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1,314,259,993,463
arxiv
\section{Introduction} Let $K$ be a field, $m$ a positive integer and $n$ an integer prime to the characteristic of $K$. The Milnor-Bloch-Kato conjecture asserts that the Galois symbol \begin{equation} \label{eqn:galoisclass} K^M_m(K)/n K^M_m(K) \quad \longrightarrow \quad H^m(K, {\mathbb Z}/n{\mathbb Z}(m)) \end{e...
1,314,259,993,464
arxiv
\section{Introduction} Irrotational dust spacetimes have been widely studied, in particular as models for the late universe, and as arenas for the evolution of density perturbations and gravity wave perturbations. In linearised theory, i.e. where the irrotational dust spacetime is close to a Friedmann--Robertson--Walk...
1,314,259,993,465
arxiv
\section{Introduction}\label{section:introduction} The proliferation of smartphones and tablets equipped with 3G and 4G connectivity and the fast growing demand for downloading multimedia files have resulted in severe overload in the internet backhaul, and it is expected to be worse with the advent of 5G in near fut...
1,314,259,993,466
arxiv
\section{Introduction} It is well known that radiative transition process of emitters in media differs from those in vacuum\cite{Blo1965,Top2003}. Because of fundamental importance and relevance to various applications in low-dimensional optical materials and photonic crystals, this issue continues to attract both the...
1,314,259,993,467
arxiv
\section{\setcounter{equation}{0}\oldsection} \renewcommand\thesection{\arabic{section}} \renewcommand\theequation{\thesection.\arabic{equation}} \allowdisplaybreaks \def\pf{\it{Proof.}\rm\quad} \DeclareMathOperator*{\Cat}{\mathbf{Cat}} \DeclareMathOperator*{\sgn}{sgn} \DeclareMathOperator*{\dep}{dep} \Declar...
1,314,259,993,468
arxiv
\section{Introduction} SU UMa-type dwarf novae, a subclass of dwarf novae, exhibit two types of outbursts: normal outburst and superoutburst (for a review, see \cite{war95book}; \cite{osa96review}). During superoutburst, hump-like modulations called superhumps are visible. Basically, the light source of superhumps is...
1,314,259,993,469
arxiv
\section{Introduction and main results}\label{sec:inro} Let $\Omega \subset {\mathbb R}^N$, $N \geq 2$, be a bounded, open domain, and let $p>1$. We say that $u \in W^{1,p}_0(\Omega) \setminus \{0\}$ is an eigenfunction of the $p$-Laplacian associated to the eigenvalue $\lambda \in \mathbb{R}$ if it is a weak solution...
1,314,259,993,470
arxiv
\section{Introduction} Let $X$ be a smooth projective variety defined over an algebraically closed field $k$ and let $H$ be an ample divisor on $X$. A family ${\mathcal S}$ of isomorphism classes of coherent sheaves on $X$ is called bounded if there exists a scheme $S$ of finite type over $k$ and an $S$-flat family $...
1,314,259,993,471
arxiv
\section{Introduction} Let $\Omega\subset\subset\mathbb{C}^{2}$ be a smoothly bounded domain. Throughout, we suppose that $ \Omega$ admits a $\mathcal{C}^\infty$-smooth defining function $\rho$ which is plurisubharmonic on the boundary, $b\Omega$, of $\Omega$, i.e., \begin{align*} H_{\rho}(\xi...
1,314,259,993,472
arxiv
\section{Introduction} \figconflict \IEEEPARstart{S}{emantic} segmentation is a fundamental research field in computer vision. It aims to predict the class of each pixel in a given image. The availability of large labeled datasets~\cite{everingham2011pascal,zhou2017scene} and the development of deep neural networks~\...
1,314,259,993,473
arxiv
\section{#1}\setcounter{equation}{0}} \renewcommand{\theequation}{\thesection.\arabic{equation}} \newcommand{\begin{equation}}{\begin{equation}} \newcommand{\end{equation}}{\end{equation}} \newcommand{\begin{eqnarray}}{\begin{eqnarray}} \newcommand{\end{eqnarray}}{\end{eqnarray}} \newcommand{\nonumber}{\nonumber} \newc...
