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1201.3662

High mobility two-dimensional hole system on hydrogen-terminated silicon (111) surfaces

We have realized a two-dimensional hole system (2DHS), in which the 2DHS is induced at an atomically flat hydrogen-terminated Si(111) surface by a negative gate voltage applied across a vacuum cavity. Hole densities up to $7.5\times10^{11}$ cm$^{-2}$ are obtained, and the peak hole mobility is about $10^4$ cm$^2$/Vs at 70 mK. The quantum Hall effect is observed. Shubnikov-de Haas oscillations show a beating pattern due to the spin-orbit effects, and the inferred zero-field spin splitting can be tuned by the gate voltage.

1206.5151

Quantifying short-range correlations in nuclei

An approximate method to quantify the magnitude of the two-nucleon (2N) and three-nucleon (3N) short-range correlations (SRC) and their mass dependence is proposed. The proposed method relies on the concept of the "universality" or "local nuclear character" of the SRC. We quantify the SRC by computing the number of independent-particle model (IPM) nucleon pairs and triples which reveal beyond-mean-field behavior. It is argued that those can be identified by counting the number of nucleon pairs and triples in a zero relative orbital momentum state. A method to determine the quantum numbers of pairs and triples in an arbitrary mean-field basis is outlined. The mass dependence of the 2N and 3N SRC is studied. The predictions are compared to measurements. This includes the ratio of the inclusive inelastic electron scattering cross sections of nuclei to 2H and 3He at large values of the Bjorken variable. Corrections stemming from the center-of-mass motion of the pairs are estimated. We find that the relative probability per nucleon for 2N and 3N SRC has a soft dependence with mass number A and that the proton-neutron 2N SRC outnumber the proton-proton (neutron-neutron) 2N SRC. A linear relationship between the magnitude of the EMC effect and the predicted number of proton-neutron SRC pairs is observed. This provides support for the role of local nuclear dynamics on the EMC effect.

2007.06430

The Hausdorff dimension of self-projective sets

Given a finite set $\mathcal{A} \subseteq \mathrm{SL}(2,\mathbb{R})$ we study the dimension of the attractor $K_\mathcal{A}$ of the iterated function system induced by the projective action of $\mathcal{A}$. In particular, we generalise a recent result of Solomyak and Takahashi by showing that the Hausdorff dimension of $K_\mathcal{A}$ is given by the minimum of 1 and the critical exponent, under the assumption that $\mathcal{A}$ satisfies certain discreteness conditions and a Diophantine property. Our approach combines techniques from the theories of iterated function systems and M\"obius semigroups, and allows us to discuss the continuity of the Hausdorff dimension, as well as the dimension of the support of the Furstenberg measure.

math/0209074

On finite-dimensional maps

Let $f\colon X\to Y$ be a perfect surjective map of metrizable spaces. It is shown that if $Y$ is a $C$-space (resp., $\dim Y\leq n$ and $\dim f\leq m$), then the function space $C(X,\uin^{\infty})$ (resp., $C(X,\uin^{2n+1+m})$) equipped with the source limitation topology contains a dense $G_{\delta}$-set $\mathcal{H}$ such that $f\times g$ embeds $X$ into $Y\times\uin^{\infty}$ (resp., into $Y\times\uin^{2n+1+m}$) for every $g\in\mathcal{H}$. Some applications of this result are also given.

1704.07055

k-FFNN: A priori knowledge infused Feed-forward Neural Networks

Recurrent neural network (RNN) are being extensively used over feed-forward neural networks (FFNN) because of their inherent capability to capture temporal relationships that exist in the sequential data such as speech. This aspect of RNN is advantageous especially when there is no a priori knowledge about the temporal correlations within the data. However, RNNs require large amount of data to learn these temporal correlations, limiting their advantage in low resource scenarios. It is not immediately clear (a) how a priori temporal knowledge can be used in a FFNN architecture (b) how a FFNN performs when provided with this knowledge about temporal correlations (assuming available) during training. The objective of this paper is to explore k-FFNN, namely a FFNN architecture that can incorporate the a priori knowledge of the temporal relationships within the data sequence during training and compare k-FFNN performance with RNN in a low resource scenario. We evaluate the performance of k-FFNN and RNN by extensive experimentation on MediaEval 2016 audio data ("Emotional Impact of Movies" task). Experimental results show that the performance of k-FFNN is comparable to RNN, and in some scenarios k-FFNN performs better than RNN when temporal knowledge is injected into FFNN architecture. The main contributions of this paper are (a) fusing a priori knowledge into FFNN architecture to construct a k-FFNN and (b) analyzing the performance of k-FFNN with respect to RNN for different size of training data.

2310.10659

Exploiting Machine Unlearning for Backdoor Attacks in Deep Learning System

In recent years, the security issues of artificial intelligence have become increasingly prominent due to the rapid development of deep learning research and applications. Backdoor attack is an attack targeting the vulnerability of deep learning models, where hidden backdoors are activated by triggers embedded by the attacker, thereby outputting malicious predictions that may not align with the intended output for a given input. In this work, we propose a novel black-box backdoor attack based on machine unlearning. The attacker first augments the training set with carefully designed samples, including poison and mitigation data, to train a `benign' model. Then, the attacker posts unlearning requests for the mitigation samples to remove the impact of relevant data on the model, gradually activating the hidden backdoor. Since backdoors are implanted during the iterative unlearning process, it significantly increases the computational overhead of existing defense methods for backdoor detection or mitigation. To address this new security threat, we proposes two methods for detecting or mitigating such malicious unlearning requests. We conduct the experiment in both exact unlearning and approximate unlearning (i.e., SISA) settings. Experimental results indicate that: 1) our attack approach can successfully implant backdoor into the model, and sharding increases the difficult of attack; 2) our detection algorithms are effective in identifying the mitigation samples, while sharding reduces the effectiveness of our detection algorithms.

2204.12116

Lipids and lipid-mixtures in boundary layers: from hydration lubrication to osteoarthritis

The hydration layer surrounding the phosphocholine headgroups of single-component phosphatidylcholine (PC) lipids, or of lipid-mixtures, assembled at an interface greatly modifies the interfacial properties and interactions. As water molecules within the hydration layer are held tightly by the headgroup but are nonetheless very fluid upon shear, the boundary lipid layers, exposing the highly hydrated headgroup arrays, can provide efficient boundary lubrication when sliding against an opposing surface, at physiologically-high contact pressures. Additionally, any free lipids in the surrounding liquid can heal defects which may form during sliding on the boundary PC layer. Similar boundary lipid layers contribute to the lubricating, pressure-bearing, and wear-protection functions of healthy articular joints. This review presents a survey of the relationship between the molecular composition of the interfacial complex and the lubrication behavior of the lipid-based boundary layers, which could be beneficial for designing boundary lubricants for intra-articular injection for the treatment of early OA.

1112.3876

Generalized Parton Distributions of the Photon in Position Space

We report on a calculation of the generalized parton distributions of the photon when there is non-zero momentum transfer both in the transverse and longitudinal directions. By taking Fourier transforms of the GPDs with respect transverse and longitudinal momentum transfer, we obtain the parton distributions of the photon in position space.

1209.0353

Correlation between Ultra-high Energy Cosmic Rays and Active Galactic Nuclei from Fermi Large Area Telescope

We study the possibility that the $\gamma$-ray loud active galactic nuclei (AGN) are the sources of ultra-high energy cosmic rays (UHECR), through the correlation analysis of their locations and the arrival directions of UHECR. We use the $\gamma$-ray loud AGN with $d\le 100 {\rm Mpc}$ from the second Fermi Large Area Telescope AGN catalog and the UHECR data with $E\ge 55 {\rm EeV}$ observed by Pierre Auger Observatory. The distribution of arrival directions expected from the $\gamma$-ray loud AGN is compared with that of the observed UHECR using the correlational angular distance distribution and the Kolmogorov-Smirnov test. We conclude that the hypothesis that the $\gamma$-ray loud AGN are the dominant sources of UHECR is disfavored unless there is a large smearing effect due to the intergalactic magnetic fields.

1909.06551

Yamabe Solitons on (LCS)$_n$-manifolds

The object of the present paper is to study some properties of (LCS)$_n$-manifolds whose metric is Yamabe soliton. We establish some characterization of (LCS)$_n$-manifolds when the soliton becomes steady. Next we have studied some certain curvature conditions of (LCS)$_n$-manifolds admitting Yamabe solitons. Lastly we construct a 3-dimensional (LCS)$_n$-manifold satisfying the results.

2305.04562

Thermodynamic Trade-off Relation for First Passage Time in Resetting Process

Resetting is a strategy for boosting the speed of a target-searching process. Since its introduction over a decade ago, most studies have been carried out under the assumption that resetting takes place instantaneously. However, due to its irreversible nature, resetting processes incur a thermodynamic cost, which becomes infinite in case of instantaneous resetting. Here, we take into consideration both the cost and first passage time (FPT) required for a resetting process, in which the reset or return to the initial location is implemented using a trapping potential over a finite but random time period. An iterative generating function and counting functional method \`a la Feynman and Kac are employed to calculate the FPT and average work for this process. From these results, we obtain an explicit form of the time-cost trade-off relation, which provides the lower bound of the mean FPT for a given work input when the trapping potential is linear. This trade-off relation clearly shows that instantaneous resetting is achievable only when an infinite amount of work is provided. More surprisingly, the trade-off relation derived from the linear potential seems to be valid for a wide range of trapping potentials. In addition, we have also shown that the fixed-time or sharp resetting can further enhance the trade-off relation compared to that of the stochastic resetting.

1702.01394

Undecidability and Finite Automata

Using a novel rewriting problem, we show that several natural decision problems about finite automata are undecidable (i.e., recursively unsolvable). In contrast, we also prove three related problems are decidable. We apply one result to prove the undecidability of a related problem about k-automatic sets of rational numbers.

0904.1675

Influence of Chain Interdiffusion Between Immiscible Polymers on Dewetting Dynamics

The interface between two immiscible polymers, polystyrene (PS) and polydimethylsiloxane (PDMS), was studied by neutron reflectivity and dewetting by using free PS chains and PDMS brushes. Unexpectedly, we found that the PS chains diffuse in the PDMS brushes at temperatures well below the glass transition temperatures of PS, the dynamics being largely determined by the grafting density of the brush. By this study, we demonstrate the major influence of the chains interdiffusion on the friction properties for a couple of immiscible polymers. By the way, the puzzling ageing of PS thin films observed from dewetting experiments is found to be directly related to modifications of the PS/PDMS interface.

