP]. ",
"Then, Section 5 presents a few conditions, obtained by mild adaptation of results proposed in the output regulation literature, useful to construct the dynamic regulator which solve the problem discussed in Section 2. ",
"Finally Section 6 and 7 concludes with an example and final remarks.\\\n[**Notation**]{} For $x \\in \\Real^n$, $|x|$ denotes the Euclidean norm and, for $\\cal C$ a closed subset of $\\Real^n$, $|x|_{\\cal C}=\\min_{y \\in \\cal C}|x-y|$ denotes the distance of $x$ from $\\cal C$. ",
"For $\\cal S$ a subset of $\\Real^n$, $\\mbox{cl}\\cal S$ and $\\mbox{int}\\cal S$ are the closure of $\\cal S$ and the interior of $\\cal S$ respectively, and $\\partial {\\cal S}$ its boundary. ",
"A class-$\\cal KL$ function $\\beta(\\cdot,\\cdot)$ satisfying $|s| \\leq d$ $\\Rightarrow$ $\\beta(t,s) \\leq N\ne^{-\\lambda t} |s|$ for some positive $d$, $N$, $\\lambda$ is said to be a locally exponential class-$\\cal KL$ function. ",
"For a locally Lipschitz system of the form $\\dot z = f(z)$ the value at time $t$ of the solution passing through $z_0$ at time $t=0$ will be written as $\\phi_f(t,z_0)$ or, if the initial condition and the system are clear from the context, as $z(t)$ or $z(t,z_0)$. For a smooth system $\\dot x = f(x)$, $x \\in \\Real^\\dimx$, a compact set $\\ca$ is said to be LAS($\\cal X$) (respectively LES($\\cal X$)), with ${\\cal X} \\subset \\Real^\\dimx$ a compact set, if it is locally asymptotically (respectively exponentially) stable with a domain of attraction containing ${\\cal X}$. By ${\\cal D}(\\ca)$ we denote the domain of attraction of $\\ca$ if the latter is LAS/LES for a given dynamics. ",
"For a function $f:\\Real^n \\to \\Real^n$ and a differentiable real-valued function $q:\\Real^n \\to \\Real$, $L_fq(x)$ denote the Lie derivative at $x$ of $q$ along $f$. For a smooth system $\\dot x = f(x)$, $x \\in \\Real^\\dimx$ the $\\omega$-[*limit set*]{} of a subset $B \\subset \\Real^\\dimx$, written $\\omega(B)$, is the set of all points $x\\in\\Real^\\dimx$ for which there exists a sequence of pairs $(x_k,t_k)$, with $x_k\\in B$ and $t_k\\to \\infty$ as $k\\to \\infty$, such that $\\lim_{k\\to \\infty}\\phi_f(t_k,x_k)=x$.\n\nThe framework and the main result {#SecFramework}\n=================================\n\nThe main goal of this paper is to present a design tool to handle the presence of asymptotically but not necessarily exponentially stable zero dynamics in robust output-feedback stabilization problems of nonlinear systems. ",
"Although the tool we are going to present lends itself to be useful in a significant variety of control scenarios, in order to keep confined the discussion while maintaining a certain degree of generality, we focus our attention on the class of [*smooth*]{} systems of the form with measurable output $$y_m = C y \\qquad y_m\\in \\Real$$ in which the linear system $(A,B,C)$ is assumed to have relative degree $r$ with the pair $(A,C)$ observable, $\\kappa$ is a positive design parameter and $v$ is a control input. ",
"In the previous system the variable $w \\in \\Real^\\dimmu$ represents an exogenous variable which is governed by with $W$ a compact set which is [*invariant*]{} for (\\[exosys\\]). ",
"As a particular case, the signals $w(t)$ generated by (\\[exosys\\]) may be constant signals, i.e. $s(w)\\equiv 0$, namely constant uncertain parameters taking value in the set $W$ and affecting the system (\\[plantstab\\]). ",
"In general, the variables $w$ can be considered as exogenous signals which, depending on the considered control scenario, may represent references to be tracked and/or disturbances to be rejected.",
"\n\nAs a consequence of the fact that $W$ is a (forward and backward) invariant set for (\\[exosys\\]), the [*closed*]{} cylinder ${\\cal C}_{\\dimx + \\dimy}:=\n W \\times \\Real^{\\dimx + \\dimy}$ is invariant for (\\[plantstab\\]),(\\[exosys\\]). ",
"Thus it is natural to regard system (\\[plantstab\\]), (\\[exosys\\]) on ${\\cal C}_{\\dimx + \\dimy}$ and endow the latter with the relative topology. ",
"This will be done from now on by referring to system (\\[plantstab\\]),(\\[exosys\\]). ",
"Analogously, the dynamics described by the first $\\dimx$ equations of (\\[plantstab\\]) and by (\\[exosys\\]) will be thought as evolving on the closed set ${\\cal C}_{\\dimx}:=\n W \\times \\Real^{\\dimx}$ which will be endowed with the relative topology. ",
"$\\triangleleft$\n\nWe shall study the previous system under the following “minimum-phase\" assumption.",
"\n\n[*Assumption*]{} There exist compact sets $\\ca \\subset\n {\\cal C}_\\dimx$ which is locally asymptotically stable for the system Under this assumption, there exists a compact set ${\\cal X} \\subset {\\cal\n C}_n$ such that $\\ca \\subset \\mbox{int} \\cal X$ and $\\ca$ is LAS($\\cal X$) for system (\\[zd1\\]).\\\nIn this framework we consider the output feedback stabilization problem which consists of designing a [*locally Lipschitz*]{} regulator of the form and, given arbitrary bounded sets ${\\cal Y} \\subset \\Real^\\dimy$ and ${\\cal N} \\subset \\Real^\\dimeta$, a positive $\\kappa^\\star$, such that for all $ \\kappa \\geq \\kappa^\\star$ and for some ${\\cal B} \\subset \\Real^{\\dimeta + \\dimx}$ the set ${\\cal B} \\times \\{0\\}$ is LAS(${\\cal N} \\times {\\cal X} \\times {\\cal Y}$) for the closed-loop system (\\[plantstab\\]), (\\[etasys\\]).",
"\n\nThe important point here is that $\\varphi_k$ and $\\rho _k$ must be locally Lipschitz. ",
"This restriction has strong practical motivations like sensitivity to noise or numeric and discrete time implementation.",
"\n\nThe goal of the following part is to present a result regarding the solution of the robust stabilization problem formulated above. ",
"In order to ease the notation, in the following we shall drop in (\\[plantstab\\]) the dependence from the variable $w$ which, in turn, will be thought as embedded in the variable $x$ (with the latter varying in the set ${\\cal C}_{\\dimx}$). ",
"This, with a mild abuse of notation, will allow us to rewrite system (\\[plantstab\\]) and (\\[exosys\\]) in the more compact form and system (\\[zd1\\]) as $\\dot x = f(x,0)$.\n\nThe existence of a locally Lipschitz regulator solving the problem at hand, will be claimed under an assumption which involves the ability of asymptotically reproducing the function $q(x(t),0)$, where $x(t)$ is any solution of $\\dot x\n = f(x,0)$ which can be generated by taking initial conditions on $\\ca$, by means of a locally Lipschitz system properly defined. ",
"The following definition aims to formally state the required reproducibility conditions which will be then used in the forthcoming Theorem \\[TheoremFirst\\].",
"\n\n(LER, rLER). ",
"\\[DefinitionRegularitySoft\\] A triplet $(F(\\cdot), Q(\\cdot), {\\cal A})$, where $F: \\Real^\\dimz \\to \\Real^\\dimz$ and $Q: \\Real^\\dimz \\to \\Real$ are smooth functions and ${\\cal A}\\subset \\Real^\\dimz$ is a compact set, is said to be [*Locally Exponentially Reproducible*]{} (LER), if there exists a compact set ${\\cal R} \\supseteq \\cal A$ which is LES for $\\dot z = F(z)$ and, for any bounded set $\\cal Z$ contained in the domain of attraction of $\\cal R$, there exist an integer $\\dimxi$, [*locally Lipschitz*]{} functions $\\varphi: \\Real^\\dimxi \\to \\Real^\\dimxi$, $\\gamma:\n \\Real^\\dimxi \\to \\Real$, and $\\psi: \\Real^\\dimxi \\to \\Real^\\dimxi$, with $\\psi$ a complete vector field, and a [*locally Lipschitz*]{} function $T:\\Real^\\dimz \\to \\Real^\\dimxi$, such that and for all $\\xi_0 \\in \\Real^\\dimxi$ and $z_0 \\in \\cal Z$ the solution $(\\xi(t), z(t))$ of\n\nsatisfies where $\\beta(\\cdot,\\cdot)$ is a locally exponentially class-$\\cal\n KL$ function.",
"\n\nFurthermore the triplet in question is said to be [*robustly Locally Exponentially Reproducible*]{} (rLER) if it is LER and, in addition, for all locally essentially bounded $v(t)$, for all $\\xi_0 \\in \\Real^\\dimxi$ and $z_0 \\in \\cal Z$ the solution $(\\xi(t), z(t))$ of\n\nsatisfies where $\\beta(\\cdot,\\cdot)$ is a locally exponentially class-$\\cal\n KL$ function and $\\ell$ is a class-$\\cal K$ function. ",
"$\\triangleleft$\n\nWe postpone to Section \\[SecDigression\\] a broad discussion about this definition and to Section \\[SecSuff\\] the presentation of sufficient conditions for a triplet to be rLER.",
"\n\nWith this definition at hand, we pass to formulate the following theorem which fixes a framework where the stabilization problem previously formulated can be solved by means of a locally Lipschitz regulator. ",
"The proof of this theorem can be found in Appendix \\[ProofTheoremFirst\\].\\\n\n\\[TheoremFirst\\] Let $\\ca$ be LAS(${\\cal X}$) for the system $\\dot x = f(x,0)$ for some compact set ${\\cal X} \\subset {\\cal C}_n$. Assume, in addition, that the triplet $(f(x,0),{q}(x,0),{\\ca})$ is [*LER*]{}. ",
"Then there exist a locally Lipschitz regulator of the form (\\[etasys\\]), a compact set ${\\cal R} \\supseteq \\ca$, a continuous function $\\tau: {\\cal R} \\to \\Real^\\dimeta$, and, for any compact set ${\\cal Y} \\subset \\Real^\\dimy$ and ${\\cal N} \\subset \\Real^\\dimeta$, a positive constant $\\kappa^\\star$, such that for all $\\kappa \\geq \\kappa^\\star$ the set is LES(${\\cal N} \\times {\\cal X} \\times {\\cal Y}$) for (\\[plantstab+exo\\]), (\\[etasys\\]) and the set is LAS(${\\cal N} \\times {\\cal X} \\times {\\cal Y}$) for (\\[plantstab+exo\\]), (\\[etasys\\]). ",
"Furthermore, if $\\ca$ is also LES for the system $\\dot x =\n f(x,0)$, the set $\\cal R$ can be taken equal to $\\ca$.\n\nBy going throughout the proof of the previous theorem, it turns out that the regulator (\\[etasys\\]) solving the problem at hand has the form $$\\ba{rcl}\n \\dot \\eta &=& \\varphi(\\eta) - \\psi(\\eta)[\\gamma(\\eta) + \\kappa B\\tr A\n y]\\\\\n v &=& \\gamma(\\eta)\n \\ea$$ in which $\\kappa$ is a sufficiently large positive number and $(\\varphi(\\cdot),\\psi(\\cdot),\\gamma(\\cdot))$ are the locally Lipschitz functions which are associated to the triplet $(f(x,0),{q}(x,0),{\\ca})$ in the definition of local exponential reproducibility. ",
"$\\triangleleft$\n\nA brief digression about the problem {#SecDigression}\n====================================\n\nThe structure of (\\[plantstab\\]) and the associated problem, apparently very specific, are indeed recurrent in a number of control scenarios in which robust non linear stabilization is involved. ",
"We refer to Section \\[SecUCO\\] for the presentation of a few relevant cases where this occurs. ",
"For the time being it is interesting to note how the previous formulation presents two main peculiarities which make the problem at hand particularly challenging.\\\nThe first is that the function $q(w,x,y)$, coupling the $x$ and $y$ subsystem in (\\[plantstab\\]), is not necessarily vanishing on the desired attractor $\\ca \\times \\{0\\}$, namely the desired attractor $\\ca \\times \\{0\\}$ is not necessarily forward invariant for (\\[plantstab\\]) in the case $v\\equiv 0$. In this respect the first crucial property required to the regulator is to be able to reproduce, through the input $v$, the uncertain coupling term $q(w,x,0)$ by providing a not necessarily zero steady-state control input. ",
"This issue is intimately connected to arguments which are usually addressed in the output regulation literature (see [@SICON], [@BI03]), [@Huang], [@Pavlov]), in which the goal is precisely to make attractive a set, on which regulation objectives are met, which is not invariant for the open-loop system.",
"\n\nThe second peculiarity, apparently not correlated to the previous one, relies in the fact that the set $\\ca$ is assumed to be “only” asymptotically stable for (\\[zd1\\]) and no exponential properties are required. ",
"In this respect the study of the interconnection (\\[plantstab\\]) is particularly challenging as it is not sufficient, in general, to decrease the linear asymptotic gain ([@Te96]) between the “inputs” $x$ and the “outputs” $y$ of the $y$-subsystem (which is what one would make by increasing the value of $\\kappa$ since the matrix $A$ is Hurwitz) to infer asymptotic properties in the interconnection. ",
"Indeed the presence of a not necessarily linear asymptotic gain between the “inputs” $y$ and the “outputs” $x$ of the $x$-subsystem requires a non trivial design of the input $v$ which, intuitively, should be chosen to infer a certain locally non-Lipschitz ISS gain to the $y$-subsystem.",
"\n\nThe rich available literature on nonlinear stabilization already provides successful tools to solve the problem at hand if the previous two pathologies are dropped, namely if the assumption is strengthen by asking that the set $\\cal A$ is also LES(${\\cal X}$) for (\\[zd1\\]) and that the “coupling” term $q(w,x,y)$ is vanishing at ${\\cal A} \\times \\{ 0\\}$. As a matter of fact, under the previous conditions, it is a well-known fact that the set $\\ca \\times \\{0\\}$, which is forward invariant for (\\[plantstab\\]) with $v=0$, can be stabilized by means of a large value of $k$ as formalized in ([@TP], [@Atassi]).\\\nIn the case $\\ca$ is not exponentially stable for (\\[zd1\\]) and/or the coupling term $q(w,x,y)$ is not vanishing on the desired attractor, the problem becomes challenging and more sophisticated choices for $v$ must be envisaged. ",
"In particular, while preserving the local Lipschitz property of the regulator, the only conclusions which can be drawn if $v\\equiv 0$ is that the origin is [*semiglobally practically*]{} stable in the parameter $\\kappa$, that is the trajectories of the system can be steered arbitrary close to the set $\\ca \\times \\{0\\}$ by increasing the value of $\\kappa$ (see [@TP], [@Atassi], [@SICON]). ",
"Even in the simpler scenario in which $q(w,x,0)\\equiv 0$ for all $(w,x) \\in \\ca$, a large value of $k$ is not sufficient to enforce the desired asymptotic behavior in the case the set $\\ca$ fails to be exponentially stable for (\\[zd1\\]). ",
"In this case the asymptotic properties of the system have been studied in [@Celani] by showing how the trajectories are attracted by a manifold which, only in a particular case depending on the linear approximation of the system, collapses to the origin (see Theorem 6.2 in [@Celani]).",
"\n\nIn these critical scenarios an appropriate design of the control input $v$ becomes inevitable in order to compensate for the coupling term $q(w,x,y)$ which cannot be only dominated by a large value of $\\kappa$. In particular, a first possible option, motivated by small gain arguments and gain assignment procedures for nonlinear systems (see [@JiangBook], [@JiangTeelPraly]), is to design the control $v$ in order to assign, to the $y$-subsystem, a certain nonlinear ISS gain suitably identified according to small gain criterions and to the asymptotic gain of the $x$-subsystem (\\[plantstab\\]). ",
"This option, however, necessarily leads to design control laws which are not, in general, locally Lipschitz close to the compact attractor and, thus, which violates a basic requirement of the above problem.\\\nAn alternative option to design the control $v$ is to be inspired by nonlinear separation principles (see, besides others, [@TP], [@TPSCL], [@Atassi], [@IsBook2], [@GKbook]), namely to design an appropriate state observer yielding an asymptotic estimate $(\\hat w,\\hat x,\\hat y)$ of the state variables, and to asymptotically compensate for the coupling term $q(w,x,y)$ by implementing a “certainty equivalence” control law of the form $v = - q(\\hat w,\\hat x, \\hat\n y)$. Indeed, under suitable conditions, the tools proposed in [@TPSCL] would allow one to precisely fix the details and to solve the problem at hand in a rigorous way. ",
"This way of approaching the problem, though, presents a number of drawbacks which substantially limit its applicability. ",
"First, the design of the observer clearly requires the formulation of suitable observability assumptions[^1] on the controlled plant, and in particular of its $(w,x)$ components, not in principle necessary for the stabilization problem to be solvable, which may be not fulfilled for a number of relevant cases. ",
"Moreover, according to the state-of-the-art of the observer design literature ([@GKbook]), the design of the observer may be a challenging (if not impossible) task in case of uncertain parameters affecting the observed dynamics. ",
"Finally, it is worth noting how approaching the problem according to the previous design philosophy, leads to inherently [*redundant control structures*]{}, by requiring the explicit estimate of the full state (and of possible uncertainties) in order to reproduce the signal $q(w,x,y)$.\n\nAs opposite to the previous strategies, Theorem \\[TheoremFirst\\] provides a design procedure which does not rely upon domination of the interconnection term $q(w,x,y)$ but rather on its asymptotic reconstruction which, however, it is not based upon the design of an observer of the state variables $(w,x,y)$. In this respect the crucial property underlying the Theorem is the local exponential reproducibility property which, according to its definition, relies upon two requirements. ",
"The key first requirement, for a triplet $(F,Q,\\ca)$ to be LER, is that there exists a set $\\cal R$ which contains $\\ca$ and which is LES for the autonomous system $\\dot z = F(z)$. The second crucial requirement characterizing the definition is that there exists a [*locally Lipschitz*]{} system of the form with input $u_\\xi$ and output $y_\\xi$, such that system (\\[xisysdef\\]), modelling the cascade connection of the autonomous system $\\dot z = F(z)$ with output $y_z = Q(z)$ with the system (\\[xisys\\]), has a locally exponentially stable set described by ${\\rm graph} \\left .",
"\n T \\right |_{\\cal R}$ and, on this set, the output $y_\\xi$ equals $y_z$ (see (\\[Timmdef\\])). ",
"The domain of attraction of ${\\rm graph} \\left .",
"\n T \\right |_{\\cal R}$ is required to be of the form ${\\cal Z} \\times \\Real^\\dimxi$ with $\\cal Z$ any compact set in the domain of attraction of $\\cal R$ (note that, according to the definition, system (\\[xisys\\]) is allowed to depend on the choice of $\\cal Z$). ",
"In this respect the second requirement can be regarded as the ability, of the system (\\[xisys\\]), of [*asymptotically reproducing*]{} the output function $Q(z(t))$ of system $\\dot z(t) = F(z(t))$ with initial conditions of the latter taken in $\\cal Z$. Note how the “output reproducibility” property required to system (\\[xisys\\]) does not hide, in principle, any kind of state observability property of the system $\\dot z=F(z)$ with output $y_z= Q(z)$. In other words system (\\[xisys\\]) must be not confused with a state observer of the $z$-subsystem as its role is to reproduce the output function $Q(z(t))$ and not necessarily to estimate its state.",
"\n\nAs the definition of [*robust*]{} LER, we only note that, in addition to the previous properties, it is required that system (\\[xisysdefRob\\]) exhibits an ISS property (without any special requirement on the asymptotic gain) with respect to the exogenous input $v$.\n\nApplications\n============\n\nOutput-feedback from UCO state-feedback in presence of non-hyperbolic attractors {#SecUCO}\n--------------------------------------------------------------------------------\n\nIn this part we show how the theory of robust nonlinear separation principle presented in [@TP], [@Atassi] can be extended with the tools developed in the previous sections. ",
"In particular we are interested to extend the theory of [@TP] by showing how to design a pure output-feedback semiglobal controller stabilizing an attractor when it is known how the latter can be asymptotically ([*but not exponentially*]{}) stabilized by means of a Uniform Completely Observable (UCO) state-feedback controller.",
"\n\nConsider the smooth system in which $u$ and $y$ are respectively the control input and the measured output and $W$ is a compact set which is invariant for $\\dot w=s(w)$. As discussed in the previous section, the variables $w$ emphasize the possible presence of parametric uncertainties and/or disturbance to be rejected and/or reference to be tracked (in the latter case the measurable output $y$ plays more likely the role of regulation/tracking error). ",
"As done before, in order to simplify the notation, we drop the dependence of the variable $w$ and we compact system (\\[pla0withw\\]) in the more convenient form\n\nwhich is supposed to evolve on a closed invariant set ${\\cal C}_\\dimz$ which is endowed with the subset topology (such a closed set being, in the form (\\[pla0withw\\]), the closed cylinder ${\\cal C}_\\dimz:= W \\times\n \\Real^\\dimz$).",
"\n\nWe recall (see [@TP]) that a function $\\bar u : \\Real^\\dimz\n \\to \\Real$ is said to be UCO with respect to (\\[pla0\\]) if there exist two integers $n_y$, $n_u$ and a ${\\cal C}^1$ function $\\Psi$ such that, for each solution of we have, for all $t$ where the solution makes sense, where $y^{(i)}(t)$ denotes the $i$th derivative of $y$ at time $t$.\n\nMotivated by [@TP] we shall study system (\\[pla0\\]) under the following two assumptions:\n\n- there exist a smooth function $\\bar u : \\Real^\\dimz\n \\to \\Real$ and compact sets $\\ca \\subset {\\cal C}_\\dimz$ and ${\\cal Z} \\subset {\\cal\n C}_\\dimz$, such that the $\\ca$ is LAS($\\cal Z$) for system (\\[pla0\\]) with $u= \\bar u(z)$;[^2]\n\n- $\\bar u(z)$ is UCO with respect to (\\[pla0\\]).",
"\n\nIn this framework we shall be able to prove, under suitable reproducibility conditions specified later, that the previous two assumptions imply the existence of a locally Lipschitz dynamic output feedback regulator able to asymptotically stabilize the set $\\ca$. The main theorem in this direction is detailed next. ",
"In this theorem we refer to an integer $\\ell_u \\geq n_u$ defined as that number such that for the system\n\nthere exist smooth functions $C_i$ such that the first $n_y+1$ time derivatives of $y$ can be expressed as $$y^{(i)} = C_i(z,\\xi_0,\\ldots, \\xi_{\\ell_u}) \\qquad \\forall \\,\n i=0, \\ldots, n_y +1\\,.$$\n\n\\[TheoremMainUCO\\] Consider system (\\[pla0\\]) and assume the existence of a compact set $\\ca \\subset {\\cal C}_\\dimz$ and of a smooth function $\\bar u(z)$ such that properties (a) and (b) specified above are satisfied. ",
"Assume, in addition, that the triplets and are rLER. ",
"Then there exist a positive $\\dimzeta$, a compact set ${\\cal B} \\subset \\Real^\\dimzeta$ and, for any ${\\cal N} \\subset \\Real^\\dimzeta$, a locally Lipschitz controller of the form such that the set $\\ca \\times \\cal B$ is LAS(${\\cal Z} \\times\n \\cal N$) for the closed-loop system (\\[pla0\\]), (\\[finalregUCO\\]).",
"\n\nThis result extends Theorem 1.1 of [@TP] in three directions. ",
"First, note that we are dealing with stabilization of compact attractors for systems evolving on [*closed sets*]{}. ",
"This is a technical improvement on which, though, we would not like to put the emphasis. ",
"Second, note that the UCO control law $\\bar u(z)$ is not required to be vanishing on the attractor $\\ca$ which, as a consequence, is not required to be forward invariant for the open loop system (\\[pla0\\]) with $u\\equiv 0$. In this respect the proposed setting can be seen as also able to frame output regulation problems. ",
"Finally, the previous result claims that, by means of a pure [*locally Lipschitz*]{} output feedback controller, we are able to restore the asymptotic properties of an UCO controller without relying upon exponential stability requirements of the latter and robustly with respect to uncertain parameters. ",
"The last two extensions are conceptually very much relevant and can be seen as particular application of the tools presented in the previous sections. ",
"Following the main laying of [@TP], the proof of the claim is divided in two subsections which contain results interesting on their own.",
"\n\nRobust Asymptotic Backstepping {#SectionRobAsyBac}\n------------------------------\n\nIn this part we discuss how the UCO control law $\\bar u$ can be robustly back-step through the chain of integrators of (\\[plaextended\\]). ",
"As commented above, the forthcoming proposition extends in a not trivial way the results of [@TP] in the measure in which one considers the fact that $\\bar u(z)$ is not vanishing on the attractor and that $\\ca$ is not necessarily locally exponential stable for the closed-loop system.",
"\n\nWe show that the existence of the static UCO stabilizer for (\\[pla0\\]) implies the existence of a dynamic stabilizer for (\\[extendedzsys\\]) using the partial state $\\xi_i$, $i=0,\\ldots, \\ell_u$, and the output derivatives $y^{(i)}$, $i=1,\\ldots, n_y$. This is formally proved in the next proposition.",
"\n\n\\[theorembackstepping\\] Consider system (\\[extendedzsys\\]) under the assumption (a) previously formulated. ",
"Assume that the triplet (\\[triplet1\\]) is rLER. ",
"Then there exists a positive $\\dimeta$, a compact set ${\\cal R} \\supset \\ca$, a continuous function $\\tau: {\\cal R} \\to \\Real^{\\dimeta + \\ell_u+1}$, and, for any compact set $\\Xi' \\subset \\Real^{\\ell_u+1}$ and ${\\cal N}' \\subset \\Real^\\dimeta$, a locally Lipschitz regulator of the form with $\\xi={\\rm col}(\\xi_0,\\ldots, \\xi_{\\ell_u})$ such that the sets and $${\\rm graph} \\left . ",
"\\tau \\right |_{\\ca}\n :=\n \\{ (z,\\xi,\\eta) \\in {\\ca} \\times \\Real^{\\ell_u+1}\n \\times \\Real^{\\dimeta} \\; :(\\xi,\\eta) = \\tau(z)\\}$$ are respectively LES(${\\cal Z} \\times {\\Xi}' \\times {\\cal N}'$) and LAS(${\\cal Z} \\times {\\Xi}' \\times {\\cal N}'$) for the closed-loop system (\\[extendedzsys\\]), (\\[reg1\\]).",
"\n\nConsider the change of variables $$\\ba{rcl}\n \\xi_0 \\; \\to \\tilde \\xi_0 &:=& \\xi_0 - \\bar u(z)\\\\\n \\xi_i \\; \\to \\; \\tilde \\xi_i &:=& \\xi_i -\\bar u^{(i)}(z,\\tilde \\xi_0, \\ldots, \\tilde \\xi_{i-1})\n\\quad i=1, \\ldots, \\ell_u\n \\ea$$ where the $\\bar u^{(i)}(z)$, $i=1, \\ldots, \\ell_u$, are recursively defined as $$\\ba{rcl}\n \\bar u^{(1)}(z,\\tilde \\xi_0) &:=& \\dst {\\partial \\bar u(z) \\over \\partial z} A(z,\\tilde \\xi_0 + \\bar\n u(z))\\\\\n \\bar u^{(i)}(z, \\tilde \\xi_0, \\ldots, \\tilde \\xi_{i-1} ) &:=& \\dst {\\partial \\bar u^{(i-1)}(z,\\tilde \\xi_0,\\ldots\n \\tilde \\xi_{i-2}) \\over \\partial z} A(z,\\tilde \\xi_0 + \\bar\n u(z)) + \\\\\n && \\dst \\sum_{j=0}^{i-2} {\\partial \\bar u^{(i-1)}(z,\\tilde \\xi_0,\\ldots\n \\tilde \\xi_{i-2}) \\over \\partial \\tilde \\xi_j}\\tilde \\xi_{j+1} \\quad\\qquad\n i=2,\\ldots,\\ell_u\\,,\n \\ea$$ and the further change of variable $$\\ba{l}\n \\tilde \\xi_i,\\; \\to \\; \\zeta_i:= g^{-i} \\tilde \\xi_i \\qquad i=0,\\ldots,\n \\ell_u-1\\\\\n \\tilde \\xi_{\\ell_u} \\; \\to \\; \\zeta_{\\ell_u} := \\tilde \\xi_{\\ell_u} - \\dst \\sum_{i=0}^{\\ell_u -1}\n a_i g^{\\ell_u-i} \\tilde \\xi_i\n \\ea$$ where $g$ is a positive design parameter and the $a_i$’s are coefficients of an Hurwitz polynomial.",
"\n\nBy letting $\\zeta := \\mbox{col} (\\zeta_0, \\ldots,\n \\zeta_{\\ell_u-1})$ system (\\[extendedzsys\\]) in the new coordinates reads as where $B=\\mbox{col}(0,\\ldots, 0,1)$, $C=(1,0,\\ldots,0)$, $\\tilde A(z,C\\zeta) = A(z,\\tilde \\xi_0 + \\bar u(z))\n -A(z,\\bar u(z))$, $H$ is a Hurwitz matrix and $\\ell_g(\\cdot)$ is a smooth function such that As the triplet (\\[triplet1\\]) is rLER, there exists a compact set ${\\cal R} \\supseteq \\ca$ which is LES for $\\dot z = A(z,\\bar u(z))$ with ${\\cal D}({\\cal R}) \\supseteq {\\cal D}(\\ca)$. Furthermore, by the fact that (\\[triplet1\\]) is rLER and by definition of rLER, also the triplet $(A(z,\\bar u(z)), -L_{A(z,\\bar\nu(z))}^{(\\ell_u+1)} \\bar u(z), {\\cal R})$ is rLER. ",
"We consider now the zero dynamics, with respect to the input $u_1$ and output $\\zeta_{\\ell_u}$, of system (\\[syszxizeta\\]) given by For this system it can be proved (by means of arguments which, for instance, can be found in [@SICON]), that for any compact set ${\\cal M} \\in\n \\Real^{\\ell_u}$ there exists a $g^\\star >0$ such that for all $g \\geq\n g^\\star$ the sets ${\\cal R} \\times \\{ 0\\}$ and $\\ca \\times \\{0\\}$ are respectively LES(${\\cal Z} \\times {\\cal\n M}$) and LAS(${\\cal Z} \\times {\\cal\n M}$) for (\\[zdclosedloopproof1\\]). ",
"Fix, once for all, $g \\geq g^\\star$. By the previous facts, by (\\[ellprop\\]), by the fact that the triplet $(A(z,\\bar u(z)), -L_{A(z,\\bar\nu(z))}^{(\\ell_u+1)} \\bar u(z), {\\cal R})$ is rLER, and by Proposition \\[Propx1x2\\] in Appendix \\[AppendixAuxRes\\], it follows that the triplet $ ((\\ref{zdclosedloopproof1}),\\, \\ell_g(z,\\zeta,\n 0),\\, {\\cal R} \\times \\{ 0\\})$ is LER. ",
"Now fix where $\\kappa$ is a positive design parameters and $v$ is a residual control input. ",
"From the previous results, it follows that system (\\[syszxizeta\\]) with (\\[controlu\\]) fits in the framework of Theorem \\[TheoremFirst\\] , by which it is possible to conclude that there exists a locally Lipschitz controller of the form a continuous function $\\tau': {\\cal R}\\times \\{0\\} \\to \\Real^{\\dimxi}$ and, for any compact set ${\\cal M}_{\\ell_u} \\subset\n \\Real$ and ${\\cal N}' \\subset \\Real^{\\dimxi}$, a positive constant $\\kappa^\\star$, such that for all $\\kappa \\geq\n \\kappa^\\star$ the set $${\\rm graph }\\tau' \\times \\{0\\} = \\{((z,\\zeta),\\zeta_{\\ell_u},\\xi) \\in\n ({\\cal R} \\times \\{0\\}) \\times \\Real \\times \\Real^{\\dimxi} \\quad : \\quad\n \\zeta_{\\ell_u}=0\\,, \\; \\xi = \\tau'(z,\\zeta)\\}$$ is LES(${\\cal Z} \\times {\\cal M} \\times {\\cal M}_{\\ell_u} \\times\n{\\cal N}'$) for (\\[syszxizeta\\]), (\\[controlu\\]) and (\\[etasysprime\\]). ",
"Furthermore, by properly adapting the arguments at the end of the proof of Theorem \\[TheoremFirst\\], it is possible also to prove that the set ${\\rm graph }\\left . ",
"\\tau'\\right |_{\\ca \\times \\{0\\}} \\times\n \\{0\\}$ is LAS(${\\cal Z} \\times {\\cal M} \\times {\\cal M}_{\\ell_u} \\times {\\cal N}'$) for (\\[syszxizeta\\]), (\\[controlu\\]) and (\\[etasysprime\\]).",
"\n\nThe previous facts have shown how to solve the problem at hand by means of a [*partial state feedback*]{} regulator (namely a regulator processing $\\tilde \\xi_0 = \\xi_0 - \\bar u(z)$ and its first $\\ell_u$ time derivatives $\\tilde \\xi_i$) of the form In order to obtain a pure output feedback regulator of the form (\\[reg1\\]), we follow [@TP] and design a “dirty derivatives” observer-based regulator where $L$ is a positive design parameters, the $\\lambda_i$’s are such that the polynomial $s^{\\ell_u} + \\lambda_{\\ell_u} s^{\\ell_u-1} + \\ldots + \\lambda_2 s + \\lambda_1$ is Hurwitz and where $$\\hat {\\zeta}_{\\rm sat} = \\mbox{sat}_\\ell(\\hat {\\tilde \\xi}_{\\ell_u} - g^{\\ell_u-1} a_0 \\hat {\\tilde \\xi}_1\n -\n \\ldots - g\n a_{\\ell_u-1} \\hat {\\tilde \\xi}_{\\ell_u-1})$$ in which $\\mbox{sat}_\\ell(s)$ is the saturation function such that $\\mbox{sat}_\\ell(s)=s$ if $|s| \\leq \\ell$ and $\\mbox{sat}_\\ell(s)=\\ell \\, \\mbox{sgn}(s)$ otherwise. ",
"Letting $\\tilde \\xi=\\mbox{col}(\\tilde \\xi_1,\\ldots, \\tilde \\xi_{\\ell_u})$, $\\hat {\\tilde \\xi} = \\mbox{col}(\\hat {\\tilde \\xi}_1,\\ldots, \\hat\n {\\tilde \\xi}_{\\ell_u})$, and defining the change of variables $$\\hat {\\tilde \\xi} \\; \\mapsto \\; e := D_L (\\tilde \\xi - \\hat {\\tilde \\xi})$$ in which $D_L=\\mbox{diag}(L^{\\ell_u-1}, \\ldots, L,1)$, it turns out that the overall closed-loop system (\\[syszxizeta\\]), (\\[dirtyderReg\\]) reads as where $\n x := \\mbox{col}(z, \\zeta, \\zeta_{\\ell_u}, \\xi)\n $, $\\dot x = \\varphi(x)$ is a compact representation of (\\[syszxizeta\\]), (\\[partialstatefeedbackreg\\]), $H$ is a Hurwitz matrix and $\\Delta_1(\\cdot)$ and $\\Delta_2(\\cdot)$ are defined as $$\\Delta_1(\\cdot)=\\left(\\ba{c}0\\\\0\\\\ \\kappa(\\zeta_{\\ell_u} - \\hat {\\zeta}_{\\rm sat}) +\n \\Upsilon'_k(\\xi,\\hat {\\zeta}_{\\rm sat}) - \\Upsilon'_k(\\xi,{\\zeta}_{\\ell_u}) \\\\\n \\Phi_k'(\\xi,\\hat {\\zeta}_{\\rm sat} ) - \\Phi_k'(\\xi,{\\zeta}_{\\ell_u} ) \\ea\\right )$$ and $$\\Delta_2(\\cdot) = \\left( \\ba{c}\n 0\\\\\n \\vdots\\\\\n 0\\\\\n \\kappa(\\zeta_{\\ell_u} - \\hat {\\zeta}_{\\rm sat}) +\n \\Upsilon'_k(\\xi,\\hat {\\zeta}_{\\rm sat}) - \\Upsilon'_k(\\xi,{\\zeta}_{\\ell_u})\n \\ea\n \\right )$$ By construction the set ${\\rm graph}\\tau' \\times \\{0\\}$ is LES($\\cal X$) for the system $\\dot x = \\varphi(x)$ with ${\\cal X}:= ({\\cal Z} \\times {\\cal M}) \\times {\\cal M}_{\\ell_u} \\times {\\cal\n N}'$ and, by construction, it turns out that for any $\\ell>0$, $\\Delta_1(x,0)\\equiv 0$ and $\\Delta_2(x,0)\\equiv 0$ for all $x \\in {\\rm graph}\\tau' \\times\n \\{0\\}$. Furthermore, for any compact ${\\cal M} \\in\n \\Real^{\\ell_u-1}$, ${\\cal M}_{\\ell_u} \\in \\Real$ and $\\hat{\\cal M} \\in\n \\Real^{\\ell_u}$, there exists a compact set ${\\cal E} \\subset \\Real^{\\ell_u}$ ([*dependent on $L$*]{}) such that if $\\zeta(0) \\in {\\cal M}$, $\\zeta_{\\ell_u} \\in {\\cal\n M}_{\\ell_u}$ and $\\hat {\\tilde \\xi} (0) \\in \\hat {\\cal M}$ then $e(0) \\in \\cal E$. Furthermore, by definition of saturation function, it turns out that for all $\\bar x>0$ there exist $\\delta_1>0$ and $\\delta_2>0$ such that $|\\Delta_1(x,e)|\\leq \\delta_1$ and $\\Delta_2(x,e) \\leq \\delta_2$ for all $x$, $|x| \\leq \\bar x$, $e \\in \\Real$ and $L>0$.\n\nFrom these facts and by the result in [@TP], it follows that for any ${\\cal E} \\in\n \\Real^{\\ell_u}$ there exists a $L^\\star>0$ such that for all $L \\geq L^\\star$ the set $${\\rm graph} \\tau' \\times \\{0\\} \\times \\{0\\}\n = \\{((z, \\zeta), \\zeta_{\\ell_u}, \\xi, e) \\in ({\\cal R} \\times \\{0\\})\n \\times\\Real \\times\n \\Real^\\dimxi \\times \\Real^{\\ell_u} \\; : \\; \\zeta_{\\ell_u} =0 \\,, \\; \\xi = \\tau'(z,\\zeta)\\,, \\; e =0\\}$$ is LES(${\\cal Z} \\times {\\cal M} \\times {\\cal M}_{\\ell_u} \\times {\\cal\n N}' \\times \\cal E$).",
"\n\nFrom the previous results, the fact that $\\ca$ is LAS for the system $\\dot z\n = A(z,\\bar u(z))$, and the fact that on ${\\rm graph} \\tau' \\times \\{0\\}\n \\times \\{0\\}$ the closed-loop dynamics is described by $\\dot z = A(z,\\bar u(z))$), the desired result follows by properly adapting the omega-limit set arguments used at the end of the proof of Theorem \\[TheoremFirst\\].",
"\n\nExtended Dirty Derivatives Observer\n-----------------------------------\n\nIn this part we present a result which allows one to obtain a pure output feedback stabilizer once a partial state-feedback stabilizer (namely a stabilizer processing the output and a certain number of its time derivative) is known. ",
"Along the lines pioneered in [@EK] and [@TP], the idea is to substitute the knowledge of the time derivatives of the output with appropriate estimates provided by a “dirty derivative observer” (by using the terminology of [@TP]). ",
"In our context, though, we propose an “extended” dirty derivative observer, where the adjective “extended” is to emphasize the presence of a dynamic extension of the classical observer structure motivated by the need of handling the presence of possible not exponentially stable attractors in the partial-state feedback loop and the fact that, on this attractor, the measured output is not necessarily vanishing. ",
"More specifically we assume, for the system (\\[pla0\\]), the existence of a dynamic stabilizer of the form such that the following property hold for the closed-loop system:\n\n- there exists a compact set ${\\cal R} \\supset \\ca$ and a continuous function $\\tau: {\\cal R} \\to \\Real^\\dimvarsigma$ such that the sets ${\\rm graph} \\tau$ and ${\\rm graph} \\left . ",
"\\tau \\right\n |_{\\ca}$ are respectively LES(${\\cal Z} \\times {\\cal H}$) and LAS(${\\cal Z} \\times {\\cal H}$) for the closed-loop system (\\[pla0\\]), (\\[varsigmareg\\]) for some compact set ${\\cal H} \\subset\n \\Real^\\dimvarsigma$;\n\n- there exist smooth functions $C_i$, $i=0,\\ldots, n_y+1$, such that the output derivatives $y^{(i)}$ of the closed-loop system (\\[pla0\\]), (\\[varsigmareg\\]) can be expressed as $y^{(i)} =\n C_i(z,\\varsigma)$, $i=0,\\ldots, n_y+1$ and the following holds $$\\left . ",
"\\bar \\rho(\\varsigma, y, y^{(1)}, \\ldots, y^{(n_y)})\n \\right |_{{\\rm graph} \\tau} =\\bar u(z)\\,.$$\n\nNote that the previous conditions are automatically satisfied under the assumptions of Section \\[SecUCO\\] and by virtue of the results presented in the previous section. ",
"As a matter of fact, by bearing in mind (\\[extendedzsys\\]) and Theorem \\[theorembackstepping\\] (and specifically (\\[reg1\\])), the main outcome of the previous Section has been to design a dynamic controller of the form in which, according to (\\[ubarnot\\]) and to the definition of $\\ell_u$, System (\\[reggg\\]), (\\[ubarxi\\]) is clearly in the form (\\[varsigmareg\\]) and, according to the result of Theorem \\[theorembackstepping\\], the previous conditions (a)-(b) are satisfied. ",
"$\\triangleleft$\n\nWithin the previous framework we are able to prove the following proposition which, along with Proposition \\[theorembackstepping\\] and the previous remark, immediately yields Theorem \\[TheoremMainUCO\\].\\\n\nConsider system (\\[pla0\\]) and assume the existence of a dynamic regulator of the form (\\[varsigmareg\\]) such that the previous properties (a)-(b) are satisfied. ",
"Assume, in addition, that the triplet (\\[triplet2\\]) is rLER. ",
"Then there exist a positive $\\dimzeta$, a compact set ${\\cal B} \\subset \\Real^\\dimzeta$ and, for any compact set ${\\cal N} \\subset \\Real^\\dimzeta$, an output feedback controller of the form (\\[finalregUCO\\]) such that the set $\\ca \\times \\cal B$ is LAS(${\\cal Z} \\times \\cal N$) for the closed-loop system (\\[pla0\\]), (\\[finalregUCO\\]).",
"\n\nAs candidate controller, we consider a system of the form $$\\ba{rcl}\n \\dot \\varsigma &=& \\bar \\varphi_\\ell(\\varsigma, y, \\hat y_1, \\ldots, \\hat\ny_{n_y})\\\\[2mm]\n \\dot {\\hat y}_i &=& \\hat y_{i+1} + L^{i+1} \\lambda_i (\\hat\n y_0- y)\\\\\n \\dot {\\hat y}_{n_y} &=& L^{n_y +1} \\lambda_{n_y} (\\hat\ny_0-y) + v\\\\[2mm]\n u &=& \\bar \\rho_\\ell(\\varsigma, y, \\hat y_1, \\ldots, \\hat y_{n_y})\\\\\n \\ea$$ in which $v$ is a control input to be designed, $L$ is a positive design parameters, the $\\lambda_i$’s are the coefficients of an Hurwitz polynomial and $\\bar \\varphi_\\ell(\\cdot)$ and $\\bar\n\\rho_\\ell$ are appropriate saturated versions of the functions $\\bar \\varphi(\\cdot)$ and $\\bar \\rho(\\cdot)$ of (\\[varsigmareg\\]) satisfying $ \\bar \\varphi_\\ell(s) = \\bar\n\\varphi(s)$ if $|\\bar \\varphi(s)|\\leq \\ell$, $|\\bar\n\\varphi_\\ell(s)|\\leq \\ell$ for all $s$, and $ \\bar \\rho_\\ell(s) =\n\\bar \\rho(s)$ if $|\\bar \\rho(s)|\\leq \\ell$, $|\\bar\n\\rho_\\ell(s)|\\leq \\ell$ for all $s$, with $\\ell$ a design parameter.",
"\n\nLet now $y_d=\\mbox{col}(y, y^{(1)}, \\ldots, y^{(n_y)})$, $\\hat y =\n \\mbox{col}(\\hat y_0, \\hat y_1,$ $ \\ldots, \\hat y_{n_y})$ and consider the change of variables $\n \\hat y \\; \\mapsto \\; e =\n D_L (y_d - \\hat y)\n $ where $D_L= \\mbox{diag}( L^{n_y}, \\, L^{n_y-1},\\, \\ldots,\\, 1 )$. ",
"In this coordinate setting, by denoting $\n {x} = \\mbox{col}(\\ba{cc} z & \\varsigma \\ea )\n $, the overall closed-loop system reads as in which $H$ is a Hurwitz matrix in observability canonical form, $B=\\left(\\ba{cccc}0 & \\ldots & 0& 1 \\ea \\right )\\tr$ $\\dot x = {f}(x)$ is a compact representation of the system (\\[pla0\\]), (\\[varsigmareg\\]), ${q}(x) = C_{n_y\n+1}(z,\\varsigma)$ and\n\n$$\\Delta(x,e) = \\left ( \\ba{c} 0\\\\\n A(z,\\bar \\rho_\\ell(\\varsigma, y, \\hat y_{1}, \\ldots, \\hat y_{n_y}) )\n-A(z, \\bar \\rho(\\varsigma, y, y^{(1)}, \\ldots, y^{(n_y)}) )\\\\\n \\bar \\varphi_\\ell(\\varsigma, y, \\hat y_{1}, \\ldots, \\hat y_{n_y}) ) - \\bar \\varphi(\\varsigma,\ny, y^{(1)}, \\ldots, y^{(n_y)}) ) \\ea \\right )$$ in which, in the latter, we have left the “original” coordinates $\\hat y_i$ for notational convenience.",
"\n\nBy definition of $\\Delta$, of $\\bar \\rho_\\ell$ and of $\\bar\n\\varphi_\\ell$, it turns out that for any bounded set ${\\cal Z}'_M$ and ${\\cal H} \\subset \\Real^{\\dimxi + \\dimeta}$, there exists an $\\ell^\\star$ such that for any $\\ell \\geq \\ell^\\star$ $$\\Delta(x, 0) =0 \\qquad \\forall \\; x \\in {\\cal Z}'_M \\times {\\cal\nH}\\,.$$\n\nFurthermore, by the fact that the triplet (\\[triplet2\\]) is rLER it follows that there exists a compact set ${\\cal R}' \\supset \\ca$ which is LES for $\\dot z = A(z,\\bar u(z))$ with ${\\cal D}({\\cal\nR}') \\supseteq {\\cal D}(\\ca)$. Let ${\\cal R}'' := {\\cal R} \\bigcap {\\cal R'}$. By item (a) above and by going throughout the proof of Proposition \\[theorembackstepping\\], it turns out that ${\\rm\ngraph} \\left . ",