1,314,259,993,474
arxiv
\section{INTRODUCTION} Usability and accessibility are the commonly used terms in the context of enhancing the user experience for users of the world wide web~\cite{hanson2013progress}. While there is no universally accepted view or definition for usability, a commonly accepted definition presented in ISO 9241-11 sta...
1,314,259,993,475
arxiv
\section{Introduction} The $\psi(3770)$ resonance is the lowest-mass $c\bar c$ state lying above the open charm-pair threshold (3.73~GeV$/c^2$). Since its width is 2 orders of magnitude larger than that of the $\psi(3686)$ resonance, it is traditionally expected to decay to $D\bar D$ meson pairs with a branching frac...
1,314,259,993,476
arxiv
\section{\label{Introduction}Introduction} Understanding the interaction of matter with strong and ultrastrong laser pulses is a fundamental and rapidly developing field of research. With the remarkable advances in laser technology in the past few decades, experimental investigation of the interaction bec...
1,314,259,993,477
arxiv
\section{Introduction} Nowadays, with the rapid development of analyzing player performance by collecting the past matches they have played, researchers have cooperated with sports teams and players to boost the advancement of sports analytics. However, it is difficult for novel algorithms to be verified in real-time m...
1,314,259,993,478
arxiv
\section{Introduction} \label{Se1} \begin{figure}[ht] \begin{center} \includegraphics[width=0.8\linewidth]{prior.png} \end{center} \caption{ The diagram of VaDE\xspace. The data generative process of VaDE\xspace is done as follows: 1) a cluster is picked from a GMM model; 2) a latent embedding is generated base...
1,314,259,993,479
arxiv
\section{Introduction} \input{intro.tex} \section{Related Work} \input{relat.tex} \section{Methodology} \input{method.tex} \section{Experiments} \input{exper.tex} \section{Conclusion} \input{conclu.tex} \bibliographystyle{splncs04} \subsection{Datasets} Two large-scale datasets, nuScenes dataset and Lyft datas...
1,314,259,993,480
arxiv
\section{Introduction} In recent years, the quantity of available source code has been growing exponentially \cite{source_growth}. Code reuse at this scale is predicated on understanding and searching through a massive number of projects and source code documents. The ability to generate meaningful, semantic labels is...
1,314,259,993,481
arxiv
\section{Introduction} The majority of nuclides heavier than iron are produced via neutron capture reactions \cite{B2FH57, Kappeler11-RMP, Arnould07-PR,Thielemann17-ARNPS}. However, there are a few dozens of nuclides on the proton rich side of the valley of stability, the so-called $p$-nuclei, which cannot be reac...
1,314,259,993,482
arxiv
\section{Introduction} According to the World Health Organization 2019 statistics, Cardiovascular Diseases (CVDs) contribute to nearly 34\% of all deaths worldwide. The most critical risk factor for CVD is elevated blood pressure, also known as hypertension \cite{paper28}. Thereby early diagnosis of abnormal BP can ai...
1,314,259,993,483
arxiv
\section{Introduction} Hierarchical structure formation scenarios suggest that galaxies form by continuous accretion of small, dark--matter dominated satellites. The possibility of an extragalactic deployment of high--velocity clouds has long been considered, and in various contexts, by Oort (1966, 1970, 1981...
1,314,259,993,484
arxiv
\section{Introduction} Seiberg and Witten showed that the low-energy effective theory of $N=2$ supersymmetric gauge theory in four dimensions is determined by the prepotential, a holomorhic function of the period integrals of the meromorphic one-form (the Seiberg-Witten differential) on a Riemann surface\cite{SeWi}...
1,314,259,993,485
arxiv
\section{Introduction} Probabilistic programming is a rapidly developing discipline at the interface of programming and Bayesian statistics \cite{GordonHNR14,Goodman2014,VandeMeent2018}. The idea is to express probabilistic models (incorporating the prior distributions) and the observed data as programs, and to use a ...
1,314,259,993,486
arxiv
\section{Introduction} A first order phase transition from hadronic to exotic matter phases may proceed through the nucleation of droplets of the new phase. The formation of droplets of quark matter \citep{Bombaci1, Mintz, Bombaci2} and antikaon condensed matter \citep{Norsen, NorsenReddy} in neutrino-free neutron st...
