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2,121,713,845,741
arxiv
\section{Introduction} \label{sec:intro} A major outstanding goal in cosmology is to piece together the history of the Universe between Cosmic Dawn, the emergence of the first stars and galaxies, and the end of reionization, when the radiation from these objects had ionized the intergalactic medium (IGM). Advances in...
2,121,713,845,742
arxiv
\section{Introduction} In~\cite{macmahon:indices} MacMahon proved that two \emph{permutation statistics\/}, namely the \emph{length\/} (or \emph{inversion number\/}) and the \emph{major index\/}, are equidistributed over the symmetric group $S_n$ for every $n>0$ (see also~\cite{macmahon:combinatory}). The question of ...
2,121,713,845,743
arxiv
\section*{\indexname} \special{header=pstricks.pro} \newgray{gray}{0.50} \newrgbcolor{royalblue}{0.25 0.41 0.88} \newrgbcolor{green}{0.1 0.8 0.2} \newrgbcolor{lightgreen}{0 1 0} \newrgbcolor{ygreen}{0.7 1 0.7} \newrgbcolor{lblue}{0.8 0.83 1} \theoremstyle{plain} \newtheorem*{einlsatz}{Satz} \newtheorem{satz}{Satz}[sect...
2,121,713,845,744
arxiv
\section{\label{sec:sec1}Introduction} The nucleation which occurs within the bulk metastable material is called {\it homogeneous nucleation}~\cite{Kelton10,Oxtoby88}. However, it is frequently assisted by the presence of a surface. The nucleation in this case is called {\it heterogeneous nucleation}~\cite{Kelton1...
2,121,713,845,745
arxiv
\section{Introduction} The main theorem of this paper is inspired by two results in two seemingly unrelated areas of probability: the Cox-Durrett shape theorem well known in the theory of first passage percolation, and our recent subadditive ergodic theorem for double sequences which proved useful in studying IARCH ...
2,121,713,845,746
arxiv
\section{Introduction} The Fibonacci sequence 0,1,1,2,3,5,8,.... given by Italian mathematician Leonardo of Pisano has continued to produce a lot of research interest over the years. Things took a turn for the different when Matijasevich [2,3] first derived a fibonacci identity to complete the proof that computably en...
2,121,713,845,747
arxiv
\section{I. Introduction} The trapped-ion system is a leading platform for the construction of universal quantum computers, offering long coherence time, high-fidelity quantum operations, and reliable state preparation and measurement \cite{leibfried2003quantum,Haffner08Quantum,Wineland08Entangled,Ladd10Quantum,Monroe2...
2,121,713,845,748
arxiv
\section{Introduction} There has been considerable analysis \cite{FNAL} of the value of a high energy muon storage ring for the purpose of producing well-defined, high energy beams of neutrinos. This approach takes advantage of the relatively long muon lifetime to allow for collection at modest energies and accelerati...
2,121,713,845,749
arxiv
\section{Introduction} Let $R$ be a local or graded Cohen-Macaulay ring which admits a canonical module $\omega_R$. The trace of an $R$-module $M$, denoted $\tr(M)$, is the sum of all ideals $\varphi(M)$, where the sum is taken over all $R$-module homomorphisms $\varphi \:\; M\to R$. It is noticed in \cite{HHSTrace...
2,121,713,845,750
arxiv
\section*{Abstract} Reaction networks are systems in which the populations of a finite number of species evolve through predefined interactions. Such networks are found as modeling tools in many biological disciplines such as biochemistry, ecology, epidemiology, immunology, systems biology and synthetic biology. It is...
2,121,713,845,751
arxiv
\section{Introduction} A spatial point process $\bX$ is briefly speaking a random subset of the $d$-dimensional Euclidean space $\mathbb R^d$, where $d=2,3$ are the cases of most practical importance. We refer to the (random) elements of $\bX$ as `events' to distinguish them from other possibly fixed points in $\...
2,121,713,845,752
arxiv
\section{Introduction :} Multi-component quantum fluids described by a vector or tensor order parameter are often richer than their scalar counterparts. Examples in condensed matter are superfluid $^3$He \cite{vollhardt3He} or some unconventional superconductors with spin-triplet Cooper pairing \cite{norman2011a}....
2,121,713,845,753
arxiv
\section{Introduction} Let $G(n,p)$ denote the binomial random graph on vertex set $[n]:= \{1,2,\ldots,n\}$, where each edge is included independently with probability $p$. The following classic question has been extensively studied in the theory of random graphs: given a large graph $H$, does $G(n,p)$ contain a cop...
2,121,713,845,754
arxiv
\section{Introduction} Human activity recognition is a research challenge mainly tackled by computer vision researchers using videos captured by security cameras to understand individuals' behaviors. However, recording people's activities with their identities brings certain privacy concerns due to lack of anonymity. M...