"\\tau \\right |_{{\\cal R}''}$ is LES for $\\dot x = f(x)$. Moreover, the set ${\\cal\nR}''$ is LES for $\\dot z = A(z,\\bar u(z))$ with ${\\cal D}({\\cal R}'') \\supseteq {\\cal D}(\\ca)$ and, by definition of rLER, it is possible to claim that the triplet $(A(z,\\bar u(z)), L_{A(z,\\bar\nu(z))}^{(n_y+1)} C(z), {\\cal R}'')$ is rLER. ",
"From the previous facts, from the item (b) above, which implies that $$\\left . {",
"q}(x) \\right |_{{\\rm graph} \\left . ",
"\\tau \\right |_{{\\cal R}''}} = C_{n_y +1}(z,\n\\tau(z))= L_{A(z, \\bar u(z))}^{(n_y+1)}C(z)\\,,$$ and by Proposition \\[Propx1x2\\] in Appendix \\[AppendixAuxRes\\], it follows that the triplet $$({f}(x), {q}(x), {\\rm graph} \\left . ",
"\\tau \\right |_{{\\cal R}''})$$ is LER. ",
"Thus system (\\[closedloopcompact\\]) fits in the framework of Theorem \\[TheoremFirst\\] (with graph$\\left . ",
"\\tau \\right\n|_{{\\cal R}''}$ playing the role of the set $\\ca$) by which the result follows (by using the fact that graph$\\left . ",
"\\tau \\right\n|_\\ca$ is LAS for $\\dot x = f(x)$ and by adapting the omega-limit set arguments at the end of the proof of Theorem \\[TheoremFirst\\]). ",
"$\\triangleleft$\n\nSufficient conditions for exponential reproducibility {#SecSuff}\n=====================================================\n\nHaving established with Theorems \\[TheoremFirst\\] and \\[TheoremMainUCO\\] the interest of local exponential reproducibility for solving the problem of (robust) output feedback stabilization via a locally Lipschitz regulator, in this section we present a number of results which are useful to test when a triplet $(F,Q,\\ca)$ is rLER (and thus LER) and, eventually, to design the functions $(\\varphi, \\psi,\\gamma)$.\n\nAs also commented in Section \\[SecSuff\\], the first requirement behind the definition is the existence of a compact set ${\\cal\n R} \\supseteq \\ca$ which is LES for $\\dot z = F(z)$. In this respect we present a result which claims that the existence of a set $\\cal R$ which is LES for $\\dot z = F(z)$ is automatically guaranteed if the set $\\ca$ is LAS for $\\dot z=F(z)$. Thus, put in the context of Theorem \\[TheoremFirst\\], the first requirement of the definition is not restrictive at all. ",
"Details of this fact are reported in the following proposition whose proof can be found in [@MPBook].\\\n\n\\[toolPropositionAp\\] Consider system evolving on an invariant closed set ${\\cal C}_\\dimz \\subset \\Real^\\dimz$. Let $\\ca \\subset {\\cal C}_\\dimz$ be a compact set which is LAS with domain of attraction ${\\cal\n D}(\\ca) \\subseteq {\\cal C}_\\dimz$. For any compact set ${\\cal S} \\subset {\\cal C}_\\dimz$ such that $\\ca \\subset {\\rm int}\\cal S$, there exists a compact set ${\\cal R}$ satisfying $\\ca \\subseteq {\\cal R}\n \\subset {\\cal S}$ which is LES for (\\[toolsys2\\]) with domain of attraction ${\\cal D}({\\cal R})\\equiv{\\cal D}(\\ca)$.\n\nWe pass now to analyze the second crucial requirement behind the definition of rLER, namely the existence of [*locally Lipschitz*]{} functions $(\\varphi, \\psi, \\gamma)$ and $T$ such that conditions (\\[Timmdef\\]) and (\\[condstabdefRob\\]) are satisfied for system (\\[xisysdefRob\\]). ",
"Being the property in question related to the ability of reproducing any signal $Q(z(t))$ generated by the system $\\dot\nz(t) = F(z(t))$ by taking its initial conditions in the set $\\cal\nR$, it is not surprising that the theory of nonlinear output regulation, and specifically the design techniques proposed in the related literature to construct internal models, can be successfully used to this purpose (see [@CASYMI]). ",
"In particular, in the following, we present two techniques which are directly taken, with minor adaptations, from the literature of output regulation.",
"\n\nFirst, we follow [@BI03bis] and we present a method which draws its inspiration from high-gain design techniques of nonlinear observers. ",
"Specifically it is possible to state the following proposition which comes from Lemma \\[toolPropositionAp\\] and from minor adaptations[^3] of the main result of [@BI03bis] (see the quoted work for the proof).",
"\n\n\\[PropositionPhase\\] Let $F: \\Real^\\dimz \\to \\Real^\\dimz$ and $Q: \\Real^\\dimz \\to\n \\Real$ be given smooth functions and $\\ca \\subset \\Real^m$ be a given compact set which is LAS for $\\dot z = F(z)$. Assume, in addition, that there exist a $\\tilde \\dimz >0$, a compact set $\\cal S$ such that $\\ca \\subset {\\rm int } \\cal S$ and a locally Lipschitz function $f: \\Real^{\\tilde \\dimz} \\to \\Real$ such that the following differential equation holds Then the triplet $(F,Q,\\ca)$ is rLER. ",
"In particular $(\\varphi,\\psi,\\gamma)$ can be taken as the functions $\\varphi: \\Real^{\\tilde \\dimz} \\to \\Real^{\\tilde \\dimz}$, $\\psi:\n\\Real^{\\tilde \\dimz} \\to \\Real^{\\tilde \\dimz}$, $ \\gamma:\n\\Real^{\\tilde \\dimz} \\to \\Real$ defined as $$\\varphi( \\xi) = \\left( \\ba{c} \\xi_2 + \\lambda_0 L \\xi_1\\\\\n \\xi_3 + \\lambda_1 L^2 \\xi_1\\\\\n \\vdots\\\\\n \\xi_{ \\tilde \\dimz} + \\lambda_{ \\tilde \\dimz -2} L^{ \\tilde \\dimz -1}\n \\xi_1\\\\\n f_c({\\xi}_1,\\, {\\xi}_2,\\, \\ldots, \\, {\\xi}_{\\tilde \\dimz}) + \\lambda_{\\dimz -1} L^{ \\tilde \\dimz}\n \\xi_1\\\\\n \\ea\n\\right )\\,, \\qquad\n \\psi( \\xi) = \\left( \\ba{c} -\\lambda_0 L\\\\\n-\\lambda_1 L^2\\\\ \\vdots\\\\\n -\\lambda_{\\tilde \\dimz -2} L^{ \\tilde \\dimz -1}\\\\\n -\\lambda_{\\tilde \\dimz -1} L^{\\tilde \\dimz}\n \\ea \\right )$$ and $\\gamma(\\xi) =\\xi_1$, where $L$ is a positive design parameter to be taken sufficiently large, $\\lambda_i$, $i=0,\\ldots, \\tilde\n\\dimz-1$, are such the polynomial $s^{\\tilde \\dimz} +\n\\lambda_{\\tilde \\dimz-1} s^{\\tilde \\dimz-1} + \\ldots + \\lambda_1 s\n+ \\lambda_0$ is Hurwitz, and $f_c(\\cdot)$ is any bounded function such that $f_c \\circ \\tau(z) = f(z)$ for all $z \\in \\cal S$ where $\\tau: \\Real^{\\dimz} \\to \\Real^{\\tilde \\dimz}$ is defined as $$\\tau(z) = \\left (\\ba{cccc}Q(z) & L_{F(z)}Q(z) & \\cdots & L_{F(z)}^{\\tilde \\dimz -1} Q(z) \\ea \\right\n )\\tr\\,.$$\n\n\\[remarkNoDiffObs\\] It is well-known (see, for instance, [@GKbook]) that a sufficient condition for a pair $(F,Q)$ to satisfy property (\\[immobser\\]) locally with respect to a point $z_0$ is that its observability distribution at $z_0$ (see [@HerKre]) has dimension $\\dimz$ at $z=z_0$, namely if the system $\\dot z = F(z)$ with output $y_z=Q(z)$ satisfies the [*observability rank condition*]{} (by using the terminology of [@HerKre]) at $z_0$. Such a condition represents an observability condition for the system $\\dot z = F(z)$ with output $y_z=Q(z)$ which, however, is far to be necessary to fulfill the property of rLER. ",
"In this respect it must be stressed again that the property of local exponential reproducibility does not involve any state observability property of system $\\dot z = F(z)$ with output $y_z=Q(z)$ but rather a property of output reproducibility. ",
"$\\triangleleft$\n\nClearly the high-gain technique to design output observer behind Proposition \\[PropositionPhase\\] is not the only tool which can be used to design the functions $(\\varphi,\\psi,\\gamma)$ for a triplet which is rLER. ",
"In order to enrich the available tools, we present now a result motivated by the theory of state observers pioneered in [@KaKr] (and developed in [@Andrieu], [@Krener]) which, in turn, has inspired the technique to design internal models developed in [@SICON] in the context of nonlinear output regulation (see also [@MPTAC]). ",
"In this respect it is interesting to observe that if instead of asking $(\\varphi, \\psi, \\gamma)$ to be locally Lipschitz these functions were required to be only continuous, the theoretical tools presented in [@SICON] are sufficient to prove that any smooth triplet $(F,Q,\\ca)$ is rLER if $\\ca$ is LAS for $\\dot z=F(z)$. In particular, if $(H,G) \\in \\Real^{\\dimxi \\times \\dimxi}\n \\times \\Real^{\\dimxi \\times 1}$, $\\dimxi >0$, is an arbitrary controllable pair with $H$ a Hurwitz matrix, and $\\cal R$ is the set which is LES for $\\dot z = F(z)$ (whose existence is guaranteed by Lemma \\[toolPropositionAp\\] since $\\ca$ is LAS for these dynamics), then it turns out that if the functions $\\varphi$ and $\\psi$ in (\\[xisysdefRob\\]) are chosen as $$\\varphi(\\xi) = H \\xi \\qquad\\mbox{and}\\qquad \\psi(\\xi) = G$$ then property (\\[condstabdefRob\\]) holds true with (see Propositions 1 in [@SICON])\n\nFurthermore, if $\\dimxi$ is chosen so that $\\dimxi \\geq 2 \\dimz + 2$ and the matrix $H$ is taken so that $\\sigma(H) \\in \\{\\zeta \\in \\Compl: \\Re(\\zeta ) < -\\ell\\} \\setminus \\cal S$ where ${\\cal S} \\in \\Compl$ is a set of zero Lebesgue measure and $\\ell$ is a sufficiently large positive number, then there always exists a class-$\\cal K$ function $\\rho(\\cdot)$ such that the following partial injectivity condition holds (see Proposition 2 in [@SICON]) and, in turn, the latter guarantees the existence of a [*continuous*]{} function $\\gamma:\n \\Real^\\dimxi \\to \\Real$ such that also property (\\[Timmdef\\]) holds true (see Proposition 3 in [@SICON]). ",
"As shown in [@MPTAC] (see Proposition 4 there), a possible expression of such a $\\gamma(\\cdot)$ is given by\n\nThe previous arguments, however, are not conclusive if system (\\[xisys\\]) is required to be locally Lipschitz. ",
"In this respect an extra condition (see the forthcoming (\\[Omegadef\\]), (\\[rankcond\\])) is needed to guarantee the existence of a locally Lipschitz $\\gamma$ as precisely proved in [@AddendumSICON]. ",
"The main results in this direction are presented in the next lemma (whose proof is a minor adaptation of the main result of [@AddendumSICON]).\\\n\n\\[lemmarank\\] Let $\\cal O$ be an open bounded set which is backward invariant for $\\dot z = F(z)$ with $F:\\Real^\\dimz \\to \\Real^\\dimz$ a smooth function. ",
"Let $\\ca \\subset \\cal O$ be a compact set which is LAS for $\\dot z = F(z)$ and let $Q: \\Real^\\dimz \\to \\Real$ be a $C^\\infty$ function. ",
"Let $\\Omega (z)$ be the distribution defined as If there exists a constant $c \\leq \\dimz$ such that then for any compact set ${\\cal R} \\subset \\cal O$, with ${\\cal R} \\supseteq\n \\ca$, the function $\\rho$ in (\\[partialinj\\]) can be taken linear and the function $\\gamma$ in (\\[gammaMCS\\]) is Locally Lipschitz. ",
"As a consequence the triplet $(F, Q, {\\cal A})$ is rLER.",
"\n\nBy also bearing in mind Remark \\[remarkNoDiffObs\\], it is worth noting how condition (\\[rankcond\\]) [*does not*]{} require the observability distribution (\\[ObsvDistr\\])to be full rank, namely the system $\\dot z = F(z)$ with output $y_z = Q(z)$ to be observable in any sense. ",
"Rather, condition (\\[rankcond\\]) can be regarded as a regularity condition of the observable part of system $\\dot z = F(z)$ with output $y_z =\n Q(z)$. $\\triangleleft$\n\nBy going throughout the technical details in [@AddendumSICON], it is possible to observe that the requirement about the existence of an open bounded set $\\cal O$ which is [*backward invariant*]{} for $\\dot z = F(z)$ is [*uniquely*]{} motivated by the need of having the function $T(z)$ in (\\[Tdefinition\\]) well-defined and $C^2$. In this respect the requirement about the existence of a bounded invariant set $\\cal O$ can be substituted by the requirement that the function $T(z)$ in (\\[Tdefinition\\]) is well-defined and $C^2$ for all $z \\in {\\rm int} \\cal R$ for a proper choice of the matrix $H$. In this case, by the details in [@AddendumSICON], it turns out that the rank condition (\\[rankcond\\]) must be substituted by $${\\rm dim} \\Omega (z) = c \\qquad \\forall \\; z \\in\n \\{\\Phi_F(t,\\varsigma)\\quad : \\quad t\\leq 0\\,, \\; \\varsigma \\in {\\cal\n R}\\}\\,.\\,\\triangleleft$$\n\n\\[remarkclipping\\] The requirement in Lemma \\[lemmarank\\] about the existence of a bounded set $\\cal O$ which is backward invariant for $\\dot z = F(z)$, may be practically overtaken by properly “clipping” the function $F(z)$ outside the set $\\ca$. As a matter of fact, being the property of rLER related to the ability of reproducing the signals $Q(z(t))$ generated by the system $\\dot z(t) = F(z(t))$ by taking its initial conditions in a neighborhood of $\\ca$, it turns out that any triplet $(F_c,Q_c,\\ca)$, with $F_c : \\Real^\\dimz \\to \\Real^\\dimz$, $Q_c:\\Real^\\dimz \\to \\Real$ functions which agree with $F$ and $Q$ on some compact $\\cal S$ containing $\\ca$ in its interior, can be used in place of $(F,Q,\\ca)$ to check whether the latter is rLER and eventually to design the functions $(\\varphi,\\psi,\\gamma)$. In this respect, the presence of a bounded backward invariant set $\\cal O$ may be forced by properly clipping to zero the vector field $F(z)$ outside $\\ca$. Alternatively, by bearing the previous remark, the function $T$ be forced to be well-defined and $C^2$ by properly clipping the function $Q(z)$ outside $\\ca$. For reason of space we omit the technical details to rigorously prove the previous intuition and we refer the reader to the example in Section \\[SecExample\\] for an illustrative example.",
"\n\nExample {#SecExample}\n=======\n\nConsider the system with control input $u \\in \\Real$, measured output $y\\in \\Real$ in which $w$ is a constant signal taking value in the interval $W:=[\\underline{w},\n \\overline{w}]$. By defining ${\\cal C}_1 :=W \\times \\Real$ and $$\\ca:= \\{(w,x) \\in {\\cal C}_1\\; : \\; x = \\sqrt[3]{w} \\}$$ we address the problem of stabilizing the set $\\ca \\times \\{0\\}$, which is invariant for the previous system with $u=0$, by means of a $y$-feedback. ",
"The set $\\ca$ is LAS for the zero dynamics of (\\[sysExa\\]) with domain of attraction ${\\cal D}(\\ca) = {\\cal C}_1$ and, by defining $u= - \\kappa y + v$, the previous problem fits in the framework of Section \\[SecFramework\\]. ",
"Note, in particular, that by only increasing the value of $k$ while setting $v=0$ the desired asymptotic stabilization objective can not be met. ",
"As a matter of fact, different equilibria characterize the system according to the value of $w$. For $w=0$, the $y$-component of the system has three equilibria given by $(0,\\sqrt{1/\\kappa^3}, -\\sqrt{1/\\kappa^3})$ which, for $w \\neq\n 0$, collapse in one equilibrium, solution of $w+y = \\kappa^3y^3$, which tends to $0$ as $k$ tends to $\\infty$. So, with $v=0$, only [*practical*]{} stabilization of the set $\\ca \\times \\{0\\}$ in the parameter $k$ can be achieved. ",
"In order to apply Theorem \\[TheoremFirst\\] and to obtain asymptotic stabilization of the set $\\ca \\times \\{0\\}$ by means of dynamic feedback, we let $z:= \\mbox{col}(w,x)$, $$F(z) := \\left ( \\ba{c} 0\\\\ -x^3 + w \\ea \\right ) \\qquad Q(z) := x$$ and we check the exponential reproducibility of the triplet $(F(z),Q(z),\\ca)$. To this purpose, let $\\cal S$ be a compact set of the form $${\\cal S} = \\{(w, x) \\in {\\cal C}_1 \\; : \\; \\sqrt[3]{\\underline{w}}- {1 \\over 2} \\leq x \\leq \\sqrt[3]{\\overline{w}} +\n {1 \\over 2} \\}$$ so that $\\ca \\subset {\\rm int} \\cal S$, and note that, by Lemma \\[toolPropositionAp\\], there exists a set ${\\cal R}$, $\\ca \\subseteq {\\cal R} \\subset \\mbox{int} \\cal\n S$, which is LER with ${\\cal D}({\\cal R}) = {\\cal D}(\\ca)$. Both Proposition \\[PropositionPhase\\] and \\[lemmarank\\] can be used to prove that the triplet in question is rLER and, indeed, to design the functions $(\\varphi,\\psi,\\gamma)$.\n\nBy following Proposition \\[PropositionPhase\\], it is easy to check that $$L_{F(z)}^2Q (z) = -3 \\, Q^2(z) \\, L_{F(z)}Q (z) \\qquad \\forall \\,\n z \\in {\\cal C}_1\\,,$$ namely condition (\\[immobser\\]) holds (with $\\tilde m =2$), and thus the triplet $(F(z),Q(z),\\ca)$ is rLER. ",
"According to the proposition, the functions $(\\varphi,\\psi,\\gamma)$ can be designed as where $\\lambda_0$ and $\\lambda_1$ are such that $s^2 + \\lambda_1 s +\n \\lambda_0$ is an Hurwitz polynomial, $L$ is a sufficiently large design parameter and $f_c(\\cdot)$ is any smooth bounded function such that $$f_c(x, \\,-x^3+w) = -3 x^2 (-x^3+w) \\qquad \\forall \\, (x,w) \\in {\\cal\n S}\\,.$$\n\nThe functions $(\\varphi,\\psi,\\gamma)$ can be designed according to Proposition \\[lemmarank\\] as well. ",
"However note that this proposition cannot be applied as such due to the absence of a bounded invariant set containing ${\\ca}$ (indeed finite escape time occur in backward time for initial conditions outside $\\ca$). ",
"To overtake this obstacle and by bearing in mind Remark \\[remarkclipping\\], pick a smooth function $a:\\Real \\to \\Real_{\\geq 0}$ such that $a(s) =1$ for all $\\sqrt[3]{\\underline{w}}- {1 \\over 2} \\leq s\n\\leq \\sqrt[3]{\\overline{w}} + {1 \\over 2}$ and $a(s) = 0$ for all $s \\leq \\sqrt[3]{\\underline{w}}- 1$ and $s \\geq\n\\sqrt[3]{\\underline{w}}+ 1$, and consider the system $\\dot {z} =\na(x) F(z)$. For this system the bounded set $\\cal O$ defined as $${\\cal O} = \\{ z \\in {\\cal C}_1 \\; : \\; \\sqrt[3]{\\underline{w}}- 1 \\leq x \\leq\n \\sqrt[3]{\\overline{w}} + 1 \\}\\,,$$ which is open with respect to the subset topology induced by ${\\cal\n C}_1$, is invariant. ",
"Thus, Lemma \\[lemmarank\\] can be applied to the triplet $(a(x)F(z), Q(z), {\\ca})$. In this specific case $$\\Omega(z) = {\\rm span} \\left( \\ba{cc} 0 & 1\\\\\n a(x) & \\ast \\ea \\right )$$ where $\\ast$ is a junk term, from which it follows that $${\\rm dim}\\Omega(z) \\equiv 2 \\qquad \\forall \\; z\\in {\\cal O}$$ which implies, by Proposition \\[lemmarank\\], that the triplet $(a(x) F(z), Q(z), {\\ca})$ is rLER. ",
"But, as the functions $F(z)$ and $a(x)F(z)$ agree on $\\cal\n S$, the fact that the triplet $(a(x) F(z), Q(z),\n {\\ca})$ is rLER can be shown to imply that also the triplet $(a(x) F(z), Q(z),\n {\\ca})$ is such. ",
"Thus, according to Proposition \\[lemmarank\\], the functions $(\\varphi,\\psi,\\gamma)$ can be also designed as where $(H,G) \\in \\Real^{5\\times 5} \\times \\Real^{5 \\times 1}$ is an arbitrary controllable pair with the matrix $H$ such that $\\sigma(H) \\in \\{\\zeta \\in \\Compl: \\Re(\\zeta ) < - \\ell\\}\n\\setminus \\cal S$ where ${\\cal S} \\in \\Compl$ is a set of zero Lebesgue measure and $\\ell$ is a sufficiently large positive number, the function $T$ defined as in (\\[Tdefinition\\]) and $\\rho$ a sufficiently large positive number.\\\nAs a result the problem of output feedback stabilization of the set $\\ca \\times \\{0\\}$ can be achieved, by bearing in mind Theorem \\[TheoremFirst\\] and the subsequent remark, by the following dynamic controller $$\\ba{rcl}\n \\dot \\xi &=& \\varphi(\\xi) - \\psi(\\xi)[\\gamma(\\xi) - \\kappa y]\\\\\n u &=& - \\kappa y + \\gamma(\\xi)\n \\ea$$ with the functions $(\\varphi,\\psi,\\gamma)$ designed as in (\\[Ex1Triplet1\\]) or (\\[Ex1Triplet2\\]) and $\\kappa$ a sufficiently large number.",
"\n\nProof of Theorem \\[TheoremFirst\\] {#ProofTheoremFirst}\n=================================\n\nBy the definition of LER of the triplet $({f}(x,0),{q}(x,0),\n {\\ca})$ there exists a set ${\\cal R}\\supseteq\n \\ca$ which is LES for $\\dot x = f(x,0)$ and , for any compact set ${\\cal X}_1 \\subset {\\cal D}({\\cal\n R})$, there exist an integer $\\dimeta$, locally Lipschitz functions $\\varphi:\\Real^\\dimeta \\to\n \\Real^\\dimeta$, $\\psi: \\Real^\\dimeta \\to \\Real^\\dimeta$, $\\gamma: \\Real^\\dimeta \\to\n \\Real$ and a smooth function $T: \\Real^\\dimx \\to \\Real^\\dimeta$ such that and for all $\\xi_0 \\in \\Real^\\dimxi$ and $x_0 \\in {\\cal X}_1$ the solution $(\\xi(t), x(t))$ of\n\nsatisfies where $\\beta(\\cdot,\\cdot)$ is a locally exponentially class-$\\cal\n KL$ function. ",
"As $\\ca$ is LAS($\\cal X$) and ${\\cal R}\\supseteq \\ca$, we have ${\\cal D}(\\cal R) = {\\cal D}(\\ca)$ and thus the previous properties hold, in particular, with ${\\cal X}_1 = \\cal\n X$. Furthermore, in case $\\ca$ is LES for $\\dot x = f(x,0)$, it is possible to show[^4] that (\\[TimmdefProof\\]) and (\\[condstabdefProof\\]) hold also with $\\cal R$ replaced by $\\ca$ possibly with a different class-$\\cal KL$ function $\\beta(\\cdot,\n \\cdot)$.\n\nAssume, without loss of generality (as $(A,B,C)$ has relative degree $r$ and $(A,C)$ is observable), that the pair $(A,C)$ is in the canonical observability form and that $B=(0,\\ldots, 0,1)\\tr$, and choose, as candidate controller, the system which, by the structure of $A$ and $B$, is of the form (\\[etasys\\]) since $B^T A y = a_r y_m$ for some real number $a_r$.\n\nConsider now the change of variables Note that such a change of variables is well-defined for all $y$ and $\\eta$ as $\\psi$ is complete.",
"\n\nSince $${\\partial \\phi_{\\psi}(t',\\eta) \\over \\partial t'} -\n {\\partial \\phi_{\\psi}(t',\\eta) \\over \\partial \\eta} \\psi(\\eta)\n \\equiv 0$$ and using the fact that $$\\left . {",
"\\partial \\phi_{\\psi}(t',\\eta) \\over \\partial t'}\n \\right |_{t'=0} = \\psi(\\eta)\n \\qquad \\quad\n \\left . {",
"\\partial \\phi_{\\psi}(t',\\eta) \\over \\partial \\eta}\n \\right |_{t'=0} = I\\,,$$ it turns out that the closed-loop dynamics (\\[plantstab\\]), (\\[regth1\\]) in the new coordinates can be described as the feedback interconnection of a system of the form and a system of the form\n\nin which $\\tilde f(x,y)$, $\\tilde \\ell_1(x,\\chi,y)$ and $\\tilde \\ell_2(x,\\chi,y)$ are [*locally Lipschitz*]{} functions satisfying $\\tilde f(x,0)=0$, $\\tilde \\ell_1(x,\\chi,0)=0$ and $\\tilde \\ell_2(x,\\chi,0)=0$ for all $x \\in \\cal C$ and $\\chi \\in\n\\Real^\\dimeta$ and with $\\tilde \\ell_1$ and $\\tilde \\ell_2$ possibly dependent on ${\\cal X}$.\n\nLet $\\cal N$ be an arbitrary compact set of $\\Real^\\dimeta$ and denote by $\\Xi$ the image of $\\cal N$ under the function (\\[chi-etachange\\]) (note that $\\cal N$ may depend on ${\\cal X}$). ",
"Since system (\\[upperth1\\]) with $y=0$ is nothing but (\\[xisysdefProof\\]), it turns out that ${\\rm graph}\n\\left . ",
"T \\right |_{\\cal R}$ is LES(${\\cal X} \\times \\Xi$) for system (\\[upperth1\\]) with $y=0$. Furthermore, by (\\[TimmdefProof\\]), the term ${q}(x,0) + \\gamma(\\chi)$ in (\\[lowerth1\\]) is identically zero for $(x,\\chi) \\in {\\rm graph} \\left . ",
"T \\right |_{\\cal R}$. From these facts and the results in [@TP], [@Atassi], it follows that for any compact set ${\\cal Y} \\in \\Real^\\dimy$ there exists a $\\kappa^\\star>0$ such that for all $\\kappa \\geq \\kappa^\\star$ the set ${\\rm graph}\\left . ",
"T\\right |_{\\cal R} \\times \\{0\\}$ is LES(${\\cal X} \\times\n\\Xi \\times \\cal Y$) for (\\[upperth1\\]), (\\[lowerth1\\]). ",
"By taking $\\tau = \\left . ",
"T \\right |_{\\cal R}$ the previous result proves the first part of the theorem, namely that ${\\rm graph}\\,\n\\tau \\times \\{ 0\\}$ is LES(${\\cal X} \\times {\\cal Y} \\times \\cal\nN$) for the closed-loop system (\\[plantstab\\]), (\\[regth1\\]).",
"\n\nWe prove now the second claim of the theorem, namely that ${\\rm\ngraph}\\left . ",
"\\tau \\right|_\\ca \\times \\{0\\}$ is LAS(${\\cal X}\n\\times {\\cal Y} \\times \\cal N$). ",
"Let $\\kappa \\geq \\kappa^\\star$ be fixed and note that, as ${\\rm graph}\\tau \\times \\{0\\}$ attracts uniformly the closed-loop trajectories leaving ${\\cal X} \\times {\\cal\n Y} \\times \\cal N$, Proposition \\[toolPropomega\\] yields that $$\\omega( {\\cal X} \\times {\\cal Y} \\times {\\cal N}) =\n \\omega({\\rm graph}\\tau \\times \\{0\\}) \\subseteq {\\rm graph}\\tau \\times \\{0\\}$$ in which $\\omega(S)$ denotes the omega limit set of the set $S$ associated to the closed-loop system. ",
"We prove now that if $(x,y,\\chi) \\in \\omega( {\\rm graph}\\tau \\times \\{0\\})$ then necessarily $x \\in \\omega({\\cal R})$ in which $\\omega({\\cal R})$ denotes the omega limit set of the set ${\\cal R}$ associated to the system $\\dot x = f(x,0)$.\n\nIndeed, consider a sequence $\\{x_n, y_n, \\chi_n\\}$ with $(x_n,\\chi_n)\\in\n{\\rm graph}\\tau$ and so in particular $x_n \\in {\\cal R}$, and $y_n\n\\equiv 0$, and a divergent sequence $\\{t_n\\}$, such that, the following holds where $x(t, x_n)$ and $\\chi((x_n,\\chi_n),t)$ denotes the solution of with initial conditions $(x_n,\\chi_n)$. $x_n$ being in ${\\cal R}$, this implies $\\bar x \\in \\omega ({\\cal\nR})$. Now, considering the system given by the first dynamics in (\\[triangular\\]) and using the fact that $\\ca \\subseteq \\cal R$ uniform attracts the trajectories of this system leaving $\\cal X$, Proposition \\[toolPropomega\\] in Appendix yields that $\\omega({\\cal X}) = \\omega({\\cal R}) = \\omega(\\ca)\n \\subseteq \\ca$. By this and the previous arguments we conclude that the $x$ components of the closed-loop trajectories are uniformly attracted by $\\omega(\\ca) \\subseteq \\ca$. From this the result follows by standard arguments. ",
"$\\triangleleft$\n\nAuxiliary results {#AppendixAuxRes}\n=================\n\n\\[toolPropomega\\] Let be a given smooth system and let $S$ be a compact set which is forward invariant for (\\[Fsysapp\\]) and which uniformly (in the initial condition) attracts the trajectories of (\\[Fsysapp\\]) originating in a compact set $D \\supset S$. Then $\\omega(D) = \\omega(S) \\subseteq S$.\n\n[*Proof*]{} First of all note that $\\omega(D)$ and $\\omega(S)$ exist and that, by definition, $\\omega(S) \\subseteq \\omega(D)$. Furthermore $\\omega(S) \\subseteq S$ as $S$ is forward invariant for (\\[Fsysapp\\]). ",
"To prove that $\\omega(D) = \\omega(S)$ suppose that it is not, namely that there exist a $\\bar z \\in \\omega(D)$ and an $\\epsilon>0$ such that $|\\bar z|_S \\geq \\epsilon$. As $S$ uniformly attracts the trajectories of (\\[Fsysapp\\]) originating from $D$, there exists a $t_{\\epsilon/2}>0$ such that $|z(t, z_0)|_S\n \\leq \\epsilon/2$ for all $z_0 \\in D$ and for all $t \\geq t_{\\epsilon/2}$. Moreover, by definition of $\\omega(D)$, there exist sequences $\\{z_n\\}_0^\\infty$ and $\\{t_n\\}_0^\\infty$, with $z_n \\in D$ and $\\lim_{n \\rightarrow \\infty}t_n = \\infty$, such that $\\lim_{n \\rightarrow \\infty}z(t_n, z_n) =\\bar z$. This, in particular, implies that for any $\\nu>0$ there exists a $n_\\nu>0$ such that $|z(t_n,z_n)\n -\\bar z| \\leq \\nu$ for all $n \\geq n_\\nu$. But, by taking $\\nu = \\min\\{\n \\epsilon/2,\\nu_1\\}$ with $\\nu_1$ such that $t_n \\geq t_{\\epsilon/2}$ for all $n \\geq n_{\\nu_1}$, this contradicts that $S$ uniformly attracts the trajectories of the system originating from $D$. $\\triangleleft$\n\n\\[Propx1x2\\] Consider a system of the form and assume that there exist a compact set $\\ca \\subset\n \\Real^{\\dimx_1}$ and a smooth function $\\tau : \\Real^{\\dimx_1} \\to\n \\Real^{\\dimx_2}$ such that the set $${\\rm graph} \\left . ",
"\\tau \\right |_\\ca = \\{(x_1,x_2)\\in \\ca \\times \\Real^{\\dimx_2} \\quad : \\quad x_2 =\n \\tau(x_1)\\}$$ is LES for (\\[x1x2sys\\]) and the set $\\ca$ is LES for the system $\\dot x_1 = f_1(x_1,\\tau(x_1))$. Let $q : \\Real^{\\dimx_1} \\times \\Real^{\\dimx_2} \\to \\Real$ be a smooth function. ",
"If the triplet $(f_1(x_1,\\tau(x_1)),$ $ q(x_1, \\tau(x_1)),\n \\ca)$ is rLER then the triplet $({\\rm col}(f_1(x_1,x_2),\\, f_2(x_1,x_2)), q(x_1,x_2),\n {\\rm graph} \\left . ",
"\\tau \\right |_\\ca)$ is LER.",
"\n\nLet $\\bar f_1(x_1) = f_1(x_1,\\tau(x_1))$ and $\\bar q(x_1) =\n q(x_1,\\tau(x_1))$. Since $\\ca$ is LES for $\\dot x_1 = \\bar f_1(x_1)$ and the triplet $(\\bar f_1(x_1),$ $ \\bar q(x_1), \\ca)$ is rLER, for any compact set $\\bar X_1 \\subset {\\cal D}({\\ca})$, there exist an integer $\\bar \\dimxi$ and locally Lipschitz functions $\\bar \\varphi:\n \\Real^{\\bar \\dimxi} \\to \\Real^{\\bar \\dimxi}$, $\\bar \\psi: \\Real^{\\bar \\dimxi}\n \\to \\Real$, $\\bar \\gamma: \\Real^{\\bar \\dimxi} \\to \\Real$ and $\\bar T: \\Real^{\\dimx_1} \\to \\Real^{\\bar \\dimxi}$ such that, for all $\\bar x_{10} \\in \\bar X_1$ and $\\bar \\xi_0 \\in \\Real^{\\bar\n \\dimxi}$ and for all locally essentially bounded $v(t)$, the solution $(\\bar x_1(t), \\bar \\xi(t))$ of the system $$\\ba{rcll}\n \\dot {\\bar x}_1 &=& \\bar f_1(\\bar x_1) & \\qquad \\bar x_1(0) =\n \\bar x_{10}\\\\\n \\dot {\\bar \\xi} &=& \\bar \\varphi(\\bar \\xi) + \\bar \\psi(\\bar\n \\xi)[\\bar q(\\bar x_1) + v] & \\qquad \\bar \\xi(0) = \\bar \\xi_0\n \\ea$$ satisfies where $\\beta_1(\\cdot,\\cdot)$ and $\\ell(\\cdot)$ are respectively a locally exponential class-$\\cal KL$ and a class-$\\cal K$ functions, and $$\\bar \\gamma(\\bar T(\\bar x_1)) + \\bar q(\\bar x_1) =0 \\qquad\n \\forall \\, \\bar x_1 \\in {\\ca }\\,.$$ Furthermore, by the assumption that ${\\rm graph} \\left . ",
"\\tau\n\\right |_\\ca$ is LES for (\\[x1x2sys\\]), for any $(x_{10},\nx_{20}) \\in {\\cal D}({\\rm graph} \\left . ",
"\\tau \\right |_\\ca)$ the solution $(x_1(t), x_2(t))$ of (\\[x1x2sys\\]) with initial condition $(x_1(0), x_2(0)) = (x_{10}, x_{20})$ satisfies where $\\beta_2(\\cdot,\\cdot)$ is a locally exponential class-$\\cal\nKL$ function.",
"\n\nNow pick a compact set $\\bar X_1 \\subset {\\cal D}({\\ca})$ and the functions $(\\bar \\varphi(\\cdot), \\bar \\psi(\\cdot), \\bar\n\\gamma(\\cdot))$ accordingly, and denote by $(x_1(t),x_2(t),\\xi(t))$ the solution of the system\n\nwith initial conditions $(x_{10}, x_{20}, \\xi_0) \\in \\Real^{\\dimx_1} \\times \\Real^{\\dimx_2} \\times\n \\Real^{\\bar \\dimxi}$ at time $t=0$. Let $X \\subset \\Real^{\\dimx_1} \\times \\Real^{\\dimx_2}$ be an arbitrary compact set such that $X \\subset {\\cal D}({\\rm graph} \\left . ",
"\\tau \\right\n |_{\\ca})$, let ${\\cal R} := {\\rm graph} \\left . ",
"\\tau \\right\n |_{\\ca}$ and let $T:\\Real^{\\dimx_1} \\times \\Real^{\\dimx_2} \\to \\Real^{\\bar\n \\dimxi}$ be the locally Lipschitz function defined as $T(x_1,x_2) = \\bar T(x_1)$. We shall prove in the following that for any initial condition $(x_{10}, x_{20}, \\xi_0)\n \\in X \\times \\Real^{\\bar \\dimxi}$ the trajectory $(x_1(t),x_2(t),\\xi(t))$ of (\\[eq2\\]) satisfies\n\nwhere $\\beta_3(\\cdot,\\cdot)$ is a locally exponential class-$\\cal\nKL$ function and $${\\rm graph}\\left . ",
"T \\right |_{\\cal R} = \\{((x_1,x_2),\\xi) \\in {\\rm graph} \\left . ",
"\\tau \\right\n |_{\\ca} \\times \\Real^{\\bar \\dimxi} \\; : \\; \\xi = T(x_1,x_2) \\}\\,.$$ To this purpose, pick any $\\bar x_{10} \\in \\ca \\subset \\bar\n X_1$ and note that $(x_1(t),x_2(t),\\xi(t))$ satisfies\n\nwhere $$v(t) = q(x_1(t),x_2(t)) - \\bar q(\\bar x_1(t))$$ and $\\bar x_1(t) = \\Phi_{\\bar f_1}(t,\\bar x_{10})$. Let $x_1^\\star \\in \\ca$ be such that $(x_1^\\star,\\tau(x_1^\\star))$ is the projection of $(x_1,x_2)$ on ${\\rm graph} \\left . ",
"\\tau \\right\n |_\\ca$. Since $\\bar x_1(t) \\in\n \\ca$ and $x_1^\\star(t) \\in \\ca$ for all $t \\geq 0$, $X$ is compact and (\\[ineq11\\]) holds, and $\\bar q$ is locally Lipschitz, for any initial condition $(x_{10}, x_{20}) \\in\n X$ of (\\[eq3\\]) the term $v(t)$ can be bounded as $$\\ba{rcl}\n |v(t)| &=& |q(x_1(t),x_2(t)) - \\bar q(x_1^\\star(t)) + \\bar q(x_1^\\star(t))- \\bar q(\\bar\n x_1(t))| \\\\\n &\\leq& |q(x_1(t),x_2(t)) - \\bar q(x_1^\\star(t))| + |\\bar q(x_1^\\star(t))- \\bar q(\\bar\n x_1(t))| \\\\\n & \\leq& L_q |(x_1(t),x_2(t))|_{{\\rm graph} \\left . ",
"\\tau \\right\n |_\\ca} + 2 \\sup_{s \\in {\\ca}} |\\bar q(s)|\\\\\n &\\leq& v_M\n \\ea$$ for all $t\\geq 0$, where $L_q$ is a bound of the Lipschitz constant of $q$ on the forward flow of (\\[x1x2sys\\]) originated from $X$ and $v_M$ a positive constant, both dependent on $X$. Hence, from estimate (\\[estim1\\]), it follows that $|(\\bar x_1(t), \\xi(t))|_{{\\rm graph} \\left . ",
"\\bar T\n \\right |_{{\\ca}}}$ is bounded and, since $\\bar x_1(t) \\in\n \\ca$ and ${{\\rm graph} \\left . ",
"\\bar T\n \\right |_{{\\ca}}}$ is compact, also $\\xi(t)$ is bounded. ",
"This, in turn, implies that also the trajectories of (\\[eq2\\]) originated from $X \\times \\Real^{\\bar \\dimxi}$ are ultimately bounded, namely there exists a compact set $S \\subset \\Real^{\\dimx_1+\\dimx_2+\\bar \\dimxi} $ such that for any $\\Xi \\subset \\Real^{\\bar \\dimxi}$ there exists a $T>0$ such that $\\forall \\, (x_{10} , x_{20} , \\xi_0) \\in X \\times \\Xi$, $(x_1(t),x_2(t),\\xi(t)) \\in S$ for all $t \\geq T$. As a consequence, the trajectories of (\\[eq2\\]) are uniformly attracted by $\\omega(S)$, the $\\omega$-limit set of the set $S$ of system (\\[eq2\\]), which is a bounded invariant set.",
"\n\nWe prove now that $\\omega(S)$ is a subset of ${\\rm graph} \\left .",
"\nT \\right |_{{\\cal R}}$. For, let $ (x_{10}', x_{20} ', \\xi_0')$ be a point of $\\omega(S)$ and note that, by (\\[ineq11\\]) which implies that ${\\rm graph} \\left . ",
"\\tau \\right |_\\ca$ is uniform attractive for the $(x_1,x_2) $ dynamics in (\\[eq2\\]), and by Proposition \\[toolPropomega\\] in Appendix \\[AppendixAuxRes\\], it turns out that necessarily $x_{10}' \\in \\ca$ and $ x_{20}'\n=\\tau(x_{10}')$. Furthermore it can be proved that $\\xi_0' =\\bar\nT(x_{10}')$. In fact, suppose that it is not true, namely that there exists an $\\epsilon>0$ such that As $\\omega(S)$ is invariant for (\\[eq2\\]), for any $(x_{10} , x_{20}, \\xi_0) \\in \\omega(S)$ the corresponding trajectory $(x_1(t), x_2(t), \\xi(t))\\in \\omega(S)$ for all $t \\in\n\\Real$, and thus $x_1(t) \\in \\ca \\subset \\bar X_1$ and $x_2(t) =\n\\tau(x_1(t))$ $\\forall \\, t \\in \\Real$. So, inequality (\\[estim1\\]) with $v=0$ yields that, using compactness of $\\omega(S)$, there exists a $t_\\epsilon\n>0$ such that for all $(x_{10} , x_{20}, \\xi_0) \\in \\omega(S)$, $|(x_1(t),\\xi(t))|_{{\\rm graph} \\left . ",
"\\bar T \\right |_\\ca} <\n\\epsilon/2$ for all $t \\geq t_{\\epsilon}$. The previous facts, specialized with $(x_{10},x_{20},\\xi_0) =\n\\Phi_{(\\ref{eq2})}(-t_\\epsilon, (x_{10}', x_{20}', \\xi_0'))$, yield that $(x_{10}', x_{20}',\n\\xi_0')=\\Phi_{(\\ref{eq2})}(t_\\epsilon, (x_{10}, x_{20}, \\xi_0))$ are such that $|(x_{10}',\\xi_0')|_{{\\rm graph} \\left . ",
"\\bar T\n\\right |_\\ca} < \\epsilon/2$ which contradicts (\\[epsest\\]). ",
"Hence, $\\omega(S)$ is necessarily a subset of ${\\rm graph} \\left .",
"\n\\bar T \\right |_{ {\\ca}}$. Since $S$ can be taken, without loss of generality, such that ${\\rm graph} \\left . ",
"\\bar T \\right |_{\n{\\ca}} \\subset {\\rm int} S$, the previous facts prove (\\[beta3\\]) with the only exception that the class $\\cal KL$ function $\\beta_3(\\cdot,\\cdot)$ is not necessarily locally exponential (see [@BI03]). ",
"To prove local exponential stability we follow a Lyapunov approach. ",
"First, note that, by defining $p_1 = {\\rm col}(x_1, \\xi)$, the first and third dynamics of (\\[eq2\\]) can be rewritten as $$\\dot p_1 = F_1(p_1) + G_1(p_1,x_2)(x_2 - \\tau(x_1))$$ where $F_1(p_1) ={\\rm col}(\\bar f_1(x_1), \\bar \\phi(\\xi) \\bar\n\\psi(\\xi) \\bar q_1(x_1))$, $G_1(p_1,x_2) = {\\rm col}(r_1(x_1,x_2),\n\\bar \\psi(\\xi)r_2(x_1,x_2))$ in which $r_1(\\cdot,\\cdot)$ and $r_2(\\cdot,\\cdot)$ are properly defined smooth functions. ",
"By assumption and by standard converse Lyapunov results, there exist a smooth function $V_1 : {\\cal D}({\\rm graph} \\left . ",
"\\bar T\n\\right |_{\\ca}) \\to \\Real$ and positive numbers $c_1$, $\\underline\na_1 \\leq \\bar a_1$, such that and Similarly, by letting $p_2= {\\rm col}\n(x_1,x_2)$ and by rewriting (\\[x1x2sys\\]) as $\\dot p_2 =\nF_2(p_2)$, it turns out that there exist a smooth function $V_2 :\n{\\cal D}({\\rm graph} \\left . ",
"\\tau\\right |_{\\ca}) \\to \\Real$ and positive numbers $c_2$, $\\underline a_2 \\leq \\bar a_2$, such that and Furthermore, note that there exists a positive $\\bar \\tau$ such that As a matter of fact, given $(x_1,x_2, \\xi) \\in S$, let $\\bar x_1 \\in \\ca$ be such that $|x_1 -\\bar x_1, x_2 -\n \\tau(\\bar x_1)| = |(x_1,x_2)|_{{\\rm graph} \\left .",
"\n\\tau \\right |_{\\ca}}$. As $|x_1 - \\bar x_1| \\leq |(x_1,x_2)|_{{\\rm\ngraph} \\left . ",
"\\tau \\right |_{\\ca}}$ and $|x_2 - \\tau(\\bar x_1)|\n\\leq |(x_1,x_2)|_{{\\rm graph} \\left . ",
"\\tau \\right |_{\\ca}}$, and denoting by $\\bar \\tau'$ an upper bound of the Lipschitz constant of $\\tau$ on $S$, it turns out that $$\\ba{rcl}\n |x_2 - \\tau(x_1)| &=& |x_2 - \\tau(\\bar x_1) + \\tau(\\bar x_1)-\n \\tau(x_1)|\\\\\n &\\leq& |x_2 - \\tau(\\bar x_1)| + |\\tau(\\bar x_1)- \\tau(x_1)|\\\\\n &\\leq&\n |(x_1,x_2)|_{{\\rm graph} \\left . ",
"\\tau \\right |_{\\ca}} + \\bar\n \\tau' |x_1 - \\bar x_1|\\\\\n &\\leq& (1 + \\bar \\tau') |(x_1,x_2)|_{{\\rm graph} \\left . ",
"\\tau \\right\n |_{\\ca}}\n := \\bar \\tau |(x_1,x_2)|_{{\\rm graph} \\left .",
"\n\\tau \\right |_{\\ca}} \\ea$$ for all $(x_1,x_2,\\xi) \\in S$, namely (\\[boundtau\\]) holds. ",
"Consider now the candidate Lyapunov function $V(x_1,x_2,\\xi) = V_1(p_1) + \\beta V_2(p_2)$ for system (\\[eq2\\]) with $\\beta>0$. By (\\[boundLyap1\\]) and (\\[boundLyap2\\]), there exist positive numbers $\\underline a \\leq \\bar\n a$ (dependent on $\\beta$) such that $$\\underline a |(x_1,\\xi)|^2_{{\\rm graph} \\left .",
"\n\\bar T \\right |_{\\ca}} + \\underline a |(x_1,x_2)|^2_{{\\rm\ngraph} \\left . ",
"\\tau \\right |_{\\ca}} \\leq V(x_1,x_2,\\xi)\n\\leq \\bar a |(x_1,\\xi)|^2_{{\\rm graph} \\left . ",
"\\bar T \\right\n|_{\\ca}} + \\bar a |(x_1,x_2)|^2_{{\\rm graph} \\left . ",
"\\tau \\right\n|_{\\ca}}$$\n\nBy (\\[Lyap1\\]), (\\[Lyap2\\]), (\\[boundLyap2\\]) and (\\[boundtau\\]), and by the fact that $G_1(p_1)$ is locally Lipschitz, it turns out that there exists a $\\beta^\\star>0$ such that for all $\\beta \\geq \\beta^\\star$ and for all $(x_1,x_2,\\xi) \\in S$ $$\\left . ",
"\\dot V(x_1,x_2,\\xi) \\right |_{(\\ref{eq2})} \\leq - c \\, V(x_1,x_2,\\xi)$$ where $c$ is a positive constant. ",
"Combining the previous facts with by (\\[ineq11\\]), standard arguments yields (\\[beta3\\]) with $\\beta_3(\\cdot,\n \\cdot)$ a locally exponential class-[KL]{} function. ",
"This, in turn, proves the proposition with the functions $(\\varphi,\\psi,\\gamma)$ associated to the triplet $({\\rm col}(f_1(x_1,x_2),\\, f_2(x_1,x_2)),$ $q(x_1,x_2),\n {\\rm graph} \\left . ",
"\\tau \\right |_\\ca)$ in the definition of LER given by $(\\bar \\varphi, \\bar \\psi, \\bar \\gamma)$. $\\triangleleft$\n\n[99]{}\n\nV. Andrieu and L. Praly, On the existence of a Kazantis-Kravaris/Luenberger observer. [",
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"\n\n[^1]: It must be noted that only [*local*]{} observability notion are potentially needed at this level as a consequence of the fact that practical stability is already guaranteed by the high-gain law $\\kappa$.\n\n[^2]: By referring to (\\[pla0withw\\]), a meaningful case to be considered is when $\\ca = W \\times \\{0\\}$, in which case this assumption amounts to require the existence of a state feedback stabilizer, possibly dependent on the uncertainties, able to asymptotically stabilize the origin with a certain domain of attraction.",
"\n\n[^3]: The adaptation consists only in proving the ISS property which is behind the definition of rLER.",
"\n\n[^4]: Internal remark: to be checked.",
"\n"
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"Computational analysis of fluid dynamics in pharmaceutical freeze-drying.",
"\nAnalysis of water vapor flows encountered in pharmaceutical freeze-drying systems, laboratory-scale and industrial, is presented based on the computational fluid dynamics (CFD) techniques. ",
"The flows under continuum gas conditions are analyzed using the solution of the Navier-Stokes equations whereas the rarefied flow solutions are obtained by the direct simulation Monte Carlo (DSMC) method for the Boltzmann equation. ",
"Examples of application of CFD techniques to laboratory-scale and industrial scale freeze-drying processes are discussed with an emphasis on the utility of CFD for improvement of design and experimental characterization of pharmaceutical freeze-drying hardware and processes. ",
"The current article presents a two-dimensional simulation of a laboratory scale dryer with an emphasis on the importance of drying conditions and hardware design on process control and a three-dimensional simulation of an industrial dryer containing a comparison of the obtained results with analytical viscous flow solutions. ",
"It was found that the presence of clean in place (CIP)/sterilize in place (SIP) piping in the duct lead to significant changes in the flow field characteristics. ",
"The simulation results for vapor flow rates in an industrial freeze-dryer have been compared to tunable diode laser absorption spectroscopy (TDLAS) and gravimetric measurements."