1,314,259,993,487
arxiv
\section{Introduction} All graphs considered in this paper will be finite, undirected, and may have loops and multiple edges, unless stated otherwise (in which case the graph will be referred to as a simple graph). We consider five types of walks in graphs: general walks, trails, paths, induced paths, and isometric pa...
1,314,259,993,488
arxiv
\section{Introduction} Different search operators have been proposed and applied in EAs~\cite{fogel1997handbook}. Each search operator has its own advantage. Therefore an interesting research issue is to combine the advantages of variant operators together and then design more efficient hybrid EAs. Currently hybrid...
1,314,259,993,489
arxiv
\section{Datasets and Evaluation Setup} \label{sec:supp-datasets} We evaluate our proposed approach for joint 3D pose and focal length estimation in the wild on three challenging real-world dataset with different object categories: Pix3D~\cite{Sun2018pix3d} (\textit{bed}, \textit{chair}, \textit{sofa}, \textit{table}...
1,314,259,993,490
arxiv
\section{Introduction} Permutation complexity of aperiodic words is a relatively new notion of word complexity which was first introduced and studied by Makarov $\cite{Makar06}$ based on ideas of S.V. Avgustinovich (see the acknowledgements in $\cite{FlaFrid}$), and is based on the idea of an infinite permutation as...
1,314,259,993,491
arxiv
\section{Introduction} The plan for this article is a follows. I'll start by describing a simple example of the Riemannian version of the prolongation procedure of \cite{BCEG}. Next, I will explain how the direct observations used in this example can be replaced by tools from representation theory to make the procedure...
1,314,259,993,492
arxiv
\section{Introduction} Calorimetric methods are the most exact for measurement of energy of high-energy nuclei and they are widely applied in experiments on accelerators and with cosmic radiation \cite{1}. The most of methods of calorimetric measurements of energy are based on full absorption of energy of a parti...
1,314,259,993,493
arxiv
\section{The Carmen Sandiego game} The work described here\footnote{The ideas of the present paper were formulated in Dec. 2013 - Jan. 2014, and discussed (in varying detail) in early 2014 with Scott Aaronson, Laci Babai, Sasha Razborov, and Avi Wigderson.} concerns the following ``game'' involving three parties: Al...
1,314,259,993,494
arxiv
\section{Introduction} \label{intro} The problem of the existence of the operator with dimension 2, whose contribution to QCD sum rules ~\cite{SVZtf79} is proportional to~$1/Q^2$, and search for relevant OPE corrections are performed already for quite a long time \cite{ShortString, ZakharovOther, BodDominEidel2012}. ...
1,314,259,993,495
arxiv
\section{Introduction} Even though Quantum chromodynamics (QCD) is universally accepted as the theory of strong interactions, color confinement still remains an unsolved problem. Although the well established phenomenon of the confinement of quarks and gluons inside hadrons is without any doubt encoded into the QCD Lag...
1,314,259,993,496
arxiv
\section{Introduction} \label{Sec-Introduction} Microwave engineering relies on time-consuming electromagnetic simulations to carry out robust electrical designs. The electromagnetic complexity in microwave devices is such that \emph{only} detailed, full-wave simulations, i.e., solving Maxwell's equations directly, can...
1,314,259,993,497
arxiv
\section{Introduction}\label{sec:intro} In this paper we consider the Cauchy problem for the following log-modified nonlinear Schr\"odinger equation (NLS) on $\mathbb R^2$: \begin{equation}\label{eq:nls} \left\{ \begin{aligned} & i{\partial}_t u +\frac{1}{2}\Delta u =\lambda u|u|^2\ln |u|^2,\quad x\in \mathbb R^2,\ ...
1,314,259,993,498
arxiv
\section{Introduction} The estimation of treatment effects is one of the core problems in causal inference. A treatment effect is a measure used to compare interventions in randomized experiments, policy analysis, and medical trials. The treatment effect measures the difference in outcomes between units assigned to the...
1,314,259,993,499
arxiv
\section{Introduction} Studying edge-on galaxies opens up the possibility to observe something that is not feasible with face-on galaxies: the halo of the galaxy. It is now clear that sufficiently deep and well-resolved radio observations of edge-on galaxies show emission high above their galactic discs \citep{changes...