1703.06929

The Coldest Place in the Universe: Probing the Ultra-Cold Outflow and Dusty Disk in the Boomerang Nebula

Our Cycle 0 ALMA observations confirmed that the Boomerang Nebula is the coldest known object in the Universe, with a massive high-speed outflow that has cooled significantly below the cosmic background temperature. Our new CO 1-0 data reveal heretofore unseen distant regions of this ultra-cold outflow, out to $\gtrsim120,000$ AU. We find that in the ultra-cold outflow, the mass-loss rate (dM/dt) increases with radius, similar to its expansion velocity ($V$) - taking $V\propto r$, we find $dM/dt \propto r^{0.9-2.2}$. The mass in the ultra-cold outflow is $\gtrsim3.3$ Msun, and the Boomerang's main-sequence progenitor mass is $\gtrsim4$ Msun. Our high angular resolution ($\sim$0".3) CO J=3-2 map shows the inner bipolar nebula's precise, highly-collimated shape, and a dense central waist of size (FWHM) $\sim$1740 AU$\times275$ AU. The molecular gas and the dust as seen in scattered light via optical HST imaging show a detailed correspondence. The waist shows a compact core in thermal dust emission at 0.87-3.3 mm, which harbors $(4-7)\times10^{-4}$ Msun~of very large ($\sim$mm-to-cm sized), cold ($\sim20-30$ K) grains. The central waist (assuming its outer regions to be expanding) and fast bipolar outflow have expansion ages of $\lesssim1925$ yr and $\le1050$ yr: the "jet-lag" (i.e., torus age minus the fast-outflow age) in the Boomerang supports models in which the primary star interacts directly with a binary companion. We argue that this interaction resulted in a common-envelope configuration while the Boomerang's primary was an RGB or early-AGB star, with the companion finally merging into the primary's core, and ejecting the primary's envelope that now forms the ultra-cold outflow.

1112.5542

Quantum key distribution with finite resources: Taking advantage of quantum noise

We compare the effect of different noise scenarios on the achievable rate of an epsilon-secure key for the BB84 and the six-state protocol. We study the situation where quantum noise is added deliberately, and investigate the remarkable benefit for the finite key rate. We compare our results to the known case of added classical noise and the asymptotic key rate, i.e. in the limit of infinitely many signals. As a complementary interpretation we show that under the realistic assumption that the noise which is unavoidably introduced by a real channel is not fully dedicated to the eavesdropper, the secret key rate increases significantly.

1011.5788

Paperfolding morphisms, planefilling curves, and fractal tiles

An interesting class of automatic sequences emerges from iterated paperfolding. The sequences generate curves in the plane with an almost periodic structure. We generalize the results obtained by Davis and Knuth on the self-avoiding and planefilling properties of these curves, giving simple geometric criteria for a complete classification. Finally, we show how the automatic structure of the sequences leads to self-similarity of the curves, which turns the planefilling curves in a scaling limit into fractal tiles. For some of these tiles we give a particularly simple formula for the Hausdorff dimension of their boundary.

2002.11930

Auto-Encoding Twin-Bottleneck Hashing

Conventional unsupervised hashing methods usually take advantage of similarity graphs, which are either pre-computed in the high-dimensional space or obtained from random anchor points. On the one hand, existing methods uncouple the procedures of hash function learning and graph construction. On the other hand, graphs empirically built upon original data could introduce biased prior knowledge of data relevance, leading to sub-optimal retrieval performance. In this paper, we tackle the above problems by proposing an efficient and adaptive code-driven graph, which is updated by decoding in the context of an auto-encoder. Specifically, we introduce into our framework twin bottlenecks (i.e., latent variables) that exchange crucial information collaboratively. One bottleneck (i.e., binary codes) conveys the high-level intrinsic data structure captured by the code-driven graph to the other (i.e., continuous variables for low-level detail information), which in turn propagates the updated network feedback for the encoder to learn more discriminative binary codes. The auto-encoding learning objective literally rewards the code-driven graph to learn an optimal encoder. Moreover, the proposed model can be simply optimized by gradient descent without violating the binary constraints. Experiments on benchmarked datasets clearly show the superiority of our framework over the state-of-the-art hashing methods. Our source code can be found at https://github.com/ymcidence/TBH.

2104.11001

Global stability for a nonlinear system of anisotropic wave equations

In this paper, we initiate the study of global stability for anisotropic systems of quasilinear wave equations. Equations of this kind arise naturally in the study of crystal optics, and they exhibit birefringence. We introduce a physical space strategy based on bilinear energy estimates that allows us to prove decay for the nonlinear problem. This uses decay for the homogeneous wave equation as a black box. The proof also requires us to interface this strategy with the vector field method and take advantage of the scaling vector field. A careful analysis of the spacetime geometry of the interaction between waves is necessary in the proof.

2310.01820

Towards Robust Fidelity for Evaluating Explainability of Graph Neural Networks

Graph Neural Networks (GNNs) are neural models that leverage the dependency structure in graphical data via message passing among the graph nodes. GNNs have emerged as pivotal architectures in analyzing graph-structured data, and their expansive application in sensitive domains requires a comprehensive understanding of their decision-making processes -- necessitating a framework for GNN explainability. An explanation function for GNNs takes a pre-trained GNN along with a graph as input, to produce a `sufficient statistic' subgraph with respect to the graph label. A main challenge in studying GNN explainability is to provide fidelity measures that evaluate the performance of these explanation functions. This paper studies this foundational challenge, spotlighting the inherent limitations of prevailing fidelity metrics, including $Fid_+$, $Fid_-$, and $Fid_\Delta$. Specifically, a formal, information-theoretic definition of explainability is introduced and it is shown that existing metrics often fail to align with this definition across various statistical scenarios. The reason is due to potential distribution shifts when subgraphs are removed in computing these fidelity measures. Subsequently, a robust class of fidelity measures are introduced, and it is shown analytically that they are resilient to distribution shift issues and are applicable in a wide range of scenarios. Extensive empirical analysis on both synthetic and real datasets are provided to illustrate that the proposed metrics are more coherent with gold standard metrics.

1907.00890

A volume-of-fluid method for interface-resolved simulations of phase-changing two-fluid flows

We present a numerical method for interface-resolved simulations of evaporating two-fluid flows based on the volume-of-fluid (VoF) method. The method has been implemented in an efficient FFT-based two-fluid Navier-Stokes solver, using an algebraic VoF method for the interface representation, and extended with the transport equations of thermal energy and vaporized liquid mass for the single-component evaporating liquid in an inert gas. The conservation of vaporizing liquid and computation of the interfacial mass flux are performed with the aid of a reconstructed signed-distance field, which enables the use of well-established methods for phase change solvers based on level-set methods. The interface velocity is computed with a novel approach that ensures accurate mass conservation, by constructing a divergence-free extension of the liquid velocity field onto the entire domain. The resulting approach does not depend on the type of interface reconstruction (i.e.\ can be employed in both algebraic and geometrical VoF methods). We extensively verified and validated the overall method against several benchmark cases, and demonstrated its excellent mass conservation and good overall performance for simulating evaporating two-fluid flows in two and three dimensions.

1103.5443

Anomaly-induced charges in nucleons

We show a novel charge structure of baryons in electromagnetic field due to the chiral anomaly. A key connection is to treat baryons as solitons of mesons. We use Skyrmions to calculate the charge distributions in a single nucleon and find an additional charge. We also perform calculations of charge distribution for classical multi-baryons with B=2, 3,...,8 and 17; they show amusing charge distributions.

2208.13817

Multi-functional interface between integrated photonics and free space

The combination of photonic integrated circuits and free-space meta-optics has the ability to unclasp technological knots that require advanced light manipulation due their conjoined ability to guide and shape electromagnetic waves. The need for large scale access and component interchangeability is essential for rapid prototyping of optical systems. Such capability represents a functional challenge in terms of fabrication and alignment of compound photonic platform. Here, we report a multi-functional interface that demonstrates the capabilities of a flexible and interchangeable combination of a photonic integrated circuit to a free-space coupling chip with different designs of low-loss meta-optics at a wavelength of 780 nm. We show that robustness and fidelity of the designed optical functions can be achieved without prior precise characterization of the free-space input nor stringent alignment between the photonic integrated chip and the meta-optics chip. A diffraction limited spot of approximately 3 micron for a hyperboloid metalens of numerical aperture 0.15 was achieved despite an input Gaussian elliptical deformation of up to 35% and misalignments of the components of up to 20 micron. A holographic display with a peak signal-to-noise ratio of more than 10 compared to its ground truth is also reported using this platform making this work the first interface to shape photonic integrated modes into free space using different diffractive optical functions.

2006.02674

Growth of Sobolev norms for linear Schr{\"o}dinger operators

We give an example of a linear, time-dependent, Schr{\"o}dinger operator with optimal growth of Sobolev norms. The construction is explicit, and relies on a comprehensive study of the linear Lowest Landau Level equation with a time-dependent potential.

2001.08984

Smoothing and growth bound of periodic generalized Korteweg-de Vries equation

For generalized KdV models with polynomial nonlinearity, we establish nonlinear smoothing property in $H^s$ for $s>\frac{1}{2}$. Such smoothing effect persists globally, provided that the $H^1$ norm does not blow up in finite time. More specifically, we show that a translate of the nonlinear part of the solution gains $\min(2s-1,1)-$ derivatives for $s>\frac{1}{2}$. Following a new simple method, which is of independent interest, we establish that, for $s>1$, $H^s$ norm of a solution grows at most by $\langle t\rangle^{s-1+}$ if $H^1$ norm is a priori controlled.

1409.0082

Role of axion electrodynamics in Weyl metal: Violation of Wiedemann-Franz law

Recently, enhancement of the longitudinal magneto-electrical conductivity (LMEC) has been observed in Bi$_{1-x}$Sb$_{x}$ around $x \sim 3\%$ under $\bm{E} \parallel \bm{B}$ ($\bm{E}$: external electric field and $\bm{B}$: external magnetic field) [Phys. Rev. Lett. {\bf 111}, 246603 (2013)], where an enhancement factor proportional to $B^{2}$ is suggested to result from the $\bm{E} \cdot \bm{B}$ term. In the present study, we show that this $B^{2}$ enhancement is not limited on the LMEC, where both the Seebeck and thermal conductivities in the longitudinal setup ($\bm{E} \parallel \bm{B}$) are predicted to show essentially the same enhancement proportional to $B^{2}$. In particular, the $B^{2}$ enhancement factor of the LMEC turns out to differ from that of the longitudinal thermal conductivity, responsible for breakdown of Wiedemann-Franz (WF) law, which means that anomalous currents flowing through the dissipationless channel differ from each other. Since the breakdown of the WF law appears in spite of the existence of electron quasiparticles, regarded to be a purely topological character (chiral anomaly), the Weyl metallic state cannot be identified with the Landau's Fermi-liquid fixed point. We propose the violation of the WF law as another hallmark of the Weyl metallic phase, which originates from axion electrodynamics.