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[
"Introduction {#sec1}\n============\n\nPolymers are multifunctional ingredients widely used in cosmetic formulas for different purposes, such as thickening, emulsifying, stabilizing, and enhancing the product texture properties. ",
"The most common polymers used for these aims are the synthetic ones belonging to the family of polyacrylates, which are versatile and high-performing materials.^[@ref1]^ Nowadays, the interest on natural polymers is increasing, together with a major interest for environmental issues and sustainability that is becoming an imperative for the cosmetic companies which must be aware of the environmental impact of the whole life cycle of the cosmetic product.^[@ref2]−[@ref5]^ In the last few years, in Europe, there has been a heated debate on the topic of microplastics and the damage of the aquatic ecosystem: these solid and spherical plastic particles less than 5 mm in size are banned from cosmetic products.^[@ref6]^ Besides that, there is a growing concern on the overall impact of liquid plastics, such as polyacrylic polymers, which can be dispersed or emulsified in cosmetic formulas with functional purposes.^[@ref7]^ These polymeric materials are also mainly responsible for the texture tactile properties of skin care products.^[@ref8],[@ref9]^ It is well-known that consumers immediately evaluate the sensory characteristics of the product when applied on the skin, and this aspect is the main driver of the purchase process.^[@ref10]^ For this reason, it is important for cosmetic industries to find viable natural alternatives, without losing the sensorial characteristics and the functional-stability aspects impaired by synthetic polymers.",
"\n\nXanthan gums, celluloses, starches, and gums are widely used ingredients not only in the natural cosmetic market but also in food, pharmaceutical, and adhesives industries. ",
"Polysaccharides are complex carbohydrates which, according to their chemical structure, can influence the mechanical properties of the system.^[@ref11]^ In fact, they are characterized by the presence of many hydroxyl groups which, once dispersed in water, can strongly interact with water molecules and increase the viscosity of the system.^[@ref12]^ From a technical point of view, replacing high-performing synthetic polymers in formulas with natural alternatives can be quite challenging, and considering the wide variety of plant-based polysaccharides available for cosmetic use, manufacturers are continuously more interested in instrumental methodologies to be used as time-saving and reproducible prescreening tools to evaluate the applicative specificities of new natural ingredients and assess the product design.",
"\n\nThe importance of rheology for the characterization of semisolid materials has been widely proven. ",
"In particular, the results obtained from the analyses, conducted both in continuous and oscillatory flow conditions, are used in the research and development of cosmetics, to investigate the spreading properties of products, their internal structure, and physical stability.^[@ref13],[@ref14]^ The texture analysis is frequently used in the food sector for determining the textural properties of foods.^[@ref15]−[@ref17]^ In recent times, this instrumental test has been also introduced in the cosmetic industry to quantify multiple textural properties, which are related to the sensory characteristics of products, such as gels and emulsions.^[@ref18]^ Recent studies have described the usefulness of rheology and texture measurements used in combination to compare different cosmetic products and to obtain objective information on their physical--mechanical attributes.^[@ref19],[@ref20]^ This work is intended to investigate the rheological and textural properties of water dispersions prepared using various acrylic and natural-derived polymers at different concentrations. ",
"The textural properties known as firmness, consistency, adhesiveness, cohesiveness, and stringiness have been evaluated through an immersion/deimmersion test by means of a texture analyzer. ",
"The rheological curves have been obtained with measurements conducted both in continuous and oscillatory flow conditions. ",
"To verify the existence of any correlations between these two instrumental techniques, the obtained data have been statistically analyzed.",
"\n\nResults and Discussions {#sec2}\n=======================\n\nThe dataset made of the polymer dispersions as observations and the texture attributes as variables has been statistically processed with principal component analysis (PCA), which allowed examining the differences between the mechanical characteristics of the samples prepared in this work and pointing out the relations that occur between the parameters investigated ([Figure [1](#fig1){ref-type=\"fig\"}](#fig1){ref-type=\"fig\"}). ",
"In order to better visualize the properties conferred to the system by the raw materials and to get as close as possible to the conditions of actual use in the formulation, only the representative concentration of each polymer, among the concentration range indicated in the technical data sheets, was reported in the PCA graph. ",
"The first axis *F*~1~ represented the stiffness and the solidity of the analyzed systems because it was positively related to the parameters of firmness, consistency, cohesiveness, and adhesiveness. ",
"The second axis *F*~2~, instead, which was positively related to stringiness and negatively related to all the other variables, could represent product picking and film-forming properties. ",
"In detail, adhesiveness, cohesiveness, and stringiness were positively related to *F*~2~, whereas firmness and consistency were negatively related to it. ",
"The positioning of the polymeric raw materials inside the PCA plot was a consequence of the physical--mechanical properties they gave to the aqueous systems in which they were dispersed. ",
"From a general point of view, there was a clear distinction between the synthetic polymers and the natural-derived ones. ",
"A majority of the natural raw materials were positioned on the left side of the graph because they had lower values of firmness, consistency, cohesiveness, and adhesiveness and were more likely to form fluid systems. ",
"On the contrary, the major part of the synthetic polymers was distributed in the right area of the graph because they were characterized by higher textural parameters than the polysaccharides except for stringiness, indicating the ability to form stiffer gelled systems.",
"\n\n{#fig1}\n\nThe synthetic polymers S1 (carbomer) and S2 (sodium polyacrylate) are positively loaded on both *F*~1~ and *F*~2~. They are high molecular weight polymers derived from the crosslinking of the polyacrylic acid. ",
"Acrylic polymers when dispersed in water and neutralized with a common base such as sodium hydroxide (NaOH), converting the acidic polymer into a salt, form a three-dimensional network: the polymer chains begin to swell and partially uncoil because of electrostatic repulsion among the negative charges, conferring high viscosity, consistency, and shear thinning characteristics to aqueous systems. ",
"These polymers differ for the position on *F*~1~, probably due to the different crosslinking degree and the conformation of the microgel structure. ",
"S1, in particular, leads to the formation of stiffer hydrogels, resistant to external deforming forces. ",
"It registered high levels of firmness, consistency, cohesiveness, and adhesiveness, and for this reason, it is located on the very right side of the graph. ",
"The dispersion made of S2, which is a preneutralized form of the acrylic polymer, showed high values of cohesiveness and adhesiveness but lower firmness. ",
"The textural and the rheological profiles of the samples prepared by dispersing these acrylic polymers in water were deeply investigated in our previous work.^[@ref21]^\n\nThe other polymers analyzed in this work can be split into three distinct clusters. ",
"SN (hydroxypropyl guar gum), N4 (*Caesalpinia spinosa* gum), and N5 (*Ceratonia siliqua* gum) belong to the same cluster (group A), negatively loaded on *F*~1~ and positively loaded on *F*~2~. They are characterized by the highest values of stringiness and the lowest values of consistency and firmness. ",
"The latter is a parameter described as the force needed to reach a certain degree of deformation, and it is directly connected to the product spreadability. ",
"The lower the firmness, the easier the application because less force is needed to make the product flow on the skin.^[@ref9]^ The dispersions formulated with these natural-derived raw materials are fluid systems with high spreadability and good pickup properties.",
"\n\nThe synthetic polymer S3 (polyacrylate cross-polymer-11) and the natural polymers N1 (xanthan gum), N2 (succinoglycan), and N3 (sclerotium gum) form a second cluster (group B) because they are negatively loaded on *F*~1~ and on *F*~2~ too. ",
"These materials dispersed in the solution formed weak interactions with water, determining the formation of systems with medium--low textural parameters. ",
"Even if they belong to the same cluster, they differ from each other for their values on *F*~1~. Among the materials belonging to this group, in fact, the synthetic polymer S3 showed the highest adhesive and cohesive properties, and this is a consequence of the stronger molecular interactions between the polymeric chains which formed the three-dimensional gelled network.",
"\n\nA third cluster (group C) is made of the hydrophobically modified synthetic polymers S4 (ammonium acryloyldimethyltaurate/beheneth-25 methacrylate cross-polymer) and S5 (acrylates/C10-30 alkyl acrylate cross-polymer) and the polysaccharides N6 (gellan gum) and N7 (carrageenan). ",
"These samples, positively loaded on *F*~1~ and negatively loaded on *F*~2~, were characterized by the presence of stronger intermolecular interactions, and for this reason, they showed high firmness and consistency but the lowest values of adhesiveness and stringiness. ",
"These parameters are typical of no-stringy bouncy systems with low pickup properties.",
"\n\nGroup A {#sec2.1}\n-------\n\nThe polymers included in this group (SN, N4, and N5) when dispersed in water formed fluid systems, whose predominant textural characteristic is stringiness because a strand was formed during the withdrawal of the probe from the analyzed sample.",
"\n\n[Table S1](http://pubs.acs.org/doi/suppl/10.1021/acsomega.0c01306/suppl_file/ao0c01306_si_001.pdf) presents the numerical values of the five textural parameters measured with an immersion/deimmersion test conducted with a texture analyzer on the samples prepared with different concentrations of the raw materials belonging to group A. As expected, increasing the polymer amount, an increase of the values of firmness, consistency, cohesiveness, and adhesiveness was registered. ",
"On increasing the polymer concentration, the force needed to deform the system was higher because more polymer--solvent interactions were formed, and the three-dimensional network became more and more structured. ",
"The polymer concentration also had an impact at the end of the texture curve: the stringiness increased at higher concentrations. ",
"These results obtained for the stringiness differ from the results obtained in our previous work for the hydrophilic gels prepared with synthetic acrylic polymers, whose stringiness decreased with increasing polymer concentrations.^[@ref21]^ The high values of stringiness shown by SN and the materials belonging to the same cluster are related to the sensorial expression of \"long flow\" used in formulation practice, opposite to that of \"short flow\" which indicates a cosmetic system whose overall rigidity is due to the presence of a highly crosslinked rheological modifier, which determines a reduction in stringiness.^[@ref22]^\n\nA comparison between the curves obtained from the texture analyses of the dispersions prepared with SN (hydroxypropyl guar gum), N4 (*C. spinosa* gum), and N5 (*C. siliqua* gum) at the same concentration of 1.5% w/w is reported in [Figure [2](#fig2){ref-type=\"fig\"}](#fig2){ref-type=\"fig\"}.",
"\n\n{#fig2}\n\nThe samples showed a similar textural behavior. ",
"They had almost the same values of stringiness (\\>20 mm) because the three curves have the same endpoint on the graph. ",
"However, the sample prepared with N5 showed lower values of firmness, adhesiveness, and cohesiveness than the samples prepared with N4 and SN. ",
"We can assume that N5 in solution blindly interacts with water and is more likely to form liquid systems and fluid textures. ",
"The textural curves of N4 and SN are overlapped in the negative part, showing very similar values of adhesiveness and cohesiveness, but SN slightly reached higher values of firmness (0.13 N).",
"\n\nThe controlled shear rate (CSR) test allowed studying the viscosity trend with an increasing shear rate. ",
"The viscosity values of the dispersions made with the polysaccharides of group A gradually decreased in function of the shear application, and this behavior is called shear-thinning. [",
"Figure [3](#fig3){ref-type=\"fig\"}](#fig3){ref-type=\"fig\"} shows the flow curves of the samples prepared with an increasing concentration of SN. ",
"The viscosity remained almost unchanged at lower shear rates, forming a Newtonian plateau region. ",
"As the shear rate increased, the viscosity was reduced because the polymer chains tended to align toward the flow direction. ",
"The viscosity of SN dispersions increased with the polymer concentration as a result of the stronger interactions between the polysaccharidic chains and the solvent. [",
"Table S2](http://pubs.acs.org/doi/suppl/10.1021/acsomega.0c01306/suppl_file/ao0c01306_si_001.pdf) reports the viscosity at rest (η~0~) values, calculated with the Carreau--Yasuda model, of the samples prepared with the three polymers belonging to group A. One can note that N5 dispersions reached lower values of firmness than the other two materials, in accordance with the lower textural values.",
"\n\n{#fig3}\n\nThe viscoelastic properties as a function of frequency, using a fixed oscillation amplitude within the linear viscoelastic range, have been investigated ([Figure [4](#fig4){ref-type=\"fig\"}](#fig4){ref-type=\"fig\"}). ",
"SN solutions showed that both the storage *G*′ and the loss *G*″ moduli were significantly dependent on the frequency with a cross-over point, which is characteristic of the viscoelastic materials ([Figure [4](#fig4){ref-type=\"fig\"}](#fig4){ref-type=\"fig\"}a). ",
"The viscous *G*″ modulus was predominant at lower frequencies and the storage *G*′ modulus became higher than the viscous modulus when high frequencies were applied. ",
"By increasing the polymer concentration, the elastic character of the systems increased, and the frequency value correspondent to the cross-over point decreased (cross-over point frequency values: SN 1% 7.67 rad/s, SN 1.5% 2.89 rad/s, and SN 2% 1.13 rad/s). ",
"The water dispersions made of N4 showed a viscoelastic behavior similar to that of SN dispersions, but the frequencies corresponding to the cross-over point were higher, thus indicating a more liquid-like behavior than SN (cross-over point frequency values: N4 1% 20.02 rad/s, N4 1.5% 6.28 rad/s, and N4 2% 3.12 rad/s) ([Figure [4](#fig4){ref-type=\"fig\"}](#fig4){ref-type=\"fig\"}b). ",
"N5 solutions showed a transition from viscous liquid to a viscoelastic material as a function of the polymer concentration ([Figure [4](#fig4){ref-type=\"fig\"}](#fig4){ref-type=\"fig\"}c). ",
"Up to 1%, the viscous *G*″ modulus was greater than the elastic *G*′ modulus in all of the frequency range investigated. ",
"By increasing the polymer concentration at 1.5%, *G*′ became higher than the viscous modulus when high frequencies were applied, showing a cross-over point (cross-over point frequency values: N5 1.5% 14.92 rad/s and N5 2% 8.38 rad/s).",
"\n\n{#fig4}\n\nIn [Figure [5](#fig5){ref-type=\"fig\"}](#fig5){ref-type=\"fig\"} the viscoelastic properties measured varying the frequency values of the water dispersions prepared at 1.5% w/w of SN, N4 and N5, are compared. ",
"The damping factor tan δ is calculated from the ratio between the loss modulus *G*″ and the storage modulus *G*′, and it represents a way to describe the weight of the elastic components. ",
"N5 dispersion had the highest values of tan δ, having a predominant viscous behavior, and this indicated a higher dissipative capacity than the other materials. ",
"SN was characterized by the lowest values of tan δ and a more elastic behavior.",
"\n\n{#fig5}\n\nThese rheological modifiers are galactomannans consisting of a mannose backbone with side groups of galactoses branched on the six positions. ",
"These three glucomannans differ from their degree of substitution, that is, the number of side units per unit length of the main chain. ",
"The galactopyranose units prevent the formation of hydrogen bonds and inhibit the aggregation of the polysaccharidic main chains. ",
"N5 (*C. siliqua* gum, also known as the carob gum) is unevenly substituted because it has a ratio of 1:4 between mannose and galactose units. ",
"N4 (*C. spinosa* gum, also known as the tara gum) has a ratio of 1:3, while that of SN (hydroxypropyl guar gum) is of 1:2.^[@ref23]^ For these reasons, SN can be easily dissolved in cold water, while N4 and N5 are less soluble and needed higher temperature to break the hydrogen bonds. ",
"The differences in the chemical structure also have an impact on the rheological and textural properties they impaired to aqueous dispersions. ",
"N5, in fact, showed lower viscosity and a more liquid-viscous rheological behavior than S4 and SN, which have a higher substitution degree. ",
"Moreover SN, besides having more galactose side chains, is a chemically modified polysaccharide: the hydrophobic side chains which establish stronger intermolecular interactions lead to the formation of a system with higher viscosity.",
"\n\nGroup B {#sec2.2}\n-------\n\nThe microbial-derived materials of this group, N1 (xanthan gum), N2 (succinoglycan), and N3 (sclerotium gum) and the synthetic polymer S3, when dispersed, determined the formation of weak interactions with water, forming aqueous systems with balanced textural parameters. ",
"In particular, they exhibited lower values of stringiness than the materials of group A. [Table S3](http://pubs.acs.org/doi/suppl/10.1021/acsomega.0c01306/suppl_file/ao0c01306_si_001.pdf) reports the numerical values of the textural parameters measured through an immersion/deimmersion test performed on the samples prepared at increasing concentrations of the raw materials belonging to group B. The instrument registered increasing values of firmness, consistency, and adhesiveness in function of the polymer concentration. ",
"On the other hand, stringiness decreased at increasing polymer concentrations, contrary to what happened for the raw materials of group A. The interactions between the polymers of group B and the solvent were stronger to that formed by the polymers of group A, determining a more structured, less deformable network. [",
"Figure [6](#fig6){ref-type=\"fig\"}](#fig6){ref-type=\"fig\"} shows a comparison between the textural parameters of firmness ([Figure [6](#fig6){ref-type=\"fig\"}](#fig6){ref-type=\"fig\"}a) and adhesiveness ([Figure [6](#fig6){ref-type=\"fig\"}](#fig6){ref-type=\"fig\"}b) of the samples prepared at the same concentrations (1% and 1.5% w/w) of the raw materials belonging to group B.\n\n{#fig6}\n\nThe polymeric dispersions at 1% w/w showed values of firmness between 0.11 and 0.16 N. The natural-derived raw materials N2 and N3, at higher concentrations (1.5% w/w), reached even greater values of firmness than the synthetic polymer S3. ",
"Among the natural polymers, N2 showed higher values of adhesiveness. ",
"However, the natural-derived materials did not reach the textural characteristics of the synthetic polymer S3 in terms of adhesiveness, even at higher concentrations.",
"\n\nThe rheological analyses conducted in continuous flow conditions highlighted the shear-thinning behavior of the samples prepared with the polymers of group B ([Figure S1](http://pubs.acs.org/doi/suppl/10.1021/acsomega.0c01306/suppl_file/ao0c01306_si_001.pdf)), and the values of the zero-shear viscosity (η~0~) calculated with the Carreau--Yasuda model are reported in [Table S4](http://pubs.acs.org/doi/suppl/10.1021/acsomega.0c01306/suppl_file/ao0c01306_si_001.pdf). ",
"The pseudo-plastic behavior of the polysaccharides N1, N2, and N3 was due to the rod-like conformation assumed in water: the highly ordered helices, stabilized by intramolecular H-bonds, were aligned toward the flux direction, determining a progressive decrease in viscosity when shear is applied.",
"\n\nThe frequency sweep tests were conducted on the water dispersions choosing a strain value that falls within the linear viscoelastic region (LVR), in which both the elastic *G*′ and viscous *G*″ moduli have a parallel trend independent of the strain. ",
"The mechanical spectra registered are shown in [Figure [7](#fig7){ref-type=\"fig\"}](#fig7){ref-type=\"fig\"}.",
"\n\n{#fig7}\n\n*G*′ was larger than *G*″ throughout the entire range of frequencies investigated. ",
"The moduli were parallel and dependent on the frequency applied and they settled between the first and the second decades. ",
"This behavior, typical of that of the weak gels, indicated that the elastic components always dominated over the viscous ones and that the system's structure was held by physical bonds between the macromolecules. ",
"By increasing the concentration of S3, there were only a few variations of the moduli values because the system was saturated at 0.5% of polymer concentration ([Figure [7](#fig7){ref-type=\"fig\"}](#fig7){ref-type=\"fig\"}a). ",
"For the natural polymers N1, N2, and N3, the higher their amounts, the higher the moduli ([Figure [7](#fig7){ref-type=\"fig\"}](#fig7){ref-type=\"fig\"}b--d). ",
"In fact, increasing the polysaccharide concentration, the helicoidal structures became entangled, and a three-dimensional network was formed, in which water remained entrapped. ",
"The synthetic polymer S3 showed higher values of the complex modulus *G*\\*, defined as the ratio between the total stress and the deformation to which the material is subjected at a given frequency. ",
"The natural polymers N2 and N3 used at a concentration of 1.5% w/w reached higher values of moduli than N1, close to that of the synthetic one S3 at 1% w/w (*G*\\* values at 1.7 Hz: S3 1% 125.68 Pa, N1 1.5% 46.35 Pa, N2 1.5% 98.11 Pa, and N3 1.5% 98.93 Pa) ([Figure [8](#fig8){ref-type=\"fig\"}](#fig8){ref-type=\"fig\"}a), but they did not reach the tan δ values of the synthetic polymer S3, which showed lower values, indicating a more elastic behavior, which was a consequence of the more complex crosslinked structure ([Figure [8](#fig8){ref-type=\"fig\"}](#fig8){ref-type=\"fig\"}b).",
"\n\n{#fig8}\n\nThe differences among these microbial-derived polysaccharides are due to the chemical structures and the different modality of interaction with water molecules. ",
"The xanthan gum has a cellulose-like backbone of glucose residues substituted with a trisaccharide side chain on alternating glucose units which consists of two mannose and a glucuronic acid residue. ",
"Noncarbohydrate substituents include an acetyl group on the inner mannose and a pyruvate group on the terminal mannose. ",
"The pyruvic acid content of xanthan can vary according to the producing bacterial strain and can affect the performance of the gum in water. ",
"Succinoglycan is an octasaccharide repeating unit consisting of seven glucose and one galactose with acetyl, pyruvyl, and succinyl substitutions. ",
"The long and flexible side chains of succinoglycan, which extrude from the double helices formed in solution, can establish more intermolecular interactions than the side chains of the xanthan gum determining the formation of stiffer gels.^[@ref24]^ A sclerotium gum is a nonionic polysaccharide characterized by a linear chain of (1,3)-β-[d]{.smallcaps}-glucose with a single (1,6)-β-[d]{.smallcaps}-glucose every third unit of the main chain. ",
"In water, it assumes a triple helix conformation held by intramolecular H-bonds, which determines a more rigid and elastic gel than the xanthan gum at high concentrations.^[@ref25]^\n\nGroup C {#sec2.3}\n-------\n\nFor the raw materials of group C, which includes N6 (gellan gum), N7 (carrageenan), and S4 and S5 (crosslinked hydrophobically modified acrylic polymers), firmness and consistency were the predominant texture parameters. ",
"Considering [Table S5](http://pubs.acs.org/doi/suppl/10.1021/acsomega.0c01306/suppl_file/ao0c01306_si_001.pdf), the values of cohesiveness and adhesiveness were lower than firmness and consistency and remained almost constant at increasing concentrations. ",
"Stringiness decreased at increasing concentrations of polymers, as for the raw materials of group B. In [Figure [9](#fig9){ref-type=\"fig\"}](#fig9){ref-type=\"fig\"} the texture curves obtained with an immersion/deimmersion test performed on the samples prepared with increasing concentrations of the polysaccharides N6 and N7 are shown.",
"\n\n{#fig9}\n\nBoth the polysaccharidic materials formed soft and elastic gels. ",
"Firmness and consistency increased at increasing polymer concentrations, maintaining low values of cohesiveness, adhesiveness, and stringiness, which is a typical profile of a gel with bouncy characteristics, poor film-forming properties, and low pickup. ",
"The positive curve can be divided into two areas: the immersion area (displacement from 0 to 10 mm) and deimmersion area (displacement from 10 to 20 mm). ",
"The ratio between the deimmersion area and the immersion area is called resilience. ",
"This is a textural parameter which indicates the ability of the sample to return to its original form after being deformed, compressed, or stretched. ",
"A complete resilient material has a resilience of 1, whereas materials which modify their structure after applying an external force show values of resilience much lower than 1, close to zero. ",
"The dispersions containing N6 and N7 showed high resilience (values between 0.8 and 0.9) because they were resistant to the deformation carried out by the probe and could almost completely recover their original shape. ",
"N6 showed higher values of firmness and consistency than N7 at the same concentrations. ",
"It is reasonable to think that the different structuring capabilities of these polymers are due to their different chemistry. ",
"N6 is a high acyl gellan gum consisting of a linear chain of glucose, rhamnose, and glucuronic acid (molar ratio 2:1:1). ",
"When dispersed in hot water in the presence of a monovalent salt, the polysaccharidic chains are uncoiled; after cooling, they assume a double helix conformation, stabilized by hydrogen bonds and by the presence of acyl groups, which determines the formation of a crosslinked network.^[@ref26]^ On the other hand, N7 is an iota-carrageenan characterized by the presence of galactose dimers, with acidic sulfate groups. ",
"This polysaccharide forms double helices in water, stabilized by the presence of bivalent cations, which form cationic bridges between the negatively charged sulfate groups.^[@ref27]^ As a result, the gels formed by the iota-carrageenan were less firm than those formed by the gellan gum, in which the physical interactions between the acyl ramifications lead to a more structured system even at lower concentrations. ",
"The systems formed by N6 (0.25% w/w) showed higher values of firmness not only than the gels formed by N7 at higher concentrations (0.75% w/w) but also than the gels formed by the synthetic acrylic polymers S4 and S5 (0.75% w/w) ([Figure [10](#fig10){ref-type=\"fig\"}](#fig10){ref-type=\"fig\"}a). ",
"However, the synthetic polymers reached higher values of adhesiveness than N6 and N7 because it was more difficult to overcome the attractive forces between the sample and the probe ([Figure [10](#fig10){ref-type=\"fig\"}](#fig10){ref-type=\"fig\"}b). ",
"The dispersions of the raw materials belonging to group C did not show significant differences in the values of stringiness ([Figure [10](#fig10){ref-type=\"fig\"}](#fig10){ref-type=\"fig\"}c).",
"\n\n{#fig10}\n\nThe flow curves obtained with a CSR test highlighted the pseudoplastic nature of the dispersions prepared with the polymers of group C ([Figure S2](http://pubs.acs.org/doi/suppl/10.1021/acsomega.0c01306/suppl_file/ao0c01306_si_001.pdf)), and the values of the zero-shear viscosity (η~0~) at increasing concentrations are reported in [Table S6](http://pubs.acs.org/doi/suppl/10.1021/acsomega.0c01306/suppl_file/ao0c01306_si_001.pdf). ",
"Viscosity increased at increasing polymer concentrations, and the samples formulated with N6 showed the highest viscosity values. ",
"The frequency sweep rheological analyses conducted on the dispersions made with the raw materials of group C revealed that the elastic *G*′ modulus was higher than the viscous *G*″ modulus throughout the whole frequency range investigated. ",
"The moduli were located between the first and the second decade ([Figure [11](#fig11){ref-type=\"fig\"}](#fig11){ref-type=\"fig\"}a). ",
"The synthetic polymer S5 (at 0.75% w/w) reached higher values of moduli than the other rheological modifiers, but it showed a more prevalent viscous component, as indicated by the higher tan δ values ([Figure [11](#fig11){ref-type=\"fig\"}](#fig11){ref-type=\"fig\"}b). ",
"The natural-derived polymer N6 showed the lowest values of tan δ especially when high frequencies were applied, indicating more elastic characteristics even at lower concentrations (0.25% w/w) in accordance with the higher values of firmness measured with the texture analysis. ",
"The polysaccharide N7 formed a gel with rheological properties similar to that formed by the synthetic polymer S4 at the same concentration (0.75% w/w) because the tan δ curves were superimposed throughout the entire frequency range applied.",
"\n\n{#fig11}\n\nCorrelations between the Textural and the Rheological Parameters {#sec2.4}\n----------------------------------------------------------------\n\nPearson's coefficients have been calculated starting from the data obtained by measuring the textural and the rheological properties of the polymeric aqueous dispersions prepared and analyzed in this work. ",
"The textural parameters of firmness and consistency resulted to be positively correlated to the viscosity values obtained with the rheological tests conducted in continuous shear flow (Pearson's coefficient calculated for η~0~ was 0.9 and for the η at 0.1 s^--1^ was 0.8). ",
"The textural parameters of adhesiveness and cohesiveness were significantly correlated to the viscoelastic properties measured through the oscillatory rheological tests (Pearson's coefficient for the complex modulus *G*\\* taken at 1 Hz was 0.8). ",
"For the materials of group B and C, which showed a weak-gel rheology pattern, stringiness was negatively correlated to the η values (Pearson's −0.7) because the length of the string formed when the probe was withdrawn from the sample decreased with an increasing material concentration, as the three-dimensional network becomes more and more structured. ",
"On the contrary, for the materials of group A, the stringiness values were significantly positively correlated to η and *G*\\* (Pearson's coefficient 0.7--0.8), in accordance with their viscoelastic behavior.",
"\n\nConclusions {#sec3}\n===========\n\nThe results of this work proved that objective data about rheology and texture obtained, studying the behavior of the aqueous dispersions of the single raw materials, are useful to predict the sensorial properties they can confer to cosmetic products. ",
"Our protocol based on rheological and texture analyses, which are significantly correlated, turned out to be a powerful prescreening tool to characterize and categorize each polymeric raw material, according to their applicative specificities. ",
"As expected, natural-derived polysaccharides do not reach the mechanical properties of highly crosslinked acrylic polymers such as carbomer, which showed higher physical parameters. ",
"Matching the performance of synthetic polymers by replacing them with polysaccharides is difficult because each raw material has its own sensorial specificities and synthetic polymers are artificially created to have a specific performance in formulation. ",
"However, some of the acrylic polymers analyzed in this study, which formed aqueous systems with medium--low viscosity and high spreadability, showed some significative similarities with natural polymers. ",
"The water dispersions of succinoglycans (N2) and sclerotium gums (N3) had values of firmness and consistency similar to that of polyacrylate cross-polymer-11 (S3). ",
"In addition, they showed a weak-gel rheological pattern and similar values of moduli, but they differed from the values of adhesiveness and the damping factor tan δ because the acrylic polymer had a more elastic behavior. ",
"Carrageenan (N7) showed a rheological trend very similar to that showed by the hydrophobically modified polymer S4, and they both formed soft and elastic gels when dispersed in water. ",
"However, the natural-derived polymer N7 did not reach the values of adhesiveness calculated for S4. ",
"In conclusion, the combined use of texture analyses and rheology proved to be a simple time and money-saving system to avoid the traditional *trial and error* approach to the formulation of natural cosmetic products, especially during a revision of the formulation design or the substitution of an ingredient, in reference to the concern around liquid plastics, is required.",
"\n\nExperimental Section {#sec4}\n====================\n\nMaterials {#sec4.1}\n---------\n\n13 raw materials recently introduced in the market as rheological modifiers were selected for the study.",
"\n\nSynthetic raw materials are as follows: S1---carbomer (Carbopol Ultrez 10 by Lubrizol), S2---sodium polyacrylate (Cosmedia SP by BASF), S3---polyacrylate cross-polymer-11 (Aristoflex Velvet by Clariant), S4---ammonium acryloyldimethyltaurate/Beheneth-25 methacrylate cross-polymer (Aristoflex Blv by Clariant), and S5---acrylates/C10-30 alkyl acrylate cross-polymer (Pemulen EZ4U by Lubrizol).",
"\n\nThe semisynthetic raw material is the SN---hydroxypropyl guar gum (Jaguar HP-105 by Solvay Novecare).",
"\n\nNatural raw materials are the N1---xanthan gum (Satiaxane VPC 911 by Cargill), N2---succinoglycan (Rheozan SH by Solvay Novecare), N3---sclerotium gum (Actigum CS 11 QD by Cargill), N4---*C. spinosa* gum (Vari Tara by Variati), N5---*C. siliqua* gum (Vari Carruba by Variati), N6---gellan gum (Kelcogel CG-HA by CP Kelco), and N7---carrageenan (Genuvisco CG-131 by CP Kelco).",
"\n\nPreparation of the Samples {#sec4.2}\n--------------------------\n\nThe synthetic polymers (S1--S5) were dispersed in hot water (70--75 °C) at increasing concentrations by means of the Silverson L5T homogenizer at 2500 rpm until homogeneity. ",
"Polymers S1 and S5 needed neutralization with NaOH solution 10% w/w.\n\nSemisynthetic (SN) and natural polymers (N1--N7) were dispersed in water at increasing amounts under continuous stirring with a magnetic stirrer. ",
"SN, N1, N2, and N3 were dispersed in cold water. ",
"N4, N5, N6, and N7 needed higher temperature to be dispersed (70 °C for N4, N5 and N6, 45 °C for N7). ",
"Salt was needed for the dispersion of polymers N6 and N7.",
"\n\nThe pH of the dispersions obtained was between 5 and 6.",
"\n\nThe sample preparation modality, including the concentration ranges used in this work, is summarized in [Table S7](http://pubs.acs.org/doi/suppl/10.1021/acsomega.0c01306/suppl_file/ao0c01306_si_001.pdf).",
"\n\nTexture Analysis {#sec4.3}\n----------------\n\nA Texture Analyzer TMS-Pro, from the Food Technology Corporation (Sterling, Virginia, USA), was used equipped with a load cell of 10N and a nylon, spherical probe (2 cm diameter). ",
"The samples were poured in jars with a volume of 50 mL and a diameter of 5.3 cm. ",
"An immersion/deimmersion test was conducted in triplicates at room temperature: through a vertical displacement, the probe penetrated the samples for 10 mm at a rate of 1.3 mm s^--1^ and then turned back to its initial position. ",
"Software Texture Lab Pro was used to register and display the data. [",
"Figure [12](#fig12){ref-type=\"fig\"}](#fig12){ref-type=\"fig\"} shows the texture parameters collected from the curve load (N) vs cumulative displacement (mm): firmness, consistency, cohesiveness, adhesiveness, and stringiness. ",
"Firmness is the positive peak, that is, the maximum value of force needed to obtain a deformation and is expressed as newton (N); consistency is the area under the positive curve (N mm) and represents the total work the sample opposes against the deformation. ",
"These two parameters obtained from the first part of the curve are related to the viscosity of the sample and depend on the material molecular weight and crosslinking degree. ",
"Cohesiveness is the negative peak (N) registered during the movement of the probe upward and is related to the intramolecular forces of the analyzed material; adhesiveness is the area under the negative portion of the curve (N mm) and is the work necessary to break the attractive forces established between the surface of the sample and the surface of the instrument probe. ",
"These parameters obtained from the negative part of the curve are related to the elastic properties of the sample. ",
"Stringiness is the distance (mm) to which the product stretches during the withdrawal of the probe that returns to its initial position.^[@ref18]^ This parameter describes the viscoelasticity of the product.",
"\n\n{#fig12}\n\nRheological Analyses {#sec4.4}\n--------------------\n\nThe instrument used is the rheometer Physica MCR-101 from Anton Paar. ",
"All the analyses were performed both in continuous and oscillatory flow conditions, at a controlled temperature (23 ± 0.05 °C), using the CP50-1 sensor, which consisted in a parallel plate geometry set at a fixed gap of 0.1 mm. ",
"The measurements were conducted in triplicates, ensuring the reproducibility of the results. ",
"The sample flow curves were obtained in continuous flow conditions, with a CSR test, by recording viscosity values (η) at an increasing shear rate, from 0.001 to 1000 s^--1^. Fitting the flow curves with the Carreau--Yasuda mathematical model that describes the shear thinning behavior of the material ([eq [1](#eq1){ref-type=\"disp-formula\"}](#eq1){ref-type=\"disp-formula\"}), the viscosity of the samples in the plateau region (zero-shear viscosity) was calculated, as an indication of the viscosity at rest.",
"\n\nThe tests performed in oscillatory conditions allowed highlighting the viscoelastic properties of the polymer dispersions. ",
"An amplitude sweep test was conducted increasing the strain (γ) from 0.01 to 1000%, maintaining the frequency at 1 Hz, in order to identify the LVR. ",
"Frequency sweep tests, were performed decreasing the frequency from 10 to 0.01 Hz, at a fixed strain chosen from the LVR. ",
"These tests were used to study the inner structure of the dispersion and the trend of the storage (*G*′) and loss (*G*″) moduli.",
"\n\nStatistical Analysis {#sec4.5}\n--------------------\n\nXLSTAT software (Addinsoft, Paris, France) was used to elaborate the data obtained from the analytical tests. ",
"PCA was performed on the correlation matrix made with the average values of the textural parameters measured for each sample. ",
"This analysis allowed evaluating the differences and the similarities between the raw materials subjected to the analyses. ",
"Pearson's correlation coefficient was calculated considering the numerical values of the textural and rheological parameters, to highlight which ones were significantly correlated (*p*-value \\< 0.05).",
"\n\nThe Supporting Information is available free of charge at [https://pubs.acs.org/doi/10.1021/acsomega.0c01306](https://pubs.acs.org/doi/10.1021/acsomega.0c01306?goto=supporting-info).List of the rheological modifier used in this work and the dispersion modality for the preparation of samples; numerical values of the textural parameters measured for the samples prepared at increasing concentrations of the raw material of group A; zero shear viscosity (η~0~) values, calculated with the Carreau--Yasuda model, for the samples prepared with increasing concentrations of the raw materials of group A; numerical values of the textural parameters measured for the samples prepared at increasing concentrations of the raw material of group B; flow curves of the samples prepared with the polymers of group B at 1% w/w; zero shear viscosity (η~0~) values, calculated with the Carreau--Yasuda model, for the samples prepared with increasing concentrations of the raw materials of group B; numerical values of the textural parameters measured for the samples prepared at increasing concentration of the raw material of group C; flow curves of the samples prepared with the polymers of group C at 0.5% w/w; and zero shear viscosity (η~0~) values, calculated with the Carreau--Yasuda model, for the samples prepared with increasing concentrations of the raw materials of group C ([PDF](http://pubs.acs.org/doi/suppl/10.1021/acsomega.0c01306/suppl_file/ao0c01306_si_001.pdf))\n\nSupplementary Material\n======================\n\n###### \n\nao0c01306_si_001.pdf\n\nThe authors declare no competing financial interest.",
"\n\nThe authors would like to acknowledge Dr Giulia Galizia from Unired s.r.l. ",
"for the writing assistance and language editing. ",
"We also thank the reviewers for their comments and suggestions.",
"\n"
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"---\nabstract: 'Ten years of photometric observations of SN 1987A are reviewed. ",
"The optical and near-infrared colors are now declining at $\\lesssim 1$ magnitude per 1000 days, which is consistent with both the infrared “freeze-out” and the possible energy sources powering the nebula. ",
"The “uvoir” bolometric luminosity at ten years is estimated to be log$_{10}$(L) $\\sim 36.1-36.4$ ergs s$^{-1}$. The most recent photometric measurements are given in Table \\[t1\\]. ",
"A deep color-magnitude diagram shows that the young stars are concentrated within a projected distance of $\\sim 25$ (6pc) in a field out to $\\sim3$ from the supernova. ",
"It is likely that Stars 2 and 3 which project to within 0.7pc of the supernova are associated with Sk –69202.'",
"\nauthor:\n- 'Nicholas B. Suntzeff'\ntitle: 'The Ten-Year Photometric Evolution of SN 1987A'\n---\n\nIntroduction\n============\n\nWith the announcement of a supernova in the Large Magellanic Cloud (Shelton 1987), many astronomers in the southern hemisphere stopped the projects they were working on, and began programs of the long-term monitoring of this unique object. ",
"A tremendous literature has developed on the observation and theory of the supernova. ",
"At the time of this conference, there are more than 1000 refereed papers listed under “SN 1987A” by the Astrophysics Data System of NASA. ",
"In this short contribution, I would like to summarize the observational work on the photometry and spectrophotometry of SN 1987A, and discuss the stellar population surrounding the supernova.",
"\n\nPhotometry of SN 1987A\n======================\n\nIn the years following the explosion of Sanduleak –69202 on UT 7:36 23 Feb 1987 or JD 2446849.8165 (Bratton [*et al.*]{} ",
"1988, Hirata [*et al.*]{} ",
"1988), all major southern hemisphere observatories followed the photometric evolution SN 1987A in optical and infrared colors. ",
"In addition, IUE and later HST measured photometric indices. ",
"For ground-based observatories, it was not always easy finding a telescope [*small*]{} enough to follow the supernova. ",
"The ground-based observations were also complicated by the fact that the only detector generally available was a single channel device such as a photoelectric photometer. ",
"A measurement therefore required photometric weather (not a problem today with CCD detectors and fainter SNe) or at least scattered clouds so that quick differential photometry could be done relative to a nearby standard like $\\delta$ Doradus. ",
"At maximum light on day 84.5, the supernova was $V=2.975$ (Hamuy & Suntzeff 1990). ",
"At this brightness, we had to reduce the aperture of the 0.4m telescope at CTIO by using the Hartmann mask, and masking off all but 5 holes, leaving a collecting area of only 26 cm$^2$! ",
"Future bright events may leave observatories unprepared as small telescopes are closed in the face of financial pressures.",
"\n\nAtlases of Photometry\n---------------------\n\nEach observatory published the photometric data in a number of different papers. ",
"Generally the last paper in the series contains references to the earlier papers. ",
"Here I will list only the latest paper from the series of publications of a particular observatory group. ",
"The number is parenthesis gives the date (since explosion) of the last observation. ",
"In some cases the data are only presented in graphical form.",
"\n\n- [**AAO/MSSSO:**]{} near-infrared spectrophotometry (day 1114), Meikle [*et al.*]{} (",
"1993)\n\n- [**CTIO:**]{} $UBVRI$ photoelectric photometry (day 813), Hamuy & Suntzeff (1990); CCD optical photometry (day 1469), Walker & Suntzeff (1991); $UBVRIJHK[10][20]$ and “uvoir” bolometric luminosities (day 1594), Suntzeff [*et al.*]{} (",
"1992); optical spectrophotometry (day 805) Phillips [*et al.*]{} (",
"1990); near-infrared spectrophotometry (day 1445), Bautista [*et al.*]{} (",
"1995)\n\n- [**ESO:**]{} Near and mid-infrared photometry and spectrophotometry (day 1493), Bouchet & Danziger (1993), Bouchet [*et al.*]{} (",
"1996); Stromgren photometry(day 330), Helt [*et al.*]{} (",
"1991); spectrophotometry (day 314), Hanuschik [*et al.*]{} (",
"1994); Walraven photometry (day 120, some data quoted up to day 393 in Pun [*et al.*]{} ",
"1995), Pel [*et al.*]{} (",
"1987); Geneva photometry (day 917), Burki [*et al.*]{} (",
"1991)\n\n- [**KAO:**]{} Near and mid-infrared spectrophotometry (day 775), Wooden [*et al.*]{} (",
"1993)\n\n- [**IUE:**]{} Spectrophotometry and ultraviolet magnitudes (day 1567), Pun [*et al.*]{} (",
"1995); FES ($V_{IUE}$) light curve (day 760) Kirshner & Gilmozzi (1989) (see also Sonneborn 1988)\n\n- [**LCO:**]{} $UBVRI$ photoelectric photometry and early photographic photometry (day 156), Shelton(1993a,b), Shelton & Lapasset (1993)\n\n- [**HST:**]{} Ultraviolet magnitudes (day 2431), Pun [*et al.*]{} (",
"1995)\n\n- [**SAAO:**]{} $UBVRIJHKLM$ single-channel and CCD photometry (day 1770), Caldwell [*et al.*]{} (",
"1993). ",
"Also uvoir bolometric magnitudes.",
"\n\n- [**Astron station:**]{} ultraviolet spectrophotometry (day 394), Lyubimkov (199)\n\nI also list a number of papers which are relevant to the photometric data: finding chart and star names, Walborn [*et al.*]{} ",