2,121,713,845,755
arxiv
\section{Introduction} \label{sec:introduction} \noindent Multimedia information retrieval on a large scale database has to address at the same time both issues related to effectiveness and efficiency. Search results should be pertinent to the submitted queries, and should be obtained quickly, even in presence of ve...
2,121,713,845,756
arxiv
\section{Introduction} Wireless networks have greatly changed our daily life in recent years, using various mobile devices such as smartphones, tablets and smartwatches. Innovative mobile applications utilize location proximity to provide interesting services, such as proximity-based social networks and online taxi ser...
2,121,713,845,757
arxiv
\section{Introduction} Low-dimensional quantum magnets are at the heart of current interest in strongly correlated electron systems. These systems are driven by strong correlations and large quantum fluctuations - especially when frustration comes into play - and can exhibit various unconventional phases and quantum...
2,121,713,845,758
arxiv
\section{Introduction} \mypara The recent excitement surrounding van der Waals (vdW) heterostructures stems from the diverse emergent phenomena that can arise by layering two-dimensional (2D) materials like graphene and other xenes, or transition metal dichalcogenides \cite{Ajayan2016Two-dimensionalMaterials,Novoselo...
2,121,713,845,759
arxiv
\chapter{Basics of Random Access - ALOHA and Slotted ALOHA} \label{chapter1} \acresetall \ifpdf \graphicspath{{chapter1/Images/}} \fi \thispagestyle{empty} \epigraph{Computers are only capable of a certain kind of randomness because computers are finite devices}{Tristan Perich} The focus of the first Chapter is o...
2,121,713,845,760
arxiv
\section{Introduction} Optoelectronic oscillators (OEOs) combine a nonlinear modulation of laser light with optical storage to generate ultra-pure microwaves for lightwave telecommunication and radar applications \cite{YaoMalekiJOSAB,YaoMalekiJQE}. Their principal specificity is their extremely low phase noise, which c...
2,121,713,845,761
arxiv
\section{Introduction} A standard approach to the solution of generalized eigenproblems \begin{equation} \label{eq:gen_eig_problem} Fc = \lambda Sc, \end{equation} where $F$ and $S$ are Hermitian and $S$ is positive definite, makes use of an inverse factor of $S$ to transform the eigenvalue problem to standard form~\...
2,121,713,845,762
arxiv
\section{Introduction} It is clear that the computation of line bundle cohomology classes over $D$-dimensio\-nal varieties is an interesting mathematical question of its own. Our motivation for approaching this problem, however, originates from the appearance of this problem in various classes of compactifications o...
2,121,713,845,763
arxiv
\section{Introduction} Differential privacy (DP) is the standard for privacy-preserving statistical summaries \cite{dwork2006calibrating}. Companies such as Microsoft \cite{pereira2021us}, Google \cite{2020google}, Apple \cite{tang2017privacy}, and government organizations such as the US Census \cite{abowd2018us}, h...
2,121,713,845,764
arxiv
\section{Introduction} The MICROSCOPE (Micro-Satellite \`a tra\^in\'ee Compens\'ee pour l'Observation du Principe d'Equivalence) mission was fully dedicated to the in-orbit test of the Universality of free fall, the so-called Weak Equivalence Principle (WEP) \cite{einstein08, einstein16}. The accuracy objective was exp...
2,121,713,845,765
arxiv
\section{Results} \label{sec:results} \Cref{ssec:qual_mapping_quality} and \cref{ssec:quan_mapping_quality} show a qualitative and quantitative evaluation of our proposed 3D mesh reconstruction algorithm, with respect to the baseline and state-of-the-art approaches, on the EuRoC\xspace dataset, using the subset of s...
2,121,713,845,766
arxiv
\section{Introduction} Reinforcement learning agents have recently begun to be deployed in real world applications, but these systems still tend to be repetitive tasks with well defined state spaces. Better generalization is needed for applications that interact with the more dynamics parts of the real world. Towards ...
2,121,713,845,767
arxiv
\section{Introduction} \label{intro} An exciting result from heavy-ion experiments performed at the Relativistic Heavy-Ion Collider (RHIC) is the creation of a state of deconfined quarks and gluons known as the {\it quark-gluon plasma} (QGP) (see, for example, \cite{Adcox:2004mh}). Fast partons (partons which propagat...
2,121,713,845,768
arxiv
\section{Introduction} \ \ \ We consider the eigenvalue problem \begin{align} \label{ZSeq} L\bm{u}(x) = \lambda \bm{u}(x), \end{align} for the first order $2\times 2$ differential system on the line: \begin{align*} L:= \begin{pmatrix} \displaystyle ih\frac{d}{dx} & -iA(x) \\ iA(x) & \displaystyle -ih\frac{d}{dx} \end...