2302.14141

Linear pretraining in recurrent mixture density networks

We present a method for pretraining a recurrent mixture density network (RMDN). We also propose a slight modification to the architecture of the RMDN-GARCH proposed by Nikolaev et al. [2012]. The pretraining method helps the RMDN avoid bad local minima during training and improves its robustness to the persistent NaN problem, as defined by Guillaumes [2017], which is often encountered with mixture density networks. Such problem consists in frequently obtaining "Not a number" (NaN) values during training. The pretraining method proposed resolves these issues by training the linear nodes in the hidden layer of the RMDN before starting including non-linear node updates. Such an approach improves the performance of the RMDN and ensures it surpasses that of the GARCH model, which is the RMDN's linear counterpart.

1710.04121

Towards In-Transit Analytics for Industry 4.0

Industry 4.0, or Digital Manufacturing, is a vision of inter-connected services to facilitate innovation in the manufacturing sector. A fundamental requirement of innovation is the ability to be able to visualise manufacturing data, in order to discover new insight for increased competitive advantage. This article describes the enabling technologies that facilitate In-Transit Analytics, which is a necessary precursor for Industrial Internet of Things (IIoT) visualisation.

1808.03777

Non-stationary thermal electromotive force generated by third sound

It is predicted that oscillations of temperature during propagation of third sound in a thin superfluid film cause appearance of an alternating electric field in the surrounding space (a peculiar non-stationary thermoelectric effect). The magnitude of this field depends significantly on the substrate type and the method of its coating. It is shown that the differential thermal EMF (the ratio of electric potential amplitude to the film temperature amplitude) can exceed such one in metals and reach $10^{-4}$ V/K.

2211.05339

Writing summary for the state-of-the-art methods for big data clustering in distributed environment

Big Data processing systems handle huge unstructured and structured data to store, process, and analyze through cluster analysis which helps in identifying unseen patterns to find the relationships between them. Clustering analysis over the shared machines in big data technologies helps in deriving the relations and making decisions using data in context. It can handle every form of raw, tabular data along with structured, semi-structured, and unstructured data. The data doesn't have to possess linearity property. It can reflect associative and correlative patterns and groupings. The main contribution and findings of this paper are to gather and summarize the recent big data clustering techniques, and their strengths, and weaknesses in any distributed environment.

1902.09163

Experimental Determination of Momentum-Resolved Electron-Phonon Coupling

We provide a novel experimental method to quantitatively estimate the electron-phonon coupling and its momentum dependence from resonant inelastic x-ray scattering (RIXS) spectra based on the detuning of the incident photon energy away from an absorption resonance. We apply it to the cuprate parent compound NdBa$_2$Cu$_3$O$_6$ and find that the electronic coupling to the oxygen half-breathing phonon mode is strongest at the Brillouin zone boundary, where it amounts to $\sim 0.17$ eV, in agreement with previous studies. In principle, this method is applicable to any absorption resonance suitable for RIXS measurements and will help to define the contribution of lattice vibrations to the peculiar properties of quantum materials.

astro-ph/9701246

Distortion of gamma-ray burst light curves by gravitational microlensing

If at cosmological distances, a small fraction of gamma-ray bursts should be multiply imaged by intervening galaxies or clusters, resulting in the appearance of two very similar bursts from the same location with a relative time delay of hours to a year. We show that microlensing by individual stars in the lensing galaxy can smear out the light curves of the multiply imaged bursts on millisecond time scales. Therefore, in deciding whether two bursts are similar enough to qualify as multiple images, one must look at time scales longer than a few tens of milliseconds, since shorter time scales are possibly rendered dissimilar by microlensing.

2011.14525

Inter-layer Transition in Neural Architecture Search

Differential Neural Architecture Search (NAS) methods represent the network architecture as a repetitive proxy directed acyclic graph (DAG) and optimize the network weights and architecture weights alternatively in a differential manner. However, existing methods model the architecture weights on each edge (i.e., a layer in the network) as statistically independent variables, ignoring the dependency between edges in DAG induced by their directed topological connections. In this paper, we make the first attempt to investigate such dependency by proposing a novel Inter-layer Transition NAS method. It casts the architecture optimization into a sequential decision process where the dependency between the architecture weights of connected edges is explicitly modeled. Specifically, edges are divided into inner and outer groups according to whether or not their predecessor edges are in the same cell. While the architecture weights of outer edges are optimized independently, those of inner edges are derived sequentially based on the architecture weights of their predecessor edges and the learnable transition matrices in an attentive probability transition manner. Experiments on five benchmarks confirm the value of modeling inter-layer dependency and demonstrate the proposed method outperforms state-of-the-art methods.

2207.04946

Search for Astrophysical Neutrinos from 1FLE Blazars with IceCube

The majority of astrophysical neutrinos have undetermined origins. The IceCube Neutrino Observatory has observed astrophysical neutrinos but has not yet identified their sources. Blazars are promising source candidates, but previous searches for neutrino emission from populations of blazars detected in $\gtrsim$ GeV gamma-rays have not observed any significant neutrino excess. Recent findings in multi-messenger astronomy indicate that high-energy photons, co-produced with high-energy neutrinos, are likely to be absorbed and reemitted at lower energies. Thus, lower-energy photons may be better indicators of TeV-PeV neutrino production. This paper presents the first time-integrated stacking search for astrophysical neutrino emission from MeV-detected blazars in the first Fermi-LAT low energy catalog (1FLE) using ten years of IceCube muon-neutrino data. The results of this analysis are found to be consistent with a background-only hypothesis. Assuming an E$^{-2}$ neutrino spectrum and proportionality between the blazars' MeV gamma-ray fluxes and TeV-PeV neutrino flux, the upper limit on the 1FLE blazar energy-scaled neutrino flux is determined to be $1.64 \times 10^{-12}$ TeV cm$^{-2}$ s$^{-1}$ at 90% confidence level. This upper limit is approximately 1% of IceCube's diffuse muon-neutrino flux measurement.

0902.3623

A Self-Contained and Easily Accessible Discussion of the Method of Descente Infinie and Fermat's Only Explicitly Known Proof by Descente Infinie

We present the only proof of Pierre Fermat by descente infinie that is known to exist today. As the text of its Latin original requires active mathematical interpretation, it is more a proof sketch than a proper mathematical proof. We discuss descente infinie from the mathematical, logical, historical, linguistic, and refined logic-historical points of view. We provide the required preliminaries from number theory and develop a self-contained proof in a modern form, which nevertheless is intended to follow Fermat's ideas closely. We then annotate an English translation of Fermat's original proof with terms from the modern proof. Including all important facts, we present a concise and self-contained discussion of Fermat's proof sketch, which is easily accessible to laymen in number theory as well as to laymen in the history of mathematics, and which provides new clarification of the Method of Descente Infinie to the experts in these fields. Last but not least, this paper fills a gap regarding the easy accessibility of the subject.

nucl-th/0112021

Chemical factors in canonical statistical models for relativistic heavy ion collisions

We study the effect of enforcing exact conservation of charges in statistical models of particle production for systems as large as those relevant to relativistic heavy ion collisions. By using a numerical method developed for small systems, we have been able to approach the large volume limit keeping the exact canonical treatment of all relevant charges, namely baryon number, strangeness and electric charge. Hence, we hereby give the information needed in a hadron gas model whether the canonical treatment is necessary or not in actual cases. Comparison between calculations and experimental particle multiplicities is shown. Also, a discussion on relative strangeness chemical equilibrium is given.

2207.00754

Renormalization group improved $m_s$ and $\vert V_{us}\vert$ determination from hadronic $\tau$ decays

We determine the strange quark mass ($m_s$) and quark mixing element $\vert V_{us}\vert $, and their joint determination from the Cabibbo suppressed hadronic $\tau$ decays in various perturbative schemes. Compared to the previous analysis based on the optimal renormalization or the renormalization group summed perturbation theory (RGSPT) scheme, we have improved this analysis by replacing the theoretical longitudinal contributions with phenomenological parametrization, and the RGSPT coefficients are used for the dimension-4 Adler functions. The improved analysis results in the extraction of $m_s(2\,\mathrm{GeV})=98\pm19\,\mathrm{MeV}$ and $\vert V_{us}\vert=0.2191\pm0.0043$ from the RGSPT scheme.

1812.05656

Polygon Simplification by Minimizing Convex Corners

Let $P$ be a polygon with $r>0$ reflex vertices and possibly with holes and islands. A subsuming polygon of $P$ is a polygon $P'$ such that $P \subseteq P'$, each connected component $R$ of $P$ is a subset of a distinct connected component $R'$ of $P'$, and the reflex corners of $R$ coincide with those of $R'$. A subsuming chain of $P'$ is a minimal path on the boundary of $P'$ whose two end edges coincide with two edges of $P$. Aichholzer et al. proved that every polygon $P$ has a subsuming polygon with $O(r)$ vertices, and posed an open problem to determine the computational complexity of computing subsuming polygons with the minimum number of convex vertices. We prove that the problem of computing an optimal subsuming polygon is NP-complete, but the complexity remains open for simple polygons (i.e., polygons without holes). Our NP-hardness result holds even when the subsuming chains are restricted to have constant length and lie on the arrangement of lines determined by the edges of the input polygon. We show that this restriction makes the problem polynomial-time solvable for simple polygons.

1301.1689

PRIMUS: An observationally motivated model to connect the evolution of the AGN and galaxy populations out to z~1

We present an observationally motivated model to connect the AGN and galaxy populations at 0.2<z<1.0 and predict the AGN X-ray luminosity function (XLF). We start with measurements of the stellar mass function of galaxies (from the Prism Multi-object Survey) and populate galaxies with AGNs using models for the probability of a galaxy hosting an AGN as a function of specific accretion rate. Our model is based on measurements indicating that the specific accretion rate distribution is a universal function across a wide range of host stellar mass with slope gamma_1 = -0.65 and an overall normalization that evolves with redshift. We test several simple assumptions to extend this model to high specific accretion rates (beyond the measurements) and compare the predictions for the XLF with the observed data. We find good agreement with a model that allows for a break in the specific accretion rate distribution at a point corresponding to the Eddington limit, a steep power-law tail to super-Eddington ratios with slope gamma_2 = -2.1 +0.3 -0.5, and a scatter of 0.38 dex in the scaling between black hole and host stellar mass. Our results show that samples of low luminosity AGNs are dominated by moderately massive galaxies (M* ~ 10^{10-11} M_sun) growing with a wide range of accretion rates due to the shape of the galaxy stellar mass function rather than a preference for AGN activity at a particular stellar mass. Luminous AGNs may be a severely skewed population with elevated black hole masses relative to their host galaxies and in rare phases of rapid accretion.