1,314,259,993,500
arxiv
\section{Introduction} Rapid theoretical and experimental development of quantum computers has led to a productive crossover of ideas between the fields of many-body condensed matter physics and of quantum information and computation \cite{Augusiak2012,Zeng2019}. On the one hand, a principal application of quantum devi...
1,314,259,993,501
arxiv
\section{Introduction} \setcounter{equation}{0} \hskip 1em In this paper, we study the following free boundary problem modeling tumor growth in necrotic phase: \begin{equation}\label{1.1} \left\{ \begin{array}{rll} \Delta\sigma\,&=\sigma \chi_{\Omega^+(t)}\qquad \qquad & \mbox{in}\;\; \Omega^+(t)\cup\Omega^...
1,314,259,993,502
arxiv
\section{Introduction} \Ma{The Chiral Magnetic Effect (CME) is the generation of an electric current $\bm J$ in presence of an external magnetic field $\bm B$~ \cite{FKW08}}: \begin{equation} \braket{\bm{J}}=\frac{e^2}{2\pi^2}\mu_5\bm{B}.\label{CMEdef} \end{equation} \Ma{The current~\eq{CMEdef} appears naturally in ...
1,314,259,993,503
arxiv
\section{Introduction} Motivated by limited communication capacity in physical systems, control with quantized feedback \cite{elia2001stabilization,fu2005sector,you2011attainability,kang2015coarsest,zhou2019adaptive} has been an active research area for decades, dating back to an early work \citep{kalman1956nonlinear}...
1,314,259,993,504
arxiv
\section{Introduction} Artificial neural networks (ANNs) give unprecedented results in machine learning tasks \cite{AlexNet2012, resnet2015, InceptionResNetV4, ViTOG, EffNetV2OG} though they continue to be little understood. Theoretical studies focus on the equivalence between ANNs trained with (full-batch) gradient de...
1,314,259,993,505
arxiv
\section{Introduction} Diffusion phenomena arise from a Markovian stochastic modeling and as a solution of SDEs with or without jumps in many areas of applied mathematics. Their investigation concerns different mathematical branches and therefore research interest in questions such as existence and regularity of soluti...
1,314,259,993,506
arxiv
\section{Introduction} \label{sec:intro} Explaining how a feature impacts a model prediction is a crucial question in machine learning (ML) as it provides a deeper understanding of how the model behaves and what insights have been extracted from data. In many real-world applications, it has been increasingly common to ...
1,314,259,993,507
arxiv
\section{Introduction} \label{sec:1.Introduction} \vspace{-0.15cm} Image retrieval is a long-standing problem in computer vision. This task aims to sort a database of images based on their similarities to the given query image. For this task, global retrieval through global descriptor matching and geometric verificatio...
1,314,259,993,508
arxiv
\section{Introduction}\label{sec-1} The aim of the present contribution consists in providing a topological proof of the existence of chaotic dynamics for a planar Hamiltonian system considered in different formulations and with different interpretations in the literature, by using the ``Linked Twist Maps'' (from now ...
1,314,259,993,509
arxiv
\section{Introduction} Music source separation is a problem that has been studied for a few decades now: given an audio track with several instruments mixed together (a regular MP3 file, for example), how can it be separated into its component instruments? The obvious application of this problem is in music production...
1,314,259,993,510
arxiv
\section{Introduction} We consider the initial-value problem for the focusing energy-critical nonlinear Schr\"odinger equation in dimension $d\geq 3$, \begin{equation}\label{nls} \begin{cases} \ iu_t+\Delta u=F(u)\\ \ u(t_0)=u_0\in \dot H^1_x({\mathbb{R}}^d), \end{cases} \end{equation} where the nonlinearity is given b...
1,314,259,993,511
arxiv
\section{\label{sec:intro}Introduction} Amino acids form the basis of peptides and proteins, which are fundamental building blocks of life, and they are of great scientific interest for a multitude of reasons, first and foremost due to their role in biology and related use in pharmacology and medicine. Their systemati...