2,121,713,845,769
arxiv
\subsection*{Disclaimer} \label{disclaimer} If the reader does not believe that physics is a rigorous science based on facts of nature - which I will call natural philosophy in this essay on the core of the beyond the Standard Model physics - no argument, no matter how logical and/or physical, could help in my expe...
2,121,713,845,770
arxiv
\section{Introduction} \label{s1} \setcounter{equation}{0} In this paper, we consider the nonlinear Schr\"{o}dinger equation with wave operator (NLSW) in $d$ ($d=1,2,3$) dimensions as \cite{Baoc,Mach,Colin1,Colin2,Schoene,Tsu, BDX,Xin} \begin{equation}\label{eq:nls_wave_full} \begin{cases} i\p_t \psi(\bx...
2,121,713,845,771
arxiv
\section{Introduction} Multilingual embeddings are useful because they provide word representations of source and target language in the same space in machine translation and because they are a basis for transfer learning. In contrast to prior multilingual work \cite{zeman08crosslanguage,mcdonald11delexicalized,ts...
2,121,713,845,772
arxiv
\section{Introduction} \label{x1} How and when the galaxies assembled their stars are two of the most pressing questions of modern cosmology. In the last decade, it has become clear that the dusty star-forming galaxies are significant contributors to this process as they pin down the episodes of galaxy-scale star form...
2,121,713,845,773
arxiv
\section*{References}} \renewcommand{\eqref}[1]{Eq.~\ref{#1}} \newcommand{\eqsref}[1]{Eqs.~\ref{#1}} \newcommand{\figref}[1]{Figure~\ref{#1}} \newcommand{\figsref}[1]{Figures~\ref{#1}} \newcommand{\secref}[1]{Sec.~\ref{#1}} \newcommand{\secsref}[1]{Secs.~\ref{#1}} \newcommand{\appref}[1]{Appendix~\ref{#1}} \newcommand...
2,121,713,845,774
arxiv
\section{Introduction} Let $\mathsf{Est}$ be a randomized algorithm that estimates some quantity $\mu(C) \in \R^d$ when given input $C$. The canonical example is the case when $C$ is a Boolean circuit, $d = 1$, $\mu(C) \stackrel{\text{def}}{=} \Pr_x[C(x) = 1]$, and $\mathsf{Est}$ estimates $\mu(C)$ by evaluating $...
2,121,713,845,775
arxiv
\section{Introduction} Quantum behavior at the microscopic scale is well established both theoretically and experimentally. Strictly quantum phenomena observed so far have confirmed the validity of quantum mechanics postulates, in particular its non-local character.\cite{aspect1981} Entanglement is certainly one of t...
2,121,713,845,776
arxiv
\section{Introduction} One of the most peculiar and fascinating manifestations of topology in condensed matter physics is the appearance of nondissipative transport coefficients in insulating systems. The paradigmatic example is the Hall conductivity, which is quantized in a two-dimensional insulator, and proportional...
2,121,713,845,777
arxiv
\section{Introduction} Stochastic optimization (SO) problems frequently arise in engineering disciplines such as transportation systems, machine learning, service systems, manufacturing etc. Practical limitations, lack of model information and the large dimensionality of these problems prohibit analytic solutions to th...
2,121,713,845,778
arxiv
\section{Introduction} By fast magnetic reconnection, we mean magnetic field lines changing their connections on a time scale determined by Alfv\'enic, not resistive, physics. Fast magnetic reconnection is prevalent in both natural and laboratory plasmas \cite{Liu:2017}. As shown by Newcomb\cite{Newcomb}, magnetic f...
2,121,713,845,779
arxiv
\section{Introduction}\label{s:intro} Conventionally, Low-Earth Orbits (LEOs) have a maximum altitude of $\sim 2000$ km, with a $\sim 300$ km lower limit given by the rapid orbital decay caused by the atmospheric drag. The inner Van Allen radiation belt (\cite{allen1958observation}), with a high level of trapped radia...
2,121,713,845,780
arxiv
\section*{Introduction} The two principal problems of QCD are confinement and spontaneous breaking of chiral invariance. Both of them take place in the strongly interacting domain where the theory becomes nonperturbative. Most probably the two are interrelated. However, usually they were considered separately. Up to n...
2,121,713,845,781
arxiv
\section{Introduction} A \emph{shrinking Ricci soliton} is a Riemannian manifold $(M, g)$ for which \begin{equation}\label{eq:soliton} 2\Rc(g) + \mathcal{L}_{X}g = g \end{equation} for some smooth vector field $X$ on $M$. The soliton is \emph{gradient} if $X = \nabla f$ for some $f\in C^{\infty}(M)$. When $(M, g)$ is ...