"1987 and Walker & Suntzeff (1990); detailed photometry and spectroscopy of Stars 2 and 3, Walborn [*et al.*]{} (",
"1993) ; “uvoir” bolometric luminosities from optical and infrared spectrophotometry, Suntzeff & Bouchet (1990), Hamuy [*et al.*]{} (",
"1990), and Bouchet [*et al.*]{} (",
"1991); summary of polarization measurements through day 600, Wang & Wheeler (1996); HST spectrophotometry of Star 2 (and a discussion of age and reddening of this star), Scuderi [*et al.*]{} (",
"1996).",
"\n\nAlthough there is a good local photometric sequence near SN 1987A in the optical (Walker & Suntzeff 1991, Walborn [*et al.*]{} ",
"1993), the photometric observations are by no means easy. ",
"The supernova, which is now at $m \\sim 17-20$, is within 3 of Stars 2 and 3 which have magnitudes of $15 < V < 16$. Walborn [*et al.*]{} (",
"1993) show that Star 3 is a variable Be star with $\\delta(V) \\sim 0\\fm6$ and star 2 shows signs of also being a star Be star. ",
"Even with excellent local standards and image quality, there can be systematic differences as large as $\\delta(m) \\sim 0\\fm4$ in the photometric data published by different observatories due to the non-stellar flux distribution of the supernova in the nebular phase coupled with the different CCD quantum efficiency/filter combinations (Menzies 1989, Hamuy [*et al.*]{} ",
"1990). ",
"The near-infrared photometry is more accurate since the crowding hot stars are fainter and the image quality is generally better, but the local standards are only accurate to about 01 (Suntzeff [*et al.*]{} ",
"1991, Walborn [*et al.*]{} ",
"1993).",
"\n\nThe Light Curve of SN 1987A\n---------------------------\n\nIn Table \\[t1\\] I list the most recent photometric data for SN 1987A. The HST WFPC2 optical photometry was measured by P. Challis, The near-infrared photometry was measured from CTIO 4m telescope IR imager data.",
"\n\n[lccccc]{} & & & & &\\\n2927 (3 Mar 95) & ... & 19.68& 19.72& 18.63& 19.07\\\n3267 (6 Feb 96) & 19.85 & 19.93& 19.96& 18.88& 19.37\\\ndecline rate & 0.89: & 1.03(13)&0.63(05) &0.82(03)&0.96(02)\\\n&&&\\\n&& & &\\\n3274 (10 Feb 96) && 17.71& 17.28& 17.14&\\\n3558 (20 Nov 96) && 18.24& 17.63& 17.46&\\\n3616 (17 Jan 97) && 18.01& 17.41& 17.34&\\\n3621 (22 Jan 97) && 18.11& 17.54& 17.22&\\\ndecline rate && 0.75(13) & 0.78(10) & 0.45(11)\\\n\nThe ground-based $JHK$ magnitudes were measured with DAOPHOT (Stetson 1987) psf fitting techniques and do not include flux from the inner ring. ",
"The inner ring adds about 03 on day 3274. ",
"The psf errors are 005 (01 on 3616) and the photometric zero point error is about 007. ",
"The (preliminary) HST magnitudes were measured through a digital aperture of diameter 0.6, with an estimated error of 015. ",
"I also list the decline rate for the data starting around day 2500. ",
"In Figure \\[f1\\] I plot the $UBVRI$ data from CTIO and HST the $JHK$ data from CTIO and ESO.",
"\n\nThe supernova light curve is declining at 1 magnitude per 1000 days or less, consistent with the possible sources of energy powering the nebula ($^{44}$Ti, $^{22}$Na, and a pulsar) and the effects of the infrared “freeze out” (Woosley [*et al.*]{} ",
"1989, Kumagai [*et al.*]{} ",
"1991, Fransson & Kozma 1993).",
"\n\nWe cannot directly measure the “uvoir” bolometric luminosity at these late times because we do not have 10-30 micron fluxes. ",
"However, we can use the bolometric corrections to the optical colors $VK$ to estimate a bolometric magnitude on the assumption that the flux distribution is indeed frozen. ",
"Under this assumption, the uvoir luminosity on day 3600 is log$_{10}$(L) $\\sim 36.1-36.4$ in units of ergs s$^{-1}$.\n\nFrom the re-analysis of the early photographic and photoelectric data, the early-time light curve has been improved (West & McNaught 1992, Shelton 1993a, Shelton & Lapasset 1993). ",
"In Figure \\[f2\\] I plot the data from these papers along with the early CTIO, SAAO, and LCO photoelectric photometry. ",
"I also include the photoelectric data published by Matthews (1987), Moreno & Walker (1987), and the visual lower limit of Jones (1987). ",
"The Jones limit happened 1.8 hours after the neutrino detections. ",
"The first optical detection was made by McNaught at 3.1 hours after outburst.",
"\n\nThe Stellar Population Near SN 1987A\n------------------------------------\n\nAs summarized by Melnick in this conference, Sk –69202 was located about 4 from the center of the loose cluster NGC 2044 (LH90) near NGC 2070 (30 Doradus). ",
"The whole region is enveloped in emission associated with the star formation in the 30 Dor complex. ",
"At the position of Sk –69202 there is no large-scale star formation activity as in NGC 2044 or NGC 2050 to the south. ",
"Walker & Suntzeff (1990) however noted a small young association within 30 of the supernova, which is called KMK80 in the catalog of Kontizas [*et al.*]{} (",
"1988). ",
"Efrevmov (1991) and Walborn [*et al.*]{} (",
"1993) have estimated the age of this association at $12\\pm4$Myrs using the CTIO photometry. ",
"Scuderi [*et al.*]{} (",
"1996) have estimated an upper limit (dependent on mass loss) to the age of Star 2 at 13Myrs. ",
"This, of course, is similar to the age estimate for Sk –69202 of 11Myrs by Arnett [*et al.*]{} (",
"1989).",
"\n\nThe field population near SN 1987A can be seen in more detail in Figure \\[f3\\]. ",
"Here I plot the $BV$ color-magnitude diagram along with the (Y,Z)=(0.25,0.008) isochrones from Bertelli [*et al.*]{} (",
"1994) and the photometry of Sk –69202 from Walborn [*et al.*]{} (",
"1987). ",
"I have used a reddening of $E(B-V)=0.16$ and a true distance modulus of 18.50. ",
"These data were taken in January and March 1996 at the CTIO 4m telescope CFCCD system by Mark Phillips. ",
"A total of seven frames in each color were used to calculate the magnitudes. ",
"The large scatter about the main sequence down to $V=20$ is not due to photometric errors, but due to variable reddening (Walborn [*et al.*]{} ",
"1993).",
"\n\nFigure \\[f3\\] shows that the young field population within 25 of the supernova is consistent with a population of $\\sim15$Myr, although this value critically depends on the accuracy of the theoretical $T_{eff}$ to $(B-V)$ conversion, the reddening, and the small number of hot stars. ",
"There is also a dominant older field population with a prominent turnoff at $V=20.4$ which corresponds to a 1.5Gyr population.",
"\n\nThese two populations are not well mixed however. ",
"Figure \\[f3\\] shows that [*the young field population is strongly concentrated towards the position of SN 1987A*]{}. ",
"This can be shown with simple statistics. ",
"Divide the field by a circle with radius of 25(projected distance of $\\sim 6$pc) around SN 1987A and count the number of hot stars, defined here simply as any star with $(B-V) <\n0.5$. Form the ratio of the number of stars with $V < 18$ and $18 < V\n< 20$. The ratios for inside and outside the circle are 14/23 and 20/178 or 61% versus 17%. ",
"Furthermore, of the eight brightest hot stars in this region ($V<16$), four are inside the circle (stars 2,3,10,30), and two are inside 3! ",
"Given such statistics, it is extremely likely that Sk –69202 was part of a loose association including KHK80 with an age of $\\sim15$Myr, and that Stars 2 and 3, which are less than 3away, are physically associated with progenitor of the supernova. ",
"However, because there is no obvious interaction of the outer rings of the supernova with Stars 2 and 3, it is unlikely that the supernova lies in precisely the same plane on the sky as the two crowding stars.",
"\n\nThis paper is the summary of the work of many astronomers who have collaborated to bring this photometry to the astronomical community. ",
"I would like to acknowledge the help of Patrice Bouchet, Peter Challis, Darren DePoy, Jay Elias, Richard Elston, Christian Gouiffes, Mario Hamuy, Jason Pun, Bob Kirshner, Jaymie Matthews, Mark Phillips, S. Elizabeth Turner, Alistair Walker, and Robert Williams. ",
"The help of Jason Spyromilio with the pronunciation of “uvoir” is always appreciated. ",
"I also gratefully acknowledge the continuing support for research on SN 1987A through the HST grants “SINS: Supernova INtesive Study, ” Robert Kirshner, PI, and, of course, NOAO.",
"\n\nArnett, W. D., Bahcall, J. N., Kirshner, R. P., & Woosley, S. E. 1989, , 27, 629 Bautista, M. A., [*et al.*]{} ",
"1995, , 109, 729 Bratton, C. B., [*et al.*]{} ",
"1988, Phys. ",
"Rev. D., 37, 3361 Bouchet, P. [*et al.*]{} ",
"1991, , 245, 490 Bouchet, P., & Danziger, I. J. 1993, , 273, 451 Bouchet, P. [*et al.*]{} ",
"1996, in Supernovae and Supernova Remnants : Proceedings IAU Colloq.",
" 145, eds. ",
"R. McCray and Z. Wang (New York, Cambridge Univ. ",
"Press), p. 201 Bertelli, G., Bressan A., Chiosi C., Fagotto F., & Nasi E. 1994, , 106, 275 Burki, G., Cramer, N., & Nicolet, B. 1991, , 87, 163 Caldwell, J. A. R. 1993, , 262, 313 Efremov, Y. N. 1991, Sov. ",
"Astron. ",
"Lett., ",
"17, 173 Fransson, C., & Kozma, C. 1993, , 408, L25 Hamuy, M., & Suntzeff, N. B. 1990, , 99, 1146 Hamuy, M., Suntzeff, N. B., Bravo, J., Phillips, M. M. 1990, , 102, 888 Hanuschik, R. W. [*et al.*]{} ",
"1994, , 281, 737 Helt, B. E., [*et al.*]{} ",
"1991, , 89, 399 Hirata, K. S. [*et al.*]{} ",
"1988, Phys. ",
"Rev. D, 38, 448 Lyubimkov, L. S. 1990, Sov. ",
"Astron., ",
"34, 239 Jones, A. 1987, IAU Circ.",
" 4340 Kirshner, R. P., & Gilmozzi, R. 1989, in Exploring the Universe with the IUE Satellite, ed. ",
"Y. Kondo (2nd ed.; ",
"Dordrecht: Reidel), 771 Kontizas, E., Metaxa, M., & Kontizas, M. 1988, , 96, 1625. ",
"Kumagai, S., Shigeyama, T., Nomoto, K., & Hashimoto, M. 1991, , 243, L13 Matthews, J. 1987, IAU Circ.",
" 4328 Meikle, W. P. S. [*et al.*]{} ",
"1993, , 261, 535 Menzies, J. W. 1989, , 237, 21p Moreno, B., & Walker, S. 1987, IAU Circ.",
" 4316 Pel, J. W. [*et al.*]{} ",
"1987, in Proc. ",
"ESO Workshop on SN 1987A, ed. ",
"I.J. Danziger (ESO:Garching), 97 Phillips, M. M. [*et al.*]{} ",
"1990, , 99, 1133 Pun, C. S. J, [*et al.*]{} ",
"1995, , 99, 223 Scuderi, S. [*et al.*]{} ",
"1996, , 465, 956 Shelton, I. K. 1987, IAU Circ., ",
"4316 Shelton, I. K. 1993a, , 105, 1886 Shelton, I. K., & Lapesset, E. 1993, , 105, 1892 Shelton, I. K. 1993b, , 105, 1895 Sonneborn, G. 1988, in A Decade of UV Astronomy with IUE, ed. ",
"E. Rolfe, ESA SP-281, 111 Stetson, P. B. 1987, , 99, 191 Suntzeff, N. B., & Bouchet, P. 1990, , 99, 650 Suntzeff, N. B., Phillips, M. M., DePoy, D. L., Elias, J. H., & Walker, A. R. 1991, , 102, 1118 Suntzeff, N. B., Phillips, M. M., Elias, J. H., DePoy, D. L., & Walker, A. R., 1992, , 384, L33 Walborn, N. R., [*et al.*]{} ",
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"1993, , 88, 477 Woosley, S. E., Pinto, P. A., & Hartmann, D. 1989, , 346, 395\n"
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"The available evidence for the use of direct oral anticoagulants (DOACs) is limited and primarily consists of case series and cohort studies, which are summarized in this chapter. ",
"Randomized trials evaluating DOACs in patients with APS are reviewed. ",
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"The Great Danes scored two-straight before Harvard answered with four of the next five – including two from Edmonds – over six minutes to take its first lead of the game, 5-4, at the 3:09 mark. ",
"UAlbany scored two-unanswered to end the quarter and hold a 6-5 advantage after 15 minutes.",
"\n\nCheek knotted the game, 6-6, five minutes into the second quarter with a spin move from 15 yards out to free himself. ",
"Irelan posted a goal off a face-off win before the Crimson ripped off consecutive scores to take an 8-7 lead. ",
"The Great Danes scored three times over 23 seconds before the end of the half to go into the break ahead, 10-8.",
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"\n\nUAlbany took its largest lead of the game, 14-11, at the 10:15 mark of the fourth quarter. ",
"Cheek found a cutting Connor McCroskey and Joe Lang sniped a shot to the top corner to pull Harvard within one, 14-13, with five minutes to play. ",
"The Great Danes were not deterred, scoring 80 seconds later to push back out two and hold on for a 15-13 win.",
"\n\nFor the full, archived replay of the game on the Ivy League Digital Network, click here.",
"\n\nGame Notes:Joe Lang extended his point-scoring streak to 26 games. ",
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"Cheek extends his goal streak to 12 games. ",
"Cheek has had a hat trick in seven games this year. ",
"Harvard moves to 13-3 over the last two years when scoring 10-plus. ",
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[
"---\nabstract: 'We summarize some of the results we obtained in arXiv:1006.2126 (Physical Review Letters 106, 071301), arXiv:1102.4637 (Physics Letters B 700, 150-156) and in arXiv:1107.3334, giving complementary characterizations of the relativity of spacetime locality that affects certain Planck-scale-deformed phase-space descriptions of free particles.'",
"\nauthor:\n- 'Niccoló LORET[^1]'\n- Leonardo BARCAROLI\n- 'Giacomo ROSATI[^2]'\ntitle: 'Longitudinal and transverse relativity of spacetime locality in Planck-scale-deformed phase spaces'\n---\n\nPreliminaries\n=============\n\nThese notes are based on our works in Refs.",
" [@bob; @kbob; @transverse]. ",
"We here plan to give a quick overall picture of these results that we derived concerning manifestations of relative locality for theories of free particles governed by DSR-deformed relativistic symmetries [@gacdsr1; @dsrPOLAND2001], in two complementary regimes: longitudinal and transverse one.\\\nIt is valuable for our purposes to observe that “relative locality\" is a natural next step in a logical line on relativistic theories that starts with the relativity of rest (Galilean Relativity) and then, accommodates “relative simultaneity\" (Special Relativity). ",
"The relativity of rest and the absoluteness of time hosted by Galilean relativity famously leads to a structureless law of composition of velocities: $\\vec{v}\\oplus\\vec{\\delta v}=\\vec{v}+\\vec{\\delta v}$. The observer-independence of the speed of light, and the relativity of simultaneity, lead to a more complex (nonlinear, noncommutative, nonassociative) law of composition of velocities, the special-relativistic law $$\\vec{v}_a\\oplus\\vec{v}_b=\\frac{\\vec{v}_a+\\vec{v}_b}{1+\\frac{\\vec{v}_a\\vec{v}_b}{c^2}}+\\frac{1}{c^2}\\frac{\\gamma_a}{1+\\gamma_a}\\frac{\\vec{v}_a\\wedge(\\vec{v}_a\\wedge\\vec{v}_b)}{1+\\frac{\\vec{v}_a\\vec{v}_b}{c^2}}\n~,$$ where $\\gamma_a=1/\\sqrt{1-|\\vec{v}_a|^2/c^2}$ is the Lorentz factor. ",
"In quantum-gravity research one finds motivation for endowing a specific momentum scale, essentially the Planck scale, with a special role, and it is conceivable [@gacdsr1; @dsrPOLAND2001] that this momentum scale, here denoted with $|\\ell|^{-1}$, be an absolute relativistic scale, to which the laws of transformation among observers could adapt in the context of a novel relativistic theory of “Doubly Special Relativity (DSR) type\" [@gacdsr1; @dsrPOLAND2001].",
"\n\nIt is emerging that this sort of constructions may require [@bob; @kbob] a relativity of spacetime locality in the same sense that the observer-independence of the speed-of-light scale requires the relativity of simultaneity. ",
"And, just like special relativity required a nonlinear law of composition of velocities, these DSR constructions require a non-linear law of composition of momenta $(p\\oplus q)_a\\neq (p+q)_a$, of the type $$p_a\\oplus dq_a=p_a+U(p)^b_a dq_b=p_a+dq_a+\\Gamma_a^{bc}p_b dq_c+... \\label{somma}$$ where we denoted with $\\Gamma_a^{bc}$ the feature $\\Gamma_a^{bc}=-\\frac{\\partial}{\\partial p_a}\\frac{\\partial}{\\partial q_b}(p\\oplus q)_c|_{q,p=0}$, implicitly referring to the fact that this may be viewed [@principle] as an affine connection on momentum space.\\\nThe liaison between our approach (which we are here going to summarize) and the one based on the study of geometry of momentum space has been investigated in [@jackgab], where a first insight of interaction vertexes in a deformed symmetries scenario is given.",
"\n\nWe shall here not rely explicitly on the geometry of momentum space and on the form of the composition law for momenta, since we do not need the full characterization of the shape of interactions to present longitudinal and transverse effect of relative locality. ",
"Instead we summarize some of the results obtained in Refs.",
" [@bob] and [@transverse], of the non-interactive case, giving usefully complementary characterizations of the relativity of spacetime locality that affects certain descriptions of free particles in Planck-scale-deformed phase-space constructions.",
"\n\nIn this paper from now on we will formalize the features of obstruction of measurability and modified momenta composition rule with $\\kappa$-Poincaré Hopf algebra. ",
"The algebric sector of $\\kappa$-Poincaré can be interpreted as a deformation of Poincaré Lie algebra with $\\ell\\sim 1/M_P$ (where $M_P$ is the Planck mass) the parameter of deformation. ",
"It is, therefore, always possible to rely on the existence of a “classical” limit by turning off this deformation ($\\ell\\rightarrow 0$). ",
"In this context moreover it is easier to give a simple interpretation of relative locality phenomena on physical observables and thus implement a phenomenology.",
"\n\nWe adopt units such that the speed-of-light scale is $1$ ($c=1$).",
"\n\nLongitudinal effects\n====================\n\nLet us start, in this section, by summarizing the main results of Ref.",
" [@bob; @kbob], where a relativistic description of momentum dependence of the speed of massless particles was given within a classical-phase-space construction inspired by properties of the $\\kappa$-Poincaré Hopf algebra [@lukie1992; @majrue; @lukieANNALS].\\\nAt the quantum level the $\\kappa$-Poincaré algebra is intimately related to the $\\kappa$-Minkowski noncommutative spacetime [@majrue; @lukieANNALS]. ",
"For classical-phase-space constructions indeed one can consider standard Minkowski spacetime coordinates in combination with a description of relativistic transformations inspired by properties of the $\\kappa$-Poincaré Hopf algebra. ",
"So we assume trivial Poisson brackets for the spacetime coordinates, $\\{ x , t \\} = 0$. One then codifies [@bob; @jurekvelISOne] boost transformations in terms of Poisson brackets with the translation generators, with deformation parameters $\\alpha,\\beta,\\gamma$, as follows [@bob]: $$\\begin{aligned}\n &\\left\\{ \\mathcal{N}_i, \\Omega \\right\\} = P_i-\\alpha\\ell\\Omega P_i\\;\\;\\;\\; , \\;\\;\\;\\;\\;\\;\\;\\; \\left\\{ P_i, \\Omega \\right\\} = 0&\\label{poinc1}\\\\\n&\\left\\{ \\mathcal{N}_i, P_j \\right\\} = \\Omega\\delta_{ij}+\\ell\\left((1+\\gamma-\\alpha)\\Omega^2+\\beta \\vec{P}^2\\right)\\delta_{ij}-\\ell\\left(\\gamma+\\beta-\\frac{1}{2}\\right)P_iP_j~,&\\label{poinc2}\\end{aligned}$$ where $\\Omega$, $P_i$ and $\\mathcal{N}_i$ are respectively time translation, space translation and boost generators.\\\nIt is easy to check that (\\[poinc1\\]),(\\[poinc2\\]) satisfy all Jacobi identities with $\\{ x , t \\} = 0$ and standard symplectic structure. ",
"And from (\\[poinc1\\]), (\\[poinc2\\]) one finds the following deformed on-shell relation: $$\\mathcal{C}_\\ell = \\Omega^2 - \\vec{P}^2 +\\ell( 2\\gamma \\Omega^3\n+ (1-2 \\gamma) \\Omega \\vec{P}^2 )~.\n\\label{casparam}$$ By a standard Hamiltonian analysis one finds [@bob; @kbob] from (\\[casparam\\]) that, in particular, the worldlines of massless particles ($\\mathcal{C}_\\ell=0$) are governed by $$(x-x_0)_i = (1-\\ell |\\vec{P}|) \\frac{P_i}{|\\vec{P}|} \\, (t-t_0)~.\\label{wordli}$$ The fact that the speed of massless particles here depends on momentum[^3] is the main intriguing feature of this relativistic framework, and was the subject of several investigations (see, [*e.g.*]{}, Refs.",
" [@jurekvelISOne; @gacMandaniciDANDREA; @mignemiVEL; @ghoshVEL]), including some which established the presence of longitudinal relative locality [@bob; @kbob; @leeINERTIALlimit; @arzkowaRelLoc].",
"\n\nThe relativity of locality is immediately seen upon studying the covariance under $\\alpha, \\beta, \\gamma$-deformed boosts of the worldlines (\\[wordli\\]). ",
"One finds [@bob] that an infinitesimal deformed boost with rapidity vector $\\xi_i$ acts as follows: $$\\begin{aligned}\n P_i' &=& P_i-\\xi_i\\Omega-\\ell\\xi_i(\\beta P^2+(1+\\gamma-\\alpha)\\Omega^2)-\\ell\\xi_k\\left(\\frac{1}{2}-\\beta-\\gamma\\right)P^kP_i \\label{tr1}\\\\\n t' &=& t-\\xi_ix^i-\\ell\\xi_i(\\alpha t P^i+2(1+\\gamma-\\alpha)x^i\\Omega)\\label{tr2}\\\\\n x_i' &=& x_i-\\xi_i t+\\ell(\\alpha\\xi_i t \\Omega + 2\\beta\\xi_k x^k P_i)-\\ell\\left(\\gamma+\\beta-\\frac{1}{2}\\right)(\\xi_kP^kx_i+\\xi_ix_kP^k)\\label{tr3}\\end{aligned}$$ We can now specialize these (\\[tr1\\]), (\\[tr2\\]) and (\\[tr3\\]) to the case of boosts along the direction $x$, which is the direction of motion of the particle according to (\\[wordli\\]), and it then follows that when a given observer Alice has the particle on the worldline (\\[wordli\\]) an observer boosted with respect to Alice along the $x$ direction sees the particle on the worldline $$(x'-x'_0)_i = (1-\\ell |\\vec{P'}|) \\frac{P'_i}{|\\vec{P'}|} \\, (t'-t'_0)~,\\label{wordli2}$$ indeed consistently with the relativistic nature of the framework.",
"\n\nAnd these results on the action of boosts also allow one to expose the relativity of spacetime locality. ",
"We first recall [@bob] that the absoluteness of spacetime locality amounts to the property that when one observer establishes that two events coincide then all other observers agree that those two events coincide.\\\nTo see that this is not the case in the framework under consideration, it suffices to consider two worldlines of massless particles with different energy, a “soft” one with momentum $p^{(s)}$ and a “hard” one with momentum $p^{(h)}$, emitted simultaneously from the origin of an observer Alice, so that we have a coincidence of (emission) events. ",
"A distant observer Bob at rest with respect to Alice would still describe the two emission events as coincident, but, using our prescription for boosting, a third observer Camilla, purely boosted with respect to Bob, would describe the two emission events as non-coincident. ",
"Details on the derivation of this relative-locality effect can be found in Ref.",
" [@bob], which focused on the case of a Bob-Camilla boost parallel to the Alice-Bob translation direction. ",
"And for that case Ref.",
" [@bob] exposed a “longitudinal relative locality\" in the sense that the nonlocality attributed to the emission events by distantly boosted observer Camilla was found to be along the direction connecting Camilla and the relevant pair of events.",
"\n\nTransverse effects\n==================\n\nOur next task is to summarize the results on “transverse relative locality\" of Ref.",
" [@transverse]. ",
"Again we want to first map the worldline (\\[wordli\\]), attributed to observer Alice, to the description of an observer Bob, purely translated with respect to Alice along the $x$ direction, but then we are interested in an observer Camilla purely boosted with respect to Bob along a direction $y$, orthogonal to $x$. Specializing our boost actions to the case of a boost purely in the $y$ direction[^4], we arrive at this Camilla worldline, which we characterize in the $x,y$ plane [@transverse]: $$\\begin{aligned}\ny^C(x^C)=-\\xi_y\\left(1-\\left(\\alpha-\\beta-\\gamma-\\frac{1}{2}\\right)\\ell p\\right)x^C-\\ell\\xi_y a p\\end{aligned}$$ where $\\xi_y$ is the boost parameter. ",
"Here we notice two main features that characterize this result with respect to the corresponding result that applies in the special-relativity limit ($\\ell \\rightarrow 0$):\\\n(I) when $\\ell\\xi_y a p$ is within the reach of available experimental sensitivities it will be appreciated that the worldline does not cross Camilla’s spatial origin, a feature we shall find convenient to label as “shift\";\\\n(II) when $\\ell\\xi_y p$ is within the reach of available angular resolutions (and $\\alpha-\\beta-\\gamma-\\frac{1}{2} \\neq 0$) the angle in the $x,y$ plane by which Camilla sees the arrival of the particle is momentum dependent, which is a feature that may be labeled “dual-gravity lensing\", following the terminology introduced in Ref.",
" [@leelaurentGRB], where an analogous feature was encountered in working with the relative-locality curved-momentum-space framework of Ref.",
" [@principle].\\\nBoth of these features in general contribute to the transverse relative locality: if one considers a simultaneous emission at Alice of two massless particles of different momentum our distantly transversely boosted observer Camilla ends up describing the two emission events as non-coincident and the lack of coincidence occurs along the $y$ direction (a direction orthogonal to the one connecting the observers Alice and Camilla).",
"\n\nParticularly striking are the effects of dual-gravity lensing: Alice sends out simultaneously two particles toward Camilla along the same direction, but Camilla ends up detecting them along non-parallel directions forming an angle [@transverse] $$\\theta \\simeq \\xi_y (\\alpha-\\beta-\\gamma-\\frac{1}{2}) \\, \\ell (p^{(h)} - p^{(s)}),$$ where notably the angle depends linearly on the difference of the momenta $(p^{(h)} - p^{(s)})$.\n\nIncidentally it is noteworthy that the feature of dual-gravity lensing exposed in Ref.",
" [@leelaurentGRB] was proportional to the sum of the energies(/momenta) of the two particles whose wordlines were experiencing lensing. ",
"It was already clear from Ref.",
" [@leelaurentGRB] that this result of dependence on the sum of energies had only been checked within a very specific setup for the derivation, including definite choices among the many possible chains of interactions that could be considered in the interacting-particle framework there being studied. ",
"The fact that Ref.",
" [@transverse], although within the limitations of a theory of free particles, found dual-gravity-lensing effects proportional to the difference of the energies(/momenta) of the two particles whose wordlines experience lensing can provide encouragement for the search of other chains of interactions, in which the difference of energies governs the dual-gravity lensing.",
"\n\nClosing remarks\n===============\n\nThe “theoretical evidence\" we here summarized on the basis of the results originally reported in Refs.",
" [@bob; @kbob; @transverse] suggests that transverse relative locality and longitudinal relative locality are in some ways rather different but may deserve equal priority in future investigations of relative locality. ",
"This intuition is based on relative-locality theories of free particles, but it is hard to imagine that for interacting relative-locality particles, which are described within the framework of Ref.",
" [@principle], the “balance of power\" between longitudinal and transverse relative locality could be significantly shifted.",
"\n\nAnother aspect which was here only considered somewhat implicitly is the relevance of relative locality for certain models with spacetime noncommutativity. ",
"There it will also be interesting to learn how relative locality interfaces with the most subtle aspects of those models, such as the need for adopting consistent ordering prescriptions [@aadbasis; @kowanowabasis; @meljaEPJ].",
"\n\nOf course, we are most excited about the potential implications for phenomenology. ",
"It was amusing to see that the possibility of DSR-deformations of relativistic symmetries played a significant role [@whataboutopera; @operaDSR; @synchroDSR; @fransDSROPERA; @yiDSROPERA; @dimitriDSROPERA] in the analysis of the apparent “OPERA anomaly\" for neutrinos of accelerator energies. ",
"But the truly significant prospects are the one for Planck-scale phenomenology, mostly exploiting observations of particles propagating over cosmological distances (see, [*e.g.*]{} Refs.",
" [@magicELLISnew; @unoEdue]). ",
"The relevance of longitudinal relative locality for such phenomenological studies was already established in Refs.",
" [@bob; @leelaurentGRB], and the theoretical evidence we here summarized may encourage attempts of seeking similar opportunities for transverse relative locality.",
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"\n\n[^1]: niccolo.loret@roma1.infn.it\n\n[^2]: giacomo.rosati@roma1.infn.it\n\n[^3]: The coefficients of the terms $\\ell \\Omega^3$ and $\\ell \\Omega \\vec{P}^2$ in $C_\\ell$ were arranged in Ref.",
" [@bob] just so that this speed law for massless particles, $1-\\ell |p|$, would be produced. ",
"This is how from the more general two-parameter case $\\mathcal{C}_\\ell = \\Omega^2 - \\vec{P}^2 +\\ell( \\gamma' \\Omega^3\n + \\gamma\" \\Omega \\vec{P}^2)$ one arrives at the one-parameter case considered here and in Ref.",
" [@bob]: $\\mathcal{C}_\\ell = \\Omega^2 - \\vec{P}^2 +\\ell( 2\\gamma \\Omega^3\n + (1-2 \\gamma) \\Omega \\vec{P}^2)$.\n\n[^4]: Notice that it may be useful to also note that the coordinate velocity for massless particles transforms under our boosts according to $$\\{\\mathcal{N}_j,(1-\\ell |\\vec{P}|) \\frac{P_i}{|\\vec{P}|} \\} = \\left( 1- \\ell \\left(\\alpha - \\beta - \\gamma -\\frac{1}{2}\\right)|\\vec{P}|\\right) \\left( \\delta_{ij}- \\frac{P_i P_j}{|\\vec{P}|^2} \\right) -\\ell \\delta_{ij} |\\vec{P}|.$$\n"
] | {
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"Jim Horne (Florida politician)\n\nJim Horne is a former Florida State Senator and Florida Commissioner of Education. ",
"He is an accountant and has worked in the real estate and consulting businesses. ",
"He resigned as Commissioner of Education in 2004.",
"\n\nHorne served in the Florida Legislature from 1995 to 2001 and was chairman of the Senate committee that handles the state budget. ",
"He represented Orange Park, Florida. ",
"The Florida Crossroads public television program spent a day with him while he served as Florida's education commissioner. ",
"He founded the Horne Group, a government consulting and business development company.",
"\n\nReferences\n\nCategory:Florida state senators\nCategory:People from Orange Park, Florida\nCategory:Year of birth missing (living people)\nCategory:Living people"
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"PlayStation Vita\n\nNews\n\nKingdom Hearts goes 3D for 3DS\n\nSquareEnix has revealed that one of its most popular franchises is set to make the leap into the third dimension with a new title for Nintendo's all-new 3DS.",
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"News, views and top stories in your inbox. ",
"Don't miss our must-read newsletter Sign up Thank you for subscribing We have more newsletters Show me See our privacy notice Invalid Email\n\nA teacher has been forced out of work after an online hate campaign was launched because she is a Sinn Fein councillor.",
"\n\nHer union rep said the woman has not been back to the Boys Model in North Belfast since a Facebook campaign started and graffiti appeared claiming she is not wanted at the school.",
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"\n\nThe message added that the school “declined to give any other information regarding her for private reasons”.",
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"\n\nThe message was followed by a number of comments including one person who said “I don’t want my son to take part in any of her classes”.",
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"\n\nHe added: “I can’t tell you how upset she is and how angry I am. ",
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"\n\nHe added: “This girl is only interested in carrying out her professional duties, she’s committed to this profession, she’s committed to these children and this assault on her on a social media site, and indeed in graffiti on a wall close to the school today, is all uncalled for.",
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"\n\nChris Hazzard added that no teacher “whatever their beliefs or religion, should be singled out and targeted in such a way”.",
"\n\nHe said: “It is now high time for Unionist political leaders to face down these rejectionist elements and come out to strongly defend the right of people to live and work free from sectarian harassment.”"
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"Tako-Tsubo syndrome: an important differential diagnosis in patients with acute chest pain.",
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"Significant obstructive coronary artery disease is absent. ",
"Owing to its clinical and imaging characteristics, TTC is frequently misdiagnosed as an acute coronary syndrome. ",
"Tako-Tsubo syndrome was first described in the 1990s in Japan, but meanwhile has been increasingly identified in other parts of the world also. ",
"TTC predominantly affects postmenopausal women, and may involve up to 2% of all patients with acute ST-segment elevation myocardial infarction (STEMI). ",
"Apart from single case reports, no systematic data from Austria are currently available. ",
"We analyzed prevalence, diagnostic characteristics and the clinical course of patients with TTC admitted to our cardiology department during a period of four years (May 2004 - December 2008). ",
"Diagnosis of TTC was established by the presence of the typical apical ballooning pattern of the left ventricle shown by ventriculography or echocardiography and by the absence of a significant coronary artery stenosis as demonstrated by coronary angiography. ",
"Among 448 patients with suspected acute STEMI and 963 patients with non-STEMI, 31 patients (2.2%) were diagnosed as having TTC. ",
"The majority of identified patients with TTC were postmenopausal women (90.3% women, mean age 75 +/- 10.2 years). ",
"At the time of acute hospital admission, the principal symptom was chest pain in 24 patients (77.4%), dyspnea in 10 (32.3%) and hypotension in one (3.2%). ",
"Preceding emotionally or physically stressful events were identified in 24 patients (77.4%: emotional 29%, physical 48.4%). ",
"Acute ST-segment elevation was present in 13 patients (42%) and ST/T wave abnormalities were found in 18 (58%). ",
"All patients demonstrated a distinct increase in levels of cardiac enzymes and biomarkers. ",
"Significant coronary artery stenosis was absent in all patients. ",
"After a clinical follow-up period of 172.4 +/- 342.8 days, three patients had died from non-cardiac causes, TTC had recurred in another patient 13 months after the index event, and the other 27 patients were free from cardiac symptoms and the electrocardiographic and echocardiographic abnormalities had resolved. ",
"Patients with TTC display clinical symptoms and electrocardiographic findings that mimic acute myocardial infarction. ",
"A history of a preceding stressful event in elderly women, typical echocardiographic findings of TTC, and only a mild elevation of cardiac markers will be informative. ",
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"About SmallBizDaily\nSmallBizDaily is powered by three people with a passion for entrepreneurship: Rieva Lesonsky, Maria Valdez Haubrich and Karen Axelton. ",
"We met at EntrepreneurMagazine nearly 25 years ago, when Rieva hired the rest of us as editors. ",
"We’ve been a great team ever since, so when Rieva decided it was time for her to stop talking about entrepreneurship and start living it, she naturally turned to us to be her business partners.",
"\n\nAt SmallBizDaily, we combine our decades of experience reading and writing about entrepreneurship with our new experience as startup entrepreneurs to share our unique take on the world of small business.",
"\n\nAbout Rieva Lesonsky\n\nRieva Lesonsky is CEO of GrowBiz Media, a content and consulting company specializing in small businesses and entrepreneurship. ",
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"Prior to co-founding GrowBiz Media in 2008, she was SVP/Editorial Director of Entrepreneur Magazine.",
"\n\nRieva’s energy and enthusiasm have helped inspire entrepreneurs nationwide. ",
"A nationally recognized speaker who regularly addresses audiences across the country, she has appeared on hundreds of radio shows and numerous local and national television programs, including CNN, Good Morning America, the Today Show, Fox Business News, The Martha Stewart show and Oprah and can regularly be seen on MSNBC’s Your Business. ",
"Rieva is also the author of several books about small business and entrepreneurship, including the bestseller Start Your Own Business.",
"\n\nIn addition to blogging on SmallBizDaily, Rieva regularly writes about small business for print and digital outlets including SCORE, Small Business Trends, SBA.gov, Network Solutions/Web.com, ReadWrite, American Express OPEN Forum, AT&T, Success Magazine and Groupon. ",
"She has been named to Folio Magazine’s “Folio 40” list, which honors publishing’s top innovators; has been named a Small Business Influencer by SmallBusinessTrends.com; and has been inducted into the Business Journalism Hall of Fame.",
"\n\nMany organizations have recognized Rieva’s tireless devotion to helping entrepreneurs. ",
"She served on the Small Business Administration’s National Advisory Council for six years, and was honored by the SBA as a Small Business Media Advocate and a Woman in Business Advocate. ",
"The Collegiate Entrepreneurs Organization honored her for helping drive “the entrepreneurial revolution in secondary education,” and the ASBDC awarded her a “Champion of Small Business” award. ",
"She has received the “Champion of Small Business” award from the Association of Small Business Development Centers (ASBDC) and the 2012 Lou Campanelli Award from SCORE in recognition of outstanding leadership, vision and philanthropy in support of small business and entrepreneurship.",
"\n\nAbout Maria Valdez HaubrichMaria Valdez Haubrich is former Executive Editor of Entrepreneur Magazine, where she worked for over 20 years. ",
"At Entrepreneur, Maria’s savvy marketing mind helped develop custom publications, online content and other editorial products for B-to-B marketers seeking to reach small-business owners. ",
"Along the way, she’s learned a lot about everything from printing, design and production to project management, tech troubleshooting and how to work a trade show booth.",
"\n\nAbout Karen AxeltonKaren Axelton is former Executive Editor of Entrepreneur Magazine and former Editor of Entrepreneur.com. ",
"Karen has been tracking small-business trends for more than 20 years. ",
"She loves finding out about innovative entrepreneurs, business ideas and marketing methods, as well as consumer and demographic trends. ",
"A former marketing copywriter, Karen once spent six months working at a big corporation, where she discovered that for many people, “Dilbert” isn’t a joke. ",
"The experience inspired her to support small businesses in any way possible."
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"This invention relates to a system in which a number of machines are coupled together, in particular, but not exclusively, this invention relates to an office network system in which items of office equipment such as photocopiers, facsimile machines, printers, personal computers and the like are coupled to a server."
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"An armored battle station the size of a small moon, the Death Star packed enough firepower to destroy planets. ",
"Alliance researchers have uncovered many of the secrets of the most devastating weapon in galactic history, and gathered the information together in this one volume. ",
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"Q:\n\nhow to disable Pull-Up-Refresh in PullToRefreshScrollView?",
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"\nIt includes PullDownToRefresh and PullUpToRefresh,but I don't need the PullUpToRefresh since I get a Bottom MenuDrawer; \nI guess there might be a parameter to store the refresh action in the source code.",
"Please help me to solve this problem\n\nA:\n\nIn the README file of the project, there is this link: https://github.com/chrisbanes/Android-PullToRefresh#pull-up-to-refresh\nIf you want to disable the PullUpToRefresh behavior, you can call yourView.setMode(Mode.",
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"\n\n\n\nTHE respectable Companion, Hudhayfah Bin Yaman stated, \"Individuals used to ask the Prophet (peace be upon him) about great things, yet I used to get some information about awful things since I was worried about the possibility that they may surpass me.\" ",
"What a lovely case to take after! ",
"What's more, therefore, on a comparable note, I have recorded a portion to a great degree normal misstep that scores of individuals make, after quite a long time, with the goal that we can be tired of them and shield and keep ourselves from making them. ",
"Along these lines Insha Allah our Haj will be nearer to the Sunnah and more acceptable to Allah.",
"\n\n\n\n\n\nMistake #1:\n\nThinking that Du'a is acknowledged at first look of the Ka'bahMany individuals have the wrong thought that the first occasion when they take a gander at the Ka'bah, any Du'a that they make will be replied. ",
"Not genuine! ",
"This has no proof from the Shariah. ",
"What's more, any Hadith that one may discover with respect to this issue is either amazingly powerless or manufactured. ",
"At the point when gotten some information about Du'a being acknowledged at the principal site of the Ka'bah, Sheik Sa'd Al-Humayd answered: \"This is not valid; there must be confirmed for this to be valid, in light of the fact that demonstrations of love should just be founded on proving. ",
"Also, that confirmation must be Sahih all by itself and it ought to be clear and unambiguous. ",
"What's more, Allah knows best.\"",
"\n\n\n\n\n\nMistake #2:\n\n\"Kissing\" the Black Stone from far away and stopping amid Tawaf to do as such, Kissing the Black Stone is a delightful Sunnah and respect without a doubt for the person who can do as such. ",
"Be that as it may, because of the huge group, a greater part of the general population can't achieve it. ",
"Such a variety of individuals attempt to \"kiss\" it from far away. ",
"When they are in accordance with the Black Stone, they stop in their tracks amid Tawaf, face the Black Stone, set up the two hands in favour of their head and \"kiss\" the Black Stone in the air, as though the Black Stone were directly before them. ",
"Or, on the other hand, they toss 'flying kisses' at the Black Stone.",
"\n\n\n\n\n\nOther than being a wrong work on, halting the stream of Tawaf causes interruption and pointless jamming around there, accordingly making a lot of inconvenience to fellow pilgrims. '",
"Separation kissing' is not from the Sunnah obviously. ",
"All the Prophet (peace be upon him) did while doing Tawaf was kiss the Black Stone if he easily could do so, or touch it with his hand and kiss his hand. ",
"In any case, when it was crowded, he just indicated it from far away and stated, \"Allahu Akbar.\" ",
"That's it.",
"\n\n\n\n\n\nIt was narrated that Abu Tufayl (may Allah be satisfied with him) stated, \"I saw the Messenger of Allah (peace be upon him) perform Tawaf around the House, touching the corner (where the Black Stone is) with a crooked staff which he had with him, at that point kissing the staff.\" (",
"Sahih Muslim) Ibn Abbas stated, \"The Messenger of Allah (peace be upon him) performed Tawaf on his camel, and each time he went to the corner (where the Black Stone is) he would point to it and say, Allahu Akbar.\" (",
"Al-Bukhari, no. ",
"4987) That's all we have to do.",
"\n\n\n\n\n\nIf we are far from the Black Stone, we should point to it with our right hand, say Allahu Akbar and proceed onward. ",
"No confronting the Ka'bah, no 'separation kissing', no leaving dead speechless. ",
"Continue moving and don't disturb the stream of the Tawaf. ",
"Sheik Bin Baz stated, \"It ought to be noticed that the Tawaf remains splendidly substantial without kissing the Black Stone. ",
"If one doesn't or can't kiss the Black Stone. ",
"it is adequate essentially to point to it, saying 'Allahu Akbar' when one comes parallel to it, albeit one might be at a separation from it.\" (",
"Fatawa Bin Baz)\n\n\n\n\n\nMistake #3:\n\n\n\n\n\nShouting out Du'a in unison Some individuals yell as loud as possible, as one, while making Du'a amid Tawaf. ",
"They follow an Imam or a leader who says out various Du'as so anyone might hear, and afterwards the followers all repeat after him in unison. ",
"This causes a lot of confusion and disturbs others engaged in their own Du’as, making them lose\n\nand Khushoo'. ",
"What's more, clearly, it is likewise not befitting that one should shout and bring his voice up in a place so sacred as the Haram. ",
"The best thing to do is to know before you go for Tawaf, the Du'as that you need to make, the Qur'an you need to present, and so forth.",
"\n\n\n\n\n\n\n\n\n\nAlong these lines, you won't need to tail anyone and you will be making your own Du'a, in your own dialect, from your own heart. ",
"It will give you better fixation and fulfilment. ",
"Plan your Du'as early, rehash them to yourself, with lowliness and Khushoo'. ",
"All things considered, you're making Du'a to the One Who hears all and sees all. ",
"The Prophet (peace be upon him) stated, \"Every last one of you is speaking with his Lord, so don't disturb each other or raise your voices more than each other when reading (or he said) while praying.\" (",
"Abu Dawood, Sahih by Al-Albani).",
"\n\n\n\n\n\nConclusion:\n\n\n\n\n\nUmrah and Hajj are blessings for Muslims and Allah\n\npromised to give great rewards to those who perform Umrah with true intention. ",
"So, everyone should try to perform Umrah with lesser mistakes and with a true heart. ",
"Life is too short and it never gave second chance. ",