1109.0380

Fermi Surface Reconstruction in CeTe2 Induced by Charge Density Wave: ARPES Study

Electronic structures of a charge-density-wave CDW system CeTe_2-xSb_x (x=0, 0.05) have been investigated by employing angle-resolved photoemission spectroscopy (ARPES). The observed Fermi surface (FS) agrees very well with the calculated FS for the undistorted CeTe_2 both in shapes and sizes. The metallic states crossing the Fermi level(E_F) are observed in ARPES. The carriers near E_F have mainly the Te(1) 5p character, with the negligible contribution from Ce 4f states to the CDW formation. The supercell (shadow) bands and the corresponding very weak FS's are found to arise from band-folding due to the interaction with Ce-Te(2) layers. This work shows that the origin of the CDW formation in CeTe_2 is the FS nesting and that the CDW modulation vector is along Gamma-X (Q_CDW ~ X)

1812.07374

Nonlinearly charged dyonic black holes

In this paper, we investigate the thermodynamics of dyonic black holes in the presence of Born-Infeld electromagnetic field. We show that electric-magnetic duality reported for dyonic solutions with Maxwell field is omitted in case of Born-Infeld generalization. We also confirm that generalization to nonlinear field provides the possibility of canceling the effects of cosmological constant. This is done for nonlinearity parameter with $10^{-33}\mbox{ eV}^{2}$ order of magnitude which is high nonlinearity regime. In addition, we show that for small electric/magnetic charge and high nonlinearity regime, black holes would develop critical behavior and several phases. In contrast, for highly charged case and Maxwell limits (small nonlinearity), black holes have one thermal stable phase. We also find that the pressure of the cold black holes is bounded by some constraints on its volume while hot black holes' pressure has physical behavior for any volume. In addition, we report on possibility of existences of triple point and reentrant of phase transition in thermodynamics of these black holes. Finally, We show that if electric and magnetic charges are identical, the behavior of our solutions would be Maxwell like (independent of nonlinear parameter and field). In other words, nonlinearity of electromagnetic field becomes evident only when these black holes are charged magnetically and electrically different.

cond-mat/0412434

Zero-bias anomaly in cotunneling transport through quantum-dot spin valves

We predict a new zero-bias anomaly in the differential conductance through a quantum dot coupled to two ferromagnetic leads with antiparallel magnetization. The anomaly differs in origin and properties from other anomalies in transport through quantum dots, such as the Kondo effect. It occurs in Coulomb-blockade valleys with an unpaired dot electron. It is a consequence of the interplay of single- and double-barrier cotunneling processes and their effect on the spin accumulation in the dot. The anomaly becomes significantly modified when a magnetic field is applied.

1008.2377

Inverse systems, Gelfand-Tsetlin patterns and the weak Lefschetz property

Migliore-Mir\'o-Roig-Nagel [Trans. A.M.S. 2011, arXiv: 0811.1023] show that the weak Lefschetz property (WLP) can fail for an ideal I in K[x_1,x_2,x_3,x_4] generated by powers of linear forms. This is in contrast to the analogous situation in K[x_1,x_2,x_3], where WLP always holds [H.Schenck, A.Seceleanu, Proc. A.M.S. 2010, arXiv:0911.0876]. We use the inverse system dictionary to connect I to an ideal of fat points and show that failure of WLP for powers of linear forms is connected to the geometry of the associated fat point scheme. Recent results of Sturmfels-Xu in [J. Eur. Math. Soc. 2010, arXiv:0803.0892] allow us to relate WLP to Gelfand-Tsetlin patterns. See the paper "On the weak Lefschetz property for powers of linear forms" by Migliore-Mir\'o-Roig-Nagel [arXiv:1008.2149] for related results.

2004.06377

Baryon number fluctuations induced by hadronic interactions at low temperature and large chemical potential

We investigate the density fluctuations induced by hadronic interactions at low temperatures and large chemical potentials after the hadronization of quark-gluon plasma~(QGP). We analyze the structures of net-baryon number kurtosis and skewness and elaborate on their relations with the nuclear liquid-gas~(LG) phase transition and hadronic interactions above the critical temperature. Combining with the relevant experimental projects at RHIC/NICA/FAIR/J-PARC/HIAF with collision energies from $200\,$GeV to $1.8\,$GeV, we propose a double-peak structure of kurtosis (skewness) as a function of collision energy, which can be taken to identify the chiral phase transition and the nuclear liquid-gas phase transition. In particular, the fluctuation distributions at low temperatures provide a new method to explore hadronic interactions and nuclear liquid-gas transition.

1508.03839

The FORS1 catalogue of stellar magnetic field measurements

The FORS1 instrument on the ESO Very Large Telescope was used to obtain low-resolution circular polarised spectra of nearly a thousand different stars, with the aim of measuring their mean longitudinal magnetic fields. A catalogue of FORS1 magnetic measurements would provide a valuable resource with which to better understand the strengths and limitations of this instrument and of similar low-dispersion, Cassegrain spectropolarimeters. However, FORS1 data reduction has been carried out by a number of different groups using a variety of reduction and analysis techniques. Our understanding of the instrument and our data reduction techniques have both improved over time. A full re-analysis of FORS1 archive data using a consistent and fully documented algorithm would optimise the accuracy and usefulness of a catalogue of field measurements. Based on the ESO FORS pipeline, we have developed a semi-automatic procedure for magnetic field determinations, which includes self-consistent checks for field detection reliability. We have applied our procedure to the full content of circular spectropolarimetric measurements of the FORS1 archive. We have produced a catalogue of spectro-polarimetric observations and magnetic field measurements for about 1400 observations of about 850 different objects. The spectral type of each object has been accurately classified. We have also been able to test different methods for data reduction is a systematic way. The resulting catalogue has been used to produce an estimator for an upper limit to the uncertainty in a field strength measurement of an early type star as a function of the signal-to-noise ratio of the observation. While FORS1 is not necessarily an optimal instrument for the discovery of weak magnetic fields, it is very useful for the systematic study of larger fields, such as those found in Ap/Bp stars and in white dwarfs.

2203.04779

Predictive data-driven model based on generative adversarial network for premixed turbulence-combustion regimes

Premixed flames exhibit different asymptotic regimes of interaction between heat release and turbulence depending on their respective length scales. At high Karlovitz number, the dilatation caused by heat release does not have any relevant effect on turbulent kinetic energy with respect to non-reacting flow, while at low Karlovitz number, the mean shear is a sink of turbulent kinetic energy, and counter-gradient transport is observed. This latter phenomenon is not well captured by closure models commonly used in Large Eddy Simulations that are based on gradient diffusion. The massive amount of data available from Direct Numerical Simulation (DNS) opens the possibility to develop data-driven models able to represent physical mechanisms and non-linear features present in both these regimes. In this work, the databases are formed by DNSs of two planar hydrogen/air flames at different Karlovitz numbers corresponding to the two asymptotic regimes. In this context, the Generative Adversarial Network (GAN) gives the possibility to successfully recognize and reconstruct both gradient and counter-gradient phenomena if trained with databases where both regimes are included. Two GAN models were first trained each for a specific Karlovitz number and tested using the same dataset in order to verify the capability of the models to learn the features of a single asymptotic regime and assess its accuracy. In both cases, the GAN models were able to reconstruct the Reynolds stress subfilter scales accurately. Later, the GAN was trained with a mixture of both datasets to create a model containing physical knowledge of both combustion regimes. This model was able to reconstruct the subfilter scales for both cases capturing the interaction between heat release and turbulence closely to the DNS as shown from the turbulent kinetic budget and barycentric maps.

cond-mat/0003098

Error-correcting codes and image restoration with multiple stages of dynamics

We consider the problems of error-correcting codes and image restoration with multiple stages of dynamics. Information extracted from the former stage can be used selectively to improve the performance of the latter one. Analytic results were derived for the mean-field systems using the cavity method. We find that it has the advantage of being tolerant to uncertainties in hyperparameter estimation, as confirmed by simulations.

2102.07375

Excitonic Instability and Electronic Property of Two-dimensional AlSb Limit

Motivated by the recent synthesis of two-dimensional monolayer AlSb, we theoretically investigate its ground state and electronic properties using the first-principles calculations coupled with Bethe-Salpeter equation. An excitonic instability is revealed as a result of larger exciton binding energy than the corresponding one-electron energy gap by $\sim$0.1 eV, which is an indicative of a many-body ground state accompanied by spontaneous exciton generation. Including the spin-orbit coupling is proven to be a must to correctly predict the ground state. At room temperature, the two-dimensional monolayer AlSb is a direct gap semiconductor with phonon-limited electron and hole mobilities both around 1700 cm$^2$/V$\cdot$s. These results show that monolayer AlSb may provide a promising platform for realization of the excitonic insulator and for applications in the next-generation electronic devices.

1505.01650

A modified mean curvature flow in Euclidean space and soap bubbles in symmetric spaces

In this paper, we show that small spherical soap bubbles in irreducible simply connected symmetric spaces of rank greater than one are constructed from the limits of a certain kind of modified mean curvature flows starting from small spheres in the Euclidean space of dimension equal to the rank of the symmetric space, where we note that the small spherical soap bubbles are invariant under the isotropy subgroup action of the isometry group of the symmetric space. Furthermore, we investigate the shape and the mean curvature of the small spherical soap bubbles.