1,314,259,993,512
arxiv
\section{Introduction} Hash coding has become an essential method for similarity queries due to its computational efficiency and storage cost advantages. A series of hash representation learning methods~\cite{wang2017survey,cao2017hashnet,jiang2017deep} developed from local similarity hashing further improve the hashi...
1,314,259,993,513
arxiv
\section{Introduction} Variational quantum algorithms such as the \ac{VQE} or the \ac{QAOA} \cite{Farhi_Goldstone_14} have received a lot of attention of late. They are promising candidates for gaining a quantum advantage already with \ac{NISQ} computers in areas such as quantum chemistry \cite{Cao_Aspuru-Guzik_19}, co...
1,314,259,993,514
arxiv
\section{Introduction} Complementary slackness is a fundamental optimality condition, and hence ubiquitous in optimization. In~the most general setting of nonlinear programming (formulated below in the classical language of nonlinear optimization), it requires a pair \(\pdpair{\xb}{\yb}\) of primal-dual feasible solu...
1,314,259,993,515
arxiv
\section{Introduction} Search engine users want relevant documents returned quickly when searching. Searching is often performed using an inverted index \cite{yan2009inverted}, which stores a list of occurring terms, and for each term, documents in which that term occurs are recorded, along with term frequency within ...
1,314,259,993,516
arxiv
\section{Introduction} In recent years, deep neural network based semantic segmentation models have achieved considerable success. This success is much reliant on the large pixel-level annotated dataset over which these models are trained. However, like many other deep neural network based models, semantic segmentati...
1,314,259,993,517
arxiv
\section{Introduction} Large scale studies of the human microbiome have become increasingly common thanks to advances in next generation sequencing (NGS) technologies \citep{MetaHIT, HMP}. A relevant task in these studies is to measure the association between a sample's microbial composition and individual character...
1,314,259,993,518
arxiv
\section{Introduction} \label{sec:Introduction} The inherent atomic properties, like mass or polarizability, and the very high sensitivities achievable with atom interferometers make them a very versatile tool for high-precision measurements of, for instance, fundamental constants, internal forces, accelerations or ro...
1,314,259,993,519
arxiv
\section{Introduction} For quite a long time there has been a stable interest in the physics of the massive neutrino. Investigations in this area touch, to a certain extent, the feasible phenomenon of lepton mixing and its manifestations in neutrino physics and, consequently, in astrophysics and ...
1,314,259,993,520
arxiv
\section{Introduction} HESS\,J1303$-$631\ is one of the most prominent examples of the so-called very high energy (VHE; $E>100$\,GeV) $\gamma$-ray\ \rr{``dark''} sources, those which were detected in the VHE band but do not have counterparts at other energy bands. It was discovered in 2005 \citep{2005A&A...439.1013A...
1,314,259,993,521
arxiv
\section{Motivation and Overview}\label{sec:introduction} Since their creation in the 1940's, formal languages and grammars have found many applications in, for instance, programming languages and artificial intelligence. A rapid development of the Internet, in particular, may treat one-way finite automata as a meani...
1,314,259,993,522
arxiv
\section{Introduction} In the standard formulation of quantum mechanics, the statistical outcomes of an ideal measurement of an observable $\hat{A} |a\rangle = a |a\rangle$ are described by the spectral measure [1]: \begin{equation} p_{\psi}(a) =|\langle a | \psi \rangle|^{2} \end{equation} where $|\psi\rangle \in H$...
1,314,259,993,523
arxiv
\section{Introduction} The Lightning Network (LN) \cite{poon2016bitcoin} is emerging at the most popular layer-2 scaling technology for Bitcoin. We model the LN by a graph $G$; every vertex can be assumed to be a user and every edge is a bi-directional payment channel between two nodes\footnote{We omit private channel...
1,314,259,993,524
arxiv
\section{Introduction} \label{sec:intro} Polynomials with coefficients over a finite field $\mathbb{F}_q$ play an important role in several areas of computer science, including cryptography and coding theory~\cite{shparlinski13}. The notion of \emph{coprimality} between two polynomials $f,g \in \mathbb{F}_q[x]$---i.e. ...
1,314,259,993,525
arxiv
\section{Introduction} While Einstein's general relativity (GR) has stood all direct experimental tests~\cite{Will:2005va}, there are also reasons to try to extend GR. For example the mysterious nature of dark energy and dark matter might become resolved within a modified theory of gravity. Another reason to try t...