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"ABI-tag\", SHT_NOTE, SHF_ALLOC, 0x40021c, 0x21c, 0x20, 0x0, 0x0, 0x4, 0x0, 0x20},\n\t\t\t{\".hash\", SHT_HASH, SHF_ALLOC, 0x400240, 0x240, 0x24, 0x5, 0x0, 0x8, 0x4, 0x24},\n\t\t\t{\".gnu.hash\", SHT_LOOS + 268435446, SHF_ALLOC, 0x400268, 0x268, 0x1c, 0x5, 0x0, 0x8, 0x0, 0x1c},\n\t\t\t{\".dynsym\", SHT_DYNSYM, SHF_ALLOC, 0x400288, 0x288, 0x60, 0x6, 0x1, 0x8, 0x18, 0x60},\n\t\t\t{\".dynstr\", SHT_STRTAB, SHF_ALLOC, 0x4002e8, 0x2e8, 0x3d, 0x0, 0x0, 0x1, 0x0, 0x3d},\n\t\t\t{\".gnu.version\", SHT_HIOS, SHF_ALLOC, 0x400326, 0x326, 0x8, 0x5, 0x0, 0x2, 0x2, 0x8},\n\t\t\t{\".gnu.version_r\", SHT_LOOS + 268435454, SHF_ALLOC, 0x400330, 0x330, 0x20, 0x6, 0x1, 0x8, 0x0, 0x20},\n\t\t\t{\".rela.dyn\", SHT_RELA, SHF_ALLOC, 0x400350, 0x350, 0x18, 0x5, 0x0, 0x8, 0x18, 0x18},\n\t\t\t{\".rela.plt\", SHT_RELA, SHF_ALLOC, 0x400368, 0x368, 0x30, 0x5, 0xc, 0x8, 0x18, 0x30},\n\t\t\t{\".init\", SHT_PROGBITS, SHF_ALLOC + SHF_EXECINSTR, 0x400398, 0x398, 0x18, 0x0, 0x0, 0x4, 0x0, 0x18},\n\t\t\t{\".plt\", SHT_PROGBITS, SHF_ALLOC + SHF_EXECINSTR, 0x4003b0, 0x3b0, 0x30, 0x0, 0x0, 0x4, 0x10, 0x30},\n\t\t\t{\".text\", SHT_PROGBITS, SHF_ALLOC + SHF_EXECINSTR, 0x4003e0, 0x3e0, 0x1b4, 0x0, 0x0, 0x10, 0x0, 0x1b4},\n\t\t\t{\".fini\", SHT_PROGBITS, SHF_ALLOC + SHF_EXECINSTR, 0x400594, 0x594, 0xe, 0x0, 0x0, 0x4, 0x0, 0xe},\n\t\t\t{\".rodata\", SHT_PROGBITS, SHF_ALLOC, 0x4005a4, 0x5a4, 0x11, 0x0, 0x0, 0x4, 0x0, 0x11},\n\t\t\t{\".eh_frame_hdr\", SHT_PROGBITS, SHF_ALLOC, 0x4005b8, 0x5b8, 0x24, 0x0, 0x0, 0x4, 0x0, 0x24},\n\t\t\t{\".eh_frame\", SHT_PROGBITS, SHF_ALLOC, 0x4005e0, 0x5e0, 0xa4, 0x0, 0x0, 0x8, 0x0, 0xa4},\n\t\t\t{\".ctors\", SHT_PROGBITS, SHF_WRITE + SHF_ALLOC, 0x600688, 0x688, 0x10, 0x0, 0x0, 0x8, 0x0, 0x10},\n\t\t\t{\".dtors\", SHT_PROGBITS, SHF_WRITE + SHF_ALLOC, 0x600698, 0x698, 0x10, 0x0, 0x0, 0x8, 0x0, 0x10},\n\t\t\t{\".jcr\", SHT_PROGBITS, SHF_WRITE + SHF_ALLOC, 0x6006a8, 0x6a8, 0x8, 0x0, 0x0, 0x8, 0x0, 0x8},\n\t\t\t{\".dynamic\", SHT_DYNAMIC, SHF_WRITE + SHF_ALLOC, 0x6006b0, 0x6b0, 0x1a0, 0x6, 0x0, 0x8, 0x10, 0x1a0},\n\t\t\t{\".got\", SHT_PROGBITS, SHF_WRITE + SHF_ALLOC, 0x600850, 0x850, 0x8, 0x0, 0x0, 0x8, 0x8, 0x8},\n\t\t\t{\".got.plt\", SHT_PROGBITS, SHF_WRITE + SHF_ALLOC, 0x600858, 0x858, 0x28, 0x0, 0x0, 0x8, 0x8, 0x28},\n\t\t\t{\".data\", SHT_PROGBITS, SHF_WRITE + SHF_ALLOC, 0x600880, 0x880, 0x18, 0x0, 0x0, 0x8, 0x0, 0x18},\n\t\t\t{\".bss\", SHT_NOBITS, SHF_WRITE + SHF_ALLOC, 0x600898, 0x898, 0x8, 0x0, 0x0, 0x4, 0x0, 0x8},\n\t\t\t{\".comment\", SHT_PROGBITS, 0x0, 0x0, 0x898, 0x126, 0x0, 0x0, 0x1, 0x0, 0x126},\n\t\t\t{\".debug_aranges\", SHT_PROGBITS, 0x0, 0x0, 0x9c0, 0x90, 0x0, 0x0, 0x10, 0x0, 0x90},\n\t\t\t{\".debug_pubnames\", SHT_PROGBITS, 0x0, 0x0, 0xa50, 0x25, 0x0, 0x0, 0x1, 0x0, 0x25},\n\t\t\t{\".debug_info\", SHT_PROGBITS, 0x0, 0x0, 0xa75, 0x1a7, 0x0, 0x0, 0x1, 0x0, 0x1a7},\n\t\t\t{\".debug_abbrev\", SHT_PROGBITS, 0x0, 0x0, 0xc1c, 0x6f, 0x0, 0x0, 0x1, 0x0, 0x6f},\n\t\t\t{\".debug_line\", SHT_PROGBITS, 0x0, 0x0, 0xc8b, 0x13f, 0x0, 0x0, 0x1, 0x0, 0x13f},\n\t\t\t{\".debug_str\", SHT_PROGBITS, SHF_MERGE + SHF_STRINGS, 0x0, 0xdca, 0xb1, 0x0, 0x0, 0x1, 0x1, 0xb1},\n\t\t\t{\".debug_ranges\", SHT_PROGBITS, 0x0, 0x0, 0xe80, 0x90, 0x0, 0x0, 0x10, 0x0, 0x90},\n\t\t\t{\".shstrtab\", SHT_STRTAB, 0x0, 0x0, 0xf10, 0x149, 0x0, 0x0, 0x1, 0x0, 0x149},\n\t\t\t{\".symtab\", SHT_SYMTAB, 0x0, 0x0, 0x19a0, 0x6f0, 0x24, 0x39, 0x8, 0x18, 0x6f0},\n\t\t\t{\".strtab\", SHT_STRTAB, 0x0, 0x0, 0x2090, 0x1fc, 0x0, 0x0, 0x1, 0x0, 0x1fc},\n\t\t},\n\t\t[]ProgHeader{\n\t\t\t{PT_PHDR, PF_R + PF_X, 0x40, 0x400040, 0x400040, 0x1c0, 0x1c0, 0x8},\n\t\t\t{PT_INTERP, PF_R, 0x200, 0x400200, 0x400200, 0x1c, 0x1c, 1},\n\t\t\t{PT_LOAD, PF_R + PF_X, 0x0, 0x400000, 0x400000, 0x684, 0x684, 0x200000},\n\t\t\t{PT_LOAD, PF_R + PF_W, 0x688, 0x600688, 0x600688, 0x210, 0x218, 0x200000},\n\t\t\t{PT_DYNAMIC, PF_R + PF_W, 0x6b0, 0x6006b0, 0x6006b0, 0x1a0, 0x1a0, 0x8},\n\t\t\t{PT_NOTE, PF_R, 0x21c, 0x40021c, 0x40021c, 0x20, 0x20, 0x4},\n\t\t\t{PT_LOOS + 0x474E550, PF_R, 0x5b8, 0x4005b8, 0x4005b8, 0x24, 0x24, 0x4},\n\t\t\t{PT_LOOS + 0x474E551, PF_R + PF_W, 0x0, 0x0, 0x0, 0x0, 0x0, 0x8},\n\t\t},\n\t\t[]string{\"libc.so.6\"},\n\t},\n\t{\n\t\t\"testdata/hello-world-core.gz\",\n\t\tFileHeader{ELFCLASS64, ELFDATA2LSB, EV_CURRENT, ELFOSABI_NONE, 0x0, binary.",
"LittleEndian, ET_CORE, EM_X86_64, 0x0},\n\t\t[]SectionHeader{},\n\t\t[]ProgHeader{\n\t\t\t{Type: PT_NOTE, Flags: 0x0, Off: 0x3f8, Vaddr: 0x0, Paddr: 0x0, Filesz: 0x8ac, Memsz: 0x0, Align: 0x0},\n\t\t\t{Type: PT_LOAD, Flags: PF_X + PF_R, Off: 0x1000, Vaddr: 0x400000, Paddr: 0x0, Filesz: 0x0, Memsz: 0x1000, Align: 0x1000},\n\t\t\t{Type: PT_LOAD, Flags: PF_R, Off: 0x1000, Vaddr: 0x401000, Paddr: 0x0, Filesz: 0x1000, Memsz: 0x1000, Align: 0x1000},\n\t\t\t{Type: PT_LOAD, Flags: PF_W + PF_R, Off: 0x2000, Vaddr: 0x402000, Paddr: 0x0, Filesz: 0x1000, Memsz: 0x1000, Align: 0x1000},\n\t\t\t{Type: PT_LOAD, Flags: PF_X + PF_R, Off: 0x3000, Vaddr: 0x7f54078b8000, Paddr: 0x0, Filesz: 0x0, Memsz: 0x1b5000, Align: 0x1000},\n\t\t\t{Type: PT_LOAD, Flags: 0x0, Off: 0x3000, Vaddr: 0x7f5407a6d000, Paddr: 0x0, Filesz: 0x0, Memsz: 0x1ff000, Align: 0x1000},\n\t\t\t{Type: PT_LOAD, Flags: PF_R, Off: 0x3000, Vaddr: 0x7f5407c6c000, Paddr: 0x0, Filesz: 0x4000, Memsz: 0x4000, Align: 0x1000},\n\t\t\t{Type: PT_LOAD, Flags: PF_W + PF_R, Off: 0x7000, Vaddr: 0x7f5407c70000, Paddr: 0x0, Filesz: 0x2000, Memsz: 0x2000, Align: 0x1000},\n\t\t\t{Type: PT_LOAD, Flags: PF_W + PF_R, Off: 0x9000, Vaddr: 0x7f5407c72000, Paddr: 0x0, Filesz: 0x5000, Memsz: 0x5000, Align: 0x1000},\n\t\t\t{Type: PT_LOAD, Flags: PF_X + PF_R, Off: 0xe000, Vaddr: 0x7f5407c77000, Paddr: 0x0, Filesz: 0x0, Memsz: 0x22000, Align: 0x1000},\n\t\t\t{Type: PT_LOAD, Flags: PF_W + PF_R, Off: 0xe000, Vaddr: 0x7f5407e81000, Paddr: 0x0, Filesz: 0x3000, Memsz: 0x3000, Align: 0x1000},\n\t\t\t{Type: PT_LOAD, Flags: PF_W + PF_R, Off: 0x11000, Vaddr: 0x7f5407e96000, Paddr: 0x0, Filesz: 0x3000, Memsz: 0x3000, Align: 0x1000},\n\t\t\t{Type: PT_LOAD, Flags: PF_R, Off: 0x14000, Vaddr: 0x7f5407e99000, Paddr: 0x0, Filesz: 0x1000, Memsz: 0x1000, Align: 0x1000},\n\t\t\t{Type: PT_LOAD, Flags: PF_W + PF_R, Off: 0x15000, Vaddr: 0x7f5407e9a000, Paddr: 0x0, Filesz: 0x2000, Memsz: 0x2000, Align: 0x1000},\n\t\t\t{Type: PT_LOAD, Flags: PF_W + PF_R, Off: 0x17000, Vaddr: 0x7fff79972000, Paddr: 0x0, Filesz: 0x23000, Memsz: 0x23000, Align: 0x1000},\n\t\t\t{Type: PT_LOAD, Flags: PF_X + PF_R, Off: 0x3a000, Vaddr: 0x7fff799f8000, Paddr: 0x0, Filesz: 0x1000, Memsz: 0x1000, Align: 0x1000},\n\t\t\t{Type: PT_LOAD, Flags: PF_X + PF_R, Off: 0x3b000, Vaddr: 0xffffffffff600000, Paddr: 0x0, Filesz: 0x1000, Memsz: 0x1000, Align: 0x1000},\n\t\t},\n\t\tnil,\n\t},\n\t{\n\t\t\"testdata/compressed-32.obj\",\n\t\tFileHeader{ELFCLASS32, ELFDATA2LSB, EV_CURRENT, ELFOSABI_NONE, 0x0, binary.",
"LittleEndian, ET_REL, EM_386, 0x0},\n\t\t[]SectionHeader{\n\t\t\t{\"\", SHT_NULL, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0},\n\t\t\t{\".text\", SHT_PROGBITS, SHF_ALLOC | SHF_EXECINSTR, 0x0, 0x34, 0x17, 0x0, 0x0, 0x1, 0x0, 0x17},\n\t\t\t{\".rel.text\", SHT_REL, SHF_INFO_LINK, 0x0, 0x3dc, 0x10, 0x13, 0x1, 0x4, 0x8, 0x10},\n\t\t\t{\".data\", SHT_PROGBITS, SHF_WRITE | SHF_ALLOC, 0x0, 0x4b, 0x0, 0x0, 0x0, 0x1, 0x0, 0x0},\n\t\t\t{\".bss\", SHT_NOBITS, SHF_WRITE | SHF_ALLOC, 0x0, 0x4b, 0x0, 0x0, 0x0, 0x1, 0x0, 0x0},\n\t\t\t{\".rodata\", SHT_PROGBITS, SHF_ALLOC, 0x0, 0x4b, 0xd, 0x0, 0x0, 0x1, 0x0, 0xd},\n\t\t\t{\".debug_info\", SHT_PROGBITS, SHF_COMPRESSED, 0x0, 0x58, 0xb4, 0x0, 0x0, 0x1, 0x0, 0x84},\n\t\t\t{\".rel.debug_info\", SHT_REL, SHF_INFO_LINK, 0x0, 0x3ec, 0xa0, 0x13, 0x6, 0x4, 0x8, 0xa0},\n\t\t\t{\".debug_abbrev\", SHT_PROGBITS, 0x0, 0x0, 0xdc, 0x5a, 0x0, 0x0, 0x1, 0x0, 0x5a},\n\t\t\t{\".debug_aranges\", SHT_PROGBITS, 0x0, 0x0, 0x136, 0x20, 0x0, 0x0, 0x1, 0x0, 0x20},\n\t\t\t{\".rel.debug_aranges\", SHT_REL, SHF_INFO_LINK, 0x0, 0x48c, 0x10, 0x13, 0x9, 0x4, 0x8, 0x10},\n\t\t\t{\".debug_line\", SHT_PROGBITS, 0x0, 0x0, 0x156, 0x5c, 0x0, 0x0, 0x1, 0x0, 0x5c},\n\t\t\t{\".rel.debug_line\", SHT_REL, SHF_INFO_LINK, 0x0, 0x49c, 0x8, 0x13, 0xb, 0x4, 0x8, 0x8},\n\t\t\t{\".debug_str\", SHT_PROGBITS, SHF_MERGE | SHF_STRINGS | SHF_COMPRESSED, 0x0, 0x1b2, 0x10f, 0x0, 0x0, 0x1, 0x1, 0xb3},\n\t\t\t{\".comment\", SHT_PROGBITS, SHF_MERGE | SHF_STRINGS, 0x0, 0x265, 0x2a, 0x0, 0x0, 0x1, 0x1, 0x2a},\n\t\t\t{\".note.",
"GNU-stack\", SHT_PROGBITS, 0x0, 0x0, 0x28f, 0x0, 0x0, 0x0, 0x1, 0x0, 0x0},\n\t\t\t{\".eh_frame\", SHT_PROGBITS, SHF_ALLOC, 0x0, 0x290, 0x38, 0x0, 0x0, 0x4, 0x0, 0x38},\n\t\t\t{\".rel.eh_frame\", SHT_REL, SHF_INFO_LINK, 0x0, 0x4a4, 0x8, 0x13, 0x10, 0x4, 0x8, 0x8},\n\t\t\t{\".shstrtab\", SHT_STRTAB, 0x0, 0x0, 0x4ac, 0xab, 0x0, 0x0, 0x1, 0x0, 0xab},\n\t\t\t{\".symtab\", SHT_SYMTAB, 0x0, 0x0, 0x2c8, 0x100, 0x14, 0xe, 0x4, 0x10, 0x100},\n\t\t\t{\".strtab\", SHT_STRTAB, 0x0, 0x0, 0x3c8, 0x13, 0x0, 0x0, 0x1, 0x0, 0x13},\n\t\t},\n\t\t[]ProgHeader{},\n\t\tnil,\n\t},\n\t{\n\t\t\"testdata/compressed-64.obj\",\n\t\tFileHeader{ELFCLASS64, ELFDATA2LSB, EV_CURRENT, ELFOSABI_NONE, 0x0, binary.",
"LittleEndian, ET_REL, EM_X86_64, 0x0},\n\t\t[]SectionHeader{\n\t\t\t{\"\", SHT_NULL, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0},\n\t\t\t{\".text\", SHT_PROGBITS, SHF_ALLOC | SHF_EXECINSTR, 0x0, 0x40, 0x1b, 0x0, 0x0, 0x1, 0x0, 0x1b},\n\t\t\t{\".rela.text\", SHT_RELA, SHF_INFO_LINK, 0x0, 0x488, 0x30, 0x13, 0x1, 0x8, 0x18, 0x30},\n\t\t\t{\".data\", SHT_PROGBITS, SHF_WRITE | SHF_ALLOC, 0x0, 0x5b, 0x0, 0x0, 0x0, 0x1, 0x0, 0x0},\n\t\t\t{\".bss\", SHT_NOBITS, SHF_WRITE | SHF_ALLOC, 0x0, 0x5b, 0x0, 0x0, 0x0, 0x1, 0x0, 0x0},\n\t\t\t{\".rodata\", SHT_PROGBITS, SHF_ALLOC, 0x0, 0x5b, 0xd, 0x0, 0x0, 0x1, 0x0, 0xd},\n\t\t\t{\".debug_info\", SHT_PROGBITS, SHF_COMPRESSED, 0x0, 0x68, 0xba, 0x0, 0x0, 0x1, 0x0, 0x72},\n\t\t\t{\".rela.debug_info\", SHT_RELA, SHF_INFO_LINK, 0x0, 0x4b8, 0x1c8, 0x13, 0x6, 0x8, 0x18, 0x1c8},\n\t\t\t{\".debug_abbrev\", SHT_PROGBITS, 0x0, 0x0, 0xda, 0x5c, 0x0, 0x0, 0x1, 0x0, 0x5c},\n\t\t\t{\".debug_aranges\", SHT_PROGBITS, SHF_COMPRESSED, 0x0, 0x136, 0x30, 0x0, 0x0, 0x1, 0x0, 0x2f},\n\t\t\t{\".rela.debug_aranges\", SHT_RELA, SHF_INFO_LINK, 0x0, 0x680, 0x30, 0x13, 0x9, 0x8, 0x18, 0x30},\n\t\t\t{\".debug_line\", SHT_PROGBITS, 0x0, 0x0, 0x165, 0x60, 0x0, 0x0, 0x1, 0x0, 0x60},\n\t\t\t{\".rela.debug_line\", SHT_RELA, SHF_INFO_LINK, 0x0, 0x6b0, 0x18, 0x13, 0xb, 0x8, 0x18, 0x18},\n\t\t\t{\".debug_str\", SHT_PROGBITS, SHF_MERGE | SHF_STRINGS | SHF_COMPRESSED, 0x0, 0x1c5, 0x104, 0x0, 0x0, 0x1, 0x1, 0xc3},\n\t\t\t{\".comment\", SHT_PROGBITS, SHF_MERGE | SHF_STRINGS, 0x0, 0x288, 0x2a, 0x0, 0x0, 0x1, 0x1, 0x2a},\n\t\t\t{\".note.",
"GNU-stack\", SHT_PROGBITS, 0x0, 0x0, 0x2b2, 0x0, 0x0, 0x0, 0x1, 0x0, 0x0},\n\t\t\t{\".eh_frame\", SHT_PROGBITS, SHF_ALLOC, 0x0, 0x2b8, 0x38, 0x0, 0x0, 0x8, 0x0, 0x38},\n\t\t\t{\".rela.eh_frame\", SHT_RELA, SHF_INFO_LINK, 0x0, 0x6c8, 0x18, 0x13, 0x10, 0x8, 0x18, 0x18},\n\t\t\t{\".shstrtab\", SHT_STRTAB, 0x0, 0x0, 0x6e0, 0xb0, 0x0, 0x0, 0x1, 0x0, 0xb0},\n\t\t\t{\".symtab\", SHT_SYMTAB, 0x0, 0x0, 0x2f0, 0x180, 0x14, 0xe, 0x8, 0x18, 0x180},\n\t\t\t{\".strtab\", SHT_STRTAB, 0x0, 0x0, 0x470, 0x13, 0x0, 0x0, 0x1, 0x0, 0x13},\n\t\t},\n\t\t[]ProgHeader{},\n\t\tnil,\n\t},\n}\n\nfunc TestOpen(t *testing.",
"T) {\n\tfor i := range fileTests {\n\t\ttt := &fileTests[i]\n\n\t\tvar f *File\n\t\tvar err error\n\t\tif path.",
"Ext(tt.file) == \".gz\" {\n\t\t\tvar r io.",
"ReaderAt\n\t\t\tif r, err = decompress(tt.file); err == nil {\n\t\t\t\tf, err = NewFile(r)\n\t\t\t}\n\t\t} else {\n\t\t\tf, err = Open(tt.file)\n\t\t}\n\t\tif err !",
"= nil {\n\t\t\tt.Errorf(\"cannot open file %s: %v\", tt.file, err)\n\t\t\tcontinue\n\t\t}\n\t\tdefer f.Close()\n\t\tif !",
"reflect.",
"DeepEqual(f.",
"FileHeader, tt.hdr) {\n\t\t\tt.Errorf(\"open %s:\\n\\thave %#v\\n\\twant %#v\\n\", tt.file, f.FileHeader, tt.hdr)\n\t\t\tcontinue\n\t\t}\n\t\tfor i, s := range f.Sections {\n\t\t\tif i >= len(tt.sections) {\n\t\t\t\tbreak\n\t\t\t}\n\t\t\tsh := &tt.sections[i]\n\t\t\tif !",
"reflect.",
"DeepEqual(&s.",
"SectionHeader, sh) {\n\t\t\t\tt.Errorf(\"open %s, section %d:\\n\\thave %#v\\n\\twant %#v\\n\", tt.file, i, &s.SectionHeader, sh)\n\t\t\t}\n\t\t}\n\t\tfor i, p := range f.Progs {\n\t\t\tif i >= len(tt.progs) {\n\t\t\t\tbreak\n\t\t\t}\n\t\t\tph := &tt.progs[i]\n\t\t\tif !",
"reflect.",
"DeepEqual(&p.",
"ProgHeader, ph) {\n\t\t\t\tt.Errorf(\"open %s, program %d:\\n\\thave %#v\\n\\twant %#v\\n\", tt.file, i, &p.ProgHeader, ph)\n\t\t\t}\n\t\t}\n\t\ttn := len(tt.sections)\n\t\tfn := len(f.",
"Sections)\n\t\tif tn !",
"= fn {\n\t\t\tt.Errorf(\"open %s: len(Sections) = %d, want %d\", tt.file, fn, tn)\n\t\t}\n\t\ttn = len(tt.progs)\n\t\tfn = len(f.",
"Progs)\n\t\tif tn !",
"= fn {\n\t\t\tt.Errorf(\"open %s: len(Progs) = %d, want %d\", tt.file, fn, tn)\n\t\t}\n\t\ttl := tt.needed\n\t\tfl, err := f.ImportedLibraries()\n\t\tif err !",
"= nil {\n\t\t\tt.Error(err)\n\t\t}\n\t\tif !",
"reflect.",
"DeepEqual(tl, fl) {\n\t\t\tt.Errorf(\"open %s: DT_NEEDED = %v, want %v\", tt.file, tl, fl)\n\t\t}\n\t}\n}\n\n// elf.",
"NewFile requires io.",
"ReaderAt, which compress/gzip cannot\n// provide. ",
"Decompress the file to a bytes.",
"Reader.",
"\nfunc decompress(gz string) (io.",
"ReaderAt, error) {\n\tin, err := os.",
"Open(gz)\n\tif err !",
"= nil {\n\t\treturn nil, err\n\t}\n\tdefer in.",
"Close()\n\tr, err := gzip.",
"NewReader(in)\n\tif err !",
"= nil {\n\t\treturn nil, err\n\t}\n\tvar out bytes.",
"Buffer\n\t_, err = io.",
"Copy(&out, r)\n\treturn bytes.",
"NewReader(out.",
"Bytes()), err\n}\n\ntype relocationTestEntry struct {\n\tentryNumber int\n\tentry *dwarf.",
"Entry\n}\n\ntype relocationTest struct {\n\tfile string\n\tentries []relocationTestEntry\n}\n\nvar relocationTests = []relocationTest{\n\t{\n\t\t\"testdata/go-relocation-test-gcc441-x86-64.obj\",\n\t\t[]relocationTestEntry{\n\t\t\t{0, &dwarf.",
"Entry{\n\t\t\t\tOffset: 0xb,\n\t\t\t\tTag: dwarf.",
"TagCompileUnit,\n\t\t\t\tChildren: true,\n\t\t\t\tField: []dwarf.",
"Field{\n\t\t\t\t\t{Attr: dwarf.",
"AttrProducer, Val: \"GNU C 4.4.1\", Class: dwarf.",
"ClassString},\n\t\t\t\t\t{Attr: dwarf.",
"AttrLanguage, Val: int64(1), Class: dwarf.",
"ClassConstant},\n\t\t\t\t\t{Attr: dwarf.",
"AttrName, Val: \"go-relocation-test.c\", Class: dwarf.",
"ClassString},\n\t\t\t\t\t{Attr: dwarf.",
"AttrCompDir, Val: \"/tmp\", Class: dwarf.",
"ClassString},\n\t\t\t\t\t{Attr: dwarf.",
"AttrLowpc, Val: uint64(0x0), Class: dwarf.",
"ClassAddress},\n\t\t\t\t\t{Attr: dwarf.",
"AttrHighpc, Val: uint64(0x6), Class: dwarf.",
"ClassAddress},\n\t\t\t\t\t{Attr: dwarf.",
"AttrStmtList, Val: int64(0), Class: dwarf.",
"ClassLinePtr},\n\t\t\t\t},\n\t\t\t}},\n\t\t},\n\t},\n\t{\n\t\t\"testdata/go-relocation-test-gcc441-x86.obj\",\n\t\t[]relocationTestEntry{\n\t\t\t{0, &dwarf.",
"Entry{\n\t\t\t\tOffset: 0xb,\n\t\t\t\tTag: dwarf.",
"TagCompileUnit,\n\t\t\t\tChildren: true,\n\t\t\t\tField: []dwarf.",
"Field{\n\t\t\t\t\t{Attr: dwarf.",
"AttrProducer, Val: \"GNU C 4.4.1\", Class: dwarf.",
"ClassString},\n\t\t\t\t\t{Attr: dwarf.",
"AttrLanguage, Val: int64(1), Class: dwarf.",
"ClassConstant},\n\t\t\t\t\t{Attr: dwarf.",
"AttrName, Val: \"t.c\", Class: dwarf.",
"ClassString},\n\t\t\t\t\t{Attr: dwarf.",
"AttrCompDir, Val: \"/tmp\", Class: dwarf.",
"ClassString},\n\t\t\t\t\t{Attr: dwarf.",
"AttrLowpc, Val: uint64(0x0), Class: dwarf.",
"ClassAddress},\n\t\t\t\t\t{Attr: dwarf.",
"AttrHighpc, Val: uint64(0x5), Class: dwarf.",
"ClassAddress},\n\t\t\t\t\t{Attr: dwarf.",
"AttrStmtList, Val: int64(0), Class: dwarf.",
"ClassLinePtr},\n\t\t\t\t},\n\t\t\t}},\n\t\t},\n\t},\n\t{\n\t\t\"testdata/go-relocation-test-gcc424-x86-64.obj\",\n\t\t[]relocationTestEntry{\n\t\t\t{0, &dwarf.",
"Entry{\n\t\t\t\tOffset: 0xb,\n\t\t\t\tTag: dwarf.",
"TagCompileUnit,\n\t\t\t\tChildren: true,\n\t\t\t\tField: []dwarf.",
"Field{\n\t\t\t\t\t{Attr: dwarf.",
"AttrProducer, Val: \"GNU C 4.2.4 (Ubuntu 4.2.4-1ubuntu4)\", Class: dwarf.",
"ClassString},\n\t\t\t\t\t{Attr: dwarf.",
"AttrLanguage, Val: int64(1), Class: dwarf.",
"ClassConstant},\n\t\t\t\t\t{Attr: dwarf.",
"AttrName, Val: \"go-relocation-test-gcc424.c\", Class: dwarf.",
"ClassString},\n\t\t\t\t\t{Attr: dwarf.",
"AttrCompDir, Val: \"/tmp\", Class: dwarf.",
"ClassString},\n\t\t\t\t\t{Attr: dwarf.",
"AttrLowpc, Val: uint64(0x0), Class: dwarf.",
"ClassAddress},\n\t\t\t\t\t{Attr: dwarf.",
"AttrHighpc, Val: uint64(0x6), Class: dwarf.",
"ClassAddress},\n\t\t\t\t\t{Attr: dwarf.",
"AttrStmtList, Val: int64(0), Class: dwarf.",
"ClassLinePtr},\n\t\t\t\t},\n\t\t\t}},\n\t\t},\n\t},\n\t{\n\t\t\"testdata/go-relocation-test-gcc482-aarch64.obj\",\n\t\t[]relocationTestEntry{\n\t\t\t{0, &dwarf.",
"Entry{\n\t\t\t\tOffset: 0xb,\n\t\t\t\tTag: dwarf.",
"TagCompileUnit,\n\t\t\t\tChildren: true,\n\t\t\t\tField: []dwarf.",
"Field{\n\t\t\t\t\t{Attr: dwarf.",
"AttrProducer, Val: \"GNU C 4.8.2 -g -fstack-protector\", Class: dwarf.",
"ClassString},\n\t\t\t\t\t{Attr: dwarf.",
"AttrLanguage, Val: int64(1), Class: dwarf.",
"ClassConstant},\n\t\t\t\t\t{Attr: dwarf.",
"AttrName, Val: \"go-relocation-test-gcc482.c\", Class: dwarf.",
"ClassString},\n\t\t\t\t\t{Attr: dwarf.",
"AttrCompDir, Val: \"/tmp\", Class: dwarf.",
"ClassString},\n\t\t\t\t\t{Attr: dwarf.",
"AttrLowpc, Val: uint64(0x0), Class: dwarf.",
"ClassAddress},\n\t\t\t\t\t{Attr: dwarf.",
"AttrHighpc, Val: int64(0x24), Class: dwarf.",
"ClassConstant},\n\t\t\t\t\t{Attr: dwarf.",
"AttrStmtList, Val: int64(0), Class: dwarf.",
"ClassLinePtr},\n\t\t\t\t},\n\t\t\t}},\n\t\t},\n\t},\n\t{\n\t\t\"testdata/go-relocation-test-gcc492-arm.obj\",\n\t\t[]relocationTestEntry{\n\t\t\t{0, &dwarf.",
"Entry{\n\t\t\t\tOffset: 0xb,\n\t\t\t\tTag: dwarf.",
"TagCompileUnit,\n\t\t\t\tChildren: true,\n\t\t\t\tField: []dwarf.",
"Field{\n\t\t\t\t\t{Attr: dwarf.",
"AttrProducer, Val: \"GNU C 4.9.2 20141224 (prerelease) -march=armv7-a -mfloat-abi=hard -mfpu=vfpv3-d16 -mtls-dialect=gnu -g\", Class: dwarf.",
"ClassString},\n\t\t\t\t\t{Attr: dwarf.",
"AttrLanguage, Val: int64(1), Class: dwarf.",
"ClassConstant},\n\t\t\t\t\t{Attr: dwarf.",
"AttrName, Val: \"go-relocation-test-gcc492.c\", Class: dwarf.",
"ClassString},\n\t\t\t\t\t{Attr: dwarf.",
"AttrCompDir, Val: \"/root/go/src/debug/elf/testdata\", Class: dwarf.",
"ClassString},\n\t\t\t\t\t{Attr: dwarf.",
"AttrLowpc, Val: uint64(0x0), Class: dwarf.",
"ClassAddress},\n\t\t\t\t\t{Attr: dwarf.",
"AttrHighpc, Val: int64(0x28), Class: dwarf.",
"ClassConstant},\n\t\t\t\t\t{Attr: dwarf.",
"AttrStmtList, Val: int64(0), Class: dwarf.",
"ClassLinePtr},\n\t\t\t\t},\n\t\t\t}},\n\t\t},\n\t},\n\t{\n\t\t\"testdata/go-relocation-test-clang-arm.obj\",\n\t\t[]relocationTestEntry{\n\t\t\t{0, &dwarf.",
"Entry{\n\t\t\t\tOffset: 0xb,\n\t\t\t\tTag: dwarf.",
"TagCompileUnit,\n\t\t\t\tChildren: true,\n\t\t\t\tField: []dwarf.",
"Field{\n\t\t\t\t\t{Attr: dwarf.",
"AttrProducer, Val: \"Debian clang version 3.5.0-10 (tags/RELEASE_350/final) (based on LLVM 3.5.0)\", Class: dwarf.",
"ClassString},\n\t\t\t\t\t{Attr: dwarf.",
"AttrLanguage, Val: int64(12), Class: dwarf.",
"ClassConstant},\n\t\t\t\t\t{Attr: dwarf.",
"AttrName, Val: \"hello.c\", Class: dwarf.",
"ClassString},\n\t\t\t\t\t{Attr: dwarf.",
"AttrStmtList, Val: int64(0x0), Class: dwarf.",
"ClassLinePtr},\n\t\t\t\t\t{Attr: dwarf.",
"AttrCompDir, Val: \"/tmp\", Class: dwarf.",
"ClassString},\n\t\t\t\t\t{Attr: dwarf.",
"AttrLowpc, Val: uint64(0x0), Class: dwarf.",
"ClassAddress},\n\t\t\t\t\t{Attr: dwarf.",
"AttrHighpc, Val: int64(48), Class: dwarf.",
"ClassConstant},\n\t\t\t\t},\n\t\t\t}},\n\t\t},\n\t},\n\t{\n\t\t\"testdata/go-relocation-test-gcc5-ppc.obj\",\n\t\t[]relocationTestEntry{\n\t\t\t{0, &dwarf.",
"Entry{\n\t\t\t\tOffset: 0xb,\n\t\t\t\tTag: dwarf.",
"TagCompileUnit,\n\t\t\t\tChildren: true,\n\t\t\t\tField: []dwarf.",
"Field{\n\t\t\t\t\t{Attr: dwarf.",
"AttrProducer, Val: \"GNU C11 5.0.0 20150116 (experimental) -Asystem=linux -Asystem=unix -Asystem=posix -g\", Class: dwarf.",
"ClassString},\n\t\t\t\t\t{Attr: dwarf.",
"AttrLanguage, Val: int64(12), Class: dwarf.",
"ClassConstant},\n\t\t\t\t\t{Attr: dwarf.",
"AttrName, Val: \"go-relocation-test-gcc5-ppc.c\", Class: dwarf.",
"ClassString},\n\t\t\t\t\t{Attr: dwarf.",
"AttrCompDir, Val: \"/tmp\", Class: dwarf.",
"ClassString},\n\t\t\t\t\t{Attr: dwarf.",
"AttrLowpc, Val: uint64(0x0), Class: dwarf.",
"ClassAddress},\n\t\t\t\t\t{Attr: dwarf.",
"AttrHighpc, Val: int64(0x44), Class: dwarf.",
"ClassConstant},\n\t\t\t\t\t{Attr: dwarf.",
"AttrStmtList, Val: int64(0), Class: dwarf.",
"ClassLinePtr},\n\t\t\t\t},\n\t\t\t}},\n\t\t},\n\t},\n\t{\n\t\t\"testdata/go-relocation-test-gcc482-ppc64le.obj\",\n\t\t[]relocationTestEntry{\n\t\t\t{0, &dwarf.",
"Entry{\n\t\t\t\tOffset: 0xb,\n\t\t\t\tTag: dwarf.",
"TagCompileUnit,\n\t\t\t\tChildren: true,\n\t\t\t\tField: []dwarf.",
"Field{\n\t\t\t\t\t{Attr: dwarf.",
"AttrProducer, Val: \"GNU C 4.8.2 -Asystem=linux -Asystem=unix -Asystem=posix -msecure-plt -mtune=power8 -mcpu=power7 -gdwarf-2 -fstack-protector\", Class: dwarf.",
"ClassString},\n\t\t\t\t\t{Attr: dwarf.",
"AttrLanguage, Val: int64(1), Class: dwarf.",
"ClassConstant},\n\t\t\t\t\t{Attr: dwarf.",
"AttrName, Val: \"go-relocation-test-gcc482-ppc64le.c\", Class: dwarf.",
"ClassString},\n\t\t\t\t\t{Attr: dwarf.",
"AttrCompDir, Val: \"/tmp\", Class: dwarf.",
"ClassString},\n\t\t\t\t\t{Attr: dwarf.",
"AttrLowpc, Val: uint64(0x0), Class: dwarf.",
"ClassAddress},\n\t\t\t\t\t{Attr: dwarf.",
"AttrHighpc, Val: uint64(0x24), Class: dwarf.",
"ClassAddress},\n\t\t\t\t\t{Attr: dwarf.",
"AttrStmtList, Val: int64(0), Class: dwarf.",
"ClassLinePtr},\n\t\t\t\t},\n\t\t\t}},\n\t\t},\n\t},\n\t{\n\t\t\"testdata/go-relocation-test-gcc492-mips64.obj\",\n\t\t[]relocationTestEntry{\n\t\t\t{0, &dwarf.",
"Entry{\n\t\t\t\tOffset: 0xb,\n\t\t\t\tTag: dwarf.",
"TagCompileUnit,\n\t\t\t\tChildren: true,\n\t\t\t\tField: []dwarf.",
"Field{\n\t\t\t\t\t{Attr: dwarf.",
"AttrProducer, Val: \"GNU C 4.9.2 -meb -mabi=64 -march=mips3 -mtune=mips64 -mllsc -mno-shared -g\", Class: dwarf.",
"ClassString},\n\t\t\t\t\t{Attr: dwarf.",
"AttrLanguage, Val: int64(1), Class: dwarf.",
"ClassConstant},\n\t\t\t\t\t{Attr: dwarf.",
"AttrName, Val: \"hello.c\", Class: dwarf.",
"ClassString},\n\t\t\t\t\t{Attr: dwarf.",
"AttrCompDir, Val: \"/tmp\", Class: dwarf.",
"ClassString},\n\t\t\t\t\t{Attr: dwarf.",
"AttrLowpc, Val: uint64(0x0), Class: dwarf.",
"ClassAddress},\n\t\t\t\t\t{Attr: dwarf.",
"AttrHighpc, Val: int64(100), Class: dwarf.",
"ClassConstant},\n\t\t\t\t\t{Attr: dwarf.",
"AttrStmtList, Val: int64(0), Class: dwarf.",
"ClassLinePtr},\n\t\t\t\t},\n\t\t\t}},\n\t\t},\n\t},\n\t{\n\t\t\"testdata/go-relocation-test-gcc531-s390x.obj\",\n\t\t[]relocationTestEntry{\n\t\t\t{0, &dwarf.",
"Entry{\n\t\t\t\tOffset: 0xb,\n\t\t\t\tTag: dwarf.",
"TagCompileUnit,\n\t\t\t\tChildren: true,\n\t\t\t\tField: []dwarf.",
"Field{\n\t\t\t\t\t{Attr: dwarf.",
"AttrProducer, Val: \"GNU C11 5.3.1 20160316 -march=zEC12 -m64 -mzarch -g -fstack-protector-strong\", Class: dwarf.",
"ClassString},\n\t\t\t\t\t{Attr: dwarf.",
"AttrLanguage, Val: int64(12), Class: dwarf.",
"ClassConstant},\n\t\t\t\t\t{Attr: dwarf.",
"AttrName, Val: \"hello.c\", Class: dwarf.",
"ClassString},\n\t\t\t\t\t{Attr: dwarf.",
"AttrCompDir, Val: \"/tmp\", Class: dwarf.",
"ClassString},\n\t\t\t\t\t{Attr: dwarf.",
"AttrLowpc, Val: uint64(0x0), Class: dwarf.",
"ClassAddress},\n\t\t\t\t\t{Attr: dwarf.",
"AttrHighpc, Val: int64(58), Class: dwarf.",
"ClassConstant},\n\t\t\t\t\t{Attr: dwarf.",
"AttrStmtList, Val: int64(0), Class: dwarf.",
"ClassLinePtr},\n\t\t\t\t},\n\t\t\t}},\n\t\t},\n\t},\n\t{\n\t\t\"testdata/go-relocation-test-gcc620-sparc64.obj\",\n\t\t[]relocationTestEntry{\n\t\t\t{0, &dwarf.",
"Entry{\n\t\t\t\tOffset: 0xb,\n\t\t\t\tTag: dwarf.",
"TagCompileUnit,\n\t\t\t\tChildren: true,\n\t\t\t\tField: []dwarf.",
"Field{\n\t\t\t\t\t{Attr: dwarf.",
"AttrProducer, Val: \"GNU C11 6.2.0 20160914 -mcpu=v9 -g -fstack-protector-strong\", Class: dwarf.",
"ClassString},\n\t\t\t\t\t{Attr: dwarf.",
"AttrLanguage, Val: int64(12), Class: dwarf.",
"ClassConstant},\n\t\t\t\t\t{Attr: dwarf.",
"AttrName, Val: \"hello.c\", Class: dwarf.",
"ClassString},\n\t\t\t\t\t{Attr: dwarf.",
"AttrCompDir, Val: \"/tmp\", Class: dwarf.",
"ClassString},\n\t\t\t\t\t{Attr: dwarf.",
"AttrLowpc, Val: uint64(0x0), Class: dwarf.",
"ClassAddress},\n\t\t\t\t\t{Attr: dwarf.",
"AttrHighpc, Val: int64(0x2c), Class: dwarf.",
"ClassConstant},\n\t\t\t\t\t{Attr: dwarf.",
"AttrStmtList, Val: int64(0), Class: dwarf.",
"ClassLinePtr},\n\t\t\t\t},\n\t\t\t}},\n\t\t},\n\t},\n\t{\n\t\t\"testdata/go-relocation-test-gcc492-mipsle.obj\",\n\t\t[]relocationTestEntry{\n\t\t\t{0, &dwarf.",
"Entry{\n\t\t\t\tOffset: 0xb,\n\t\t\t\tTag: dwarf.",
"TagCompileUnit,\n\t\t\t\tChildren: true,\n\t\t\t\tField: []dwarf.",
"Field{\n\t\t\t\t\t{Attr: dwarf.",
"AttrProducer, Val: \"GNU C 4.9.2 -mel -march=mips2 -mtune=mips32 -mllsc -mno-shared -mabi=32 -g\", Class: dwarf.",
"ClassString},\n\t\t\t\t\t{Attr: dwarf.",
"AttrLanguage, Val: int64(1), Class: dwarf.",
"ClassConstant},\n\t\t\t\t\t{Attr: dwarf.",
"AttrName, Val: \"hello.c\", Class: dwarf.",
"ClassString},\n\t\t\t\t\t{Attr: dwarf.",
"AttrCompDir, Val: \"/tmp\", Class: dwarf.",
"ClassString},\n\t\t\t\t\t{Attr: dwarf.",
"AttrLowpc, Val: uint64(0x0), Class: dwarf.",
"ClassAddress},\n\t\t\t\t\t{Attr: dwarf.",
"AttrHighpc, Val: int64(0x58), Class: dwarf.",
"ClassConstant},\n\t\t\t\t\t{Attr: dwarf.",
"AttrStmtList, Val: int64(0), Class: dwarf.",
"ClassLinePtr},\n\t\t\t\t},\n\t\t\t}},\n\t\t},\n\t},\n\t{\n\t\t\"testdata/go-relocation-test-gcc540-mips.obj\",\n\t\t[]relocationTestEntry{\n\t\t\t{0, &dwarf.",
"Entry{\n\t\t\t\tOffset: 0xb,\n\t\t\t\tTag: dwarf.",
"TagCompileUnit,\n\t\t\t\tChildren: true,\n\t\t\t\tField: []dwarf.",
"Field{\n\t\t\t\t\t{Attr: dwarf.",
"AttrProducer, Val: \"GNU C11 5.4.0 20160609 -meb -mips32 -mtune=mips32r2 -mfpxx -mllsc -mno-shared -mabi=32 -g -gdwarf-2\", Class: dwarf.",
"ClassString},\n\t\t\t\t\t{Attr: dwarf.",
"AttrLanguage, Val: int64(12), Class: dwarf.",
"ClassConstant},\n\t\t\t\t\t{Attr: dwarf.",
"AttrName, Val: \"hello.c\", Class: dwarf.",
"ClassString},\n\t\t\t\t\t{Attr: dwarf.",
"AttrCompDir, Val: \"/tmp\", Class: dwarf.",
"ClassString},\n\t\t\t\t\t{Attr: dwarf.",
"AttrLowpc, Val: uint64(0x0), Class: dwarf.",
"ClassAddress},\n\t\t\t\t\t{Attr: dwarf.",
"AttrHighpc, Val: uint64(0x5c), Class: dwarf.",
"ClassAddress},\n\t\t\t\t\t{Attr: dwarf.",
"AttrStmtList, Val: int64(0), Class: dwarf.",
"ClassLinePtr},\n\t\t\t\t},\n\t\t\t}},\n\t\t},\n\t},\n\t{\n\t\t\"testdata/go-relocation-test-gcc493-mips64le.obj\",\n\t\t[]relocationTestEntry{\n\t\t\t{0, &dwarf.",
"Entry{\n\t\t\t\tOffset: 0xb,\n\t\t\t\tTag: dwarf.",
"TagCompileUnit,\n\t\t\t\tChildren: true,\n\t\t\t\tField: []dwarf.",
"Field{\n\t\t\t\t\t{Attr: dwarf.",
"AttrProducer, Val: \"GNU C 4.9.3 -mel -mabi=64 -mllsc -mno-shared -g -fstack-protector-strong\", Class: dwarf.",
"ClassString},\n\t\t\t\t\t{Attr: dwarf.",
"AttrLanguage, Val: int64(1), Class: dwarf.",
"ClassConstant},\n\t\t\t\t\t{Attr: dwarf.",
"AttrName, Val: \"hello.c\", Class: dwarf.",
"ClassString},\n\t\t\t\t\t{Attr: dwarf.",
"AttrCompDir, Val: \"/tmp\", Class: dwarf.",
"ClassString},\n\t\t\t\t\t{Attr: dwarf.",
"AttrLowpc, Val: uint64(0x0), Class: dwarf.",
"ClassAddress},\n\t\t\t\t\t{Attr: dwarf.",
"AttrHighpc, Val: int64(100), Class: dwarf.",
"ClassConstant},\n\t\t\t\t\t{Attr: dwarf.",
"AttrStmtList, Val: int64(0), Class: dwarf.",
"ClassLinePtr},\n\t\t\t\t},\n\t\t\t}},\n\t\t},\n\t},\n\t{\n\t\t\"testdata/go-relocation-test-gcc720-riscv64.obj\",\n\t\t[]relocationTestEntry{\n\t\t\t{0, &dwarf.",
"Entry{\n\t\t\t\tOffset: 0xb,\n\t\t\t\tTag: dwarf.",
"TagCompileUnit,\n\t\t\t\tChildren: true,\n\t\t\t\tField: []dwarf.",
"Field{\n\t\t\t\t\t{Attr: dwarf.",
"AttrProducer, Val: \"GNU C11 7.2.0 -march=rv64imafdc -mabi=lp64d -g -gdwarf-2\", Class: dwarf.",
"ClassString},\n\t\t\t\t\t{Attr: dwarf.",
"AttrLanguage, Val: int64(12), Class: dwarf.",
"ClassConstant},\n\t\t\t\t\t{Attr: dwarf.",
"AttrName, Val: \"hello.c\", Class: dwarf.",
"ClassString},\n\t\t\t\t\t{Attr: dwarf.",
"AttrCompDir, Val: \"/tmp\", Class: dwarf.",
"ClassString},\n\t\t\t\t\t{Attr: dwarf.",
"AttrLowpc, Val: uint64(0x0), Class: dwarf.",
"ClassAddress},\n\t\t\t\t\t{Attr: dwarf.",
"AttrHighpc, Val: uint64(0x2c), Class: dwarf.",
"ClassAddress},\n\t\t\t\t\t{Attr: dwarf.",
"AttrStmtList, Val: int64(0), Class: dwarf.",
"ClassLinePtr},\n\t\t\t\t},\n\t\t\t}},\n\t\t},\n\t},\n\t{\n\t\t\"testdata/go-relocation-test-clang-x86.obj\",\n\t\t[]relocationTestEntry{\n\t\t\t{0, &dwarf.",
"Entry{\n\t\t\t\tOffset: 0xb,\n\t\t\t\tTag: dwarf.",
"TagCompileUnit,\n\t\t\t\tChildren: true,\n\t\t\t\tField: []dwarf.",
"Field{\n\t\t\t\t\t{Attr: dwarf.",
"AttrProducer, Val: \"clang version google3-trunk (trunk r209387)\", Class: dwarf.",
"ClassString},\n\t\t\t\t\t{Attr: dwarf.",
"AttrLanguage, Val: int64(12), Class: dwarf.",
"ClassConstant},\n\t\t\t\t\t{Attr: dwarf.",
"AttrName, Val: \"go-relocation-test-clang.c\", Class: dwarf.",
"ClassString},\n\t\t\t\t\t{Attr: dwarf.",
"AttrStmtList, Val: int64(0), Class: dwarf.",
"ClassLinePtr},\n\t\t\t\t\t{Attr: dwarf.",
"AttrCompDir, Val: \"/tmp\", Class: dwarf.",
"ClassString},\n\t\t\t\t},\n\t\t\t}},\n\t\t},\n\t},\n\t{\n\t\t\"testdata/gcc-amd64-openbsd-debug-with-rela.obj\",\n\t\t[]relocationTestEntry{\n\t\t\t{203, &dwarf.",
"Entry{\n\t\t\t\tOffset: 0xc62,\n\t\t\t\tTag: dwarf.",
"TagMember,\n\t\t\t\tChildren: false,\n\t\t\t\tField: []dwarf.",
"Field{\n\t\t\t\t\t{Attr: dwarf.",
"AttrName, Val: \"it_interval\", Class: dwarf.",
"ClassString},\n\t\t\t\t\t{Attr: dwarf.",
"AttrDeclFile, Val: int64(7), Class: dwarf.",
"ClassConstant},\n\t\t\t\t\t{Attr: dwarf.",
"AttrDeclLine, Val: int64(236), Class: dwarf.",
"ClassConstant},\n\t\t\t\t\t{Attr: dwarf.",
"AttrType, Val: dwarf.",
"Offset(0xb7f), Class: dwarf.",
"ClassReference},\n\t\t\t\t\t{Attr: dwarf.",
"AttrDataMemberLoc, Val: []byte{0x23, 0x0}, Class: dwarf.",
"ClassExprLoc},\n\t\t\t\t},\n\t\t\t}},\n\t\t\t{204, &dwarf.",
"Entry{\n\t\t\t\tOffset: 0xc70,\n\t\t\t\tTag: dwarf.",
"TagMember,\n\t\t\t\tChildren: false,\n\t\t\t\tField: []dwarf.",
"Field{\n\t\t\t\t\t{Attr: dwarf.",
"AttrName, Val: \"it_value\", Class: dwarf.",
"ClassString},\n\t\t\t\t\t{Attr: dwarf.",
"AttrDeclFile, Val: int64(7), Class: dwarf.",
"ClassConstant},\n\t\t\t\t\t{Attr: dwarf.",
"AttrDeclLine, Val: int64(237), Class: dwarf.",
"ClassConstant},\n\t\t\t\t\t{Attr: dwarf.",
"AttrType, Val: dwarf.",
"Offset(0xb7f), Class: dwarf.",
"ClassReference},\n\t\t\t\t\t{Attr: dwarf.",
"AttrDataMemberLoc, Val: []byte{0x23, 0x10}, Class: dwarf.",
"ClassExprLoc},\n\t\t\t\t},\n\t\t\t}},\n\t\t},\n\t},\n}\n\nfunc TestDWARFRelocations(t *testing.",
"T) {\n\tfor i, test := range relocationTests {\n\t\tf, err := Open(test.file)\n\t\tif err !",
"= nil {\n\t\t\tt.Error(err)\n\t\t\tcontinue\n\t\t}\n\t\tdwarf, err := f.DWARF()\n\t\tif err !",
"= nil {\n\t\t\tt.Error(err)\n\t\t\tcontinue\n\t\t}\n\t\tfor _, testEntry := range test.entries {\n\t\t\treader := dwarf.",
"Reader()\n\t\t\tfor j := 0; j < testEntry.entryNumber; j++ {\n\t\t\t\tentry, err := reader.",
"Next()\n\t\t\t\tif entry == nil || err !",
"= nil {\n\t\t\t\t\tt.Errorf(\"Failed to skip to entry %d: %v\", testEntry.entryNumber, err)\n\t\t\t\t\tcontinue\n\t\t\t\t}\n\t\t\t}\n\t\t\tentry, err := reader.",
"Next()\n\t\t\tif err !",
"= nil {\n\t\t\t\tt.Error(err)\n\t\t\t\tcontinue\n\t\t\t}\n\t\t\tif !",
"reflect.",
"DeepEqual(testEntry.entry, entry) {\n\t\t\t\tt.Errorf(\"#%d/%d: mismatch: got:%#v want:%#v\", i, testEntry.entryNumber, entry, testEntry.entry)\n\t\t\t\tcontinue\n\t\t\t}\n\t\t}\n\t}\n}\n\nfunc TestCompressedDWARF(t *testing.",
"T) {\n\t// Test file built with GCC 4.8.4 and as 2.24 using:\n\t// gcc -Wa,--compress-debug-sections -g -c -o zdebug-test-gcc484-x86-64.obj hello.c\n\tf, err := Open(\"testdata/zdebug-test-gcc484-x86-64.obj\")\n\tif err !",
"= nil {\n\t\tt.Fatal(err)\n\t}\n\tdwarf, err := f.DWARF()\n\tif err !",
"= nil {\n\t\tt.Fatal(err)\n\t}\n\treader := dwarf.",
"Reader()\n\tn := 0\n\tfor {\n\t\tentry, err := reader.",
"Next()\n\t\tif err !",
"= nil {\n\t\t\tt.Fatal(err)\n\t\t}\n\t\tif entry == nil {\n\t\t\tbreak\n\t\t}\n\t\tn++\n\t}\n\tif n !",
"= 18 {\n\t\tt.Fatalf(\"want %d DWARF entries, got %d\", 18, n)\n\t}\n}\n\nfunc TestCompressedSection(t *testing.",
"T) {\n\t// Test files built with gcc -g -S hello.c and assembled with\n\t// --compress-debug-sections=zlib-gabi.",
"\n\tf, err := Open(\"testdata/compressed-64.obj\")\n\tif err !",
"= nil {\n\t\tt.Fatal(err)\n\t}\n\tsec := f.Section(\".debug_info\")\n\twantData := []byte{\n\t\t182, 0, 0, 0, 4, 0, 0, 0, 0, 0, 8, 1, 0, 0, 0, 0,\n\t\t1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n\t\t0, 27, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 8, 7,\n\t\t0, 0, 0, 0, 2, 1, 8, 0, 0, 0, 0, 2, 2, 7, 0, 0,\n\t\t0, 0, 2, 4, 7, 0, 0, 0, 0, 2, 1, 6, 0, 0, 0, 0,\n\t\t2, 2, 5, 0, 0, 0, 0, 3, 4, 5, 105, 110, 116, 0, 2, 8,\n\t\t5, 0, 0, 0, 0, 2, 8, 7, 0, 0, 0, 0, 4, 8, 114, 0,\n\t\t0, 0, 2, 1, 6, 0, 0, 0, 0, 5, 0, 0, 0, 0, 1, 4,\n\t\t0, 0, 0, 0, 0, 0, 0, 0, 27, 0, 0, 0, 0, 0, 0, 0,\n\t\t1, 156, 179, 0, 0, 0, 6, 0, 0, 0, 0, 1, 4, 87, 0, 0,\n\t\t0, 2, 145, 108, 6, 0, 0, 0, 0, 1, 4, 179, 0, 0, 0, 2,\n\t\t145, 96, 0, 4, 8, 108, 0, 0, 0, 0,\n\t}\n\n\t// Test Data method.",
"\n\tb, err := sec.",
"Data()\n\tif err !",
"= nil {\n\t\tt.Fatal(err)\n\t}\n\tif !",
"bytes.",
"Equal(wantData, b) {\n\t\tt.Fatalf(\"want data %x, got %x\", wantData, b)\n\t}\n\n\t// Test Open method and seeking.",
"\n\tbuf, have, count := make([]byte, len(b)), make([]bool, len(b)), 0\n\tsf := sec.",
"Open()\n\tif got, err := sf.",
"Seek(0, io.",
"SeekEnd); got !",
"= int64(len(b)) || err !",
"= nil {\n\t\tt.Fatalf(\"want seek end %d, got %d error %v\", len(b), got, err)\n\t}\n\tif n, err := sf.",
"Read(buf); n !",
"= 0 || err !",
"= io.",
"EOF {\n\t\tt.Fatalf(\"want EOF with 0 bytes, got %v with %d bytes\", err, n)\n\t}\n\tpos := int64(len(buf))\n\tfor count < len(buf) {\n\t\t// Construct random seek arguments.",
"\n\t\twhence := rand.",
"Intn(3)\n\t\ttarget := rand.",
"Int63n(int64(len(buf)))\n\t\tvar offset int64\n\t\tswitch whence {\n\t\tcase io.",
"SeekStart:\n\t\t\toffset = target\n\t\tcase io.",
"SeekCurrent:\n\t\t\toffset = target - pos\n\t\tcase io.",
"SeekEnd:\n\t\t\toffset = target - int64(len(buf))\n\t\t}\n\t\tpos, err = sf.",
"Seek(offset, whence)\n\t\tif err !",
"= nil {\n\t\t\tt.Fatal(err)\n\t\t}\n\t\tif pos !",
"= target {\n\t\t\tt.Fatalf(\"want position %d, got %d\", target, pos)\n\t\t}\n\n\t\t// Read data from the new position.",
"\n\t\tend := pos + 16\n\t\tif end > int64(len(buf)) {\n\t\t\tend = int64(len(buf))\n\t\t}\n\t\tn, err := io.",
"ReadFull(sf, buf[pos:end])\n\t\tif err !",
"= nil {\n\t\t\tt.Fatal(err)\n\t\t}\n\t\tfor i := 0; i < n; i++ {\n\t\t\tif !",
"have[pos] {\n\t\t\t\thave[pos] = true\n\t\t\t\tcount++\n\t\t\t}\n\t\t\tpos++\n\t\t}\n\t}\n\tif !",
"bytes.",
"Equal(wantData, buf) {\n\t\tt.Fatalf(\"want data %x, got %x\", wantData, buf)\n\t}\n}\n\nfunc TestNoSectionOverlaps(t *testing.",
"T) {\n\t// Ensure cmd/link outputs sections without overlaps.",
"\n\tswitch runtime.",
"GOOS {\n\tcase \"aix\", \"android\", \"darwin\", \"js\", \"nacl\", \"plan9\", \"windows\":\n\t\tt.Skipf(\"cmd/link doesn't produce ELF binaries on %s\", runtime.",
"GOOS)\n\t}\n\t_ = net.",
"ResolveIPAddr // force dynamic linkage\n\tf, err := Open(os.",
"Args[0])\n\tif err !",
"= nil {\n\t\tt.Error(err)\n\t\treturn\n\t}\n\tfor i, si := range f.Sections {\n\t\tsih := si.",
"SectionHeader\n\t\tif sih.",
"Type == SHT_NOBITS {\n\t\t\tcontinue\n\t\t}\n\t\tfor j, sj := range f.Sections {\n\t\t\tsjh := sj.",
"SectionHeader\n\t\t\tif i == j || sjh.",
"Type == SHT_NOBITS || sih.",
"Offset == sjh.",
"Offset && sih.",
"Size == 0 {\n\t\t\t\tcontinue\n\t\t\t}\n\t\t\tif sih.",
"Offset >= sjh.",
"Offset && sih.",
"Offset < sjh.",
"Offset+sjh.",
"Size {\n\t\t\t\tt.Errorf(\"ld produced ELF with section %s within %s: 0x%x <= 0x%x..0x%x < 0x%x\",\n\t\t\t\t\tsih.",
"Name, sjh.",
"Name, sjh.",
"Offset, sih.",
"Offset, sih.",
"Offset+sih.",
"Size, sjh.",
"Offset+sjh.",
"Size)\n\t\t\t}\n\t\t}\n\t}\n}\n"
] | {
"pile_set_name": "Github"
} | [
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"According to reserve bank of india guidelines, banks have to clarify what a flat rate is and how the a loan against the car is.",
"It can be availed by all resident individuals (except those engaged in a car hiring business); the loan is for the purchase of a new or second hand car (not older.",
"\n\nBad Credit History - Get Car Loan - Call 88000 90480 - Auto Loan ...\n\nA lease buyout loan gives you the money to buy your currently leased car, either *private party loans must be closed in person at a wells fargo branch. ",
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"Ltd., incorporated in june 2010, is a one stop solution for all your auto at autofocus our car loans cost you best! ",
"we have.",
"Home products personal vehicle loans two wheeler loan to ensure that you enjoy the best deal, we have tailored our two-wheeler loans accordingly.",
"Compare the best car loan offers in town and locate the lowest what car models are financed by the standard car loan in india? ",
"auto insurance; axis car loan;.Oct 30, 2013 - the closure notice came despite his companys annual turnover of about though his credit standing is good, his record shows hes got bigger some banks have taken to naming and shaming loan."
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"Hanging with Soul Clap on the Roof deck of Canibal Royal (Photo by Ashlyn Fulton)\n\nWhen we met up with Eli Goldstein and Charles Levine at Canibal Royal, the two looked as though they had just ransacked a thrift shop on Bedford Ave. ",
"Goldstein’s retro jumpsuit, aviator glasses and thick black beard made him instantly recognizable amidst a crowd of performers hanging backstage. ",
"To his side, I see the approachable Levine wearing a colorful, geometrically inspired button-up paired with his signature smile. ",
"He went in for a kiss on the cheek before making introductions.",
"\n\nIt was Soul Clap‘s sixth annual appearance at The BPM Festival in Playa Del Carmen, Mexico. ",
"Once again billed as a top act on Crew Love lineup, the two were most certainly in their element, despite the fact that they would be taking the stage earlier than expected. ",
"Former neighbors Greg Paulus and Nick DeBruyn (No Regular Play) were running late due to flight delays. ",
"But this little switch up caused them no sweat. ",
"After all, these two are pros.",
"\n\nSince 2001, Goldstein and Levine have offered their funky perspective to America’s house music scene. ",
"Largely inspired by the 70s disco and funk era, Soul Clap has managed to solidify their voice in a crowded space. ",
"Now living in Brooklyn (by way of Beantown) they are keeping the spirit alive by participating in local collaborations and playing major music events, from steamy warehouse raves to sold-out club shows.",
"\n\nWhile Soul Clap’s musicianship has undoubtedly shaped the borough, their reach goes far beyond Brooklyn night life. ",
"These guys are men about town, having boasted residencies at numerous New York nightclubs and making regular appearances at citywide festivals throughout the year. ",
"Plus, Goldstein has recently dipped his toes into culinary endeavors with the opening of Black Flamingo – a vegan-friendly Latin haunt and disco cave located near the Marcy Ave. ",
"M stop at 168 Borinquen Place.",
"\n\nSee what I mean? ",
"Vintage gear. ",
"Veggie tacos. ",
"Vinyl. ",
"Their craft might bring them to scenic spots around the globe, but it’s easy to see why these boys just belong in Brooklyn. ",
"We found a quiet spot on the beach club’s top deck to discuss their foundations, Funk Bomb, and of course, fashion.",
"\n\nPhoto by Ashlyn Fulton\n\nFW: 2016 was huge for Soul Clap! ",
"You released a new album, you played a sold out New Year’s Eve party at Good Room . . . ",
"how did it feel to close out the year?",
"\n\nCharles: It was a crazy year, 2016! ",
"It’s true. ",
"Musically, it had been four years since the last album, so that was a big accomplishment. ",
"Plus, it was full of a lot of exciting memorable firsts for us, like playing Coachella for the first time.",
"\n\nEli: For us, 2016 was definitely significant. ",
"We did a track with Louie Vega on his album which got nominated for a Grammy.",
"\n\nFW: Whoa, Grammy nominated artists, Soul Clap!",
"\n\nCharles and Eli: Well . . . (",
"laughs)\n\nEli: We don’t actually get a Grammy. ",
"If the song wins a Grammy, then the engineers get one, for sure. ",
"Now, if it gets a platinum or gold disc, then we get that.",
"\n\nCharles: So we don’t get the statue, but we get credit as being on a Grammy nominated album. ",
"Whatever, we can say we’re grammy winners. ",
"We’ll have to print some statues on 3-D printers. ",
"In fact, let’s print all kinds of awards! (",
"laughs) So there were those high points, and then, with Prince dying and us coming around and doing a tribute to him – it really was a pretty impactful time. ",
"We experienced lots of big things in a very weighted musical year.",
"\n\nSean and Megan catch up with Soul Clap at BPM Festival (Photo by Ashlyn Fulton)\n\nFW: I remember last year during BPM, the Crew Love party took place the day after Bowie died. ",
"It was very sad, but wow, it made for a great day of music!",
"\n\nEli: Yes, that was super emotional. ",
"It was a celebration of his achievements, and of course, the power of music. ",
"It’s great to celebrate [the legends]. ",
"Being DJs, it really gives us the power to play their music and celebrate artists of the past. ",
"Colonel Abrams was the last one big one that we lost. ",
"Surprisingly enough, not as many people seemed to know a whole lot about him. ",
"He was an 80s funk and soul singer, who turned into a significant voice in house music.",
"\n\nFW: So you’re not going to play a Leonard Cohen heavy set today then?",
"\n\nEli: You know, he died right after Trump got elected. ",
"That was especially demoralizing. ",
"I was playing Leonard Cohen tracks that weekend. ",
"And, David Mancuso! ",
"None of this [club] culture would be here without Mancuso. ",
"He reminds us what the core of this whole dance music thing is supposed to be: friends coming together in a safe comfortable space, to really come together and dance and be free. ",
"It’s the heart of it, you know. ",
"Him passing really reminds us of that.",
"\n\nFW: Speaking of inspirations, what inspired you two to record Funk Bomb?",
"\n\nCharles: It started as a jam session between Eli and myself at my house. ",
"The first synth we ever had was the Korg MS2000, and I was dialing in on that. [",
"Meanwhile,] Eli was laying down some awesome drum stuff, and programming samples. ",
"So it all began as just that one synth and us.",
"\n\nEli: We started calling those beats the MS2000-Funk Bomb. ",
"But, we went ahead and knocked that off because it was way too nerdy.",
"\n\nCharles: We created those sounds, and then ended up at Red Bull Studios. ",
"Billy Bass Nelson from Funkadelic came in and did the bass line. ",
"Wiley from Midnight Magic came and played some keys, and then John King – he’s another guy in Crew Love – a fantastic jazz pianist who grew up with Greg Paulus and Nick DeBruyn from No Regular Play, brought in a jazz element. ",
"We filled it all out at Red Bull, and it took on a life of its own. ",
"Doc Martin, who we brought [with us] on Holy Ship, just did a remix of Funk Bomb, which will come out soon.",
"\n\nFW: You just mentioned fellow Brooklyners, No Regular Play. ",
"How have your close ties to Brooklyn helped you in your collaborative efforts?",
"\n\nEli: The whole Crew Love thing started with Wolf+Lamb at the Marcy Hotel in Williamsburg. ",
"That started back in 2005 I believe, and then closed in 2015.",
"\n\nFW: And the Marcy Hotel was akin to an artist co-op, correct?",
"\n\nCharles: Artist co-op? ",
"Yeah, pretty close.",
"\n\nEli: It was a building, and the first floor was a space that’s now the Boiler Room. ",
"Actually, we just did a Boiler Room event there recently. ",
"Zev and Gadi of Wolf + Lamb kind of developed the space and had friends move into the apartments. ",
"They eventually took over the whole building and they were throwing parties. ",
"It became a space for an extended family of artists and musicians to stay when they were coming through New York. ",
"Then we came into the picture around 2008. ",
"The first round was the Vision Quest guys (Ryan Crossen, Shaun Reeves, Lee Curtis, Seth Troxler). ",
"So then we arrived, and No Regular Play came in the second wave as well. ",
"We were all working together. ",
"That was the center for collaboration and doing parties, and that developed into the Crew Love collective.",
"\n\nCharles: And circling back to Funk Bomb – all of those studio musicians are New York-based. ",
"Without the New York connections, those collaborations might not have ever happened.",
"\n\nFW: So the setting isn’t the Marcy Hotel anymore, but you’re still playing parties in New York all the time. ",
"We had a great time at I Feel Love, and then you sold-out Good Room on NYE!",
"\n\nEli: Good Room was great. ",
"New Years is always kind of weighted, because you get the crowd who doesn’t always go out. ",
"But that was a really good vibe. ",
"We had another good party with the MATTE Project at The Marina [in Inwood].",
"\n\nCharles: That was pretty dope, that was a real Crew Love party in New York, and the venue is awesome because you’re dancing in the sand! ",
"Plus we did a lot of cool stuff at Output, and it was a big year for Eli’s club, Black Flamingo.",
"\n\nBlack Flamingo Night Club (Photo credit: Insomniac)\n\nFW: Yeah, how’s that going? ",
"I know you had your album release party there late last year.",
"\n\nEli: It’s been going really well! ",
"It’s my baby. ",
"There are a bunch of investors, and this guy Bryce who’s the GM and the heart and soul that makes it tick. ",
"I do the bookings and help with all that.",
"\n\nFW: And what is Black Flamingo bringing to Brooklyn that hasn’t been served before?",
"\n\nEli: Things happen so fast in New York, but when we opened the doors a year and a half ago there weren’t any small bars paying warmer electronic music like house and disco. ",
"You had Bossa Nova in Bushwick, but that was about it. ",
"We wanted a DJ spot that was intimate but focused on house and disco. ",
"Black Flamingo is in Williamsburg, right by the bridge.",
"\n\nFW: We can get down with that. ",
"Did you set a fierce dress code, because we have to know, what is the inspiration behind your outfits? ",
"Every time we see you guys, you bring something fun. ",
"You know, you’re kind of like the “David Bowies” of house music!",
"\n\nEli: Oh wow, that’s such a compliment! ",
"Vintage shopping is a key element, late 80s early 90s, era specifically, Charles’ shirt we got in Tokyo at this place called Pin Nap.",
"\n\nCharles: Yep. ",
"Pin. ",
"Nap. ",
"The dude who works there is very funny. ",
"He’s a Japanese guy with a full afro, and he’s got a bunch of 90s nostalgia gear. ",
"He’s always like, “Come. ",
"Come. ",
"Let me show you.” ",
"He’s got lots of Alf.",
"\n\nEli: That place is absolutely smashing. ",
"They have a whole Cosby sweater section. ",
"Every time we go to Tokyo we’ve ended up in that spot.",
"\n\nFW: So he’s like your wacky clothes dealer?",
"\n\nEli: For sure. ",
"The other place I love is KOKO ROKOKO. ",
"That’s my main go-to in Chicago. ",
"They buy a bunch of awesome 80s and 90s stuff, plus they are friends from Boston. ",
"I don’t want to give away too much of the secret, but I always want to shout them out, because it’s one of the best places in the world!",
"\n\nFW: So what’s next for you guys? ",
"Gonna chill after the big year, or just keep chugging along?",
"\n\nCharles: We’re just going to keep on pushing!",
"\n\nEli: We’ve been playing around with a live element, which we’ll showcase at some festivals this summer, like Movement and Electric Forest. ",
"That’s been new for us, and that really came [to fruition] while we were working on the album. ",
"We’ve got some new releases coming out on Classic Records. ",
"Classic started with Derrick Carter and Luke Solomon. ",
"It was big in the early 2000s, but they are back now, so we’re excited to be doing house records for them. ",
"Also we’re doing a Fabric mix that’s coming out in April.",
"\n\nCharles: And that was another big thing that shook the scene – Fabric closing, and then reopening! ",
"Wow, I guess 2016 really was a weird year.",
"\n\nFW: . . . ",
"And with that, I think we can all agree that 2017 is off to a pretty weird start as well. ",
"Thanks Trump.",
"\n\nIn the sake of tradition, Soul Clap shows no signs of slowing down. ",
"You can catch Eli Goldstein vs. Eli Escobar at Black Flamingo this Saturday, February 25th. ",
"You can also catch Soul Clap Records veteran Ahmed Hashid’s special birthday set at the Bushwick A/V event at Studio 299 next weekend."