1902.05504

Epitaxial Integration on Si(001) of Ferroelectric Hf0.5Zr0.5O2 Capacitors with High Retention and Endurance

Epitaxial ferroelectric Hf0.5Zr0.5O2 films have been successfully integrated in a capacitor heterostructure on Si(001). The orthorhombic Hf0.5Zr0.5O2 phase, [111] out-of-plane oriented, is stabilized in the films. The films present high remnant polarization Pr close to 20 {\mu}C/cm2, rivaling with equivalent epitaxial films on single crystalline oxide substrates. Retention time is longer than 10 years for writing field of around 5 MV/cm, and the capacitors show endurance up to 1E9 cycles for writing voltage of around 4 MV/cm. It is found that the formation of the orthorhombic ferroelectric phase depends critically on the bottom electrode, being achieved on La0.67Sr0.33MnO3 but not on LaNiO3. The demonstration of excellent ferroelectric properties in epitaxial films of Hf0.5Zr0.5O2 on Si(001) is relevant towards fabrication of devices that require homogeneity in the nanometer scale, as well as for better understanding of the intrinsic properties of this promising ferroelectric oxide.

astro-ph/0604463

Millimetric Properties of Gamma Ray Burst Host Galaxies

We present millimetre (mm) and submillimetre (submm) photometry of a sample of host galaxies of Gamma Ray Bursts (GRBs), obtained using the MAMBO2 and SCUBA bolometer arrays respectively. These observations were obtained as part of an ongoing project to investigate the status of GRBs as indicators of star formation. Our targets include two of the most unusual GRB host galaxies, selected as likely candidate submm galaxies: the extremely red (R-K approx 5) host of GRB 030115, and the extremely faint (R>29.5) host of GRB 020124. Neither of these galaxies is detected, but the deep upper limits for GRB 030115 impose constraints on its spectral energy distribution. As a framework for interpreting these data, and for predicting the results of forthcoming submm surveys of Swift-derived host samples, we model the expected flux and redshift distributions based on luminosity functions of both submm galaxies and GRBs, assuming a direct proportionality between the GRB rate density and the global star formation rate density. We derive the effects of possible sources of uncertainty in these assumptions, including an anticorrelation between GRB rate and the global average metallicity.

1612.00690

A Bayesian Heteroscedastic GLM with Application to fMRI Data with Motion Spikes

We propose a voxel-wise general linear model with autoregressive noise and heteroscedastic noise innovations (GLMH) for analyzing functional magnetic resonance imaging (fMRI) data. The model is analyzed from a Bayesian perspective and has the benefit of automatically down-weighting time points close to motion spikes in a data-driven manner. We develop a highly efficient Markov Chain Monte Carlo (MCMC) algorithm that allows for Bayesian variable selection among the regressors to model both the mean (i.e., the design matrix) and variance. This makes it possible to include a broad range of explanatory variables in both the mean and variance (e.g., time trends, activation stimuli, head motion parameters and their temporal derivatives), and to compute the posterior probability of inclusion from the MCMC output. Variable selection is also applied to the lags in the autoregressive noise process, making it possible to infer the lag order from the data simultaneously with all other model parameters. We use both simulated data and real fMRI data from OpenfMRI to illustrate the importance of proper modeling of heteroscedasticity in fMRI data analysis. Our results show that the GLMH tends to detect more brain activity, compared to its homoscedastic counterpart, by allowing the variance to change over time depending on the degree of head motion.

0911.0590

An explicit approach to residues on and dualizing sheaves of arithmetic surfaces

We develop a theory of residues for arithmetic surfaces, establish the reciprocity law around a point, and use the residue maps to explicitly construct the dualizing sheaf of the surface. These are generalisations of known results for surfaces over a perfect field. In an appendix, explicit local ramification theory is used to recover the fact that in the case of a local complete intersection the dualizing and canonical sheaves coincide.

hep-th/0509070

Numerical evidence for the Maldacena conjecture in two-dimensional N=(8,8) super Yang-Mills theory

The N=(8,8) super Yang-Mills theory in 1+1 dimensions is solved at strong coupling to directly confirm the predictions of supergravity at weak coupling. The calculations are done in the large-N_c approximation using Supersymmetric Discrete Light-Cone Quantization. The stress-energy correlator is obtained as a function of the separation r; for intermediate values of r, the correlator behaves in a manner consistent with the 1/r^5 behavior predicted by weak-coupling supergravity.

0912.1938

The Spacetime View of the Information Paradox

In semiclassical gravity, the final state of black-hole evaporation cannot be described by a pure state. Nevertheless, we point out that the system can be described by a generalized pure state, which is not defined on a 3-dimensional hypersurface but on the 4-dimensional spacetime describing the whole Universe at all times. Unlike the conventional quantum state, such a generalized state treats time on an equal footing with space, which makes it well suited for systems that are both quantum and relativistic. In particular, such a generalized state contains a novel type of information encoded in the correlations between future and past, which avoids the black-hole information paradox.

2111.07639

Second-virial theory for shape-persistent living polymers templated by discs

Living polymers composed of non-covalently bonded building blocks with weak backbone flexibility may self-assemble into thermoresponsive lyotropic liquid crystals. We demonstrate that the reversible polymer assembly and phase behavior can be controlled by the addition of (non-adsorbing) rigid colloidal discs which act as an entropic reorienting ``template" onto the supramolecular polymers. Using a particle-based second-virial theory that correlates the various entropies associated with the polymers and discs, we demonstrate that small fractions of discotic additives promote the formation of a polymer nematic phase. At larger disc concentrations, however, the phase is disrupted by collective disc alignment in favor of a discotic nematic fluid in which the polymers are dispersed anti-nematically. We show that the anti-nematic arrangement of the polymers generates a non-exponential molecular-weight distribution and stimulates the formation of oligomeric species. At sufficient concentrations the discs facilitate a liquid-liquid phase separation which can be brought into simultaneously coexistence with the two fractionated nematic phases, providing evidence for a four-fluid coexistence in reversible shape-dissimilar hard-core mixtures without cohesive interparticle forces. We stipulate the conditions under which such a phenomenon could be found in experiment.

2203.06228

CoDA21: Evaluating Language Understanding Capabilities of NLP Models With Context-Definition Alignment

Pretrained language models (PLMs) have achieved superhuman performance on many benchmarks, creating a need for harder tasks. We introduce CoDA21 (Context Definition Alignment), a challenging benchmark that measures natural language understanding (NLU) capabilities of PLMs: Given a definition and a context each for k words, but not the words themselves, the task is to align the k definitions with the k contexts. CoDA21 requires a deep understanding of contexts and definitions, including complex inference and world knowledge. We find that there is a large gap between human and PLM performance, suggesting that CoDA21 measures an aspect of NLU that is not sufficiently covered in existing benchmarks.

hep-th/9711045

Loop Homotopy Algebras in Closed String Field Theory

Barton Zwiebach constructed the `string products' on the Hilbert space of combined conformal field theory of matter and ghosts. It is well-known that the `tree level' specialization of these products forms a strongly homotopy Lie algebra. A strongly homotopy Lie algebra is given by a square zero coderivation on the cofree cocommutative connected coalgebra, on the other hand, strongly homotopy Lie algebras are algebras over the cobar construction on the commutative algebras operad. The aim of our paper is to give two similar characterizations of the structure formed by the `string products' of arbitrary genera. Our first characterization will be based on the notion of a higher order coderivation, the second characterization will be based on the machinery of modular operads. We will also discuss possible generalizations to open string field theory.

1706.01253

Initial-boundary value problems in a rectangle for two-dimensional Zakharov-Kuznetsov equation

Initial-boundary value problems in a bounded rectangle with different types of boundary conditions for two-dimensional Zakharov-Kuznetsov equation are considered. Results on global well-posedness in the classes of weak and regular solution are established. As applications of the developed technique results on boundary controllability and long-time decay of weak solutions are also obtained.

2103.00852

CrossMap Transformer: A Crossmodal Masked Path Transformer Using Double Back-Translation for Vision-and-Language Navigation

Navigation guided by natural language instructions is particularly suitable for Domestic Service Robots that interacts naturally with users. This task involves the prediction of a sequence of actions that leads to a specified destination given a natural language navigation instruction. The task thus requires the understanding of instructions, such as ``Walk out of the bathroom and wait on the stairs that are on the right''. The Visual and Language Navigation remains challenging, notably because it requires the exploration of the environment and at the accurate following of a path specified by the instructions to model the relationship between language and vision. To address this, we propose the CrossMap Transformer network, which encodes the linguistic and visual features to sequentially generate a path. The CrossMap transformer is tied to a Transformer-based speaker that generates navigation instructions. The two networks share common latent features, for mutual enhancement through a double back translation model: Generated paths are translated into instructions while generated instructions are translated into path The experimental results show the benefits of our approach in terms of instruction understanding and instruction generation.

2207.09640

Test-Time Adaptation via Conjugate Pseudo-labels

Test-time adaptation (TTA) refers to adapting neural networks to distribution shifts, with access to only the unlabeled test samples from the new domain at test-time. Prior TTA methods optimize over unsupervised objectives such as the entropy of model predictions in TENT [Wang et al., 2021], but it is unclear what exactly makes a good TTA loss. In this paper, we start by presenting a surprising phenomenon: if we attempt to meta-learn the best possible TTA loss over a wide class of functions, then we recover a function that is remarkably similar to (a temperature-scaled version of) the softmax-entropy employed by TENT. This only holds, however, if the classifier we are adapting is trained via cross-entropy; if trained via squared loss, a different best TTA loss emerges. To explain this phenomenon, we analyze TTA through the lens of the training losses's convex conjugate. We show that under natural conditions, this (unsupervised) conjugate function can be viewed as a good local approximation to the original supervised loss and indeed, it recovers the best losses found by meta-learning. This leads to a generic recipe that can be used to find a good TTA loss for any given supervised training loss function of a general class. Empirically, our approach consistently dominates other baselines over a wide range of benchmarks. Our approach is particularly of interest when applied to classifiers trained with novel loss functions, e.g., the recently-proposed PolyLoss, where it differs substantially from (and outperforms) an entropy-based loss. Further, we show that our approach can also be interpreted as a kind of self-training using a very specific soft label, which we refer to as the conjugate pseudolabel. Overall, our method provides a broad framework for better understanding and improving test-time adaptation. Code is available at https://github.com/locuslab/tta_conjugate.

1711.03717

Binegativity of two qubits under noise

Recently, it was argued that the binegativity might be a good quantifier of entanglement for two-qubit states. Like the concurrence and the negativity, the binegativity is also analytically computable quantifier for all two qubits. Based on numerical evidence, it was conjectured that it is a PPT (positive partial transposition) monotone and thus fulfills the criterion to be a good measure of entanglement. In this work, we investigate its behavior under noisy channels which indicate that the binegativity is decreasing monotonically with respect to increasing noise. We also find that the binegativity is closely connected to the negativity and has closed analytical form for arbitrary two qubits. Our study supports the conjecture that the binegativity is a monotone.

1407.3813

Circular single domains in hemispherical small size Permalloy clusters

We have studied ferromagnetic Permalloy clusters obtained by electrodeposition on n-type silicon. Magnetization measurements reveal hysteresis loops almost independent on temperature and very similar in shape to those obtained in nanodisks with diameter bigger than 150nm. The spin configuration for the ground state, obtained by micromagnetic simulation, shows topological vortices with random chirality and polarization. This behaviour in the small diameter clusters (~80nm), is attributed to the Dzyaloshinskii-Moriya interaction that arises in its hemispherical geometries. This magnetization behaviour can be utilized to explain the magnetoresistance measured with magnetic field in plane and out of sample plane.