1,314,259,993,526
arxiv
\section{Introduction} \label{sec:intro} Past observational studies have revealed that disc galaxies often exhibit an $m=1$ distortion or lopsidedness in the outskirts of the disc. Lopsidedness is common in the spatial distribution of the neutral hydrogen (H~{\sc i}) which extends further out than the stellar disc \c...
1,314,259,993,527
arxiv
\section{Introduction} \label{sec:intro} Recent years saw a revival of the idea originally put forward by S. Hawking \cite{1971MNRAS.152...75H}, that Primordial Black Holes (PBH) could make up the so far elusive Dark Matter. LIGOs first detection of gravitational waves from merging binary black holes of approximately ...
1,314,259,993,528
arxiv
\section{Introduction} The rapid and violent form of combustion called detonation \cite{Fickett1979} propagates through detonation wave which is a shock wave with chemical reaction. Given a wide range of application in science and engineering, shock and detonation have always been of great concern in the field of sc...
1,314,259,993,529
arxiv
\section{Introduction} \label{sec:intro} A gravitating mass that traverses a sea of other particles builds up an overdense wake behind it. This wake tugs back on the mass, providing an effective drag. The background sea may itself consist of non-interacting point masses. For this collisionless case, \citet{c43} fir...
1,314,259,993,530
arxiv
\section{Introduction}\label{sec:Introduction} The oscillation modes of neutron stars (NSs) provide a means to probe the internal composition and state of dense matter. NSs have rich oscillation spectra, with modes associated with different physical origins, such as the internal ingredients, the elasticity of the cru...
1,314,259,993,531
arxiv
\@ifstar{\@ssection}{\@section}{\@ifstar{\@ssection}{\@section}} \def\@section#1 \if@nobreak \everypar{}% \ifnum\LastMac=\Hae \addvspace{\half}\fi \else \addpen{\gds@cbrk}% \addvspace{\two}% \fi \bgroup \ninepoint\bf \Raggedright \ifAutoNumber \global\advance\Sec \@ne \...
1,314,259,993,532
arxiv
\section{Problem description} \label{sec:1} Reinforcement learning is aimed at the solution of the Markov decision problems without the exact knowledge of an underlying model. In this paper we address only the case of finite state-action Markov decision processes (MDP). Moreover, for concreteness we discuss only the...
1,314,259,993,533
arxiv
\section{Introduction} This paper concerns a version of the fractional $\mathrm{\bf p}$-Laplace operator, which has been introduced in \cite{BCF2}. More precisely, for $\mathrm{\bf p}\geq 2$, $s\in (\frac{1}{2},1)$, and for a given bounded function $u:\mathbb{R}^N\to\mathbb{R}$ that is of regularity $C^{1,1}(x)$ with ...
1,314,259,993,534
arxiv
\section{Introduction} Since their inception, sequential Monte Carlo (SMC) resampling methods (a.k.a., particle filters)~\cite{Doucet2000,Doucet2001} have emerged as a useful tool to estimate and track targets with non-linear and/or non-Gaussian dynamics. Unlike the Kalman filter~\cite{Kalman1960} and its variants~\ci...
1,314,259,993,535
arxiv
\subsection{An Illustrative Example} To further illustrate our MaTrust trust inference problem (Problem~\ref{P:matrust}), we give an intuitive example as shown in Fig.~\ref{F:example}. \begin{figure*}[!t] \centering \subfigure[The observed locally-generated pair-wise trust relationships]{ \label{F:example:even...
1,314,259,993,536
arxiv
\section{Introduction} It has long been known that interactions can have drastic effects in low dimensional systems \cite{TG}. A striking example of this was elucidated by Kane and Fisher \cite{KF}. It was shown that a local impurity can be a relevant or irrelevant perturbation to a Luttinger Liquid depending on the si...
1,314,259,993,537
arxiv
\section{Introduction} In this paper we further explore the relation between string theory and some 4-dimensional structures such that these structures do not appear as a result of usual compactification or model-buildings in string theory. These structures are rather involved in the mathematics of string theory but t...