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"Popular Posts\n\nSponsored Link\n\nSponsored Link\n\nThe Total Beauty Prepped and Primed Collection & Giveaway\n\nWhen it comes to sample boxes and makeup collections, Total Beauty curates some of the best with luxury offerings at budget friendly prices. ",
"Their latest and greatest is the Prepped and Prime Collection, which is just plain sublime.",
"\n\nTotal Beauty boxes are great because there is no subscription required. ",
"You can buy boxes as you wish, and there are several available in their shops right now.",
"\n\nThe Prepped and Primed box was designed specifically for the cold, harsh conditions of these frigid Winter months we’re in. ",
"Of course, it’s a different story here in California, but we are just a fraction of the rest of the world, most of which is in the middle of the Polar Vortex! ",
"The products in this particular box soothe, smoothe, nourish, protect, and add a touch of shimmery goodness to your life. ",
"Who can say no to that?!",
"\n\nI love Total Beauty’s boxes, including the one I helped curate a few months ago. ",
"The Prepped and Primed Collection is valued at $90 and priced at $25 with free shipping. ",
"To purchase one, visit Total Beauty.",
"\n\nIf you’d like to get your hands on this box, you can win one right here! ",
"Contest ends Saturday, January 18, 2014 at 12 am, PST. ",
"Enter using the Rafflecopter widget below. ",
"Good luck!",
"\n\nI’m not subscribed to any right now but the Wantable beauty subscription box or the QVC Test Tube are the ones I’m most interested in.",
"\n\ntrinashere\n\nI’m not a subscriber to any yet, but I’ve read such good things about Ipsy and Wantable. ",
"It’s now just deciding which!",
"\n\ncpbebe\n\nNo but I am scoping out Ipsy. ",
"Right now I subscribe to Lacquerous.",
"\n\nLisa Hill Felger\n\nSo far I’ve only subscribed to Ipsy and I really like it. ",
"I really want to subscribe to Wantable. ",
"Their accessories boxes look amazing. ",
"Oh, and I have Dollar Shave Club for my husband and he loves it. ",
"Great quality razors.",
"\n\nBeka\n\nI have Ipsy. ",
"I love it. ",
"I’m looking at getting another one, because make up is addicting. ",
"^_^\n\nNancy Baker Tatarek\n\nNever heard of this but would love to try it–it looks like a wonderful collection!",
"\n\nPatricia Brousseau Caradonna\n\nNo I do not, but it sounds interesting and I definitely would like to consider.",
"\n\nhttp://sandysandmeyer.wordpress.com/ Sandy\n\nI love makeup! ",
"I think it would be fun to try. ",
"I’ve tried BeautyBox5 and I like buying inexpensive makeup at the dollar stores.",
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"I believe it used to be called beautyfix,can’t remember it’s been awhile since I’ve had it.",
"\n\nCaitlyn\n\nMy favorite is FabFitFun but popsugar is pretty close.",
"\nPopsugar would be better if it was more beauty less home stuff but that’s just me!",
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"\n\nNikki\n\nI like Runnerbox.",
"\n\nanonymous\n\nthe eye palette <3\n\nMelissa Loy\n\nWould love this.",
"\n\nMelissa Loy\n\nI like birch box\n\nKomal Kadav\n\nThe eye palette and the sibu sea buckthron seed oil looks like a catch! ",
"I hope to get it\n\nAnji Lynn\n\nIt’s the Buckthorn ♥\n\nhttp://www.beautythesis.net/ Beauty Thesis\n\nNo. ",
"Though it’s really only for the fact that I’m so fussy with products.. #beautybloggerproblems\n\nJenn\n\nHi! ",
"Actually, I don’t but have been interested in the past.",
"\n\nSusan Pertierra\n\nI have not subscribed to any subscription boxes, yet.",
"\n\nAnna Sholl\n\nNo! ",
"I’ve been thinking about subscribing to Birchbox, though.",
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"\n\nShannoninBC\n\nI’ve subscribed to a number of services available in Canada but ended up cancelling all but Beauty Box 5; I’m tempted to try Ipsy, though! ",
"What a great prize, thanks for all your effort and generosity\n\nelizabeth @ hobbylobbyist\n\nI have not signed up for any but Ipsy is on my list to try out!",
"\n\ntopkat\n\nno\n\nEmily\n\nI’ve tried Wantable, Ipsy, Birchbox and Starlooks\n\nJen\n\nI actually haven’t tried a subscription box before! ",
"I know I’m probably the last person on earth to say that….",
"\n\nIrma Tufek\n\nI’m not subscribed to any,but think about Wantable….",
"\n\nlatanya t\n\nI like Naturebox\n\nStella\n\nNaturebox is my fave! ",
"Who will turn down siracha cashew nuts snack?! ",
"<3\n\nSenny\n\nI love all of them but my favorite is probably glossybox!",
"\n\nColleen Boudreau\n\nI like Glossybox.",
"\n\nAndrea Darst\n\nI like Glossybox, but it was a bit too expensive and I love the Popsugar Must Have, but same problem.",
"\n\nKassie Colbert\n\nMy favorite right now is Ipsy\n\nneha dalmia\n\nright now my favorite is Ipsy for makeup\n\nCalli\n\nI like birchbox, but I haven’t ordered in a few months.",
"\n\njoni\n\nI like the IPSY subscription box, you get quality product to try at a very low cost!",
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"Mt. Joy. ",
"The Revivalists. ",
"Nathaniel Rateliff. ",
"I can’t tell them apart and neither can you, because they all sound like Hozier. ",
"Folk-soul has reigned ascendant since the Irish singer-songwriter’s “Take Me to Church” blew up in 2014, and if he wasn’t the first on the scene—Mumford & Sons already existed, and so did the Sam Smith/Dan Smith voice—he may be the most influential.",
"\n\nThese fellows make anguished, soul-approximate noises over creaky, dust-inflected folk-rock. ",
"Their strained singing is supposed to correlate with depth of feeling, but it also establishes distance from the source material, cuing listeners that yes, the singer is indeed a white dude. ",
"They’ll never sound like their vocal role models, but boy, will they scream, pant, and bellow trying.",
"\n\nHozier does understand the dynamics of his relationship to black music, and he feels bad about it. ",
"As a nice, well-intentioned liberal he doesn’t want to be considered a cultural appropriator. ",
"He wants to practice humility—he’s part of a tradition bigger than himself, after all. ",
"Hozier’s second album, Wasteland, Baby!, ",
"opens with “Nina Cried Power,” a “song about protest songs” that drops the names of Nina Simone, Billie Holiday, Mavis Staples, Curtis Mayfield, Patti LaBelle, John Lennon, James Brown, B.B. King, Joni Mitchell, Pete Seeger, Marvin Gaye, Bob Dylan, and Woody Guthrie, like he’s practicing his Grammy acceptance speech. ",
"To render the song immune from criticism, he invites Staples herself to sing the chorus and bridge, although she’s promptly drowned out by clunky bass and a blaring gospel choir.",
"\n\nThe lilting rhythm guitar on “Almost (Sweet Music)” suggests a sweeter love song; then you notice that the lyrics have been pieced together from the titles of about 20 jazz classics, a reverent reference stew. ",
"If the chorus had been “Be still my beating heart/don’t ruin this song for me” rather than “Don’t ruin this on me,” “Almost” would have captured how music and memories mingle, but the soft focus doesn’t click.",
"\n\nWasteland, Baby! ",
"taps into a mood of contemporary political malaise, situating several songs on the edge of some ruinous, perhaps climate-related catastrophe, but the album also stars the moaning loverboy who covered Destiny’s Child’s “Say My Name” in January. ",
"Sometimes romance and apocalypse collide in Princean ways. ",
"On the closing title track, Hozier and his beloved fall in love while watching “the death of the sun”; on “No Plan,” he offers to keep you company before the world ends, as quivery fuzz guitar crackles over the beat’s steady deathward march.",
"\n\nThere’s a desperation about the album, as Hozier searches for spiritual-erotic sustenance amid chaos. “",
"Shrike,” a hushed acoustic trifle, is lovely, as the plucked guitar melody projects a cool unflappability and sounds for once like folk music. ",
"Hozier casts himself as “the shrike to your sharp and glorious thorn,” a shrike being a bird that impales its prey on thorns. ",
"He doesn’t expand on the conceit, and he doesn’t have to. ",
"It’s better left obscure: stark, simple, with eerie tinges of violence, a quiet moment of unexplained weirdness.",
"\n\nIf Wasteland, Baby! ",
"doesn’t quite carve out a peaceful aural hiding space, blame Hozier’s voice, a loud, rumbling thing, simultaneously raw and mannered. ",
"He can’t stop roaring. ",
"A soul man should sound like he at least knows how to relax, even if he isn’t relaxing at a given moment; Hozier flaunts his tortured solemnity on sad songs and love songs alike. ",
"Sex for Hozier is a strained experience, just like his singing, especially when he mixes metaphors, like one of those writers nominated for the Bad Sex in Fiction Award. ",
"There’s no reason a song whose hook is “Lover, be good to me” should also include verses like “When St. Peter loses cool and bars the gates/When Atlas acts the maggot, makes his arms shake.”",
"\n\nThe album’s watery sound heightens the bombast: Recorded as if in a cathedral, with lots of echo space between instruments, the guitars and handclaps boom and resound. ",
"Even the quieter acoustic songs are often suffused by background choral singing, sustained ohhhs and ooohs, generating a pale glow. ",
"The louder songs are busy as hell—murky organ, kick drum, random distorted thuds, it’s all in there somewhere.",
"\n\nBut it’s too easy to call Hozier pompous. ",
"In fact, he’s guilty of a more conventionally tedious form of humility. ",
"He conceives of himself as an everyman, lucky enough to have been touched by some conflation of soul music and the muses. ",
"These exotic forces transformed his life, and he feels blessed to sing about his secular grace. ",
"Performers from Leonard Cohen to Julien Baker have demonstrated that such an approach is not incompatible with wit, eccentricity, invention. ",
"I suspect the long shadow of Hozier’s influence stems from blankness. ",
"Just by huffing and puffing, any boring white dude can elevate himself into grandeur."
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"---\nabstract: 'The electron spin in a semiconductor quantum dot can be coherently controlled by an external electric field, an effect called electric-dipole spin resonance (EDSR). ",
"Several mechanisms can give rise to the EDSR effect, among which there is a hyperfine mechanism, where the spin-electric coupling is mediated by the electron-nucleus hyperfine interaction. ",
"Here, we investigate the influence of frequency modulation (FM) on the spin-flip efficiency. ",
"Our results reveal that FM plays an important role in the hyperfine mechanism. ",
"Without FM, the electric field almost cannot flip the electron spin; the spin-flip probability is only about 20%. ",
"While under FM, the spin-flip probability can be improved to approximately 70%. ",
"In particular, we find that the modulation amplitude has a lower bound, which is related to the width of the fluctuated hyperfine field.'",
"\nauthor:\n- Rui Li\ntitle: 'Hyperfine interaction mediated electric-dipole spin resonance: the role of frequency modulation'\n---\n\nIntroduction\n============\n\nThe electron spin confined in a semiconductor quantum dot is a promising candidate for the qubit [@Hanson; @Buluta]. ",
"Since the pioneering work of Loss and DiVincenzo in 1998 [@Loss], spin quantum computing has become an important research area. ",
"There have been many theoretical and experimental advances in the subsequent decades. ",
"Qubit initialization [@Johnson; @Petta], coherent manipulation [@Koppens; @Foletti], and single shot readout [@Elzerman; @Barthel; @Morello] can be achieved with high precision. ",
"The quantum dot spin qubit has many advantages. ",
"For example, spin has a relative long coherence time (in comparison with the qubit manipulation time) [@Bluhm], the two-qubit manipulation can be easily achieved by using the Heisenberg exchange interaction [@Burkard; @Xuedong; @RuiLi5; @RuiLi4], and it is more or less much easier to achieve the qubit scalability.",
"\n\nSingle spin manipulation can be achieved by using the traditional electron spin resonance technique [@Koppens]. ",
"This method not only needs a static Zeeman field, but also needs a perpendicular ac magnetic field [@Awschalom; @Meisels]. ",
"When the frequency of the ac field matches the electron Zeeman splitting, one achieves coherent spin rotation. ",
"However, it is difficult to produce a local ac magnetic field experimentally [@Koppens]. ",
"Recently, instead of an ac magnetic field, an ac electric field has been used to manipulate a single electron spin, an effect called electric-dipole spin resonance (EDSR) [@Tokura; @Pioro; @Nowack; @Nadj1; @Nadj2; @Rashba; @Golovach; @RuiLi; @RuiLi3; @Laird; @Rashba3]. ",
"It is much easier to produce a local ac electric field in experiments.",
"\n\nWe can explain quantum dot EDSR in the following simple way. ",
"In absence of electric driving, the electron’s spin degree of freedom is mixed with its orbital degree of freedom due to some mechanisms, e.g., the slanted magnetic field [@Yoneda; @Palyi; @Szechenyi; @Scarlino], spin-orbit coupling [@Ban; @Yang; @Nowak; @Khomitsky; @Echeverria; @Romhanyi; @ZhangPeng], and the electron-nucleus hyperfine interaction [@Shafiei; @Osika; @Chesi]. ",
"Therefore, an ac electric field can induce electric-dipole transitions between the electron Zeeman levels.",
"\n\nThe hyperfine interaction mediated EDSR was first observed experimentally in 2007 [@Laird]. ",
"The hallmarks of this mechanism are listed as follows. ",
"First, under electric driving, there is no Rabi oscillation, i.e., no periodical revival of the spin polarization [@Laird]; the spin-flip probability monotonically increases to a saturating value. ",
"Second, the Rabi frequency is independent of the Zeeman field [@Laird]. ",
"Third, if there is no frequency modulation (FM) of the driving electric field, the electron spin cannot be flipped [@Shafiei]. ",
"The first theoretical investigation into the hyperfine mechanism was given by Rashba [@Rashba3], who provides deep insight into the physics behind the EDSR effect. ",
"However, the developed theory was built on the mean field approximation, and, in particular, the effects of FM were not explored.",
"\n\nIn this paper, we re-address the mechanism of hyperfine interaction mediated EDSR in the presence of FM. ",
"Our main findings are summarized as follows. ",
"First, we derive an analytical expression for the spin-flip probability where we do not take any mean field approximation. ",
"The spin-flip probability is expressed by a summation over a large number of periodic functions such that the oscillating behaviour of each periodic function is covered by the summation. ",
"Second, under fixed-frequency driving, the spin cannot be flipped. ",
"Because the electron-nucleus hyperfine interaction brings an inhomogeneous broadening to the spin splitting; the fixed driving frequency cannot match the inhomogeneously broadened spin splitting. ",
"Third, FM is used to broaden the frequency spectrum of the driving electric field. ",
"When the width of the frequency spectrum is larger than the width of the fluctuated hyperfine field, the spin-flip probability can be greatly improved.",
"\n\n\\[Sec\\_II\\]EDSR in a quantum dot with quasi-1D confinement\n==========================================================\n\nIn order to explicitly show the underlying physics of hyperfine interaction mediated EDSR, we first study this phenomena in a simple quasi-1D quantum dot. ",
"In fact, a quantum dot with quasi-1D confinement, e.g., an InAs [@Schroer; @Nadj1] or an InSb [@Nadj2] nanowire quantum dot can already be fabricated experimentally. ",
"Therefore, we confront the following total Hamiltonian $$\\begin{aligned}\nH_{\\rm tot}&=&\\frac{p^{2}_{x}}{2m_{e}}+\\frac{1}{2}m_{e}\\omega^{2}_{0}x^{2}+\\sum^{N}_{l=1}\\frac{A}{\\hbar^{2}}{\\bf S}\\cdot{\\bf I}_{l}\\delta(x-x_{l})\\nonumber\\\\\n&&+\\gamma_{e}BS_{x}+eEx\\cos\\left[\\int^{t}_{0}dt'\\nu(t')\\right],\\label{EQ_originalHamiltonian}\\end{aligned}$$ where $p_{x}=-i\\hbar\\partial_{x}$, $m_{e}$ is the effective electron mass, $\\hbar\\omega_{0}$ is the orbital energy of the quantum dot, $A$ is the strength of the electron-nucleus hyperfine coupling, $\\gamma_{e}$ is the electron gyromagnetic ratio, ${\\bf S}$ ($S=1/2$) and ${\\bf I}_{l}$ ($I=1/2$) are the electron and the $l$-th nuclear spin operators, respectively, $N$ is the total number of the nuclear spins in the dot, $x_{l}$ is the site of the $l$-th nuclear spin, and $\\nu\\,(t')$ is the modulated frequency of the driving electric field.",
"\n\nWe have introduced the concept of FM in Eq.",
" (\\[EQ\\_originalHamiltonian\\]), where the frequency of the driving field is time dependent. ",
"In this paper, we will study both the fixed-frequency driving case, i.e., $\\nu(t')=\\nu_{0}$, and the modulated-frequency driving case, i.e., $\\nu(t')=\\nu_{0}+\\delta\\nu\\cos(\\nu_{\\rm fm}t')$, where $\\delta\\nu$ and $\\nu_{\\rm fm}$ are the modulation amplitude and the modulation frequency, respectively.",
"\n\nThe mixing of spin and orbital degrees of freedom owing to hyperfine interaction\n--------------------------------------------------------------------------------\n\nOur first step is to calculate the spin splitting and the corresponding wavefunctions in the quantum dot in the presence of both an external magnetic field and a hyperfine field. ",
"The Hamiltonian of the quantum dot in the absence of the driving term can be divided into two parts $$\\begin{aligned}\nH&=&H_{0}+H_{1},\\nonumber\\\\\nH_{0}&=&\\frac{p^{2}_{x}}{2m_{e}}+\\frac{1}{2}m_{e}\\omega^{2}_{0}x^{2}+\\gamma_{e}BS_{x},\\nonumber\\\\\nH_{1}&=&\\sum^{N}_{l=1}\\frac{A}{\\hbar^{2}}\\left[S_{x}I^{x}_{l}+\\frac{1}{2}(S_{+}I^{-}_{l}+S_{-}I^{+}_{l})\\right]\\delta(x-x_{l}),\\end{aligned}$$ where $S_{\\pm}=S_{y}\\pm\\,iS_{z}$ and $I^{\\pm}_{l}=I_{y}\\pm\\,iI_{z}$ are the electron and the $l$-th nuclear spin raising/lowering operators, respectively. ",
"Note that the spin quantization direction here is along the $x$-axis. ",
"The full quantum mechanical solution to the time-independent Schrödinger equation is impossible because the hyperfine term $H_{1}$ is coordinate-dependent. ",
"However, when the Zeeman field $\\gamma_{e}B$ is strong enough, i.e., the Zeeman field is much larger than the hyperfine field, we can solve the energy spectrum by treating $H_{1}$ as a perturbation. ",
"The related physical quantities should satisfy the following perturbation condition: $$\\sum^{N}_{l=1}(A_{l}/4)\\ll\\gamma_{e}B\\ll\\hbar\\omega_{0},$$ where $A_{l}$ is the $l$-th electron-nuclear hyperfine coupling coefficient. ",
"The definition of this coefficient is given in a later equation (\\[Eq\\_hyperfine\\_coeff\\]).",
"\n\nIt is easy to find the zeroth order eigenvalues and the corresponding eigenfunctions: $$\\begin{aligned}\nE^{0}_{n\\sigma_{e}\\chi_{m}}&=&(n+1/2)\\hbar\\omega_{0}+(1/2)(-1)^{\\sigma_{e}}\\gamma_{e}B,\\nonumber\\\\\n|\\Psi^{0}_{n\\sigma_{e}\\chi_{m}}\\rangle&=&\\psi_{n}(x)|\\sigma_{e}\\rangle\\otimes|\\chi_{m}\\rangle,\\label{Eq_energy_zero}\\end{aligned}$$ where $n=0,1,2\\ldots$ is the main quantum number, $\\sigma_{e}=0,1$ is the electron spin quantum number, with $|0\\rangle\\rightarrow|\\!\\uparrow_{x}\\rangle$ and $|1\\rangle\\rightarrow|\\!\\downarrow_{x}\\rangle$, $|\\chi_{m}\\rangle=|\\sigma^{m}_{1}\\sigma^{m}_{2}\\cdots\\sigma^{m}_{N}\\rangle$ is the $N$-bit binary representation of a decimal number $m=0,1,\\ldots(2^{N}-1)$, with $\\sigma^{m}_{l}=0,1$ being the $l$-th nuclear spin quantum number, and $\\psi_{n}(x)$ is the eigenfunction of the harmonic oscillator, e.g., $$\\begin{aligned}\n\\psi_{0}(x)&=&1/(\\pi^{1/4}x^{1/2}_{0}){\\rm exp}\\left[-x^{2}/(2x^{2}_{0})\\right],\\nonumber\\\\\n\\psi_{1}(x)&=&2^{1/2}/(\\pi^{1/4}x^{1/2}_{0})(x/x_{0}){\\rm exp}\\left[-x^{2}/(2x^{2}_{0})\\right],\\end{aligned}$$ with $x_{0}=\\sqrt{\\hbar/(m_{e}\\omega_{0})}$ being the characteristic length of the quantum dot. ",
"The electron in the quantum dot should occupy the lowest orbital level, i.e., $n=0$. Therefore, in the following we only focus on $n=0$ Zeeman levels $|\\Psi_{0\\sigma_{e}\\chi_{m}}\\rangle$.\n\n![",
"\\[Fig\\_energyspectrum\\]The energy spectrum of the quantum dot in the presence of the electron-nucleus hyperfine interaction.](Quantum_dot_spectrum.eps)\n\nIt should be noted that, up to the zeroth order, each energy level has a degeneracy of $2^{N}$ (see equation (\\[Eq\\_energy\\_zero\\])). ",
"However, the perturbation $H_{1}$ does not mix the states in the degenerate subspace. ",
"Therefore, in our following calculation we can use the non-degenerate perturbation formulas [@Landau] $$\\begin{aligned}\nE&=&E^{0}+\\langle\\Psi^{0}|H_{1}|\\Psi^{0}\\rangle,\\nonumber\\\\\n|\\Psi\\rangle&=&|\\Psi^{0}\\rangle+\\sum_{\\Psi'}\\frac{\\langle\\Psi'^{0}|H_{1}|\\Psi^{0}\\rangle}{E^{0}-E'^{0}}|\\Psi'^{0}\\rangle.\\end{aligned}$$ Up to the first-order perturbation, the Zeeman energies have the following rectifications: $$\\begin{aligned}\nE_{00\\chi_{m}}&=&(1/2)\\hbar\\omega_{0}+(1/2)\\gamma_{e}B+\\sum^{N}_{l=1}(A_{l}/4)(-1)^{\\sigma^{m}_{l}},\\nonumber\\\\\nE_{01\\chi_{m}}&=&(1/2)\\hbar\\omega_{0}-(1/2)\\gamma_{e}B-\\sum^{N}_{l=1}(A_{l}/4)(-1)^{\\sigma^{m}_{l}},\\label{Eq_hyperfine_coeff}\\end{aligned}$$ where $A_{l}=A\\psi^{2}_{0}(x_{l})$ is the $l$-th electron-nucleus hyperfine coupling coefficient. ",
"The hyperfine energy structure of the quantum dot is schematically shown in figure \\[Fig\\_energyspectrum\\]. ",
"The corresponding first-order perturbation wavefunctions read $$\\begin{aligned}\n|\\Psi_{00\\chi_{m}}\\rangle&=&|\\Psi^{0}_{00\\chi_{m}}\\rangle+\\sum^{N}_{l=1}\\frac{A\\psi_{1}(x_{l})\\psi_{0}(x_{l})}{2(\\gamma_{e}B-\\hbar\\omega_{0})}\\sigma^{m}_{l}\\nonumber\\\\\n&&\\times\\psi_{1}(x)|1\\rangle\\otimes\n|\\sigma^{m}_{1}\\ldots\\sigma^{m}_{l-1}0\\sigma^{m}_{l+1}\\ldots\\sigma^{m}_{N}\\rangle,\\nonumber\\\\\n|\\Psi_{01\\chi_{m}}\\rangle&=&|\\Psi^{0}_{01\\chi_{m}}\\rangle+\\sum^{N}_{l=1}\\frac{A\\psi_{1}(x_{l})\\psi_{0}(x_{l})}{2(-\\gamma_{e}B-\\hbar\\omega_{0})}\\frac{(-1)^{\\sigma^{m}_{l}}+1}{2}\\nonumber\\\\\n&&\\times\\psi_{1}(x)|0\\rangle\\otimes|\\sigma^{m}_{1}\\ldots\\sigma^{m}_{l-1}1\\sigma^{m}_{l+1}\\ldots\\sigma^{m}_{N}\\rangle.\\label{Eq_wavefunction}\\end{aligned}$$ Thus, it can be seen clearly from equation (\\[Eq\\_wavefunction\\]) that, owing to the hyperfine interaction, the spin and the orbital degrees of freedom of the electron are mixed. ",
"Therefore, it is expected that the electric field will induce the transitions between the up Zeeman level and the down Zeeman level.",
"\n\nThe spin-flip probability under fixed-frequency driving\n-------------------------------------------------------\n\nIn this subsection, we study the EDSR effect under fixed-frequency driving. ",
"The driving Hamiltonian is written as $eEx\\cos(\\nu_{0}t)$, where $\\nu_{0}$ is the driving frequency. ",
"Although the electron spin splitting is broadened by the hyperfine interaction (see equation (\\[Eq\\_hyperfine\\_coeff\\]) and figure \\[Fig\\_energyspectrum\\]), we still choose the driving frequency to satisfy the ‘resonant’ condition, i.e., $\\hbar\\nu_{0}=\\gamma_{e}B$.\n\nAs we have shown in figure \\[Fig\\_energyspectrum\\], each Zeeman (both the up and the down) level has been broadened to a series of sublevels, where $m$ is the sublevel index. ",
"So what is the initial state for the coupled electron-nuclear system? ",
"Because the nuclear Zeeman splitting is much less than the Boltzmann energy $k_{B}T$, with $T\\sim\\,m$K being the temperature of the experiments. ",
"It is a good approximation to assume that the nuclear spin ensemble is totally unpolarized. ",
"In other words, in the initial mixed state of the total electron-nucleus system, each pure state $|\\Psi_{00\\chi_{m}}\\rangle$ has the equal probability $$\\rho(0)=(1/2^{N})\\sum^{2^{N}-1}_{m=0}|\\Psi_{00\\chi_{m}}\\rangle\\langle\\Psi_{00\\chi_{m}}|.\\label{Eq_initialstate}$$ Here, we have let the electron initially be in the spin-up state $|0\\rangle$ ($|\\uparrow_{x}\\rangle$).",
"\n\n![",
"\\[Fig\\_flipflop\\]Schematic diagram of the electric-dipole transition between the state $|\\Psi_{00\\chi_{m}}\\rangle$ and the state $|\\Psi_{01\\chi'_{m}}\\rangle$. In other words, the driving electric field assists the electron-nucleus spin-flip-flop process. ",
"There is an exchange of spin polarization between the electron and the $l$-th nucleus.](Transitions.eps)\n\nUnder electric driving, we want to calculate the electron spin-flip rate for the initial mixed state given in equation (\\[Eq\\_initialstate\\]). ",
"Our first step is to calculate the spin-flip rate for the initial pure state $|\\Psi_{00\\chi_{m}}\\rangle$. From equation (\\[Eq\\_wavefunction\\]), we can calculate the electric-dipole transition element between the state $|\\Psi_{00\\chi_{m}}\\rangle$ and the state $|\\Psi_{01\\chi'_{m}}\\rangle$ $$\\begin{aligned}\ng^{m}_{l}&=&\\langle\\Psi_{00\\chi_{m}}|eEx|\\Psi_{01\\chi'_{m}}\\rangle\\nonumber\\\\\n&=&-\\frac{eEx_{0}\\times\\hbar\\omega_{0}}{\\sqrt{2}\\left(\\hbar^{2}\\omega^{2}_{0}-\\gamma^{2}_{e}B^{2}\\right)}\\sigma^{m}_{l}A\\psi_{1}(x_{l})\\psi_{0}(x_{l})\\nonumber\\\\\n&\\approx&-\\frac{eEx_{0}}{\\sqrt{2}\\hbar\\omega_{0}}\\sigma^{m}_{l}A\\psi_{1}(x_{l})\\psi_{0}(x_{l}),\\label{Eq_transitionrate}\\end{aligned}$$ where $|\\chi_{m}\\rangle=|\\sigma^{m}_{1}\\cdots\\sigma^{m}_{l}\\cdots\\sigma^{m}_{N}\\rangle$ and $|\\chi'_{m}\\rangle\\equiv|\\sigma^{m}_{1}\\cdots\\sigma^{m}_{l-1}0\\sigma^{m}_{l+1}\\cdots\\sigma^{m}_{N}\\rangle$. Similar results were also obtained in [@Rashba3; @Rudner]. ",
"The above equation tells us that the electron-nucleus spin-flip-flop process is assisted by the driving electric field (see figure \\[Fig\\_flipflop\\]). ",
"There is an exchange of the spin polarization between the electron and the $l$-th nucleus. ",
"It should be noted that the value of $\\sigma^{m}_{l}$ in equation (\\[Eq\\_transitionrate\\]) automatically guarantees the feasibility of this flip-flop process, i.e., only when $\\sigma^{m}_{l}=1$ is $g^{m}_{l}\\neq0$. The energy difference between these two states reads $$E_{00\\chi_{m}}-E_{01\\chi'_{m}}\\approx\\gamma_{e}B+\\sum^{N}_{l=1}(A_{l}/2)(-1)^{\\sigma^{m}_{l}}.\\label{Eq_broadenZeeman}$$ There arises another problem: under electric driving there are many quantum states with which the state $|\\Psi_{00\\chi_{m}}\\rangle$ can flip-flop, as long as the $l$-th bit in $|\\chi_{m}\\rangle$ has the value $\\sigma^{m}_{l}=1$ $(l\\in\\{1,\\ldots\\,N\\})$. Despite this, the spin-flip probability for the initial pure sate $|\\Psi_{00\\chi_{m}}\\rangle$ still has a simple expression (for details see appendix \\[Appendix\\_A\\]) $$P^{m}_{\\downarrow_{x}}(t)=\\frac{\\sum^{N}_{l=1}(g^{m}_{l})^{2}}{\\hbar^{2}\\Omega^{2}_{m}}\\sin^{2}\\frac{\\Omega_{m}t}{2},\\label{Eq_inversion_purestate}$$ where\n\n$$\\begin{aligned}\n\\Delta_{m}&=&-\\sum^{N}_{l=1}(A_{l}/2)(-1)^{\\sigma^{m}_{l}},\\label{Eq_detuning}\\\\\n\\Omega_{m}&=&\\frac{1}{\\hbar}\\left[\\Delta^{2}_{m}+\\sum^{N}_{l=1}(g^{m}_{l})^{2}\\right]^{1/2}.\\label{Eq_inversion_parameters}\\end{aligned}$$\n\nHere, $\\Delta_{m}$ is the detuning introduced by the hyperfine field and $\\Omega_{m}$ is the Rabi frequency in the presence of the detuning. ",
"Therefore, for the initial pure state $|\\Psi_{00\\chi_{m}}\\rangle$, we obtain a simple Rabi formula [@Scully] for the spin-flip probability. ",
"As we can see from equations (\\[Eq\\_transitionrate\\]) and (\\[Eq\\_inversion\\_parameters\\]), the Rabi frequency $\\Omega_{m}$ is independent of the magnetic field, which is consistent with experimental observations [@Laird; @Shafiei].",
"\n\nSince we have already obtained the spin-flip probability for the initial pure state, the generalization to the initial mixed state (\\[Eq\\_initialstate\\]) is simple. ",
"The spin-flip probability for the initial mixed state reads as $$P_{\\downarrow_{x}}(t)=(1/2^{N})\\sum^{2^{N}-1}_{m=0}\\frac{\\sum^{N}_{l=1}(g^{m}_{l})^{2}}{\\hbar^{2}\\Omega^{2}_{m}}\\sin^{2}\\frac{\\Omega_{m}t}{2}.\\label{Eq_inversion}$$ This is just a summation over all the pure state’s spin-flip probability. ",
"Because equation (\\[Eq\\_inversion\\]) is summed over a large number of periodic functions, $P_{\\downarrow_{x}}(t)$ may not contain the oscillating behaviour when $N$ is very large.",
"\n\nIn figure (\\[Fig\\_EDSRWithoutFM\\]), we show the spin-flip probability as a function of the driving time. ",
"As we can see, under fixed frequency driving ($\\hbar\\nu_{0}=\\gamma_{e}B$), the electron spin almost can not be flipped; the maximal spin-down probability is only $0.2$. This very low spin-flip probability has not been observed in experiment [@Shafiei]. ",
"Therefore, under fixed-frequency driving, EDSR actually can not occur. ",
"We will explain why the spin-flip probability is very low in the next subsection.",
"\n\n![",
"\\[Fig\\_EDSRWithoutFM\\]The spin down probability under the fixed-frequency driving. ",
"The quantum dot parameters are chosen as $x_{0}=100$ nm, $A/(\\hbar\\pi^{1/2}x_{0})=0.5$ MHz, and $eEx_{0}/(\\hbar\\omega_{0})=0.2$. $N$ is the total number of the nuclear spins in the quantum dot and the nuclear spins are equal-distance distributed in the quantum dot.](Inversion_withoutFMRE.eps)\n\nThe spin-flip probability under modulated-frequency driving\n-----------------------------------------------------------\n\nAs we have explicitly shown in the above subsection, each pure state $|\\Psi_{00\\chi_{m}}\\rangle$ in the initial mixed state (see equation (\\[Eq\\_initialstate\\])) brings a detuning $\\Delta_{m}$ to the spin-flip probability $P_{\\downarrow_{x}}(t)$ (see equations (\\[Eq\\_detuning\\]) and (\\[Eq\\_inversion\\])). ",
"When $m$ runs one by one from $0$ to $2^{N}-1$, the value of the detuning $\\Delta_{m}$ has a distribution function. ",
"Actually, this distribution describes the fluctuation of the hyperfine field. ",
"The distribution function approximately reads [@Merkulov] $$P(\\Delta)=\\frac{1}{(2\\pi)^{1/2}\\Delta_{\\rm flu}}e^{-\\Delta^{2}/(2\\Delta^{2}_{\\rm flu})},\\label{Eq_distribution}$$ where $\\Delta_{\\rm flu}=(1/2)\\sqrt{\\sum^{N}_{l=1}A^{2}_{l}}$ is the width of the hyperfine field fluctuation. ",
"Therefore, under fixed-frequency driving (e.g., $\\gamma_{e}B=\\hbar\\nu_{0}$), the detuning $\\Delta$ is not fixed. ",
"This is the essential reason that leads to the very low spin-flip probability.",
"\n\nFM is a concept in telecommunication and signal processing. ",
"As we will show in the following, FM can solve the above very low spin-flip probability problem. ",
"Here, we take the simplest example to explain the importance of the FM. ",
"We consider the instantaneous frequency of the driving electric field is modulated to the following form $$\\nu(t')=\\nu_{0}+\\delta\\nu\\cos(\\nu_{\\rm fm}t'),$$ where $\\nu_{0}$ is the central frequency, $\\delta\\nu$ is the modulation amplitude, and $\\nu_{\\rm fm}$ is the modulation frequency. ",
"In order to understand FM straightforwardly, we also give the experimental parameters here, where $\\nu_{0}=2.9$ GHz, $\\delta\\nu=36$ MHz, and $\\nu_{\\rm fm}=3$ kHz [@Laird]. ",
"In the presence of FM, the driving Hamiltonian can be written as [@Haykin] $$eEx\\cos\\left[\\int^{t}_{0}dt'\\nu(t')\\right]=\\sum^{\\infty}_{l=-\\infty}eExJ_{l}(\\beta)\\cos\\left[(\\nu_{0}+l\\nu_{\\rm fm})t\\right],\\label{Eq_FMdriving}\n%&\\approx&\\sum^{l=N_{\\rm max}}_{l=-N_{\\rm max}}J_{l}(\\beta)\\cos\\left[(\\nu_{0}+l\\nu_{\\rm fm})t\\right],~~~$$ where we have made a Fourier transformation, $\\beta=\\delta\\nu/\\nu_{\\rm fm}\\gg1$ is the modulation index (we only consider the wideband modulation here), and $$J_{l}(\\beta)=\\frac{1}{2\\pi}\\int^{\\pi}_{-\\pi}dx\\,{\\rm exp}[i(\\beta\\sin\\,x-lx)]\\nonumber$$ is the $n$-th order Bessel function of the first kind. ",
"In figure [\\[Fig\\_Bessel\\]]{}, we show the Bessel function as a function of the index $l$ for the large modulation index $\\beta=200$. As we can see, when $|l|>\\beta$, $J_{l}(\\beta)\\approx0$. Therefore, actually, the summation of $l$ in equation (\\[Eq\\_FMdriving\\]) is constrained to $-\\beta\\leq\\,l\\leq\\beta$.\n\n![",
"\\[Fig\\_Bessel\\]The Bessel function $J_{l}(\\beta)$ as a function of the index $l$ for large modulation index $\\beta=200$. For $|l|>\\beta$, $J_{l}(\\beta)\\approx0$.](BesselFunctionRE.eps)\n\nFrom equation (\\[Eq\\_FMdriving\\]), it is easy to find that the frequency spectrum of the driving electric field has been broadened by the FM. ",
"The frequency of the driving now can run from $\\nu_{0}-\\delta\\nu$ to $\\nu_{0}+\\delta\\nu$, where $\\delta\\nu=\\beta\\nu_{\\rm fm}$ can be considered as the width of the frequency spectrum. ",
"This frequency spectrum broadening is very useful. ",
"As we have shown in equation (\\[Eq\\_distribution\\]), the detuning $\\Delta$, i.e., the hyperfine field, also has a distribution which approximately ranges from $-\\sqrt{2}\\Delta_{\\rm flu}$ to $\\sqrt{2}\\Delta_{\\rm flu}$. Therefore, the inhomogeneously broadened spin splitting is ranged from $\\gamma_{e}B-\\sqrt{2}\\Delta_{\\rm flu}$ to $\\gamma_{e}B+\\sqrt{2}\\Delta_{\\rm flu}$. When the width of the frequency spectrum $\\delta\\nu$ is larger than the width of the fluctuating hyperfine field $\\sqrt{2}\\Delta_{\\rm flu}$, i.e., $$\\sqrt{2}\\Delta_{\\rm flu}<\\delta\\nu,$$ the detuing $\\Delta$ will not appear in the spin-flip probability $P_{\\downarrow_{x}}(t)$. Because for each initial pure state $|\\Psi_{00\\chi_{m}}\\rangle$ the broadened spin splitting is $\\gamma_{e}B-\\Delta_{m}$ (see equation (\\[Eq\\_broadenZeeman\\])), we can always find a special mode $l$ in the driving field that matches this splitting, where $$\\gamma_{e}B-\\Delta_{m}=\\nu_{0}+l\\nu_{\\rm fm}.$$ Thus, the $l$-th mode $eExJ_{l}(\\beta)\\cos\\left[(\\nu_{0}+l\\nu_{\\rm m})t\\right]$, where $l=-\\Delta_{m}/\\nu_{\\rm fm}$, is in resonance with this broadened spin splitting $\\gamma_{e}B-\\Delta_{m}$. Therefore, the spin-flip probability under the FM can be written as $$P_{\\downarrow_{x}}(t)=\\frac{1}{2^{N}}\\sum^{2^{N}-1}_{m=0}\\sin^{2}\\frac{\\Omega^{\\rm fm}_{m}t}{2},\\label{Eq_inversion_FM}$$ where $\\Omega^{\\rm fm}_{m}=\\frac{1}{\\hbar}J_{-(\\Delta_{m}/\\nu_{\\rm fm})}(\\beta)\\sqrt{\\sum^{N}_{l=1}(g^{m}_{l})^{2}}$ is the Rabi frequency under the FM. ",
"When the detuning $\\Delta_{m}$ is absent from the Rabi frequency, the spin-flip probability can been greatly improved. ",
"In figure [\\[Fig\\_EDSRFM\\]]{}, we show the spin-flip probability as a function of the driving time under FM. ",
"We find that the maximal spin-flip probability increases from 0.2 (see figure \\[Fig\\_EDSRWithoutFM\\]) to 0.7 (see figure \\[Fig\\_EDSRFM\\]). ",
"This result is consistent with the experimental observation that the EDSR can only be observed under FM [@Shafiei]. ",
"We also mention that the experimentally observed maximal spin-flip probability is also about 0.7 [@Shafiei].",
"\n\n![",
"\\[Fig\\_EDSRFM\\]The spin down probability under modulated frequency driving. ",
"The modulation parameters are chosen as $\\beta=200$ and $\\nu_{\\rm fm}=0.02$ MHz. ",
"The other parameters are the same as in figure \\[Fig\\_EDSRWithoutFM\\].](Spin_flip_FMRE.eps)\n\nBecause the spin-flip probability $P_{\\downarrow_{x}}(t)$ is still expressed by a summation over a large number of periodical functions (see equation (\\[Eq\\_inversion\\_FM\\])), the Rabi oscillation may not appear when $N$ is larger. ",
"If $N$ is not large enough, e.g., $N=30$ or $35$, as we show in figures \\[Fig\\_EDSRWithoutFM\\] and \\[Fig\\_EDSRFM\\], there is still an oscillation for the spin-flip probability, but the amplitude of the oscillation is small.",
"\n\n\\[Sec\\_III\\]EDSR in quantum dot with quasi-2D confinement\n=========================================================\n\nMost gated quantum dots fabricated from semiconductor heterostructures, e.g., GaAs/AlGaAs heterostructures, are confined in 2D. Here we move to consider the EDSR effect in a quantum dot with quasi-2D confinement. ",
"As we have already explored the physics of EDSR in a quasi-1D quantum dot, the generalization from 1D to 2D is natural. ",
"As we show in the following, the underlying physics does not change, except the calculations are a little more complicated. ",
"We focus on the following Hamiltonian $$\\begin{aligned}\nH_{\\rm tot}&=&\\frac{p^{2}_{x}+p^{2}_{y}}{2m_{e}}+\\frac{m_{e}\\omega^{2}_{0}(x^{2}+y^{2})}{2}+\\sum_{l}\\frac{A}{\\hbar^{2}}\\textbf{S}\\cdot\\textbf{I}_{l}\\delta(\\textbf{r}-\\textbf{r}_{l})\\nonumber\\\\\n&&+\\gamma_{e}BS_{x}+eEx\\cos\\left[\\int\\,dt'\\nu(t')\\right],\\label{Eq_Hamiltonian2D}\\end{aligned}$$ where $p_{x,y}=-i\\hbar\\partial_{x,y}$, $\\textbf{r}=x\\hat{e}_{x}+y\\hat{e}_{y}$, and $\\textbf{r}_{l}$ is the site of the $l$-th nuclear spin. ",
"The in-plane magnetic field is applied along the $x$ direction, the ac electric-field is also applied along this direction. ",
"This is the simplest Hamiltonian that captures the main physics of EDSR in a quantum dot with quasi-2D confinement.",
"\n\nThe calculations here are completely similar to the 1D case; the dimension $y$ in equation (\\[Eq\\_Hamiltonian2D\\]) only introduces the calculation complexities. ",
"The transition element defined in equation (\\[Eq\\_transitionrate\\]) for the 2D case is modified to $$g^{m}_{l}\\approx-\\frac{eEx_{0}}{\\sqrt{2}\\hbar\\omega}\\sigma^{m}_{l}A\\psi^{2}_{0}(y_{l})\\psi_{1}(x_{l})\\psi_{0}(x_{l}).\\label{Eq_2Dtransitionelement}$$ Also, the hyperfine coupling coefficient for the quantum dot with 2D confinement is defined as $$A_{l}=A\\psi^{2}_{0}(x_{l})\\psi^{2}_{0}(y_{l}).\\label{Eq_2Dhyperfinecoefficient}$$ Under fixed-frequency driving, the expression of the spin-flip probability is exactly the same as that given by equations (\\[Eq\\_inversion\\_purestate\\])-(\\[Eq\\_inversion\\]). ",
"Also, under FM, the expression of the spin-flip probability still has the form shown in equation (\\[Eq\\_inversion\\_FM\\]). ",
"For a realistic gated GaAs quantum dot, the total number of the nuclear spins in the quantum dot is about $N=10^{5}$. This number is too huge. ",
"Therefore, it is impossible to calculate the spin-flip probability $P_{\\downarrow_{x}}(t)$ via equations (\\[Eq\\_inversion\\]) and (\\[Eq\\_inversion\\_FM\\]). ",
"In the following, we only discuss some general properties of EDSR in a quasi-2D quantum dot. ",
"These properties are closely related to the experimental observations.",
"\n\nFirstly, for a quantum dot with quasi-2D confinement, the Rabi frequency is still independent of the external magnetic field. ",
"As we can see from equations (\\[Eq\\_inversion\\_parameters\\]) and (\\[Eq\\_inversion\\_FM\\]), where $g^{m}_{l}$ and $A_{l}$ are defined in equations (\\[Eq\\_2Dtransitionelement\\]) and (\\[Eq\\_2Dhyperfinecoefficient\\]), respectively, both $\\Omega_{m}$ and $\\Omega^{\\rm fm}_{m}$ do not depend on the magnetic field strength $B$. This is consistent with experimental observations [@Laird; @Shafiei].",
"\n\nSecondly, for a gated GaAs quantum dot, the width of the hyperfine field fluctuation is about $\\Delta_{\\rm flu}\\approx24$ MHz (0.1 $\\mu$eV) [@Merkulov]. ",
"This quantity sets a lower bound on the modulation amplitude: $$\\sqrt{2}\\Delta_{\\rm flu}\\approx34~{\\rm MHz}<\\delta\\nu.$$ In order to observe the EDSR more efficiently, it is better to let the modulation amplitude be larger than $34$ MHz. ",
"This result is also consistent with experimental observations. ",
"An early experiment used a 36 MHz modulation amplitude [@Laird] and a more recent experiment used both 40 and 75 MHz modulation amplitudes [@Shafiei].",
"\n\n\\[Sec\\_IV\\]Summary\n==================\n\nThe electron-nucleus hyperfine interaction, which commonly exists in III-V semiconductor quantum dots, is often considered as a nuisance because it can lead to spin decoherence [@Khaetskii; @Coish; @Witzel; @Yao; @Deng; @Cywinski; @RuiLi2; @Echeverria2]. ",
"On the other hand, we can make use of the hyperfine interaction. ",
"The hyperfine interaction mediates an interaction between the spin and an external electric field that can facilitate the single spin manipulation.",
"\n\nIn this paper, we give a detailed theoretical investigation to the mechanism of the hyperfine interaction mediated EDSR. ",
"We emphasize the importance of FM to the driving electric field in this hyperfine mechanism. ",
"The spin-flip probability is expressed by a summation over a large number of periodical functions such that there is no Rabi oscillation for the spin-flip probability. ",
"Because the hyperfine field gives an inhomogeneous broadening to the spin splitting, the fixed-frequency driving almost cannot flip the electron spin. ",
"FM of the driving field can greatly improve the spin-flip efficiency; there is approximately a 50% improvement in the spin-flip probability. ",
"Also, the width of hyperfine field fluctuation sets a lower bound on the modulation amplitude. ",
"Our theory is in qualitatively good agreement with the experimental observations.",
"\n\nAcknowledgements {#acknowledgements .unnumbered}\n================\n\nThis work is supported by National Natural Science Foundation of China Grant No.",
" 11404020 and Postdoctoral Science Foundation of China Grant No.",
" 2014M560039.",
"\n\n\\[Appendix\\_A\\]The spin-flip probability for the initial pure state $|\\Psi_{00\\chi_{m}}\\rangle$\n===============================================================================================\n\n![",
"\\[Fig\\_Rabiadditive\\]Schematically shown the simplified level diagram of the electron-nuclear system under the electric driving. ",
"There is an electric-dipole transition element $g^{m}_{l}$ between the state $|0\\rangle$ and the state $|1_{l}\\rangle$.](Rabi_additive.eps)\n\nIn the following, for brevity, we make some abbreviations such as $|0\\rangle\\equiv|\\Psi_{00\\chi_{m}}\\rangle$ and $|1_{l}\\rangle\\equiv\\psi_{0}(x)|1\\rangle|\\sigma^{m}_{1}\\cdots\\sigma^{m}_{l-1}0\\sigma^{m}_{l+1}\\cdots\\sigma^{m}_{N}\\rangle$. Under fixed-frequency driving $eEx\\cos(\\nu_{0}t)$, there is a transition element $g^{m}_{l}$ between the state $|0\\rangle$ and the state $|1_{l}\\rangle$ (see figure \\[Fig\\_Rabiadditive\\]). ",
"We have the following total Hamiltonian $$H=\\hbar\\omega\\sum^{N}_{l=1}|1_{l}\\rangle\\langle\\,1_{l}|+\\sum^{N}_{l=1}g^{m}_{l}(|0\\rangle\\langle\\,1_{l}|+|1_{l}\\rangle\\langle\\,0|)\\cos(\\nu_{0}\\,t),$$ where $\\hbar\\omega=-\\gamma_{e}B-\\sum^{N}_{l=1}(A_{l}/2)(-1)^{\\sigma^{m}_{l}}$ and the transition amplitude $g^{m}_{l}$ is defined in equation (\\[Eq\\_transitionrate\\]). ",
"It should be noted that we have set the energy of state $|0\\rangle$ to 0. ",
"The frequency of the driving electric field is in resonance with the Zeeman splitting, i.e., $\\gamma_{e}B=\\hbar\\nu_{0}$. In the interaction picture, the Hamiltonian reads (under the rotating-wave approximation) $$H_{\\rm int}=\\Delta_{m}\\sum^{N}_{l=1}|1_{l}\\rangle\\langle\\,1_{l}|+\\sum^{N}_{l=1}\\frac{g^{m}_{l}}{2}(|0\\rangle\\langle\\,1_{l}|+|1_{l}\\rangle\\langle\\,0|),$$ where $$\\Delta_{m}=-\\gamma_{e}B-\\sum^{N}_{l=1}(A_{l}/2)(-1)^{\\sigma^{m}_{l}}+\\hbar\\nu_{0}\\nonumber$$ is the detuning function. ",
"The system is initially in state $|\\phi(0)\\rangle=|0\\rangle$, i.e., the electron spin is in the spin-up state. ",
"We want to find the spin-down probability $P_{\\downarrow_{x}}(t)$ under electric driving. ",
"We let $|\\phi(t)\\rangle=c_{0}(t)|0\\rangle+\\sum^{N}_{l=1}c_{l}(t)|1_{l}\\rangle$, where $c_{l}(t)$ ( $l=0,1\\ldots\\,N$) is the coefficient to be determined. ",
"The equations of motion for the coefficients can be derived from the Schrödinger equation $i\\hbar\\partial_{t}|\\phi(t)\\rangle=H_{\\rm int}|\\phi(t)\\rangle$. We find that the coefficients satisfy $$\\begin{aligned}\n\\dot{c}_{0}(t)&=&-i\\sum^{N}_{l=1}\\frac{g^{m}_{l}}{2\\hbar}c_{l}(t),\\nonumber\\\\\n\\dot{c}_{l}(t)&=&-i\\frac{\\Delta_{m}}{\\hbar}\\,c_{l}(t)-i\\frac{g^{m}_{l}}{2\\hbar}c_{0}(t).\\end{aligned}$$ The solution to this equation array is very simple, we obtain $$\\begin{aligned}\nc_{0}(t)&=&e^{-i\\frac{\\Delta_{m}}{2\\hbar}t}\\left[\\cos\\frac{\\Omega_{m}t}{2}+i\\frac{\\Delta_{m}}{\\hbar\\Omega_{m}}\\sin\\frac{\\Omega_{m}t}{2}\\right],\\nonumber\\\\\nc_{l}(t)&=&-i\\frac{g^{m}_{l}}{\\hbar\\Omega_{m}}e^{-i\\frac{\\Delta_{m}}{2\\hbar}t}\\sin\\frac{\\Omega_{m}t}{2},\\end{aligned}$$ where the Rabi frequency is defined as $$\\Omega_{m}=\\frac{1}{\\hbar}\\sqrt{\\Delta^{2}_{m}+\\sum^{N}_{l=1}(g^{m}_{l})^{2}}.$$ Therefore, the spin down probability is given by $$P_{\\downarrow_{x}}(t)=\\sum^{N}_{l=1}|c_{l}(t)|^{2}=\\frac{\\sum_{l}(g^{m}_{l})^{2}}{\\hbar^{2}\\Omega^{2}_{m}}\\sin^{2}\\frac{\\Omega_{m}t}{2}.$$ So we derive the result given in equation (\\[Eq\\_inversion\\_purestate\\]).",
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"“Where there is charity and wisdom, there is neither fear nor ignorance.” ",
"Francis of Assisi\n\nMotivation Mondays: Labor & Charity collage\n\nIn recognition of the role of charity in alleviating humanitarian crises and human suffering within and among nations, as well as of the efforts of charitable organizations and individuals, including the work of Mother Teresa, the General Assembly of the United Nations in its resolution A/RES/67/105 designated the 5th of September, the anniversary of the death of Mother Teresa, as the International Day of Charity. UN Charity Day\n\nWhat do you know about International Day of Charity? ",
"Did you know that today is both Labor Day and International Day of Charity. ",
"International Day of Charity was established in 2012 by the United Nations Organization as a way to sensitize people to the issues of poverty worldwide, and also as a way to recognize the works and deeds of Mother Teresa of Calcutta who served the poor throughout her lifetime and passed away on September 5, 1997. ",
"Mother Teresa was canonized as a Saint yesterday and so this is a special day to celebrate both her death and her recognition as a modern day Saint in our world. ",
"She will now be celebrated every year on September 5th as Saint Teresa of Calcutta MC. ",
"It makes perfect sense to me because when we labor and share the benefits of our work, we take an important step by offering help to those in need. ",
"Charity and Labor go hand in hand and are great qualities that we all want to have; to provide for our loved ones and to give back to our communities. ",
"On this auspicious day of recognizing the role both play in the lives of a community, a nation, and globally, we can recommit ourselves to help sustain each other through volunteering, working hard, and giving back. ",
"Each year, the UN has a theme/focus; for 2016, UN Sec General, Ban Ki-moon, has placed the focus on volunteering and giving. ",
"This is very important because of the 2030 Agenda for sustainable development globally\n\nMany of us grew up hearing the saying that charity begins at home … and it does. ",
"When we teach our children to be conscientious about helping others in need, and when we express gratitude for what we have, we are sharing a spirit of charity. ",
"On the community level, when we contribute to foundations and groups that help our schools and the poor in our community, we are torch bearers of charity. ",
"On the national and global level, when we support NGOs and other nonprofit organizations that provide services in many parts of the world; be it for education, health training, small business , even water and electricity, our philanthropy helps create opportunities for friendship, dialogue and global peace. ",
"Each time we make a donation or volunteer to help families in war-zones, we are activating that spirit of charity and goodwill that reverberates around the world and returns to us in beneficial ways. ",
"Give to charity, share your labor of love and spread the word.",
"\n\n“A garden requires patient labor and attention. ",
"Plants do not grow merely to satisfy ambitions or to fulfill good intentions. ",
"They thrive because someone expended effort on them.” ",
"Liberty Hyde Bailey\n\nMotivation Mondays: Labor Day & International Charity Day\n\nThe first Labor Day holiday was celebrated on Tuesday, September 5, 1882, in New York City, in accordance with the plans of the Central Labor Union. ",
"The Central Labor Union held its second Labor Day holiday just a year later, on September 5, 1883.",
"\nLabor Day, the first Monday in September, is a creation of the labor movement and is dedicated to the social and economic achievements of American workers. ",
"US Dept of Labor\n\nWhat do you know about Labor Day ? ",
"Many years ago, the world of work was brutal and work related deaths were ubiquitous. ",
"There were no laws to guide workers or the movement from one dingy workplace to another. ",
"The hours were long, pay was little, and unscrupulous bosses created atrocious workplaces and conditions, while offering little or no recourse to workers wounded on the job. ",
"Because there were no labor laws to protect minors, a common practice was to use child labor for long, mind numbing work that was often unpaid. ",
"By the 19th century, workers started to agitate for change as conditions continued to deteriorate and lives were lost at the workplace. ",
"It was this backdrop that gave impetus to the growth of the labor movement that turned life around for middle and working class folks. ",
"It was the effort of men like Matthew Maguire and Peter J. McGuire who forced the hand of our government to put a stop to inhumane work practices. ",
"The death of some workers/protesters during the Pullman Strike, in 1894, led to increased pressure from workers and eventually led to Labor Day being declared a National Holiday with a unanimous vote by Congress; then sitting US President, Grover Cleveland, signed off on the new law and the movement was up and running.",
"\n\nInterestingly enough, years before the new law was signed into effect by Congress, workers organized rallies, meetings and parades to get the word out and build a union. ",
"The first Labor Day Parade was held in NYC in 1882 to honor and celebrate the efforts of all the hardworking men and women who put their lives on the line and labored daily to ensure their families had food to eat and a roof over their heads. ",