0911.2304

Higgs mediated flavor violating top quark decays t --> u_i H, u_i gamma, u_i gamma gamma, and the process gamma gamma --> t c in effective theories

The rare top quark couplings $tu_i\gamma$ and $tu_i\gamma \gamma$ ($u_i=u,c$) induced at the one-loop level by a flavor violating $tu_iH$ vertex are studied within the context of an effective Yukawa sector that incorporates $SU_L(2)\times U_Y(1)$-invariant operators of up to dimension six. Data on the recently observed $D^0-\overline{D^0}$ mixing are employed to constrain the $tu_iH$ vertex, which is then used to predict the $t\to u_iH$, $t\to u_i\gamma$, and $t\to u_i\gamma \gamma$ decays, as well as the $\gamma \gamma \to \bar{t}u_i+t\bar{u}_i$ reaction in the context of the ILC. It is found that the $t\to cH$ and $t\to c\gamma \gamma$ decays can reach sizable branching ratios as high as $5\times 10^{-3}$ and $10^{-4}$, respectively. As for the $t\to c\gamma$ decay, it can have a branching ratio of $5\times 10^{-8}$ that is about 6 orders of magnitude larger than the standard model prediction, which, however, is still very small to be detected. As for $tc$ production, it is found that, due to the presence of a resonant effect in the convoluted cross section $\sigma(e^+e^-\to \gamma \gamma \to t\bar{c}+\bar{t}c)$, about $(0.5 - 2.7)\times 10^{3}$ $tc$ events may be produced at the ILC for a value of the Higgs mass near to the top mass.

astro-ph/9508052

Probing Lyman-alpha Absorbers with Double Lines of Sight

Study of Lyman-alpha absorption lines in the spectra of double line of sight (DLOS) quasars holds the promise of diagnosing the nature of the structures that give rise to Lyman-alpha absorption. Based on simulations of DLOS with various separations through a single population of absorbers, four tests have been designed to diagnose absorber mass distributions (smoothly varying with radius or irregular), geometries (spherical or disk/slab--like), and kinematics (isotropic or systematic velocities). Applying the tests to existing data at redshifts around two we find that: (1) The observed neutral hydrogen column density (N(HI)) distributions of Lyman-alpha lines coincident to both LOS are consistent with a smooth mass distribution. (2) Observed large anticoincident N(HI) are not consistent with a single population of smooth spherical absorbers, which should exhibit sharp cut--offs at small N(HI) in the N(HI) distribution. (3) There is marginal evidence that the observed RMS value of velocity differences between coincident lines increases with DLOS separation as is expected for disk/slab--like absorbers that have systematic velocity fields. (4) The observed velocity dispersion along a single LOS is small compared to the RMS difference between widely separated LOS, which is not consistent with models of cloudlets moving isotropically within a spherical structure. Overall, only a smooth disk/slab--like model with systematic velocities remains consistent with the inferred properties of a single population of Lyman-alpha absorbers.

1205.6723

Studying conformally flat spacetimes with an elastic stress energy tensor using 1+3 formalism

Conformally flat spacetimes with an elastic stress energy tensor given by a diagonal trace-free anisotropic pressure tensor are investigated using 1+3 formalism. We show how the null tetrad Ricci components are related to the pressure components and energy density. The 1+3 Bianchi and Jacobi identities and Einstein field equations are written for this particular case. In general the commutators must be considered since they supply potentially new information on higher order derivatives of the 1+3 quantities. We solve the system for the non rotating case which consist of ODEs of a spatial coordinate.

1909.02512

Descriptional Complexity of Semi-Simple Splicing Systems

Splicing systems are generative mechanisms introduced by Tom Head in 1987 to model the biological process of DNA recombination. The computational engine of a splicing system is the "splicing operation", a cut-and-paste binary string operation defined by a set of "splicing rules" $r = (\alpha_1, \alpha_2 ; \alpha_3, \alpha_4)$ where $\alpha_1, \alpha_2, \alpha_3, \alpha_4$ are words over an alphabet $\Sigma$. For two strings $x = x_1 \alpha_1 \alpha_2 x_2$ and $y = y_1 \alpha_3 \alpha_4 y_2$, applying the splicing rule $r$ produces the string $z = x_1 \alpha_1 \alpha_4 y_2$. In this paper we focus on a particular type of splicing systems, called $(i, j)$ semi-simple splicing systems, $i = 1,2$ and $j = 3, 4$, wherein all splicing rules have the property that the two strings in positions $i$ and $j$ are singleton letters, while the other two strings are empty. The language generated by such a system consists of the set of words that are obtained starting from an initial set called "axiom set", by iteratively applying the splicing rules to strings in the axiom set as well as to intermediately produced strings. We consider semi-simple splicing systems where the axiom set is a regular language, and investigate the descriptional complexity of such systems in terms of the size of the minimal deterministic finite automata that recognize the languages they generate.

2205.01139

Coloured symmetries of rational homology 3-spheres that cover right-angled polytopes

In the present paper we study hyperbolic manifolds that are rational homology 3-spheres obtained by colouring of right--angled polytopes. We study the existence (or absence) of different kinds of symmetries of rational homology spheres that preserve the tessellation of the manifold into polytopes. We also describe how to create colourings with given symmetries.

1508.05305

On the Gevrey well-posedness of the Kirchhoff equation

This paper is devoted to proving the almost global solvability of the Cauchy problem for the Kirchhoff equation in the Gevrey space $\gamma^s_{\eta,L^2}$. Furthermore, similar results are obtained for the initial-boundary value problems in bounded domains and in exterior domains with compact boundary.

astro-ph/9912361

Extracting Neutron Star Properties from X-ray Burst Oscillations

Many thermonuclear X-ray bursts exhibit brightness oscillations. The brightness oscillations are thought to be due to the combined effects of non-uniform nuclear burning and rotation of the neutron star. The waveforms of the oscillations contain information about the size and number of burning regions. They also contain substantial information about the mass and radius of the star, and hence about strong gravity and the equation of state of matter at supranuclear densities. We have written general relativistic ray-tracing codes that compute the waveforms and spectra of rotating hot spots as a function of photon energy. Using these codes, we survey the effect on the oscillation waveform and amplitude of parameters such as the compactness of the star, the spot size, the surface rotation velocity, and whether there are one or two spots. We also fit phase lag versus photon energy curves to data from the millisecond X-ray pulsar, SAX J1808--3658.

1307.4070

Phase diagram of strongly interacting matter under strong magnetic fields

The understanding of the behaviour of strongly interacting matter at finite temperature and density is of fundamental interest and has applications in cosmology, in the astrophysics of neutron stars and in the physics of relativistic heavy ion collisions. Given the possible existence of strong magnetic fields in the mentioned situations, their effect on the QCD phase diagram has recently become a topic of increasing interest. Here, we report on the study of this issue in the framework of the two flavor Nambu-Jona-Lasinio model with Polyakov loop (PNJL) and an extension of it, the so-called entangled PNJL model (EPNJL).

1708.03003

Uniform bounds for sums of Kloosterman sums of half integral weight

For $m,n>0$ and $mn<0$ we estimate the sums \begin{equation*} \sum_{c \leq x} \frac{S(m,n,c,\chi)}{c}, \end{equation*} where the $S(m,n,c,\chi)$ are Kloosterman sums attached to a multiplier $\chi$ of weight $1/2$ on the full modular group. Our estimates are uniform in $m, n$ and $x$ in analogy with the bounds for the case $mn<0$ due to Ahlgren-Andersen, and those of Sarnak-Tsimerman for the trivial multiplier when $m,n>0$. In the case $mn<0$, our estimates are stronger in the $mn$-aspect than those of Ahlgren-Andersen. We also obtain a refinement whose quality depends on the factorization of $24m-23$ and $24n-23$ as well as the best known exponent for the Ramanujan-Petersson conjecture.

math/0602400

On the Chow ring of certain algebraic hyper-K\"ahler manifolds

We study a generalization of a conjecture made by Beauville on the Chow ring of hyper-K\"ahler algebraic varieties. Namely we prove in a number of cases that polynomial cohomological relations involving only CH^1(X) and the Chern classes of X are satisfied in CH(X). These cases are : punctual Hilbert schemes of a K3 surface S parameterizing subschemes of length n, for n<2b_2(S)_tr+5; Fano varieties of lines in a cubic fourfold.

cond-mat/9910386

The Thermodynamics of the XXZ Heisenberg Chain with Impurities

In this paper, we discuss the effect of the arbitrary spin impurities to the spin-1/2 and spin-1 XXZ model. The effect of ground state, the free energy, the magnetic susceptibility, the specific heat and the Kondo temperature are given by using the thermodynamic Bethe ansatz equation.

1407.7151

Symmetric Relative Equilibria in the Four-Vortex Problem with Three Equal Vorticities

We examine in detail the relative equilibria of the 4-vortex problem when three vortices have equal strength, that is, $\Gamma_{1} = \Gamma_{2} = \Gamma_{3} = 1$, and $\Gamma_{4}$ is a real parameter. We give the exact number of relative equilibria and bifurcation values. We also study the relative equilibria in the vortex rhombus problem.

2103.03213

Parisian Ruin for Insurer and Reinsurer under Quata-Share Treaty

In this contribution we study asymptotics of the simultaneous Parisian ruin probability of a two-dimensional fractional Brownian motion risk process. This risk process models the surplus processes of an insurance and a reinsurance companies, where the net loss is distributed between them in given proportions. We also propose an approach for simulation of Pickands and Piterbarg constants appearing in the asymptotics of the ruin probability.

hep-ph/0208216

CP-Violation in the decay B^0, (B^0)bar -> pi^+ pi^- gamma

The decay (B^0)bar -> pi^+ pi^- gamma has a bremsstrahlung component determined by the amplitude for (B^0)bar -> pi^+ pi^-, as well as a direct component determined by the penguin interaction V_tb V^*_td c_7 O_7. Interference of these amplitudes produces a photon energy spectrum d Gamma/d x = a/x + b + c_1 x + c_2 x^2 + ... (x = 2 E_gamma/m_B) where the terms c_1,2 contain a dependence on the phase alpha_eff = pi - arg[(V_tb V^*_td)^* Amp((B^0)bar -> pi^+ pi^-)]. We also examine the angular distribution of these decays, and show that in the presence of strong phases, an untagged B^0/(B^0)bar beam can exhibit an asymmetry between the pi^+ and pi^- energy spectra.