1,314,259,993,538
arxiv
\section{Introduction} \label{sec:intro} Over the past two decades, many examples of galaxies with stellar masses $\log(M_*/M_\odot) \gtrsim 11$ out to redshift $z\sim6$ have been found (e.g., \citealt{caputi2011,stefanon2015,deshmukh2018,marsan2022}). However, towards the Epoch of Re-ionisation (EoR; $z\gtrsim6$), su...
1,314,259,993,539
arxiv
\section{Introduction and preliminaries on spherical harmonics} Many parts of analysis on Euclidean spaces and in particular the theory of spherical harmonics provide an elegant and instructive application of group theoretical concepts to various questions of classical function theory. It suf\/f\/ices to mention point...
1,314,259,993,540
arxiv
\section{introduction} In this paper, a graph is understood to be undirected and have no loops or multiple edges. While graphs with multiple edges could be taken under consideration, it is not necessary to do so as multiple edges do not add any difficulty or important properties. A set of vertices in a graph $G$ is s...
1,314,259,993,541
arxiv
\section{Introduction}\label{sec:Introduction} The aim of this paper is to present a new exact solution which represents a nonlinear internal water wave. The solution in this study is constructed by adapting the celebrated Pollard's solution in order to successfully describe the internal water waves. In 1970, Pollard ...
1,314,259,993,542
arxiv
\section{introduction} \label{sec:intro} Using grid diagrams Ozsv\'{a}th, Szab\'{o} and Thurston \cite{grid} defined combinatorial invariants of Legendrian and transverse links in the tight 3-sphere. These invariants have been shown to be effective, meaning they distinguish some Legendrian and transverse knots havin...
1,314,259,993,543
arxiv
\section{Introduction} The theory of cosmological perturbations (TCP) for a perfect fluid has always been an important issue in cosmology. It enables us to understand how small fluctuations seeded in the early universe eventually evolved into the present large scale structure. Also, TCP has been extremely useful to ...
1,314,259,993,544
arxiv
\section{Introduction} \label{introduction} Reliability measures how reliable a system is by finding the probability that it will continue to provide its desirable service in a given period of time. Fault trees (FTs) \cite{DFT-survey} and reliability block diagrams (RBDs) \cite{hasan2015reliability} are the most common...
1,314,259,993,545
arxiv
\section{Introduction} Quantum gravity with a non-vanishing cosmological constant formulated in Ashtekar's spin-connection variables \cite{4,5,6,7,8} has interesting physical states given by the exponential of the Chern-Simons functional \cite{8,9,10} and appropriate transformations thereof. In order to elucidate the p...
1,314,259,993,546
arxiv
\section{Supplemental Material to Spin Drag of a Fermi Gas in a Harmonic Trap} \section{Derivation of the transport equation from Boltzmann's equation} We consider an ensemble of spin 1/2 fermions of mass $m$. In the dilute limit, the statistical properties of the system are fully captured by the single-particle ph...
1,314,259,993,547
arxiv
\subsection*{#1}\atocs{#1}} \newcommand{\aob}[2]{\ens\big({#1 \atop #2}\big)} \newcommand{\aobc}[2]{\ens\big\{{#1 \atop #2}\big\}} \newcommand{\aonb}[2]{\ens\frac{#1}{#2}} \newcommand{\aoboc}[3]{\lba{c}#1\\#2\\#3\ear} \newcommand{\aobcod}[4]{\ens\big({#1 \atop #2}{\mbox{ } #3 \atop \mbox{ } #4}\big)} \newcommand{\aobc...
1,314,259,993,548
arxiv
\section{Introduction} Supersymmetry(SUSY) is one of the most appealing theories for physics beyond the Standard Model(SM), as it solves the hierarchy problem and could provide a good candidate for the cold dark matter(CDM) in the universe. SUSY predicts the existence of a super-partner for each SM particle, sharin...
1,314,259,993,549
arxiv
\section{\@startsection{section}{1}% \z@{.7\linespacing\@plus\linespacing}{.5\linespacing} {\bfseries \centering }} \def\@secnumfont{\bfseries} \makeatother \setlength{\textheight}{19.5 cm} \setlength{\textwidth}{12.5 cm} \usepackage{amsmath,amssymb, amsbsy} \usepackage{subfigure} \usepac...