"When I think of the origins of the labor movement and Labor Day, it is a cause we should all honor because the motivation to work remains the same today. ",
"What motivates you to labor for a living? ",
"The answer is very clear for millions of people around the world, and yet, many have stood by and watched the erosion of the labor movement take place. ",
"It is not by accident that we have “The 40-hour work week, the minimum wage, family leave, health insurance, Social Security, Medicare, and retirement plans.” ",
"All have been fought for by those who believed that without proper compensation, people would be worked to death and workplace atrocities would not end. ",
"On this day, let’s stop and thank all who worked to provide for us and our communities.",
"\n\nThe details for Motivation Mondays are below. ",
"Join in! ",
"The themes for August and September 2016 are:\n\n“Labor to keep alive in your breast that little spark of celestial fire, called conscience.” ",
"George Washington\n\nMotivation Mondays: Labor & Charity collage\n\nCharity is one of the best investments we can make in our common future. ",
"On this day of International Charity, I call on people everywhere to be part of our 15-year partnership for humanity, and to help make the Sustainable Development Goals a reality for all. ",
"UN Secretary-General Ban Ki-moon\n\nHow do Labor and Charity shape our lives? ",
"I’ve told this story before, but will share it again with a new component added to the story: The charity we extend to others comes back to us tenfold. ",
"My paternal grandmother raised my dad alone after her husband died suddenly of a heart attack. ",
"They were poor farmers, in a West African village, who saw the arrival of European missionaries up-end their lives at the turn of the 20th Century. ",
"When her hubby passed away, my Grandma sent her youngest son to the only school in a nearby village. ",
"It was a Missionary school that educated a handful of boys, sent by bold parents, in a fractious climate that didn’t encourage education as a way out of poverty. ",
"Many locals were against the missionaries who were determined to force people to abandon traditional practices and Ancestral worship for a new Christian order. ",
"With the Missionaries came laws on taxation and village leaders were also against the imposition of tax levies on communities that were barely eking out a living to support their families. ",
"So you can imagine that, in such a tense climate of imminent and eventual change, education was not available to all or even considered a road out of poverty. ",
"The missionary school was free and was offered to the community as a charitable effort to gain trust. ",
"Still, many turned away from it because they couldn’t imagine how an education would help grow their crops or raise their farm animals.",
"\n\nMy Grandma, out of desperation to support her family, took a chance and sent her youngest son to the school. ",
"He was eager to learn and she was eager to find a path out of poverty. ",
"As she struggled, others in the village rallied to support and encourage her and became equally invested in seeing my Dad succeed. ",
"My dad stayed in school, holding onto the community’s dream of a better life. ",
"He received an education that led him down the path to entering the world of Accountancy, Banking and eventually Government. ",
"As his career path expanded, he took up the role of benefactor and helped educate many in our village. ",
"He never forgot the goodwill and charity that was extended to him as a little boy and repaid it tenfold. ",
"We often forget that the hand that feeds one, creates an opportunity for many more hands to feed others. ",
"When we act charitably towards others, we benefit as much as the receiver of our philanthropy.",
"\n\nPositive Motivation Tip: The labor of love and charity we extend to others comes back to us tenfold.",
"\n\nMotivation Mondays is open to anyone who wishes to share a motivational quote, photo, personal challenge or a post that encourages others to start the week on an upbeat note.",
"Basic Instructions: Each week, I will have a motivation word to help us create a response. (",
"See listed words for the months above/below)Email address: You may email or share your post as a comment and I will add it to the round-up of related posts. ",
"email it to: contact(@)mirthandmotivation(.)comCategory tag: – Share your post using Motivation MondaysTwitter hashtag: – Use this on Twitter #MotvnMDedicated Page: There is a dedicated page for Motivation Mondays. ",
"It has the same instructions and will include other helpful tools and a link to the round-upFacebook Page:MotivationOnMondays Join our page and add your post and/or any motivational piece you think will be helpful to others.",
"Facebook Community: We have a Facebook community forum to compliment the page. ",
"It serves as another way to share uplifting posts and thoughts. ",
"Please join in and add your voice.",
"\n\nBadge: – I created a fun badge using PicMonkey’s free photo editing tools. ",
"You can create your own, use WordPress’ integrated tool on your blog or you are welcome to use mine. (",
"see dedicated page)Tag: – Motivation MondaysHashtag: – #MotvnMRelated Posts"
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"Eating Fish Linked to Slower Memory Decline\n\nEating more fish may be linked to lower rates of memory decline, according to a study published in the American Journal of Epidemiology.1\n\n“In this pooled analysis including selected participants from five large cohorts of older subjects in studies from Europe and North America, we found that increasing intake of fish was modestly associated with slower rates of cognitive decline, in particular episodic memory decline– an early marker of AD risk,” wrote first author Cecilia Samieri, PhD, of the University of Bordeaux, France, and colleagues.",
"\n\nBecause the study was so large—it included data from almost 24,000 people—it could identify modest associations that smaller studies have not been able to find.",
"\n\nThe authors pointed out that even such modest effects may have a large public health impact. ",
"For example, one study has estimated that delaying AD onset by just year could decrease the prevalence of AD worldwide by over 9 million through 2050.2\n\nAn increasing body of evidence has suggested that consuming fish may slow cognitive decline and decrease the risk of AD. ",
"Fish are an excellent source of long-chain omega-3 polyunsaturated fatty acids (PUFAs). ",
"Many AD genes, like APOE, CLU and CR1, involve lipid metabolism or inflammation, and long-chain omega-3 PUFAs may act through these pathways. ",
"Fish also contain vitamin D and selenium, which are potentially neuroprotective.",
"\n\nTo evaluate the issue, researchers pooled data from the French Three-City study and four US studies (Nurses’ Health Study, Women’s Health Study, Chicago Health and Aging Project and Rusk Memory and Aging Project). ",
"The analysis included data from 23,688 adults with a mean age of 71.9-82.2 years. ",
"Participants were followed for a median of 3.9 to 9.1 years.",
"\n\nParticipants completed food frequency questionnaires before their initial cognitive assessment, and had repeat cognitive assessments every 4 to 9 years. ",
"They also provided data on APOE gene type and other genetic mutations related to AD.",
"\n\n. ",
"No evidence that consuming more fish affects APOE4 and 13 other AD genes\n\nThe lack of an association between fish consumption and AD genes likely indicates that the effect of fish on cognition is similar regardless of genetic predisposition to AD, the authors explained.",
"\n\nThey also mentioned several potential limitations. ",
"Due to small numbers of minority participants in the five pooled studies, the study included data only from Caucasian participants. ",
"Also, 88% of participants were female with generally high education levels. ",
"So the results may not generalize to men and other populations.",
"\n\nTake Home Points\n\n. ",
"Large pooled analysis of five studies in Europe and North America found that higher levels of fish consumption were linked to slower rates of global cognitive and memory decline\n\n. ",
"People who ate ≥4 servings/week had similar memory decline as people who were four years younger, compared to people who ate <1 serving/week\n\n. ",
"No evidence that consuming more fish affects APOE4 and 13 other AD genes"
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"ABS (antilock system) prevents the wheels from locking and comes into operation when greater adhesion than is transferable is demanded between a tire and the road, that is to say when the driver overbrakes. ",
"In overbraking, the central electronic control apparatus of the ABS brake system detects from rotational speed sensor signals the tendency of one or more wheels to lock and from this calculates the activation of the pressure control valve arrangement acting upon the assigned brake cylinder. ",
"The brake pressure is then set to optimal slip by the pressure control valve arrangement by lowering, holding or building up the brake pressure according to the wheel behavior and therefore the frictional conditions between the tire and road. ",
"ABS pressure control valve arrangements without a relay action, to which the exemplary embodiments and/or exemplary methods of the present invention relate, are used in vehicles, such as, for example, utility vehicles, omnibuses, tractors and trailers. ",
"Pressure control valve arrangements without a relay action mostly have 3/2 way solenoid valves as the pilot control valves of diaphragm valves, an electronic control device activating the 3/2 way solenoid valves so that the “pressure holding”, “pressure reduction” and the “pressure build-up” functions necessary for ABS operation can be carried out. ",
"During braking without the response of the ABS (no tendency of a wheel to lock), the pressure medium, mostly air, flows, unimpeded, through the pressure control valve arrangements in both directions when the brake cylinders are being ventilated and bled. ",
"This ensures that the functioning of the service brake system is not influenced by the ABS pressure control valve arrangement.",
"\nPressure control valves of the generic type, as 1-channel pressure control valves for antilock systems in motor vehicles, have in each case, inside the housing, a diaphragm valve as a holding valve and as an outlet valve and also in each case an electromagnetic control valve for the holding valve and the outlet valve. ",
"The two diaphragm valves contain in each case a diaphragm capable of being acted upon by the pressure in a pilot control space, the pilot control space being closed outwardly by a cover fastened to the housing. ",
"A generic pressure control valve arrangement of an ABS brake system is known, for example, from EP 0 266 555 A1 or from DE-A 2 855 876. ",
"In the pressure control valve arrangements of the prior art, the housing has a pressure medium connection for the action of pressure and/or the relief of pressure, which is connected to a foot-operated brake valve. ",
"Furthermore, the two diaphragm valves are arranged laterally on the housing, the corresponding pilot control spaces being closed by covers fastened laterally to the housing, that is to say, there, surface normals on the diaphragms of both diaphragm valves are arranged perpendicularly to the mid-axis of the pressure medium connection.",
"\nFurthermore, in the published references, particularly according to FIG. ",
"1 of DE-A-2 855 876, a plane of symmetry of the mid-axes of the magnet coils of the double magnet of the two electromagnetic control valves is arranged centrically with respect to a mid-axis of the pressure medium connection (there, the pressure medium inlet). ",
"In this case, the mid-axes of the two magnet coils at the same time also define the positions of the valve seats of the electromagnetic control valves of the pressure control valve arrangement, because the mid-axes of the magnet coils are arranged coaxially with the valve seats and with the magnet armatures. ",
"Furthermore, the valve seats of the electromagnetic control valves are connected to the pressure medium connection or issue into this via pressure medium ducts. ",
"These pressure medium ducts may be made coaxially with the mid-axes of the magnet coils by cutting manufacture, such as drilling, in order for reasons of cost to avoid having to rechuck the housing in order to make obliquely running pressure medium ducts or housing bores. ",
"The pressure medium ducts consequently run parallel to one another in a vertical direction.",
"\nSo that the pressure medium ducts emanating from the valve seats of the electromagnetic control valves can therefore be manufactured in a vertical direction in the housing by cutting and at the same time both of them can issue into the pressure medium connection, the inside diameter of the pressure medium connection has to be relatively large, especially since the magnet coils also cannot undershoot a certain diameter. ",
"However, because a correspondingly large diameter of the pressure medium connection is unfavorable in flow terms, in practice a reducing sleeve which reduces the effective flow diameter is inserted into the pressure medium connection.",
"\nHowever, this procedure entails additional costs for producing and mounting the reducing sleeve, and, in view of the large number of pressure control valve arrangements delivered by a supplier of vehicles, this amounts in total to a relatively high sum."
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"Treatment of advanced malignant melanoma with recombinant interferon alfa-2a in combination with DTIC: long-term follow-up of two phase II studies.",
"\nThe present studies were designed to examine whether treatment of disseminated melanoma with a combination of recombinant interferon alpha (rIFN alpha-2a) and DTIC may provide better results than either agent alone. ",
"Two dose levels of rIFN alpha-2a were examined with the same dose and schedule of DTIC administration. ",
"In the first study 76 patients were treated with rIFN alpha-2a (3 x 10(6) IU days 1-3, 9 x 10(6) IU days 4-70 then 9 x 10(6) IU TIW) plus DTIC (i.v. ",
"200 mg/m2, escalating to 800 mg/m2 each 21 d) for 6 months or longer or until failure. ",
"Responses were seen in 26% of patients overall (7CR, 13PR) with the highest responses being seen in those assessed as having a good prognosis and in patients with skin and/or lung metastases. ",
"It was notable that males showed a better response than females and that patients with metastases in lymph nodes showed low responses. ",
"Response rates in 30 patients treated with high-dose rIFN alpha-2a (18 x 10(6) IU days 7-70) were not superior to that seen at the lower dose and was accompanied by significant increase in bone marrow toxicity. ",
"The duration of responses appeared longer than expected from responses to DTIC alone and four patients remain progression free at periods in excess of 3 years. ",
"Failure in nine of the responders was due to the development of brain metastases which emphasizes the need for additional treatment approaches to treat micrometastases at this site. ",
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"DYRK1A Kinase Positively Regulates Angiogenic Responses in Endothelial Cells.",
"\nAngiogenesis is a highly regulated process essential for organ development and maintenance, and its deregulation contributes to inflammation, cardiac disorders, and cancer. ",
"The Ca2+/nuclear factor of activated T cells (NFAT) signaling pathway is central to endothelial cell angiogenic responses, and it is activated by stimuli like vascular endothelial growth factor (VEGF) A. NFAT phosphorylation by dual-specificity tyrosine phosphorylation-regulated kinases (DYRKs) is thought to be an inactivating event. ",
"Contrary to expectations, we show that the DYRK family member DYRK1A positively regulates VEGF-dependent NFAT transcriptional responses in primary endothelial cells. ",
"DYRK1A silencing reduces intracellular Ca2+ influx in response to VEGF, which dampens NFAT activation. ",
"The effect is exerted at the level of VEGFR2 accumulation leading to impairment in PLCγ1 activation. ",
"Notably, Dyrk1a heterozygous mice show defects in developmental retinal vascularization. ",
"Our data establish a regulatory circuit, DYRK1A/ Ca2+/NFAT, to fine-tune endothelial cell proliferation and angiogenesis."
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"1. ",
"Introduction {#sec1-nutrients-12-01075}\n===============\n\nSarcopenia is characterised by a progressive loss of skeletal muscle mass accompanied by the deterioration of physical function, culminating in the loss of independence and increased morbidity risk \\[[@B1-nutrients-12-01075],[@B2-nutrients-12-01075],[@B3-nutrients-12-01075]\\]. ",
"The occurrence of metabolic abnormalities, characterised by elevated fasting glucose and triglyceride levels, reduced HDL-cholesterol and increased waist circumference and blood pressure, collectively named metabolic syndrome (MetS) \\[[@B4-nutrients-12-01075],[@B5-nutrients-12-01075]\\], has been linked to the development of sarcopenia in older adults. ",
"For instance, based on the cross-sectional NHANES database, lower muscle mass is associated with a higher risk of pre-diabetes and insulin sensitivity \\[[@B6-nutrients-12-01075]\\], and an inverse relationship between skeletal muscle mass and metabolic syndrome development has been reported in a 7-year longitudinal study in a large population of men and women \\[[@B7-nutrients-12-01075]\\].",
"\n\nHealthy dietary habits and engagement in regular physical activity have been advocated by major health organisations in order to mitigate the age-related loss of muscle mass \\[[@B8-nutrients-12-01075],[@B9-nutrients-12-01075]\\]. ",
"In this respect, adherence to healthy dietary patterns, including the Mediterranean Diet and the Dietary Approach to Stop Hypertension (DASH), has been linked to beneficial health effects in older adults \\[[@B10-nutrients-12-01075],[@B11-nutrients-12-01075]\\]. ",
"A recent investigation showed that adherence to healthy dietary patterns such as the Mediterranean diet can mitigate the age-related decline in muscle mass \\[[@B12-nutrients-12-01075]\\]. ",
"Importantly, a key feature of healthy diets is the high fibre content related to fruit, vegetable, legume and whole-grain intake \\[[@B13-nutrients-12-01075],[@B14-nutrients-12-01075],[@B15-nutrients-12-01075]\\]. ",
"Dietary fibre has important physiological effects on glucose and lipid metabolism, and several studies have documented a protective effect against diabetes and cardiovascular disorders. ",
"Unfortunately, the majority of the general population, including older adults, has a dietary fibre intake (FI) below recommended daily amounts \\[[@B16-nutrients-12-01075],[@B17-nutrients-12-01075]\\].",
"\n\nAlthough dietary FI has an influence on markers of metabolic health and cardiovascular disorders \\[[@B18-nutrients-12-01075],[@B19-nutrients-12-01075],[@B20-nutrients-12-01075],[@B21-nutrients-12-01075]\\], inconclusive findings have been reported regarding the effects on body composition \\[[@B22-nutrients-12-01075],[@B23-nutrients-12-01075],[@B24-nutrients-12-01075],[@B25-nutrients-12-01075]\\]. ",
"Furthermore, there is a paucity of information about the potential impact of dietary fibres on the age-related loss of muscle mass and functional decline. ",
"Interestingly, it is suggested that dietary fibre has a beneficial effect on the systemic inflammatory milieu. ",
"Specifically, dietary fibres may delay glucose absorption and alter gut microflora, which may attenuate the release of pro-inflammatory cytokines \\[[@B26-nutrients-12-01075],[@B27-nutrients-12-01075]\\]. ",
"Thus, given the detrimental effect of inflammation on muscle mass and protein synthesis \\[[@B28-nutrients-12-01075],[@B29-nutrients-12-01075]\\], it can be suggested that an adequate intake of dietary fibre may promote the maintenance of muscle mass in older adults.",
"\n\nImportantly, in order to depict the true impact of FI on muscle mass, other features of a healthy diet must be considered. ",
"For example, we have previously shown that adherence to recommended intakes of proteins is associated with a higher muscle mass in older women \\[[@B8-nutrients-12-01075]\\]. ",
"Moreover, as regular exercise has established effects on the maintenance of muscle mass and function, information on objectively assessed physical activity (PA) levels needs to be considered when exploring the impact of diet. ",
"In this context, the NU-AGE project, comprising data on dietary intake and body composition from over a thousand European older men and women, offers a unique opportunity to close the current evidence gap on the significance of dietary fibre for the maintenance of muscle mass and function in older adults.",
"\n\nTherefore, the aim of the present study was to examine the links between FI, skeletal muscle mass and physical function in a large cohort of older men and women from the NU-AGE study.",
"\n\n2. ",
"Materials and Methods {#sec2-nutrients-12-01075}\n========================\n\n2.1. ",
"Subjects {#sec2dot1-nutrients-12-01075}\n-------------\n\nThe present study included older men and women (*n* = 981; age 65--79 years) recruited within the frame of the NU-AGE project, a multi-centre study exploring determinants of healthy aging across five European countries. ",
"At screening, subjects fulfilling frailty criteria were excluded \\[[@B30-nutrients-12-01075]\\]. ",
"A detailed description of the recruitment process and study design has been described elsewhere \\[[@B30-nutrients-12-01075],[@B31-nutrients-12-01075]\\]. ",
"In the context of the present study, data from France were not included due to a lack of information on accelerometer-based PA. ",
"Local ethical approval was provided by the Independent Ethics Committee of the Sant'Orsola-Malpighi Hospital Bologna (Italy-103/2011/U/Sper), the National Research Ethics Committee--East of England (United Kingdom-12/EE/0109), the Wageningen University Medical Ethics Committee (Netherlands-11/41 NU-AGE) and the Bioethics Committee of the Polish National Food and Nutrition Institute (Poland). ",
"Written informed consent was obtained from participants before starting and the study was conducted in accordance with the standards set by the Declaration of Helsinki. ",
"The trial was registered at [clinicaltrials.gov](clinicaltrials.gov) (NCT01754012).",
"\n\n2.2. ",
"Assessment of Body Composition {#sec2dot2-nutrients-12-01075}\n-----------------------------------\n\nHeight and weight were measured using standardised procedures and body composition was assessed using whole body Dual energy X-ray absorptiometry (DXA) as described elsewhere \\[[@B32-nutrients-12-01075]\\]. ",
"DXA scans were performed by trained technicians according to state-of-the-art technique and manufacturer recommendations. ",
"The analytical program defined six corporeal regions. ",
"Total and regional fat and lean masses were derived. ",
"Skeletal muscle mass index (SMI, %) was derived as previously described \\[[@B32-nutrients-12-01075],[@B33-nutrients-12-01075],[@B34-nutrients-12-01075]\\]: (appendicular lean mass (kg)/total body weight (kg)) × 100.",
"\n\n2.3. ",
"Assessment of Dietary Intake {#sec2dot3-nutrients-12-01075}\n---------------------------------\n\nDietary intake was assessed using a 7-day food record. ",
"Consumed foods were coded according to standardised procedures and translated into nutrients using software exploiting local food composition tables (NEVO 2011 in The Netherlands, WISP in the UK, INRAN and IEO in Italy, and NFNI in Poland). ",
"Macronutrient intakes and the amount of dietary FI were retrieved and averaged per day. ",
"In addition, adherence to healthy dietary patterns was obtained using the NU-AGE Food Based Dietary score (Mediterranean-type diet) \\[[@B35-nutrients-12-01075]\\]. ",
"Participants having a protein intake above 1.1 g/kg of body weight were classified as meeting the recommended amount of protein intake for older people \\[[@B36-nutrients-12-01075]\\].",
"\n\n2.4. ",
"Assessment of Physical Function {#sec2dot4-nutrients-12-01075}\n------------------------------------\n\nThe short-physical performance battery (SPPB), including measures of gait speed, chair stand and balance, was conducted and test scores ranging from 0 (the worst performance) to 12 (the best performance) were derived as previously described \\[[@B37-nutrients-12-01075]\\]. ",
"Handgrip strength normalised by body weight was assessed using standardised procedures with a Jamar handheld dynamometer (Patterson Medical, Warrenville, IL, USA).",
"\n\n2.5. ",
"Assessment of Adherence to Physical Activity Guidelines Using Accelerometry {#sec2dot5-nutrients-12-01075}\n--------------------------------------------------------------------------------\n\nPhysical activity was monitored using a waist-mounted Actigraph accelerometer (GT3x activity monitor, Actigraph, Pensacola, FL, USA) for a period of one week. ",
"In short, a minimum of 4 days with at least 10 h per day of wear time was required for inclusion and periods of non-wear time were determined as previously described \\[[@B38-nutrients-12-01075]\\]. ",
"Weekly time spent in moderate-to-vigorous PA (MVPA) was retrieved based on an established accelerometer count cut-point (≥2020 counts per minute) \\[[@B39-nutrients-12-01075]\\]. ",
"Participants spending a daily average of ≥22 min in MVPA, approximate to 150 min/week, were classified as adhering to the PA guidelines.",
"\n\n2.6. ",
"Assessment of Metabolic Risk {#sec2dot6-nutrients-12-01075}\n---------------------------------\n\nWaist circumference (WC) was measured to the nearest 0.1 cm. ",
"Systolic and diastolic blood pressures were assessed using an automated electronic blood pressure monitor as previously described \\[[@B40-nutrients-12-01075]\\]. ",
"All biochemical analyses including blood glucose (mmol/L), total cholesterol, HDL and LDL-cholesterol, triglycerides, adiponectin, high-sensitive C-reactive protein (hs-CRP) and white blood cell count (WB) were measured in one centre using standard methodologies. ",
"Participants were classified as having high and low metabolic risk based on the International Diabetes Federation definition of the metabolic syndrome \\[[@B4-nutrients-12-01075]\\].",
"\n\n2.7. ",
"Statistics {#sec2dot7-nutrients-12-01075}\n---------------\n\nData are presented as mean ± standard deviation, unless indicated otherwise. ",
"All variables were checked for normality and transformed when necessary. ",
"Differences in continuous variables between sex-specific SMI tertiles were assessed by one-way ANOVA, adjusted for multiple comparisons by Sidak-Holm correction. ",
"Corresponding differences in proportions were determined by chi-square tests. ",
"Differences between sex-specific groups of metabolic risk (with and without MetS) were assessed by independent samples *t*-test and chi-square tests. ",
"Given the well-established impact of gender on skeletal muscle mass, sex-specific general linear models were employed to determine the influence on SMI and physical function outcomes by groups of FI while adjusting for age, study centre, total energy intake and MetS (main effect and FI × MetS interaction) in model 1; and protein intake, adherence to healthy diet and PA guidelines in model 2. ",
"Effect sizes were estimated for each model (partial eta: η²p). ",
"Based on our sample size, an a priori power calculation revealed that small-to-moderate effect sizes are detectable with a power of \\> 80% with alpha set to 0.05. ",
"All analyses were conducted using SPSS version 26.",
"\n\n3. ",
"Results {#sec3-nutrients-12-01075}\n==========\n\nA total of 981 European participants (mean age 71 ± 4 years, 58% female) were included in the final analysis. ",
"Subject characteristics including anthropometrics, metabolic and inflammatory biomarkers across sex-specific tertiles of SMI are presented in [Table 1](#nutrients-12-01075-t001){ref-type=\"table\"}. ",
"The average SMI in men and women was 30.6 ± 3.1% and 24.4 ± 2.8%, respectively. ",
"About 54% of the total population fulfilled the guidelines of weekly MVPA time (men: 64% vs. women: 47%, *p* \\< 0.001) and 41% were classified with MetS.\n\nMen and women belonging to the highest SMI tertile had a significantly lower prevalence of MetS and higher SPPB score, handgrip strength and adherence to PA guidelines compared to lower tertiles ([Table 1](#nutrients-12-01075-t001){ref-type=\"table\"}). ",
"Additionally, belonging to the highest SMI tertile was related to lower waist circumference, as well as lower levels of blood glucose, triglycerides and hsCRP together with higher levels of HDL and adiponectin compared to those in lower tertiles ([Table 1](#nutrients-12-01075-t001){ref-type=\"table\"}). ",
"Total fat, trunk, android and gynoid fat masses were significantly lower for those belonging to the highest SMI tertile compared to the other two tertiles ([Table 1](#nutrients-12-01075-t001){ref-type=\"table\"}). ",
"Notably, participants with MetS had lower SMI, SPPB score (only female) and handgrip strength compared to those without MetS ([Table 2](#nutrients-12-01075-t002){ref-type=\"table\"}).",
"\n\nThe total energy intake and distribution of macronutrient intakes of the whole study sample were 1808 ± 425 kcal (men: 2019 ± 451 kcal vs. women: 1653 ± 327 kcal, *p* \\< 0.001), 49 ± 6 E% carbohydrates, 35 ± 6 E% fat and 17 ± 3 E% protein. ",
"The total fibre intake for the whole sample was 22.5 ± 7.8 g/day with median intakes of 23.5 (IQR 18.1--28.6) and 20.3 (IQR 16.3--24.8) for men and women, respectively. ",
"In women, 24.0% adhered to the recommended fibre intake (25 g/d), while the corresponding proportion in male was 20.2% (30 g/d). ",
"In both sexes, participants belonging to the third tertile of SMI had significantly higher fibre and protein intakes as well as a higher total energy intake compared to those in lower tertiles ([Table 3](#nutrients-12-01075-t003){ref-type=\"table\"}).",
"\n\nBased on general linear models, older women with FI above the median value had significantly higher SMI (24.6 ± 0.2% vs. 23.9 ± 0.2%, *p* = 0.003, η^2^p = 0.016) compared to those under the median FI value ([Figure 1](#nutrients-12-01075-f001){ref-type=\"fig\"}), after adjustment for metabolic risk status (model 1).",
"\n\nThe influence of FI on SMI remained after further adjustment for adherence to the PA guidelines, protein intake and adherence to a healthy diet (24.7 ± 0.2% vs. 24.2 ± 0.1%, *p* = 0.011, η^2^p = 0.012).",
"\n\nWhile no main effect was observed ([Figure 2](#nutrients-12-01075-f002){ref-type=\"fig\"}a), a significant interaction between MetS and FI on SMI was observed in older men (*p* = 0.009) (model 1). ",
"After stratification by MetS, a significant main effect of FI on SMI was observed in older men without MetS (32.4 ± 0.3% vs. 31.3 ± 0.3%, *p* = 0.005, η^2^p = 0.035) ([Figure 2](#nutrients-12-01075-f002){ref-type=\"fig\"}b), which remained after further covariate adjustments. ",
"In contrast, no corresponding effect was shown in those with MetS ([Figure 2](#nutrients-12-01075-f002){ref-type=\"fig\"}c). ",
"Interestingly, a significant difference in FI was observed between older men without and with MetS (25.8 ± 9.8 g vs. 22.5 ± 7.0 g, *p* \\< 0.001) but not in older women (21.5 ± 6.5 g vs 20.8 ± 6.7 g, NS). ",
"Given the proposed association between FI and the inflammatory status, we examined hs-CRP levels between groups of FI. ",
"The data show that participants with FI above median had significantly lower hs-CRP level compared to those below (1.32 ± 1.96 mg/L vs. 1.82 ± 2.30 mg/L in men and 1.27 ± 1.81 mg/L vs. 2.06 ± 2.58 mg/L in women, *p* \\< 0.05).",
"\n\nThere was no main effect of FI on the physical function parameters, including SPPB score and handgrip strength and, no interactions between FI and MetS were observed.",
"\n\n4. ",
"Discussion {#sec4-nutrients-12-01075}\n=============\n\nA main finding from the study was the beneficial impact of FI on skeletal muscle mass in a cohort of older European men and women, which is independent of adherence to a healthy dietary pattern, and guidelines for protein intake and objectively assessed physical activity level.",
"\n\nWhile a large body of research has focused on the role of dietary protein intake in the regulation of muscle mass, less attention has been given to the impact of healthy diets in general, particularly FI. ",
"Our findings indicate that a low FI is detrimental for the maintenance of muscle mass in older adults. ",
"This is in line with the PREDIMED-plus study reporting lower FI in participants with low muscle mass compared to those with higher muscle mass \\[[@B12-nutrients-12-01075]\\]. ",
"Dietary fibre's impact on muscle mass may be explained by its action on gut microflora and circulating free fatty acid concentration, which may attenuate systemic inflammation \\[[@B41-nutrients-12-01075],[@B42-nutrients-12-01075]\\]. ",
"Indeed, our data show that compared to those with lower FI (below median), participants with high FI had lower levels of CRP, an established clinical marker of systemic inflammation. ",
"Given the proposed interaction between systemic inflammation and the regulation of muscle mass, we suggest that a link between FI and muscle mass can be mediated through dietary fibre-induced alterations in the systemic environment.",
"\n\nThe present study addressed the potential interaction between FI and metabolic risk on muscle mass. ",
"While such an interaction was evident in older men, the metabolic risk status did not influence the link between FI and muscle mass in older women. ",
"Importantly, this sex-specific interaction may be partly explained by the fact that older men with MetS have a significantly lower FI compared to men without MetS. In contrast, FI did not differ between older women with and without MetS. Given this, it may be hypothesized that the FI observed in older men with MetS is insufficient to offset the detrimental effects of metabolic disturbances on regulation of muscle mass.",
"\n\nAltogether, our findings support the promotion of increased FI in older adults for the maintenance of muscle mass. ",
"We and others have previously highlighted the beneficial impact of adequate protein intake on muscle mass in older adults \\[[@B8-nutrients-12-01075],[@B43-nutrients-12-01075],[@B44-nutrients-12-01075]\\]. ",
"In this respect, the fact that the impact of protein intake on muscle mass was accounted for in the current study further strengthens the proposed beneficial role of adequate FI in the regulation of muscle mass.",
"\n\nPhysical activity is another important lifestyle factor with the potential to readily influence skeletal muscle mass in older adults. ",
"In the present study, the association between FI and muscle mass was evident regardless of the objectively assessed adherence to PA guidelines, which highlights the importance of adequate FI as an independent lifestyle factor in the promotion of healthy aging.",
"\n\nOf note, participants belonging to the highest SMI tertile had lower levels of CRP and higher levels of the anti-inflammatory biomarker adiponectin, highlighting interplay between systemic inflammatory milieu and muscle mass regulation. ",
"In addition, differences in blood lipid profile were observed across SMI tertiles, with those in the highest tertile showing a more favorable profile (higher HDL-cholesterol and lower triglyceride levels) compared to the rest of participants. ",
"Further research is needed to elucidate mechanistic links between blood lipid profile, inflammatory status, and dietary habits in older adults.",
"\n\nIn contrast to the link observed between FI and muscle mass, there was no relationship between FI and physical function parameters. ",
"These contrasting findings suggest that physical function is influenced by other factors than muscle mass alone. ",
"For example, age-related changes in strength capacity have been shown to be weakly related to changes in muscle mass \\[[@B45-nutrients-12-01075]\\]. ",
"However, the FI-related link to muscle mass may benefit long-term maintenance of muscle function and delay loss of independence.",
"\n\nThe main findings of the present study are strengthened by (1) the use of a large cohort of older adults covering diverse ethnic and cultural differences, which allows for generalisation to broader European populations; and (2) state-of-the-art assessment of muscle mass using DXA, together with the use of dietary record and objective measurement of PA. ",
"The following limitations should be considered: given its cross-sectional design, making inference on causality is not possible and residual confounding from unmeasured variables cannot be ruled out. ",
"Further, dietary fibre is a diverse category of insoluble and soluble components which have different physiological effects \\[[@B46-nutrients-12-01075]\\]. ",
"Potential variations in analysis of food items between countries are likely to produce slight variations in assessment of absolute fibre intakes. ",
"However, given that the present study examines links between higher/lower fibre intakes and muscle mass, rather than comparing absolute intakes of fibre between countries, such variations in FI are unlikely to alter the study conclusions.",
"\n\n5. ",
"Conclusions {#sec5-nutrients-12-01075}\n==============\n\nIn conclusion, the NU-AGE study highlights the importance of an adequate intake of dietary fibre within dietary strategies to combat the age-related decline in muscle mass and promote healthy aging.",
"\n\nWe would like to thank all principal investigators and collaborators. ",
"We also express our gratitude to the participants and staff involved in data collection and management in NU- AGE research centres.",
"\n\nConceptualization, D.M.-R., A.N., F.K., A.S. and C.F.; methodology, D.M.-R., A.N., F.K., A.S. and C.F.; validation, D.M.-R.; formal analysis, D.M.-R., A.N. and F.K.; investigation, D.M.-R., A.N., A.S., C.F., A.B. (Alberto Bazzocchi), G.B., L.C.P.G.M.d.",
"G., E.J.M.F., A.B. (Agnes Berendsen), B.P., O.J., S.F.-T., A.J., C.N. and F.K.; writing---original draft preparation, D.M.-R., A.N. and F.K.; writing---review and editing, D.M.-R., A.N., A.S., C.F., A.B. (Alberto Bazzocchi), G.B., L.C.P.G.M.d.",
"G., E.J.M.F., A.B. (Agnes Berendsen), B.P., O.J., S.F.-T., A.J., C.N. and F.K.; supervision, A.N. and F.K.; project administration, A.S.; funding acquisition, C.F. All authors have read and agreed to the published version of the manuscript.",
"\n\nThis research was funded by the European Union's Seventh Framework Programme under agreement no. ",
"266486 (NU-AGE: New dietary strategies addressing the specific needs of the elderly population for healthy aging in Europe).",
"\n\nThe authors declare no conflict of interest. ",
"The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, and in the decision to publish the results.",
"\n\n{#nutrients-12-01075-f001}\n\n{#nutrients-12-01075-f002}\n\nnutrients-12-01075-t001_Table 1\n\n###### \n\nCharacteristics of the study sample according to sex-specific tertiles of skeletal muscle mass index (SMI).",
"\n\n SMI Male SMI Female \n ---------------------------- ------------- ---------------- -------------------- -------------- ---------------- --------------------\n n 139 138 138 189 188 189\n SMI, % ≤29.1 \\>29.1--≤31.8 \\>31.8 ≤ 23.2 \\>23.2--≤25.6 \\> 25.6\n **Basic Characteristics** \n Age, y 72 ± 4 71 ± 4 70 ± 4 \\* 71 ± 4 71 ± 4 71 ± 4\n Weight, kg 89.3 ± 11.6 81.6 ± 10.4 \\* 75.8 ± 9.1 \\*^\\#^ 76.1 ± 11.4 68.0 ± 10.0 \\* 63.0 ± 8.2 \\*^\\#^\n Height, cm 172 ± 7 173 ± 6 174 ± 6 159 ± 7 159 ± 6 162 ± 7 \\*^\\#^\n Years full education, y 13 ± 4 13 ± 4 13 ± 3 12 ± 4 12 ± 3 12 ± 3\n Smoking, % never 30.2 39.1 44.2 60.3 62.2 61.9\n Medication, % yes 89.2 81.9 60.9 83.1 80.9 68.8\n PA. ",
"guidelines, % yes 56.1 60.9 74.6 39.7 48.9 51.9\n **Physical function** \n Handgrip, kg/kg BW 0.44 ± 0.08 0.49 ± 0.09 \\* 0.56 ± 0.09 \\*^\\#^ 0.32 ± 0.08 0.38 ± 0.08 \\* 0.43 ± 0.10 \\*^\\#^\n SPPB, score 11.5 ± 0.9 11.4 ± 1.0 11.8 ± 0.8 \\*^\\#^ 10.8 ± 1.5 11.3 ± 1.3 \\* 11.5 ± 0.9 \\*\n **Metabolic Risk Factors** \n WC, cm 105.5 ± 9.1 97.8 ± 8.6 \\* 90.2 ± 7.4 \\*^\\#^ 94.9 ± 9.9 88.1 ± 9.7 \\* 81.6 ± 8.1 \\*^\\#^\n BMI, kg/m^2^ 29.7 ± 3.3 27.0 ± 2.8 \\* 24.8 ± 2.6 \\*^\\#^ 29.8 ± 3.8 26.5 ± 3.5 \\* 23.9 ± 3.0 \\*^\\#^\n DBP, mmHg 76 ± 10 76 ± 11 78 ± 10 75 ± 10 74 ± 11 73 ± 11\n SBP, mmHg 142 ± 17 140 ± 19 141 ± 18 141 ± 21 140 ± 22 138 ± 21\n MetS, % yes 73.4 44.2 15.2 55.6 42.0 20.1\n Glucose, mmol/L 6.14 ± 1.02 5.69 ± 0.74 \\* 5.37 ± 0.76 \\*^\\#^ 5.67 ± 0.82 5.39 ± 0.64 \\* 5.24 ± 0.57 \\*\n Triglycerides, mmol/L 1.21 ± 0.55 1.05 ± 0.45 \\* 0.97 ± 0.43 \\* 1.15 ± 0.46 1.07 ± 0.46 0.96 ± 0.40 \\*\n TC, mmol/L 1.87 ± 0.40 1.92 ± 0.37 2.02 ± 0.40 \\* 2.16 ± 0.40 2.18 ± 0.42 2.28 ± 0.41 \\*\n HDL-cholesterol, g/L 0.46 ± 0.12 0.49 ± 0.13 0.57 ± 0.15 \\*^\\#^ 0.62 ± 0.16 0.64 ± 0.17 0.72 ± 0.19 \\*^\\#^\n LDL-cholesterol, g/L 1.17 ± 0.37 1.22 ± 0.33 1.25 ± 0.36 1.32 ± 0.37 1.33 ± 0.39 1.37 ± 0.38\n Adiponectin, µg/mL 7.96 ± 4.47 9.63 ± 6.23 9.87 ± 6.63 \\* 14.93 ± 8.44 15.68 ± 9.24 18.01 ± 9.81 \\*\n hs-CRP, mg/L 2.0 ± 2.4 1.7 ± 2.3 1.1 ± 1.6 \\*^\\#^ 2.2 ± 2.7 1.5 ± 1.9 \\* 1.3 ± 2.0 \\*^\\#^\n WBC, % total count 5.9 ± 1.2 5.7 ± 1.5 5.7 ± 1.4 5.8 ± 1.4 5.8 ± 1.5 5.9 ± 1.5\n **Fat mass** \n Total fat mass, kg 30.4 ± 5.8 22.8 ± 4.9 \\* 15.4 ± 4.6 \\*^\\#^ 34.2 ± 7.2 26.2 ± 5.5 \\* 20.3 ± 5.0 \\*^\\#^\n Trunk fat mass, kg 19.3 ± 3.9 13.9 ± 3.3 \\* 8.8 ± 3.1 \\*^\\#^ 18.1 ± 4.2 13.5 ± 3.3 \\* 9.9 ± 3.0 \\*^\\#^\n Android fat mass, kg 3.7 ± 0.8 2.5 ± 0.7 \\* 1.6 ± 0.6 \\*^\\#^ 3.3 ± 0.9 2.3 ± 0.6 \\* 1.7 ± 0.5 \\*^\\#^\n Gynoid fat mass, kg 4.1 ± 0.8 3.2 ± 0.7 \\* 2.4 ± 0.7 \\*^\\#^ 5.8 ± 1.3 4.4 ± 0.9 \\* 3.8 ± 0.8 \\*^\\#^\n\nContinuous data are expressed as mean ± SD. ",
"SMI, skeletal muscle mass index. ",
"BW, body weight. ",
"PA, physical activity. ",
"SPPB, short physical performance battery. ",
"WC, waist circumference. ",
"DBP, diastolic blood pressure. ",
"SBP, systolic blood pressure. ",
"MetS, metabolic syndrome. ",
"TC, total cholesterol. ",
"HDL, high-density lipoprotein. ",
"LDL, low-density lipoprotein. ",
"hs-CRP, high-sensitivity c-reactive protein. ",
"WBC, white blood cell count. \\* *",
"p* \\< 0.05 vs. T1. ",
"^\\#^ *p* \\< 0.05 vs. T2.",
"\n\nnutrients-12-01075-t002_Table 2\n\n###### \n\nSkeletal muscle mass index and physical function in participants with and without MetS.\n\n MetS Male MetS Female \n -------------------- ------------- ---------------- ------------- ----------------\n n (%) 231 (56%) 184 (44%) 344 (61%) 222 (39%)\n SPPB, score 11.6 ± 0.9 11.5 ± 0.9 11.3 ± 1.3 11.0 ± 1.3 \\*\n Handgrip, kg/kg BW 0.52 ± 0.10 0.47 ± 0.08 \\* 0.40 ± 0.10 0.35 ± 0.09 \\*\n SMI, % 32.0 ± 2.9 28.9 ± 2.4 \\* 25.2 ± 2.8 23.2 ± 2.4 \\*\n\nData are expressed as mean ± SD. ",
"MetS, metabolic syndrome. ",
"SPPB, short physical performance battery. ",
"BW, body weight. ",
"SMI, skeletal muscle mass index. \\* *",
"p* \\< 0.05 between sex-specific groups.",
"\n\nnutrients-12-01075-t003_Table 3\n\n###### \n\nFibre, protein and total energy intake and adherence to healthy diet in sex-specific tertiles of skeletal muscle mass index.",
"\n\n SMI Male SMI Female \n --------------------------- ------------- ---------------- -------------------- ------------- ---------------- --------------------\n Total energy intake, kcal 1902 ± 418 1968 ± 413 2189 ± 473 \\*^\\#^ 1571 ± 314 1657 ± 304 \\* 1730 ± 345 \\*^\\#^\n Fibre, g/d 21.8 ± 7.7 23.6 ± 8.7 27.5 ± 9.2 \\*^\\#^ 19.6 ± 5.8 20.6 ± 6.3 23.4 ± 7.0 \\*^\\#^\n Protein, g/kg BW 0.90 ± 0.23 0.99 ± 0.23 \\* 1.15 ± 0.25 \\*^\\#^ 0.91 ± 0.24 1.02 ± 0.21 \\* 1.12 ± 0.24 \\*^\\#^\n Adherence healthy diet, % 48.9 ± 9.1 49.4 ± 8.4 48.9 ± 9.3 50.2 ± 9.7 50.9 ± 9.3 50.9 ± 9.4\n\nData expressed as mean ± SD. ",
"SMI, skeletal muscle mass index. ",
"BW, body weight. \\* *",
"p* \\< 0.05 vs. T1. ",
"^\\#^ *p* \\< 0.05 vs. T2.",
"\n"
] | {
"pile_set_name": "PubMed Central"
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"Thirty years ago, a professor of Architecture named Roger Ulrich organized a now-classic study with a group of patients recovering from gallbladder surgery. ",
"Half of the patients were placed in hospital rooms whose windows exposed a group of deciduous trees; the other half had windows that opened to a brown brick wall. ",
"Which group do you think had an easier recovery?",
"\n\nAs you might have guessed, patients who had the view of trees tolerated pain better, appeared to nurses to have fewer negative effects, and were even released from the hospital earlier. ",
"The results of this study were clear: our environment has an impact on our bodies and minds.",
"\n\n\"Environment[10]\" can refer to the physical space around us. ",
"This includes both the natural world (water, air, earth, vegetation, and animals) and the build environment (man-made furnishings, buildings, roads, and other infrastructure). ",
"What you are seeing, hearing, and experiencing at any moment is changing not only your mood, but how your nervous, endocrine, and immune systems are working. ",
"What Ulrich's study pointed out was that we need to consider our interactions with the world around us to optimize our wellbeing, and one key way to interact in a positive way with our world is to re-connect with nature.",
"\n\nNature heals\n\nHave you ever taken a walk around the park to \"chill out\" after a particularly stressful day? ",
"Perhaps you noticed that looking up at the trees or stopping to smell a fragrant flower made you feel calmer. ",
"Research is beginning to validate what seems like common sense: being in nature or even viewing scenes of nature reduces anger, fear, and stress[11] and increases pleasant feelings. ",
"Exposure to nature not only makes you feel better emotionally, it contributes to your physical wellbeing, reducing blood pressure, heart rate, muscle tension, and the production of stress hormones. ",
"Even a simple plant in a room can have a significant impact on stress and anxiety, so if you need to re-center after a rough day but don't have the time or ability to get outside, simply spending some quiet time watering your potted fern or gazing into a picture of a quiet forest can have a positive impact on the way you feel.",
"\n\nIt's not just a stress-buster, either--nature is associated with fewer physical health complaints and may even make you live longer.",
"\n\nNature restores\n\nFurthermore, time in nature or viewing nature scenes increases our ability to take on new mental tasks and pay attention.",
"One explanation for this is that nature provides a respite from the constant effort to screen out competing stimuli in our busy lives. ",
"Because humans find nature inherently engrossing, we don't have to make an effort to focus when presented with natural views. ",
"This reduces mental fatigue and refreshes the mind. ",
"Some research in children with ADHD even shows that time spent in nature increases their attention.",
"\n\nNature connects\n\nTime in nature connects us to each other and the larger world. ",
"A series of field studies conducted by the Human-Environment Research Lab at the University of Illinois suggest that residents in Chicago public housing who had trees and green space around their building reported knowing more people and having stronger feelings of unity[12] with neighbors than tenants in buildings without trees. ",
"In addition to this greater sense of community, they had a reduced risk of street crime, lower levels of violence and aggression between domestic partners, and a better capacity to cope with life's demands, especially the stresses of living in poverty.",
"\n\nThis experience of connection may be explained by studies that used fMRI to measure brain activity. ",
"When the subjects in these studies viewed nature scenes, parts of the brain associated with heightened empathy, love, and positive mental outlook were activated. ",
"When they viewed urban scenes, they activated parts of the brain associated with fear and anxiety. ",
"It appears as though nature inspires feelings that connect us to our community and our environment.",
"\n\nToo much time in front of screens is deadly\n\nLikewise, a lack of time in the natural world can make us feel more disconnected and unhappy. \"",
"Nature deprivation,\" largely due to hours spent in front of TV or computer screens, has been associated with depression[13], loss of empathy, and lack of altruism, and even a higher risk of death. ",
"This is of particular concern in our modern, busy lives--it's very easy to spend an entire day looking at our computers, our cell phones, and our televisions, without paying any attention to the greenspace outdoors or the plants on our desk.",
"\n\nThis is an example of how you can create an environment that is not working toward your wellbeing--a living room full of screens is bad for you, much like overeating or smoking!",
"\n\nWhat You Can Do\n\nIt's simple: get outside, somewhere green, preferably under your own power (or at very least, get some plants!)",
"\n\nSpend time outdoors whenever you can. ",
"You get double benefit if you enjoy the outdoors actively--gardening, walking, or biking. ",
"If you can, walk or bike where there is vegetation or water--some elements of greenspace.",
"\n\nConsider how much time you spend each time in front of a screen (TV or computer). ",
"Could you reduce that time to go outside or interact with friends or family[14]?",
"\n\nAdd plants you find attractive to your home and office (and bring them to friends and family who are sick). ",
"Consider putting up scenes of nature that you like in your home and office. ",
"Make the interior spaces you live in feel beautiful and healing.",
"\n\nAnd finally, realize that our relationship with nature is not a one-way street. ",
"Our connection with nature demonstrates that we need to protect it--for its sake and for our own."