2311.09238

Toward Ultra-Low-Power Remote Health Monitoring: An Optimal and Adaptive Compressed Sensing Framework for Activity Recognition

Activity recognition, as an important component of behavioral monitoring and intervention, has attracted enormous attention, especially in Mobile Cloud Computing (MCC) and Remote Health Monitoring (RHM) paradigms. While recently resource constrained wearable devices have been gaining popularity, their battery life is limited and constrained by the frequent wireless transmission of data to more computationally powerful back-ends. This paper proposes an ultra-low power activity recognition system using a novel adaptive compressed sensing technique that aims to minimize transmission costs. Coarse-grained on-body sensor localization and unsupervised clustering modules are devised to autonomously reconfigure the compressed sensing module for further power saving. We perform a thorough heuristic optimization using Grammatical Evolution (GE) to ensure minimal computation overhead of the proposed methodology. Our evaluation on a real-world dataset and a low power wearable sensing node demonstrates that our approach can reduce the energy consumption of the wireless data transmission up to $81.2\%$ and $61.5\%$, with up to $60.6\%$ and $35.0\%$ overall power savings in comparison with baseline and a naive state-of-the-art approaches, respectively. These solutions lead to an average activity recognition accuracy of $89.0\%$ -- only $4.8\%$ less than the baseline accuracy -- while having a negligible energy overhead of on-node computation.

1904.04049

Simple Question Answering with Subgraph Ranking and Joint-Scoring

Knowledge graph based simple question answering (KBSQA) is a major area of research within question answering. Although only dealing with simple questions, i.e., questions that can be answered through a single knowledge base (KB) fact, this task is neither simple nor close to being solved. Targeting on the two main steps, subgraph selection and fact selection, the research community has developed sophisticated approaches. However, the importance of subgraph ranking and leveraging the subject--relation dependency of a KB fact have not been sufficiently explored. Motivated by this, we present a unified framework to describe and analyze existing approaches. Using this framework as a starting point, we focus on two aspects: improving subgraph selection through a novel ranking method and leveraging the subject--relation dependency by proposing a joint scoring CNN model with a novel loss function that enforces the well-order of scores. Our methods achieve a new state of the art (85.44% in accuracy) on the SimpleQuestions dataset.

astro-ph/0504515

Observations of the BL Lac Object 3C 66A with STACEE

We present the analysis and results of recent high-energy gamma-ray observations of the BL Lac object 3C 66A conducted with the Solar Tower Atmospheric Cherenkov Effect Experiment (STACEE). During the 2003-2004 observing season, STACEE extensively observed 3C 66A as part of a multiwavelength campaign on the source. A total of 33.7 hours of data was taken on the source, plus an equivalent-duration background observation. After cleaning the data set a total of 16.3 hours of live time remained, and a net on-source excess of 1134 events was seen against a background of 231742 events. At a significance of 2.2 standard deviations this excess is insufficient to claim a detection of 3C 66A, but is used to establish flux upper limits for the source.

cs/0201029

The Witness Properties and the Semantics of the Prolog Cut

The semantics of the Prolog ``cut'' construct is explored in the context of some desirable properties of logic programming systems, referred to as the witness properties. The witness properties concern the operational consistency of responses to queries. A generalization of Prolog with negation as failure and cut is described, and shown not to have the witness properties. A restriction of the system is then described, which preserves the choice and first-solution behaviour of cut but allows the system to have the witness properties. The notion of cut in the restricted system is more restricted than the Prolog hard cut, but retains the useful first-solution behaviour of hard cut, not retained by other proposed cuts such as the ``soft cut''. It is argued that the restricted system achieves a good compromise between the power and utility of the Prolog cut and the need for internal consistency in logic programming systems. The restricted system is given an abstract semantics, which depends on the witness properties; this semantics suggests that the restricted system has a deeper connection to logic than simply permitting some computations which are logical. Parts of this paper appeared previously in a different form in the Proceedings of the 1995 International Logic Programming Symposium.

1803.02833

Half-Metallic Superconducting Triplet Spin MultiValves

We study spin switching effects in finite-size superconducting multivalve structures. We examine $\rm F_1F_2SF_3$ and $\rm F_1F_2SF_3F_4$ hybrids where a singlet superconductor ($\rm S$) layer is sandwiched among ferromagnet ($\rm F$) layers with differing thicknesses and magnetization orientations. Our results reveal a considerable number of experimentally viable spin valve configurations that lead to on-off switching of the superconducting state. For $\rm S$ widths on the order of the superconducting coherence length $\xi_0$, non-collinear magnetization orientations in adjacent $\rm F$ layers with multiple spin-axes leads to a rich variety of triplet spin-valve effects. Motivated by recent experiments, we focus on samples where magnetizations in the $\rm F_1$ and $\rm F_4$ layers exist in a fully spin-polarized half metallic phase, and calculate the superconducting transition temperature, spatially and energy resolved density of states, and the spin-singlet and spin-triplet superconducting correlations. Our findings demonstrate that superconductivity in these devices can be completely switched on or off over a wide range of magnetization misalignment angles due to the generation of equal-spin and opposite-spin triplet pairings.

2109.11878

Ringing of the regular black hole with asymptotically Minkowski core

A Regge--Wheeler analysis is performed for a novel black hole mimicker `the regular black hole with asymptotically Minkowski core', followed by an approximation of the permitted quasi-normal modes for propagating waveforms. A first-order WKB approximation is computed for spin zero and spin one perturbations of the candidate spacetime. Subsequently, numerical results analysing the respective fundamental modes are compiled for various values of the $a$ parameter (which quantifies the distortion from Schwarzschild spacetime), and for various multipole numbers $\ell$. Both electromagnetic spin one fluctuations and scalar spin zero fluctuations on the background spacetime are found to possess shorter-lived, higher-energy signals than their Schwarzschild counterparts for a specific range of interesting values of the $a$ parameter. Analysis as to what happens when one permits perturbations of the Regge--Wheeler potential itself is then conducted, first in full generality, before specialising to Schwarzschild spacetime. A general result is presented explicating the shift in quasi-normal modes under perturbation of the Regge--Wheeler potential.

hep-th/9910175

An action for the (2,0) self-dual tensor multiplet in a conformal supergravity background

We present the action for a self-dual tensor in six dimensions, coupled to a (2,0) conformal supergravity background. This action gives rise to the expected equations of motion. An alternative look upon one of the gauge symmetries clarifies its role in the supersymmetry transformation rules and the realisation of the algebra.

1302.6813

On Modal Logics for Qualitative Possibility in a Fuzzy Setting

Within the possibilistic approach to uncertainty modeling, the paper presents a modal logical system to reason about qualitative (comparative) statements of the possibility (and necessity) of fuzzy propositions. We relate this qualitative modal logic to the many--valued analogues MVS5 and MVKD45 of the well known modal logics of knowledge and belief S5 and KD45 respectively. Completeness results are obtained for such logics and therefore, they extend previous existing results for qualitative possibilistic logics in the classical non-fuzzy setting.

2210.17417

Fashion-Specific Attributes Interpretation via Dual Gaussian Visual-Semantic Embedding

Several techniques to map various types of components, such as words, attributes, and images, into the embedded space have been studied. Most of them estimate the embedded representation of target entity as a point in the projective space. Some models, such as Word2Gauss, assume a probability distribution behind the embedded representation, which enables the spread or variance of the meaning of embedded target components to be captured and considered in more detail. We examine the method of estimating embedded representations as probability distributions for the interpretation of fashion-specific abstract and difficult-to-understand terms. Terms, such as "casual," "adult-casual,'' "beauty-casual," and "formal," are extremely subjective and abstract and are difficult for both experts and non-experts to understand, which discourages users from trying new fashion. We propose an end-to-end model called dual Gaussian visual-semantic embedding, which maps images and attributes in the same projective space and enables the interpretation of the meaning of these terms by its broad applications. We demonstrate the effectiveness of the proposed method through multifaceted experiments involving image and attribute mapping, image retrieval and re-ordering techniques, and a detailed theoretical/analytical discussion of the distance measure included in the loss function.

cond-mat/0007334

Superfluid Transition Temperature in a Fermi Gas with Repulsion. Higher Orders Perturbation Theory Corrections

High order perturbation theory corrections to the superfluid transition temperature in a weakly interacting Fermi gas with repulsive interaction are calculated. This involves calculating the contributions of third and fourth order diagrams in the gas parameter and taking into account effects of retardation. The contributions from both second, third and fourth orders result in the effective attraction in p-wave channel. It is shown that the critical temperature is mainly determined by second and third orders terms of perturbation theory. The dependence of the critical temperature on an external magnetic field is found. We discuss possible applications of the results to the diluted 3He-4He mixtures and trapped neutral-atom Fermi gases.

1603.07742

Area Functional Relation for 5D-Gauss-Bonnet-AdS Black Hole

We present \emph{area (or entropy) functional relation} for multi-horizons five dimensional (5D) Einstein-Maxwell-Gauss-Bonnet-AdS Black Hole. It has been observed by exact and explicit calculation that some complicated function of two or three horizons area is \emph{mass-independent} whereas the entropy product relation is \emph{not} mass-independent. We also study the local thermodynamic stability of this black hole. The phase transition occurs at certain condition. \emph{Smarr mass formula} and \emph{first law} of thermodynamics have been derived. This \emph{mass-independent} relation suggests they could turn out to be an \emph{universal} quantity and further helps us to understanding the nature of black hole entropy (both interior and exterior) at the microscopic level. In the \emph{Appendix}, we have derived the thermodynamic products for 5D Einstein-Maxwell-Gauss-Bonnet black hole with \emph{vanishing} cosmological constant.

2106.09406

High Cadence Optical Transient Searches using Drift Scan Imaging III: Development of an Inexpensive Drive Control System and Characterisation and Correction of Drive System Periodic Errors

In order to further develop and implement novel drift scan imaging experiments to undertake wide field, high time resolution surveys for millisecond optical transients, an appropriate telescope drive system is required. This paper describes the development of a simple and inexpensive hardware and software system to monitor, characterise, and correct the primary category of telescope drive errors, periodic errors due to imperfections in the drive and gear chain. A model for the periodic errors is generated from direct measurements of the telescope drive shaft rotation, verified by comparison to astronomical measurements of the periodic errors. The predictive model is generated and applied in real-time in the form of corrections to the drive rate. A demonstration of the system shows that that inherent periodic errors of peak-to-peak amplitude ~100'' are reduced to below the seeing limit of ~3''. This demonstration allowed an estimate of the uncertainties on the transient sensitivity timescales of the prototype survey of Tingay & Joubert (2021), with the nominal timescale sensitivity of 21 ms revised to be in the range of 20 - 22 ms, which does not significantly affect the results of the experiment. The correction system will be adopted into the final version of high cadence imaging experiment, which is currently under construction. The correction system is inexpensive (<$A100) and composed of readily available hardware, and is readily adaptable to other applications. Design details and codes are therefore made publicly available.