1,314,259,993,550
arxiv
\section{Introduction} For some years now the cosmological standard model (or $\Lambda$CDM-model) has been widely successful in explaining the vast majority of cosmological observations. Still the nature of two of its key components, dark matter and dark energy, remains a mystery. So far both of these substances have ...
1,314,259,993,551
arxiv
\section{Acknowledgements} We would like to thank the LCC generator working group and the ILD software working group for providing the simulation and reconstruction tools and producing the Monte Carlo samples used in this study. This work has benefited from computing services provided by the ILC Virtual Organization, ...
1,314,259,993,552
arxiv
\section{Introduction} \label{sec:intro} Modern face classifiers based on deep learning methods leverage large datasets to learn the essential features that make each face unique and are able to achieve high-performance on the recognition task, even outperforming human capabilities \cite{Taigman2014}. However, in prese...
1,314,259,993,553
arxiv
\section{Introduction} Let $(M,g)$ be a compact Riemannian manifold without boundary, denote by $\Delta_{g}$ its Laplace-Beltrami operator, and consider the nonlinear Klein-Gordon equation \be \label{KG} (\partial_{t}^2-\Delta_{g}+V+m^2)v=-\partial_{2}f(x,v) \ee where $m$ is a strictly positive constant, $V...
1,314,259,993,554
arxiv
\section{Introduction} Motivated by the results of Burch \cite{Bu68}, the notion of Burch ideals and Burch submodules were introduced (and studied) by Dao-Kobayashi-Takahashi and Dey-Kobayashi in \cite{DKT20} and \cite{DK22} respectively. These include large well-studied classes of ideals and modules. In this article,...
1,314,259,993,555
arxiv
\section{Motivation and Statement of the Main Results} Since the classical works of Euler and Riemann it is known that the distribution of prime numbers is intimately related to the Riemann zeta-function $\zeta(s)$. In general, many topics in analytic number theory are tied to associated Dirichlet series. With his pat...
1,314,259,993,556
arxiv
\section{Introduction} \label{sec:introduction} \sun{Random walk (RW) is an effective tool for extracting relationships between entities in a graph, and is widely used in many applications such as \emph{Personalized PageRank} (PPR) \cite{page1999pagerank}, \emph{SimRank} \cite{jeh2002simrank}, \emph{Random Walk Domin...
1,314,259,993,557
arxiv
\section{Conclusions} \textbf{Conclusions:} In this paper we present a new paradigm to infuse non-trivial topological characteristics into a trivial insulator by means of modulating the scalar potential. The scalar potential is utilised to enhance the mixing between different quantum states which in turn drives the s...
1,314,259,993,558
arxiv
\section*{Supplementary Material} \input{sections/supplementary} \clearpage \clearpage {\small \bibliographystyle{ieee_fullname} \section{Method Overview} We now present each module and the corresponding losses of our full model as shown in \reffig{model}. We formulate object detection as a keypoint dete...
1,314,259,993,559
arxiv
\section{Introduction} The question of how dynamics of a physical system depends on the choice of its Hamiltonian is one of the most important in theoretical and mathematical physics. Its significance is only enhanced by the fact that in modern theory dynamics is considered not only in physical time, but in many other...
1,314,259,993,560
arxiv
\section{Introduction}\label{sec:intro} Bochner's inequality is one of the most fundamental estimates in geometric analysis. It states that \begin{equation}\label{eq:intro-bochner} \frac12\Delta|\nabla u|^2-\langle\nabla u, \nabla\Delta u\rangle\ge K \cdot |\nabla u|^2+\frac1N \cdot |\Delta u|^2 \end{equation} for eac...
1,314,259,993,561
arxiv
\section{INTRODUCTION} Localization is one of important research topics concerning autonomous vehicles~\cite{ETHlandmark, ABLE}, robotics~\cite{Tang2019} and assistive navigation~\cite{KeyPosition, VisualLocalizer}. Generally, GNSS (global navigation satellite system) is the straightforward way to localize the autonomo...
1,314,259,993,562
arxiv
\section*{Acknowledgments} I an grateful to Daniel Schubring for useful discussions. This work is supported in part by DOE grant DE-SC0011842.