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"Brauhaus\n\nOn our last visit to Brauhaus, we complained about the atrocious soundtrack, an indelicate farrago of Deutsche-pop that included an ear-aching Atomic Kitten cover. ",
"However, we hadn’t been able to praise the food highly enough. ",
"Things, it seems, have changed somewhat in the past months. ",
"The volume of the music, thankfully, has been lowered to a pianissimo near-silence, but the quality of the food has seemingly nose-dived.",
"\n\nWe still love the venue; a purpose-built semicircular space that classily replicates a traditional German tavern. ",
"Unfortunately on our visit the place was lifeless. ",
"As much as we appreciated the toning down of the tuneless volk-jangle, something was needed to generate atmosphere. ",
"The waiting staff were perfectly friendly and efficient, but somewhat lacking in cheer.",
"\n\nThings seemed to bode well for our meal when I seized a treat from my companion’s hors d’oeuvre plate, a smoked salmon medallion on an impeccably crumbly hash brown. ",
"My goulash had a strong tasty broth, but was let down by little pieces of beef so chewy as to render the dish inedible.",
"\n\nThe main courses were adequate but uninspired. ",
"A giant portion of lamb chops came with a velvety mound of mashed potato speckled with rosemary and fennel, and a side salad with a sweet tangy dressing. ",
"The meat, however, wasn’t very tender, resolutely clinging to the bone. ",
"Dished up with fettuccine, leeks and cheese sauce, a fillet of grilled salmon was beautifully seasoned, but the fish lacked flavour beneath the crisp herb-encrusted edges. ",
"The droopy green pasta lacked dynamism and the cheese sauce and vegetables were merely bland. ",
"The staff needed some cajoling before we could retrieve the menus to order dessert and we waited ages before our lacklustre puddings arrived. ",
"Although I scoffed the adjoining kiwi slices with fleeting fingers, my tablemate’s crêpes with caramel sauce suffered from a tired predictability. ",
"My apple strudel had been doused in a colourfully chocolatised vanilla sauce, but the fruit filling was too tame; a dry, warm, light-sugary flavour lacking fruity sharpness.",
"\n\nIf Brauhaus wants to sparkle this Oktoberfest, it urgently needs a dose of vivacity.",
"\n\nBrauhaus On The Map\n\nUser reviews\n\nValueAmbienceService\n\nDecorFoodOverall\n\nUser reviews:\n\nPosted by: Kay on 24 May ' 13 at 17:00\n\nOverallDecorService\n\nFoodAmbienceValue\n\nWould you go back to this restaurant? ",
"Yes\n\nEdited by TimeOutDubai.com\n\nThis may not be the poshest restaurant in Dubai but you cannot fault the food and the price! \"",
"Stodgy\" food..... Obviously an English person wrote this, I mean English food is not stodgy at all?! ",
"Thursday evening meal deal is fantastic value for money and I will definitely be recommending this to my friends. ",
"The service we couldn't fault, our drinks were topped up continually and the staff were extremely friendly.",
"\n\nPosted by: andy on 06 Mar ' 13 at 11:23\n\nOverallDecorService\n\nFoodAmbienceValue\n\nWould you go back to this restaurant? ",
"Yes\n\nGo every few weeks. ",
"Great beers. ",
"Good stodgy food, particularly pork knuckle. ",
"Think back drop of nonstop EuroPop tad annoying. ",
"A good fun bar/rest.",
"\n\nPosted by: just_me on 09 Apr ' 11 at 14:35\n\nOverallDecorService\n\nFoodAmbienceValue\n\nWould you go back to this restaurant? ",
"Yes\n\nJust order a pork shank if you want to eat a kilo of succulent meat with crispy skin. :)",
"\n\nPosted by: Dr. Raji Mathew on 30 Sep ' 10 at 05:51\n\nOverallDecorService\n\nFoodAmbienceValue\n\nWould you go back to this restaurant? ",
"Yes\n\nCame here on th 26th and had a better expeience this time. ",
"Salmon, mix grill, chicken and sausage sword were ordered for the 4 of us. ",
"The meat dishes are usually dry with lack of any juice in them. ",
"Also I feel the prices are a little high for the quality.",
"\n\nPosted by: Dr. Raji Mathew on 02 May ' 10 at 08:49\n\nOverallDecorService\n\nFoodAmbienceValue\n\nWould you go back to this restaurant? ",
"Yes\n\nTad dissapoinred last night. ",
"We had ordered Mix grill, Royal hammour and BBQ baby ribs. ",
"The ribs were burnt in parts and dry and to make it worse there was not much meat remainig on it. ",
"Fork and knife had to be left by the side as you could only eat it with you hands. ",
"I pointed it out to the manager. ",
"The chef insisted that its to be eaten with hands but as I said there wasn't much to have and for the price you get something altogether different at other establishments. ",
"Though he didn't agree that there was anything greatly wrong with the ribs, he said I can order anything else I want, which I declined. ",
"To be fair, the other dishes were good but I just wish he had just admitted that the ribs were just not right. ",
"This was my 3rd visit to this place and don't intend to let this stop me from coming here again."
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"Anton Skerritt\n\nAnton Skerritt (born January 3, 1964) is a Trinidadian/Canadian former Sprinter, and soccer player. ",
"As a sprinter he competed in the 1984 Summer Olympics, 1988 Summer Olympics, 1987 World Championships in Athletics, 1986 Commonwealth Games, and the 1989 Jeux de la Francophonie.",
"\n\nAs a soccer player he played in the Canadian National Soccer League, and the Canadian Professional Soccer League. ",
"After his retirement from professional sports he became a vice principal for Vaughan Secondary School in Vaughan, Ontario.",
"\n\nAthletics career \n\nIn 1982, Skerritt began playing soccer at the college level with Howard University. ",
"After a recommendation from an American national track and field team coach he switched to track and field. ",
"He was chosen to represent Trinidad & Tobago in the 1984 Summer Olympics to compete in Men's 400 metres, and the Men's 4×400 metres Relay.",
"\n\nIn 1986, he switched his allegiance to Canada for the 1986 Commonwealth Games and won a bronze medal in the 4×400 metres relay. ",
"At the 1987 World Championships in Athletics he achieved a Canadian record of 45.62secs in the 400 metres event. ",
"He featured in the 1988 Summer Olympics, 1989 Jeux de la Francophonie, and the 1991 Pan American Games. ",
"In the Francophonie Games he won 3 medals in 400 metres, 4×100 metres relay, and 4×400 metres relay. ",
"He retired in 1992 to pursue his education in teaching.",
"\n\nFootball career \nIn 1994, he returned to competitive soccer to play with St. Catharines Wolves of the Canadian National Soccer League. ",
"The following season, he signed with Toronto Italia. ",
"In 1996, he returned to St. Catharines where he won the Umbro Cup and reached the CNSL Championship finals against Toronto Italia but lost the series by a score of 11-0 on goals on aggregate.",
"\n\nIn 1997, he signed with the Hamilton White Eagles, but was released midway through the season as the league suspended the organization for the remainder of the season. ",
"In 2002, he signed with expansion franchise the Metro Lions of the Canadian Professional Soccer League. ",
"In their debut season the Lions secured a postseason berth by finishing third in the Eastern Conference. ",
"In the semi-finals they faced the Ottawa Wizards, but suffered a 1-0 defeat. ",
" He returned for a second season with the Lions, and helped the club reach the finals of the Open Canada Cup tournament where they lost the match to London City 4-2 on penalties.",
"\n\nReferences \n\nCategory:1964 births\nCategory:Living people\nCategory:Athletes (track and field) at the 1984 Summer Olympics\nCategory:Athletes (track and field) at the 1988 Summer Olympics\nCategory:Olympic track and field athletes of Canada\nCategory:Olympic athletes of Trinidad and Tobago\nCategory:Athletes (track and field) at the 1986 Commonwealth Games\nCategory:Athletes (track and field) at the 1990 Commonwealth Games\nCategory:Commonwealth Games silver medallists for Canada\nCategory:Athletes (track and field) at the 1991 Pan American Games\nCategory:Pan American Games competitors for Canada\nCategory:World Athletics Championships athletes for Canada\nCategory:Trinidad and Tobago male sprinters\nCategory:Trinidad and Tobago footballers\nCategory:Canadian soccer players\nCategory:Black Canadian sportspeople\nCategory:St. Catharines (Roma) Wolves players\nCategory:Toronto Italia players\nCategory:Canadian National Soccer League players\nCategory:Brampton United players\nCategory:Canadian Professional Soccer League (1998–2005) players\nCategory:Commonwealth Games medallists in athletics\nCategory:Trinidad and Tobago emigrants to Canada\nCategory:Association football defenders"
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"Somatic mutations of the multiple endocrine neoplasia type 1 (MEN1) gene in patients with sporadic, nonfamilial primary hyperparathyroidism.",
"\nMultiple endocrine neoplasia type 1 (MEN 1) is a syndrome with tumors of many endocrine tissues. ",
"Germline MEN1 gene mutations were found in most patients with familial or sporadic MEN 1. ",
"Recently, somatic MEN1 gene mutations were also detected in sporadic non-MEN 1 endocrine tumors. ",
"We used direct sequence analysis to investigate MEN1 gene mutations in 30 parathyroid tumors obtained from 30 patients with sporadic, nonfamilial primary hyperparathyroidism. ",
"Four patients had somatic mutations of the MEN1 gene, comprising 1 small insertion (1091insAGC), one missense mutation (G42S), and 2 non-sense mutations (E388X, R460X). ",
"Identical missense and non-sense mutations were found in patients with familial and non-familial MEN 1. ",
"There were no differences between clinical features of patients with and without MEN1 gene mutations. ",
"The incidence of somatic MEN1 gene mutations (13.3%) in Japanese patients with sporadic, nonfamilial primary hyperparathyroidism is almost equal to those of such patients in the United States and Sweden. ",
"Occasionally, the MEN1 gene mutation sites in sporadic parathyroid tumors are identical to those reported in tumors from patients with familial or sporadic MEN 1."
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"UEFA Euro 2016 Group E\n\nGroup E of UEFA Euro 2016 contained Belgium, Italy, Republic of Ireland and Sweden. ",
"Italy was the only former European champion in this group, having won in 1968. ",
"Matches were played from 13 to 22 June 2016.",
"\n\nTeams\n\nNotes\n\nStandings\n\nIn the round of 16,\nThe winner of Group E, Italy, advanced to play the runner-up of Group D, Spain.",
"\nThe runner-up of Group E, Belgium, advanced to play the winner of Group F, Hungary.",
"\nThe third-placed team of Group E, Republic of Ireland, advanced as one of the four best third-placed teams to play the winner of Group A, France.",
"\n\nMatches\n\nRepublic of Ireland vs Sweden\n\nBelgium vs Italy\n\nItaly vs Sweden\n\nBelgium vs Republic of Ireland\n\nItaly vs Republic of Ireland\n\nSweden vs Belgium\n\nReferences\n\nExternal links\nUEFA Euro 2016 Group E\n\nCategory:UEFA Euro 2016\nCategory:Belgium at UEFA Euro 2016\nCategory:Italy at UEFA Euro 2016\nCategory:Sweden at UEFA Euro 2016\nCategory:Republic of Ireland at UEFA Euro 2016"
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"Minoru Tatsukawa\n\nis a volleyball coach from Japan. ",
"Currentry he serves as head coach of Denso Airybees.",
"\n\nCareer \n1975 After graduating from Osaka University of Commerce, he became an assistant coach of Unitika.",
"\n1992 Assistant coach of Women's national volleyball team in the Barcelona Olympic games.",
"\n1995 He became a head coach of Unitika.",
"\n2000 Unitika Phoenix was abolished and it moved Toray Arrows.",
"\n2005 He retired a head coach and was appointed vice general manager of Toray Arrows.",
"\n2006 Denso Airybees had invited him as a head coach.",
"\n\nHonours as a head coach \nV.League/V.Premier League\nChampion (1) 1995\nRunners-up (2) 2003, 2007–08\nKurowashiki All Japan Volleyball Tournament\nChampion (1) 2008\n\nExternal links \nDenso Airybees Official Website\n\nCategory:1952 births\nCategory:Living people\nCategory:Japanese men's volleyball players\nCategory:People from Osaka"
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"Poe’s Arkansas Cavalry Battalion was a Confederate cavalry unit that served in the Trans-Mississippi Department, entirely in Arkansas, during the American Civil War. ",
"It participated in military engagements at Mount Elba, Easling’s Farm, Poison Spring, Marks’ Mills, and Hurricane Creek, as well as undertaking scouting and picketing duties in southern Arkansas. ",
"During Price’s Missouri Raid in 1864, it was one of the few cavalry units left behind to keep watch over Federal troops in Arkansas.",
"\n\nThe unit was organized in November 1863 by a former Saline County judge, Major James T. Poe of the Eleventh Arkansas Infantry. ",
"Poe had journeyed home from Louisiana to remove his family farther south from Saline County after the fall of Little Rock (Pulaski County) to Union forces in September 1863. ",
"He raised the unit to help protect local families in the area. ",
"The battalion, although officially designated Poe’s Arkansas Cavalry, was often referred to as the Eleventh Arkansas Cavalry. ",
"After the return of Colonel John L. Logan of the Eleventh Arkansas Infantry to Arkansas, it was commonly referred to as Logan’s Cavalry. ",
"Primarily composed of former members of the Eleventh and Seventeenth Arkansas Mounted Infantry who had been captured at Port Hudson and other locales who were paroled back to Arkansas, it also included deserters and previously discharged soldiers, all of whom were organized into the battalion. ",
"The battalion was assigned to Colonel William A. Crawford’s Cavalry Brigade of Major General James F. Fagan’s Division.",
"\n\nStationed at Monticello (Drew County) in March 1864, the battalion, as part of Crawford’s Brigade along with Dockery’s Brigade, attacked and attempted to destroy a Union force under Colonel Powell Clayton at Mount Elba (Cleveland County) on March 30. ",
"Facing infantry and artillery behind hasty defensive works, the Confederates, despite their repeated assaults, were defeated, forcing a hasty retreat toward Monticello. ",
"While the Confederates were moving into position the day prior, unknown to them, Clayton’s Cavalry had attacked and captured their entire wagon train at Easling’s Farm on Longview Prairie in Ashley County. ",
"This included more than 300 men, thirteen of whom were dismounted members of Poe’s Battalion.",
"\n\nDuring the April 1864 Camden Expedition, the battalion, as part of Major General Sterling Price’s Cavalry, operated against Brigadier General Frederick Steele’s forces in southern Arkansas. ",
"Poe’s Battalion, as part of Crawford’s Brigade, engaged and assisted in the destruction of a Union supply train at Poison Springs on April 18, 1864. ",
"Seven days later, they engaged a large Federal force at Marks’ Mills, assisting in the complete destruction and capture of the entire force. ",
"When Steele’s army retreated back to Little Rock after the Engagement at Jenkins’ Ferry, the battalion continued to scout and picket areas of south-central Arkansas for the remainder of the summer.",
"\n\nIn August 1864, Major General Price started north on his disastrous Missouri Raid, leaving only a small cavalry force in Arkansas to monitor the Union army at Little Rock and Pine Bluff (Jefferson County). ",
"Poe’s Battalion was one of the few to remain behind and was placed under the command of its former commander, Colonel John L. Logan. ",
"Operating out of Princeton (Dallas County) and Tulip (Dallas County), the battalion conducted scouting operations and patrolled as far as the Saline-Pulaski county border to south of Pine Bluff.",
"\n\nOn October 21, Logan’s force was attacked by a Union scouting party sent to Princeton to destroy Confederate weapons. ",
"The Union force then headed toward Little Rock. ",
"Logan hurried his men forward and successfully prepared an ambush along Hurricane Creek on the Camden Trail near present-day Bryant (Saline County). ",
"On October 23, as the Union column crossed Hurricane Creek, the Confederates opened fire. ",
"The Confederates failed to destroy the column and eventually withdrew. ",
"Union dispatches reported losses of two killed and eleven wounded, while they captured one enemy and found twenty-seven dead on the field. ",
"The lopsided casualties may be the result of execution of Confederate wounded and captured. ",
"Colonel Logan filed the claim that his men had been summarily executed after falling into the hands of the enemy and personally delivered his report, under flag of truce, to Union authorities. ",
"Brigadier General Steele claimed no knowledge of such an incident but promised to investigate. ",
"No further information is found regarding this incident.",
"\n\nOn May 22, 1865, Poe’s Battalion was stationed at Darby’s Ferry on the Red River in Arkansas, where Colonel Logan furloughed the men home, advising them to surrender themselves to the nearest Union force and receive their paroles; most simply returned to their homes without any official surrender."
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"\nDisc indicators of this generic type have bearings for instruments on motor vehicles. ",
"In this case, the only instruments which are referred to as “disc indicators” in this context are those in which the indicator disc is not held on a shaft that is mounted such that it can rotate, but the indicator disc is mounted such that a guided ring structure allows the indicator disc to rotate. ",
"Finally, the special feature of disc indicators such as these is that there is no need for the central shaft. ",
"This results in a high degree of flexibility with regard to the design options for the instrument.",
"\nOne disc indicator of this type is disclosed, for example, in DE 199 16 221 A1, which has a disc to which the pointer is fitted, with the disc being held between two guide rollers at its outer edge. ",
"In this case, one of the rollers is driven by a stepping motor.",
"\nIn DE 199 03 202 A1, covers are fitted with pointer symbols, have a circular external contour and are mounted in the cutouts in a board or panel such that they can rotate. ",
"In this case, rolling elements are fitted in the covers in order to minimize the friction in the bearing. ",
"The drive which initiates the rotary movement is provided by an electric motor, which acts on a toothed rim on the cover.",
"\nEP 492 543 A1 describes a pointer plate which is driven by an annular ultrasound motor in such a way that the pointer plate is connected to the rotor of this ultrasound motor such that they rotate together, by the edge of the pointer plate being formed such that it is oriented orthogonally with respect to the plate plane, thus producing a holder for the rotor part of the ultrasound motor. ",
"No radial bearing is formed by this design.",
"\nIn consequence, the types of bearing specified for disc indicators are complex with a large number of components, resulting in correspondingly expensive manufacturing costs. ",
"Furthermore, instruments such as these may be less reliable in operation. ",
"Although disc indicators have a number of advantages over conventional instruments which have a pointer held at the end of a shaft, it has not until now been possible to make use of these instruments, particularly because of the high production costs."
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"The Montebello Police Department is investigating a vehicle theft that hits rather close to home.",
"\n\nA marked patrol SUV was boosted from a city parking lot last week — along with a loaded AR-15 assault rifle and two loaded shotguns that were inside, authorities said Wednesday.",
"\n\nOne of the shotguns was loaded with bean-bag rounds, the other with lethal shot.",
"\n\nPolice said all the weapons were locked and secured in the vehicle and all the keys to the SUV have been accounted for.",
"\n\n\nThe SUV — a black 2018 Ford Explorer with a white roof, white doors and the number “09” painted on the roof, front fenders and rear — was last driven by authorized police personnel around 5 p.m. Thursday. ",
"Investigators said the vehicle was taken from the Police Department’s public parking lot around 2:23 a.m. Friday.",
"\n\nSurveillance video shows a masked person entering the vehicle and then driving away about 10 seconds later, police said.",
"\n\nThe SUV was not discovered missing for four days, however, when it was assigned to be driven again Tuesday, authorities said.",
"\n\nOther law enforcement agencies have been notified about the missing car, which has a California exempt license plate number of 1429238, Montebello police said.",
"\n\n\nInvestigators are asking anyone with information about the vehicle to call (323) 887-1313. ",
"Callers also can dial 911 on their mobile phone if the cruiser is spotted.",
"\n\nThose wishing to remain anonymous can call Crime Stoppers at (800) 222-8477 or go to www.lacrimestoppers.org.",
"\n\njavier.panzar@latimes.com\n\n@jpanzar"
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"Q:\n\nSpring: После добавления регистрации перестал работать Action на форме\n\nПробую делать пример приложения Sweater с Youtube в Spring.",
"\nВсе было хорошо до тех пор, пока не добавил авторизацию пользователя с хранением в памяти.",
"\nРепозитарий GItHub тут: https://github.com/aalopatin/sweater\nПоказываю, что делал:\n\nКорневая страница, имеет ссылку на main, если пользователь не залогинился переходит на страницу login:\n\n<!",
"DOCTYPE HTML>\n<html xmlns:th=\"http://www.thymeleaf.org\">\n<head>\n <title>Приветственное начало: Serving Web Content</title>\n <meta http-equiv=\"Content-Type\" content=\"text/html; charset=UTF-8\" />\n</head>\n<body>\n <div>Hello, user</div>\n <a th:href=\"@{/main}\">Main page</a>\n</body>\n</html>\n\nГлавная страничка открывается после успешной авторизации:\n\n<!",
"DOCTYPE html>\n<html>\n<head>\n <meta http-equiv=\"Content-Type\" content=\"text/html; charset=UTF-8\" />\n</head>\n<body>\n <div>\n <form method=\"post\">\n <input type=\"text\" name=\"text\" placeholder=\"Введите сообщение\" />\n <input type=\"text\" name=\"tag\" placeholder=\"Тэг\">\n <button type=\"submit\">Добавить</button> \n </form>\n </div>\n <div>Список сообщений</div>\n <form method=\"post\" action=\"filter\">\n <input type=\"text\" name=\"filter\">\n <button type=\"submit\">Найти</button>\n </form>\n <div th:each = \"message : ${messages}\">\n <b th:text = \"${message.id}\"></b>\n <span th:text = \"${message.text}\"></span>\n <i th:text = \"${message.tag}\"></i>\n </div>\n</body>\n</html>\n\nНа этой странице выводятся message и есть фильтр для их отбора, туда вводится тэг и нажимается кнопка Найти типа submit.",
"\nВот контроллер обрабатывающий все мэппинги:\npackage com.example.sweater;\n\nimport org.springframework.beans.factory.annotation.",
"Autowired;\nimport org.springframework.stereotype.",
"Controller;\nimport org.springframework.ui.",
"Model;\nimport org.springframework.web.bind.annotation.",
"GetMapping;\nimport org.springframework.web.bind.annotation.",
"PostMapping;\nimport org.springframework.web.bind.annotation.",
"RequestParam;\n\nimport com.example.sweater.domain.",
"Message;\nimport com.example.sweater.repos.",
"MessageRepo;\n\n@Controller\npublic class GreetingController {\n\n @Autowired\n private MessageRepo messageRepo;\n\n @GetMapping(\"/\")\n public String greeting(Model model) {\n\n return \"greeting\";\n\n }\n\n @GetMapping(\"/main\")\n public String main(Model model) {\n\n Iterable<Message> messages = messageRepo.findAll();\n\n model.addAttribute(\"messages\", messages);\n\n return \"main\";\n }\n\n @PostMapping(\"/main\")\n public String add(@RequestParam String text, @RequestParam String tag, Model model) {\n\n Message message = new Message(text, tag);\n\n messageRepo.save(message);\n\n Iterable<Message> messages = messageRepo.findAll();\n\n model.addAttribute(\"messages\", messages);\n\n return \"main\";\n }\n\n @PostMapping(\"/filter\")\n public String filter(@RequestParam String filter, Model model) {\n\n Iterable<Message> messages;\n\n if (filter !",
"= null && !",
"filter.isEmpty()) {\n messages = messageRepo.findByTag(filter);\n } else {\n messages = messageRepo.findAll();\n }\n\n model.addAttribute(\"messages\", messages);\n\n return \"main\";\n\n }\n}\n\nВот WebSecurityConfig:\npackage com.example.sweater.config;\n\nimport org.springframework.context.annotation.",
"Bean;\nimport org.springframework.context.annotation.",
"Configuration;\nimport org.springframework.security.config.annotation.web.builders.",
"HttpSecurity;\nimport org.springframework.security.config.annotation.web.configuration.",
"EnableWebSecurity;\nimport org.springframework.security.config.annotation.web.configuration.",
"WebSecurityConfigurerAdapter;\nimport org.springframework.security.core.userdetails.",
"User;\nimport org.springframework.security.core.userdetails.",
"UserDetails;\nimport org.springframework.security.core.userdetails.",
"UserDetailsService;\nimport org.springframework.security.provisioning.",
"InMemoryUserDetailsManager;\n\n@Configuration\n@EnableWebSecurity\npublic class WebSecurityConfig extends WebSecurityConfigurerAdapter {\n @Override\n protected void configure(HttpSecurity http) throws Exception {\n http\n .authorizeRequests()\n .antMatchers(\"/\").permitAll()\n .anyRequest().authenticated()\n .and()\n .formLogin()\n .loginPage(\"/login\")\n .permitAll()\n .and()\n .logout()\n .permitAll();\n }\n\n @Bean\n @Override\n public UserDetailsService userDetailsService() {\n UserDetails user =\n User.withDefaultPasswordEncoder()\n .username(\"u\")\n .password(\"p\")\n .roles(\"USER\")\n .build();\n\n return new InMemoryUserDetailsManager(user);\n }\n}\n\nТут прописан один пользователь в памяти и права - корневая страница доступна всем, для других запросов нужна аутентификация.",
"\nПоказываю, скриншоты:\nКорневая страница:\n\nГлавная страница:\n\nПосле ввода в поле фильтра имени тэга и нажатия кнопки Найти появляется окно с ошибкой:\n\nВ консоль ошибок не пишет, в функцию контроллера не проваливается, отладчик не ловит(функция ниже)\n@PostMapping(\"/filter\")\npublic String filter(@RequestParam String filter, Model model)\n\nВ репозитории есть рабочий коммит без авторизации пользователей с комментарием \"Add messages\". ",
"\nТекущая версия коммита с нерабочим фильтром имеет комментарий \"Add remote repository and Login\"\n\nA:\n\nНашел решение. ",
"Необходимо в форму на главной странице добавить аттрибут th. ",
"Т.к. ",
"я использую шаблонизатор Thymeleaf защита от csrf автоматически встраивается на страницы, но только в те формы, в которых присутсвует аттрибуты Thymeleaf:\n<form method=\"post\" th:action=\"filter\">\n <input type=\"text\" name=\"filter\">\n <button type=\"submit\">Найти</button>\n</form>\n\n"
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"Alignment characteristics of magnetic fields have been used to achieve precision movement and positioning of objects. ",
"A key principle of operation of an alternating-current (AC) motor is that a permanent magnet will rotate so as to maintain its alignment within an external rotating magnetic field. ",
"This effect is the basis for the early AC motors including the “Electro Magnetic Motor” for which Nikola Tesla received U.S. Pat. ",
"No. ",
"381,968 on May 1, 1888. ",
"On Jan. 19, 1938, Marius Lavet received French Patent 823,395 for the stepper motor which he first used in quartz watches. ",
"Stepper motors divide a motor's full rotation into a discrete number of steps. ",
"By controlling the times during which electromagnets around the motor are activated and deactivated, a motor's position can be controlled precisely. ",
"Computer-controlled stepper motors are one of the most versatile forms of positioning systems. ",
"They are typically digitally controlled as part of an open loop system, and are simpler and more rugged than closed loop servo systems. ",
"They are used in industrial high speed pick and place equipment and multi-axis computer numerical control (CNC) machines. ",
"In the field of lasers and optics they are frequently used in precision positioning equipment such as linear actuators, linear stages, rotation stages, goniometers, and mirror mounts. ",
"They are used in packaging machinery, and positioning of valve pilot stages for fluid control systems. ",
"They are also used in many commercial products including floppy disk drives, flatbed scanners, printers, plotters and the like.",
"\nAlthough alignment characteristics of magnetic fields are used in certain specialized industrial environments and in a relatively limited number of commercial products, their use for precision alignment purposes is generally limited in scope. ",
"For the majority of processes where alignment of objects is important, e.g., residential construction, comparatively primitive alignment techniques and tools such as a carpenter's square and a level are more commonly employed. ",
"Moreover, long trusted tools and mechanisms for attaching objects together such as hammers and nails; screw drivers and screws; wrenches and nuts and bolts; and the like, when used with primitive alignment techniques result in far less than precise residential construction, which commonly leads to death and injury when homes collapse, roofs are blown off in storms, etc. ",
"Generally, there is considerable amount of waste of time and energy in most of the processes to which the average person has grown accustomed that are a direct result of imprecision of alignment of assembled objects. ",
"Machined parts wear out sooner, engines are less efficient resulting in higher pollution, buildings and bridges collapse due to improper construction, and so on.",
"\nIt has been discovered that various field emission properties can be put in use in a wide range of applications."
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"Inspirational Quote\n\nKit Carson Peak - North RidgeJuly 23, 2004 - July 25, 2004\n\nI woke up about 9:00am at my parents' house in Denver. ",
"The night before I'd flown in from Portland, Oregon and drove straight to my parents' house for a few hours of sleep. ",
"I had a nice breakfast, stopped by the grocery store for a few last minute items, and hit the road.",
"\n\nThe drive down to Crestone was really nice. ",
"The traffic was minimal, I had the tunes blasting, and the scenery was gorgeous. ",
"South Park, the Arkansas River Valley, and the San Luis Valley are all just beautiful. ",
"After about four hours of driving I made my way through the little town of Crestone and parked at the Willow Lake Trailhead. ",
"I got the last parking spot in the lot. ",
"I tossed on my gear and headed up the trail.",
"\n\nIt took me about three hours to reach the Summit Post camp above Willow Lake. ",
"Willow Lake was really cool and the waterfall was even more spectacular than I imagined. ",
"While I rested by the lake I saw a 15-inch Greenback swim by. ",
"I wished I had my fishing kit - maybe next time!",
"\n\nDuring the last hour or so of the hike the clouds had began to close in and I felt like it would be a real race to make it to camp and set up the tent before the storm began. ",
"When I made it camp I said hi to Allen and Jackie and they showed me a good spot to pitch my tent. ",
"I pitched my tent as fast as I could, put on my rain gear, and then grabbed my water filter and Nalgene bottles and hustled to filter some water. ",
"Just as I was finishing it started pouring. ",
"I finished filtering my water and then hustled back to the tent. ",
"By this time the rain was turning into hail and it was really coming down. ",
"I scrambled inside the tent and went to sleep.",
"\n\nI woke up an hour and a half later and the weather had subsided. ",
"Outside there were some piles of marble sized hail. ",
"I wandered around to say hi to the rest of the Summit Post crew: Aaron, Ellen, Vern, and Barry. ",
"After greeting everyone I fixed up some dinner and we chatted until it got dark and cold. ",
"The storm had dusted Kit Carson with a layer of hail/snow and Barry wasn't sure if he'd be able to do the North Ridge as planned. ",
"There was a group of climbers camped not very far away who were planning on the North Ridge also. ",
"The were determined to do it and one climber among them had done it several times previously and thought the snow/hail wouldn't be a problem. ",
"Barry decided to wait until the morning to make his decision. ",
"I was leaning toward the standard route, but I'd wait until the morning to make my final decision too.",
"\n\nWe decided on a 5:30 start time so I set my alarm and went to bed.",
"\n\n7/24/04\n\nI rolled out of bed at 5:00 and had a cup of hot cocoa while I got my stuff together. ",
"Alan, Jackie, Barry, and I got together at 5:30. ",
"Aaron and Ellen decided to sleep in a bit and catch up with us later. ",
"Barry said had decided to try the North Ridge and I decided to go with him. ",
"Barry and I set off up the valley and Alan and Jackie headed up Challenger Point's north face.",
"\n\nThe other group of climbers got a start about fifteen minutes after us. ",
"As we contoured below a cliff face on Kit Carson's north face we could see the other group of climbers following behind us. ",
"They chose to stay in the valley floor and follow Willow Creek while we contoured along Kit Carson's north face and weaved our way between a field of truck-sized boulders below us and a cliff band above us. ",
"I think staying low and following the creek was probably easier than what we did, but it was probably also wetter. ",
"Brushing against all the dew-covered grass and shrubs probably soaked their boots and pants while we were relatively dry scrambling through boulders.",
"\n\nAs we passed underneath the cliff band and the North Ridge the group of climbers down in the valley gained on us significantly. ",
"We climbed up some gullies below the North Ridge as the other group climbed up a talus slope and we met on the grassy ledges at the beginning of the North Ridge. ",
"The guy in the other group who had climbed the North Ridge several times and gave us a few bits of advice before we continued on: namely stick as close to the ridge proper as possible and stray to the right if needed, but don't stray to the left.",
"\n\nFor the next hundred feet or so we negotiated the steep grassy ledges. ",
"These were largely covered in a thin layer of hail/snow which made them tricky to climb. ",
"Soon we passed the grassy ledges and made our way onto solid rock. ",
"Barry did the route finding as we headed up.",
"\n\nThe lower sections of North Ridge were not very sharp and it looked like you could find a route almost anywhere. ",
"However I got into trouble a couple of times so I decided to follow right behind Barry whose route finding was much better than mine. ",
"As we ascended the ridge sharpened and soon we narrowed our route to the ridge proper. ",
"From the top of the grassy ledges the climbing had been steady class 4. ",
"The rock was also wet in places from the melting hail/snow which made things extra tricky. ",
"Because of the wet rock we didn't have much confidence in our footholds. ",
"I had to concentrate on every hand and foothold, making sure I had three good ones at any given moment. ",
"I did my best to keep up with Barry and follow his line, but several times I had to ask him do slow down and wait for me.",
"\n\nThe ridge was unrelenting class-4 and there were very few places where I felt comfortable enough to stop and rest or to take a photo. ",
"The ridge itself was very steep and the exposure off to our left was incredible and the exposure off to our right was nothing to sneeze at either. ",
"After climbing for quite a while we passed a notch where we could rest, have a bit to eat, and snap a few photos.",
"\n\nAfter the notch we soldiered on. ",
"The steady class 4 climbing continued. ",
"There were several places where the hand and footholds were very tricky and I had to ask Barry's advice on how to complete several moves. ",
"With Barry's coaching I managed to make it over the more difficult sections. ",
"As we neared the summit the slope of the ridge quickly decreased and soon we popped out onto a near horizontal ridge. ",
"The exposure was exhilarating as we walked across the ridge to the summit. ",
"The group that head been following us up the ridge showed up right afterwards and we chatted on the summit for a few minutes while we snacked, snapped photos, and signed the summit registry. ",
"It was about 9:30am. ",
"This group decided to go on to Columbia Point (aka Kat Carson) and Barry decided to go with them. ",
"I didn't think I had it in me and decided to wait for Alan. ",
"We had been in contact with Alan via two-way radio throughout the day and knew that he was somewhere between Kit Carson Avenue and the summit.",
"\n\nI watched Barry and the group set off for Columbia Point. ",
"During the past hour the clouds had really moved in. ",
"It started as a wisp of mist filtering in between Kit Carson and Columbia Point and gradually built. ",
"Now visibility was down to about a hundred feet. ",
"Soon Barry and group were out of site but I could hear them chattering amongst themselves. ",
"As I waited in the mist for Alan I heard many voices down below. ",
"Gradually people started to emerge from the mist. ",
"Three other people arrived on the summit before Alan showed up. ",
"He signed the summit log, tossed down a small snack, and then we set off down the mountain. ",
"The mounting clouds were a bit of a concern so we didn't feel like killing any more time on the summit.",
"\n\nAs we made our way down Kit Carson we almost missed Kit Carson Avenue. ",
"We had just passed Kit Carson Avenue and were still heading down the gully when we heard some voices above. ",
"When the hikers materialized out of the mist we asked them if they were on the avenue. ",
"They said they were and we climbed back up to and set off on the right track. ",
"It was a good thing that those people happened by or we might have spent a lot of time wandering around in the mist looking for Kit Carson Avenue. ",
"Alan and I huffed and puffed our way up Kit Carson Avenue until it made a right turn around a sharp corner and descended down to the saddle between Kit Carson and Challenger Point.",
"\n\nAt this point the clouds cleared a bit and we had a good view of Challenger Point. ",
"After passing the saddle I angled up toward Challenger Point. ",
"Since Alan had already been on the summit earlier that day he took a more gradual rate of ascent as he contoured up Challenger's north face and achieved the ridge about a hundred feet past the summit. ",
"I made the summit, took a photo of the plaque, and attempted to sign the summit log. ",
"It was a soggy mess and I couldn't find a space to sign so I gave up and put it back. ",
"As I finished up a group of guys reached the summit of Challenger Point. ",
"They asked me about what to expect on their way to Kit Carson. ",
"I told 'em what I could and then set out down the ridge. ",
"I met Alan and we continued the descent. ",
"The clouds began to roll back in and soon visibility was back down to only a couple hundred feet. ",
"The exposure down the south side of the ridge was incredible. ",
"The fact that you couldn't see more than two hundred feet down due to the clouds made it seem even more impressive.",
"\n\nSoon we made it down the ridge to the top of a large gully. ",
"Alan and I opted to descend the gully instead of wrapping around the west end of the ridge via the standard route. ",
"The gully was steep dirt and loose rock but made for a relatively quick descent. ",
"However, this terrain really sapped my legs and by the time we were halfway down my legs were pretty tired. ",
"During the descent we met a couple of guys headed up. ",
"It was already 1:00pm and they probably had close to two hours of climbing just to reach Challenger Point. ",
"Pretty crazy. ",
"Alan and I were glad to be almost off the mountain, rather than just beginning. ",
"The last bit of the hike seemed to take forever but we finally arrived back at camp at about 1:30pm. ",
"It was pretty much eight hours round trip.",
"\n\nThe Oklahoma/Texas contingent had decided to hike back down to their car this afternoon so I hung out and chatted with the group while Alan and Jackie packed up their stuff. ",
"After a while I felt like a nap so I laid down while Alan and Jackie finished packing and waited for Barry. ",
"Barry showed up a little later, packed up his stuff, and the Colorado contingent said goodbye as they headed down the trail. ",
"I didn't envy them the long hike down to the car after already spending eight hours on the mountain. ",
"Frankly I was feeling really whipped myself. ",
"I hung out a little talking with Aaron, Ellen and Vern until the storm clouds finally closed in. ",
"We all retreated to our tents and then the skies let loose with a vengeance. ",
"Hail, rain, crashing thunder, and violent flashes of lighting bombarded us for more than an hour. ",
"However, it was nice to be snuggled in the tent while this went on. ",
"I wonder how many unfortunates had to experience this up on the Challenger Point ridge. ",
"That would not be fun! ",
"As it turns out Alan, Jackie, and Barry almost made it to the car without getting dumped on . . . ",
"but not quite. ",
"The got drenched in the last half mile of their hike out.",
"\n\nAfter the storm passed I got up and fixed dinner and chatted with Aaron, Ellen, and Vern. ",
"They were still considering going after Adams the next day but I had pretty much ruled it out. ",
"I was feeling really exhausted and I didn't want to push it. ",
"I told them to wake me up in the morning before they headed out. ",
"After the sun went down the temperature began to drop rapidly and I got cold. ",
"I said my goodnights and retreated to the warmth and comfort of my sleeping bag.",
"\n\n7/25/04\n\nAaron woke me at about 8:00 saying that they were all packed up and headed back to the car. ",
"They had opted to forgo Adams because Vern's feet were hurting him, Aaron's back was hurting him, and they didn't want to get caught in afternoon weather like the day before. ",
"I said goodbye and lazed in the tent for another our before dragging myself out at 9:00. ",
"When I stumbled out of the tent I found my tent covered with a layer of ice. ",
"It must have got quite chilly that night! ",
"Everyone who had been camping in the area had already departed and I had the valley to myself as I leisurely packed up my stuff.",
"\n\nI took my time making my way back to the car and arrived about 12:30. ",
"I piled into the car and drove up to Buena Vista where I went to the hamburger joint on the main drag (I forget the name but it may be K's). ",
"They have great burgers, fries, and shakes. ",
"However when I pulled in there was huge line and tons of people milling about so I decided to pass it up and went to Seven-Eleven instead for a hotdog while I filled up the gas tank.",
"\n\nAfter that I drove down to my parents' house in Denver for a shower and dinner. ",
"My parents' had taped the network TV coverage of the Tour de France (which totally sucked) so I watched that with 'em. ",
"I realize that the mainstream public doesn't give a crap about the race except to get warm fuzzies over Lance Armstrong, but there is a lot more to the race than just Lance. ",
"For instance, it would have been nice if they'd said who won the frickin' stage! ",
"Or who won the green jersey! ",
"In other cycling news that I missed over the weekend Tom Danielson smashed the Mount Evans record by over four minutes. ",
"That guy is an animal and I hope to hear big things from him in the future. ",
"Anywho, after catching up on the cycling news I left Denver and picked up the wife at the airport on the way back up to Fort Collins.",
"\n\nIt had been a long, fun weekend. ",
"If you count Challenger Point, that makes thirteen fourteeners for me."
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"Stable aggregate fertility in a time of family change: a decomposition of trends in American fertility, 1970-1999.",
"\nPopulation-level birth rates in the United States were largely stable between 1970 and 1999. ",
"This stability contrasts with rapid change in marriage rates and fertility timing during the same period. ",
"In this article, I use decomposition techniques to analyze this seeming paradox. ",
"I decompose the general fertility rate into four components: age distribution, marital status, age-specific nonmarital fertility, and age-specific marital fertility. ",
"Absent other changes, declining time spent married would have led to substantial decline in fertility. ",
"Several factors combined to counterbalance these changes in marital behavior. ",
"Among white women in the 1970s and 1980s, marital fertility rates increased at older ages, consistent with a scenario in which women postponed both marriage and childbearing; increased nonmarital birth rates during this period were not a driving factor in overall fertility trends. ",
"Increased nonmarital fertility was more important in compensating for declining time spent married among African American women and among white women in the 1990s."
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"Russia's Khodorkovsky Has Jail Term Trimmed; Attacks Courts\n\nMOSCOW — Russia's Supreme Court cut former oil tycoon Mikhail Khodorkovsky's jail sentence by two months on Tuesday, allowing one of President Vladimir Putin's biggest critics to walk free in August 2014 after more than a decade behind bars.",
"\n\nThe court upheld Khodorkovsky's 2010 conviction for money laundering and stealing oil, but trimmed his sentence after an appeal by his defense lawyers.",
"\n\nKhodorkovsky, who was also convicted of tax evasion and fraud in 2005, was Russia's richest man before he was arrested in 2003 after falling out with Putin. ",
"He is seen by some Kremlin critics as a potential opposition leader.",
"\n\nSome leading opposition figures doubt Putin will allow Khodorkovsky, 50, to go free until he is sure he is not a political threat, but his lawyers say his spirit has not been broken.",
"\n\n\"Russian penal colonies never were, and are not, conducive to feeling better, especially after 10 years. ",
"But considering all that, his spirit is unbreakable,\" defense lawyer Vadim Klyuvgant said after the ruling in Moscow.",
"\n\nKhodorkovsky's business partner, Platon Lebedev, also had his sentence cut by two months and will be able to walk free next May.\n\nKhodorkovsky addressed the Supreme Court in a video link from his prison colony near the Arctic Circle.",
"\n\n\"In this case, the usual mantra that everything is legal and well-grounded just won't do,\" Khodorkovsky said, dressed in a black shirt and reading from notes clearly and calmly.",
"\n\nDescribing his case as political, he said: \"Faulty court rulings have already become a catalyst for the protest movement [against Putin]. ",
"A growing part of society is demanding . . . ",
"to be able to live and not be afraid.\"",
"\n\nBUSINESS EMPIRE BROKEN UP\n\nKhodorkovsky's $40-billion business empire was broken up and sold off, mainly into state hands, after his arrest and subsequent sentencing in 2005.",
"\n\nHe had fallen out with Putin by funding political parties other than the main pro-Kremlin party and suggesting some oil deals involving the state were corrupt.",
"\n\nMany foreign investors saw Khodorkovsky's jailing as a turning point in Putin's 2000-2008 presidency, giving hardliners the upper hand and ultimately increasing their control over the economy.",
"\n\nInvestors said his release would be a positive sign but they are more now concerned about the treatment of opposition leader Alexei Navalny, who is appealing against a five-year jail term after being convicted in July of theft.",
"\n\nNavalny, 37, is now widely regarded as more likely to be able to challenge Putin politically than Khodorkovsky, who has continued to criticize the president from prison but has increasingly seemed out of touch with political events.",
"\n\nPutin remains Russia's most popular politician, opinion polls show. ",
"The polls suggest Navalny and Khodorkovsky would be unlikely to be able to mount a strong challenge to the president.",
"\n\nIn their first trial, Khodorkovsky and Lebedev were sentenced to nine years in prison, later reduced to eight, for fraud and tax evasion. ",
"They both pleaded not guilty.",
"\n\nMore charges were brought against them and, found guilty of money-laundering and theft in 2010, their sentences were extended until 2017. ",
"They were later reduced to 2016 on appeal and then to 2014.",
"\n\nKhodorkovsky had been due for release in October 2014, and Lebedev in July next year.",
"\n\nThe European Court of Human Rights last month rejected suggestions that the case against Khodorkovsky had been politically motivated but found that the initial trial was unfair and the 2005 sentencing was unjustified.",
"\n\nRussia's Supreme Court cut former oil tycoon Mikhail Khodorkovsky's jail sentence by two months on Tuesday, allowing one of President Vladimir Putin's biggest critics to walk free in August 2014 after more than a decade behind bars."
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