2302.05503

Comparing velocity and passive scalar statistics in fluid turbulence at high Schmidt numbers and Reynolds numbers

Recently, Shete et al. [Phys. Rev. Fluids 7, 024601 (2022)] explored the characteristics of passive scalars in the presence of a uniform mean gradient, mixed by stationary isotropic turbulence. They concluded that at high Reynolds and Schmidt numbers, the presence of both inertial-convective and viscous-convective ranges, renders the statistics of the scalar and velocity fluctuations to behave similarly. However, their data included Schmidt numbers of 0.1, 0.7, 1.0 and 7.0, only the last of which can (at best) be regarded as moderately high. Additionally, they do not consider already available data in the literature at substantially higher Schmidt number of up to 512. By including these data, we demonstrate here that the differences between velocity and scalar statistics show no vanishing trends with increasing Reynolds and Schmidt numbers, and essential differences remain in tact at all Reynolds and Schmidt numbers.

cond-mat/9811165

The integrable open XXZ chain with broken Z_2 symmetry

The hamiltonian of an asymmetric diffusion process with injection and ejection of particles at the ends of a chain of finite length is known to be relevant to that of the spin-1/2 XXZ chain with integrable boundary terms. However, the inclusion of boundary sources and sinks of particles breaks the arrow-reversal symmetry necessary for solution via the usual Bethe Ansatz approach. Developments in solving the model in the absence of arrow-reversal symmetry are discussed.

2103.12734

On the density of eigenvalues on periodic graphs

Suppose that $\Gamma=(V,E)$ is a graph with vertices $V$, edges $E$, a free group action on the vertices $\mathbb{Z}^d \curvearrowright V$ with finitely many orbits, and a linear operator $D$ on the Hilbert space $l^2(V)$ such that $D$ commutes with the group action. Fix $\lambda \in \mathbb{R}$ in the pure-point spectrum of $D$ and consider the vector space of all eigenfunctions of finite support $K$. Then $K$ is a non-trivial finitely generated module over the ring of Laurent polynomials, and the density of $\lambda$ is given by an Euler-characteristic type formula by taking a finite free resolution of $K$. Furthermore, these claims generalize under suitable assumptions to the non-commutative setting of a finite generated amenable group acting on the vertices freely with finitely many orbits, and commuting with the operator $D$.

0907.5559

Penetrable-Square-Well fluids: Analytical study and Monte Carlo simulations

We study structural and thermophysical properties of a one-dimensional classical fluid made of penetrable spheres interacting via an attractive square-well potential. Penetrability of the spheres is enforced by reducing from infinite to finite the repulsive energy barrier in the pair potentials As a consequence, an exact analytical solution is lacking even in one dimension. Building upon previous exact analytical work in the low-density limit [Santos \textit{et al.}, Phys. Rev. E \text{77}, 051206 (2008)], we propose an approximate theory valid at any density and in the low-penetrable regime. By comparison with specialized Monte Carlo simulations and integral equation theories, we assess the regime of validity of the theory. We investigate the degree of inconsistency among the various routes to thermodynamics and explore the possibility of a fluid-fluid transition. Finally we locate the dependence of the Fisher-Widom line on the degree of penetrability. Our results constitute the first systematic study of penetrable spheres with attractions as a prototype model for soft systems.

1108.0828

Multi-Wavelength Study of the 2008-2009 Outburst of V1647 Ori

V1647 Ori is a young eruptive variable star, illuminating a reflection nebula (McNeil's Nebula). It underwent an outburst in 2003 before fading back to its pre-outburst brightness in 2006. In 2008, V1647 Ori underwent a new outburst. The observed properties of the 2003-2006 event are different in several respects from both the EXor and FUor type outbursts, and suggest that this star might represent a new class of eruptive young stars, younger and more deeply embedded than EXors, and exhibiting variations on shorter time scales than FUors. In outburst, the star lights up the otherwise invisible McNeil's nebular - a conical cloud likely accumulated from previous outbursts. We present follow-up photometric as well as optical and near-IR spectroscopy of the nebula obtainted during the 2008-2009 outburst. We will also present results from contemporaneous X-ray observations. These multi-wavelength observations of V1647 Ori, obtained at this key early stage of the outburst, provide a snapshot of the "lighting up" of the nebula, probe its evolution through the event, and enable comparison with the 2003-2006 outburst.

alg-geom/9703034

Testing S-duality conjecture and exceptional bundles

In this paper we deal with algebro-geometrical problems connected with testing S-duality conjecture for super-symmetric Yang-Mills quantum field theories in four dimensions. We describe all field configurations such that beta function coefficient for gauge groups of rank 1 and 2 is zero or negative. We also give special series of such field configurations for gauge groups of an arbitrary rank. Realization of one of the series discovers a connection with exceptional bundles. That points again at relation between S-duality and string duality.

2006.13178

Does Matter Matter? Using the mass distribution to distinguish neutron stars and black holes

Gravitational-wave detectors have opened a new window through which we can observe black holes (BHs) and neutron stars (NSs). Analyzing the 11 detections from LIGO/Virgo's first gravitational-wave catalog, GWTC-1, we investigate whether the power-law fit to the BH mass spectrum can also accommodate the binary neutron star (BNS) event GW170817, or whether we require an additional feature, such as a mass gap, in between the NS and BH populations. We find that with respect to the power-law fit to binary black hole (BBH) masses, GW170817 is an outlier at the 0.13\% level, suggesting a distinction between NS and BH masses. A single power-law fit across the entire mass range is in mild tension with: (a) the detection of one source in the BNS mass range ($\sim 1$--$2.5 \,M_\odot$), (b) the absence of detections in the "mass-gap" range ($\sim 2.5$--$5 \,M_\odot$), and (c) the detection of 10 sources in the BBH mass range ($\gtrsim 5 \,M_\odot$). Instead, the data favor models with a feature between NS and BH masses, including a mass gap (Bayes factor of 4.6) and a break in the power law, with a steeper slope at NS masses compared to BH masses (91\% credibility). We estimate the merger rates of compact binaries based on our fit to the global mass distribution, finding $\mathcal{R}_\mathrm{BNS} = 871^{+3015}_{-805} \ \mathrm{Gpc}^{-3} \ \mathrm{yr}^{-1}$ and $\mathcal{R}_\mathrm{BBH} = 47.5^{+57.9}_{-28.8} \ \mathrm{Gpc}^{-3} \ \mathrm{yr}^{-1}$. We conclude that, even in the absence of any prior knowledge of the difference between NSs and BHs, the gravitational-wave data alone already suggest two distinct populations of compact objects.

2311.14932

Hypersonic wave wall flow based on gas kinetic method

The transition of hypersonic boundary layer can lead to a several-fold increase in surface heat flux and skin friction for the aircraft, significantly impacting its flight performance. The corrugated wall, as a passive control method for boundary layer flow, also serves as a type of wall microstructure, making its study on the local rarefaction effect of considerable engineering significance. In this study, we employed the conservative discrete unified gas dynamic scheme and utilized a domain-wide numerical simulation method. Initially, we simulated the hypersonic flat plate flow with different depths of corrugated walls under the conditions of incoming flow Mach number of 6 and Reynolds number of ${{10}^{7}}$. Subsequently, we investigated the effects of corrugated walls, including flat plate corrugated walls and wedge corrugated walls, under varying Reynolds numbers for an incoming flow Mach number of 6, and discussed the impact of local rarefaction effect of corrugated walls under different Reynolds numbers. By using the local Knudsen number as the criterion, we found that under these conditions, the occurrence of local rarefaction effect near the corrugated wall due to consecutive failures does not take place when the incoming Reynolds number reaches ${{10}^{7}}$ or ${{10}^{6}}$. However, when the incoming Reynolds number drops to ${{10}^{5}}$, the local rarefaction effect near the corrugated wall becomes evident, with the appearance of non-equilibrium effects in translational and rotational temperatures of molecules. This phenomenon becomes more pronounced as the Reynolds number decreases further.

0812.1704

Spiky Strings and Spin Chains

We determine spectral curves for the known spiky string solutions in AdS space in the limit of large angular momentum. We also construct generic multi-spike solutions in this limit and compute the corresponding spectral data. The resulting spectral curves precisely match those of the classical spin chain describing the dual operators in one-loop gauge theory. Our results confirm the map between string theory and gauge theory degrees of freedom proposed in arXiv:0805.4387 [hep-th].

1501.07785

Renormalization group invariant of lepton Yukawa couplings

By using quark Yukawa matrices only, we can construct renormalization invariants that are exact at the one-loop level in the standard model. One of them $I^q$ is accidentally consistent with unity, even though quark masses are strongly hierarchical. We calculate a lepton version of the invariant $I^l$ for Dirac and Majorana neutrino cases and find that $I^l$ can also be close to unity. For the Dirac neutrino and inverted hierarchy case, if the lightest neutrino mass is 3.0 meV to 8.8 meV, an equality $I^q=I^l$ can be satisfied. These invariants are not changed even if new particles couple to the standard model particles, as long as those couplings are generation independent.

1907.11527

Measuring magnetic moments of polydisperse ferrofluids utilizing the inverse Langevin function

The dipole strength of magnetic particles in a suspension is obtained by a graphical rectification of the magnetization curves based on the inverse Langevin function. The method yields the arithmetic and the harmonic mean of the particle distribution. It has an advantage compared to the fitting of magnetization curves to some appropriate mathematical model: It does not rely on assuming a particular distribution function of the particles.

1811.07346

Propagation of Cyclonic Vortices and Intense Rainfall over Indian Peninsula: Case Studies from Northeast Monsoon Season

Four case studies of cyclonic vortices over the Indian peninsular region during northeast monsoon season are presented. It was observed that the propagation of vortices over the peninsular orography was controlled by the vortex Froude number, Frv = Vmax/(NH), where, Vmax is the maximum tangential velocity of winds in the vortex, H is the height of the orography, and N is the Brunt-Vaisala frequency of atmosphere along the orography. Strong vortices with Frv > 1 overcame the orographic barrier and crossed the peninsula. While, those with Frv < 1 were blocked by the orography. The blocked vortices remained stationary along the east coast for two to three days. In these cases, clouds formed continuously along the coast for three consecutive days. Therefore, there was intense rainfall over the coast and little rainfall over orography during this time. In unblocked vortices, the rainfall intensity showed a systematic shift from coastal to the higher orographic region within a day or two. However, significant weakening of the vortices, as well as convection, was seen as the vortex arrived over the higher plateau. These case studies will be helpful for forecasting heavy rainfall events over the Indian peninsula during northeast monsoon season.