2,121,713,845,782
arxiv
\section{Introduction} \label{sec:intro} Since the late 1980's, the field of spatial statistics has expanded into almost every area of applied research. Researchers use spatial models to analyze global temperatures, determine pubic health and safety, and investigate patterns in the brain. Much research has been done i...
2,121,713,845,783
arxiv
\section{Introduction} The Kuiper belt is a population of icy bodies beyond the orbit of Neptune (Figure~\ref{real}). The orbital structure of the Kuiper belt is an important constraint on the early evolution of the Solar System. It is thought that much of this structure, with large resonant populations and dy...
2,121,713,845,784
arxiv
\section{Introduction} \indent In a pioneering paper\cite{Bell}, Lynden-Bell and Katz introduced the concept of load and metage in the hydrodynamical flows to show that the content of Kelvin's circulation theorem is contained in the conservation of a particular function of load; if that very function is same for two fl...
2,121,713,845,785
arxiv
\section{Introduction} \label{notation.sec} Algebraic manipulation detection (AMD) codes were defined in 2008 by Cramer {\it et al.} \cite{CDFPW1,CDFPW2} as a generalization and abstraction of techniques that were previously used in the study of robust secret sharing schemes \cite{OKSS,OKS,TW}. AMD codes are studied...
2,121,713,845,786
arxiv
\section{Introduction} Gravitational microlensing, as first noted in \cite{ref:pacz86}, is a very efficient tool for the detection and the characterisation of massive astrophysical halo compact objects (MACHOs), a possible component of dark matter halos. Following the first exciting detection of microlensing events...
2,121,713,845,787
arxiv
\section{Introduction} The Hirota-Satsuma system is a system of coupled KdV equations, introduced by Hirota and Satsuma in $1981$, \cite{hirota}. In this paper, we consider the Hirota-Satsuma system with periodic boundary conditions \begin{align}\label{hir} \begin{cases} u_t+ au_{xxx}+3a (u^2)_x+\beta(v^2)_x =0, \hsp...
2,121,713,845,788
arxiv
\section{Introduction} In \cite{klyachko:89a}, Klyachko described torus-equivariant vector bundles on toric varieties in terms of collections of filtered vector spaces satisfying certain compatibility conditions. The primary goal of this article is it to generalize this description to the situation of $T$-equivariant ...
2,121,713,845,789
arxiv
\section{Introduction} \label{sec:intro} The active nucleus of galaxy M81 (hereafter M81*), at a distance of $3.96\pm0.29$\,Mpc \citep{2007ApJ...668...924B}, is one of the nearest low luminosity active galactic nuclei, LLAGN \citep{2002A&A...392..53N}. With a black hole mass of $\thicksim7\times10^7M_\odot$ determined ...
2,121,713,845,790
arxiv
\section{Introduction} \label{sec::intro} Many modern infrastructure systems depend on the delivery of electricity through a reliable and robust always-on power network. However, the stability of a particular network topology under small perturbations or malicious attack can be difficult to accurately predict, parti...
2,121,713,845,791
arxiv
\section{Introduction} Noise, vibration and harshness (NVH) issues in friction brakes are one of the most relevant customer claims in the automotive industry and also omnipresent in rail vehicles \cite{Kinkaid.2003, Brunel.2006,Hoffmann.2008,Sinou.2013}. During the last two decades, research activities, cf. Figure~\re...
2,121,713,845,792
arxiv
\section{Introduction} Let $M$ be a closed connected orientable smooth manifold. A classical theorem of H. Hopf \cite{hopf} states that $M$ admits a non-singular vector field if and only if the Euler characteristic, $\chi(M)$, of $M$ is zero. R. Brown \cite{brown} gave a generalization of Hopf's theorem for topologica...
2,121,713,845,793
arxiv
\section{Introduction} \label{sec:int} The main motivation to develop the method of topological quantization is to find an alternative to the ideas that prevail about the quantization of the gravitational fields. Nevertheless, as the method evolved we found ourselves exploring other classical theories with well establ...
2,121,713,845,794
arxiv
\section{Introduction} \label{Sec_Introduction} Owing to recent advances in heavy--ion accelerators, an increasing interest arises in exploring electromagnetic processes accompanying ion collisions. One of the dominant processes is electron--positron pair production; pertinent cross sections are large. For ultra--rela...
2,121,713,845,795
arxiv
\section{Introduction} Achieving order in the packing of elementary constituents in confined environments is an important problem arising in the study of simple liquids~\cite{scott1964random, finney1970random, hansen1990theory}, amorphous solids~\cite{zallen,weeks2015amorphous,philippe2018glass}, space tessell...
2,121,713,845,796
arxiv
\section{INTRODUCTION} The proliferation of smart devices, mobile networks and computing technology have sparked a new era of Internet of Things (IoT), which is poised to make substantial advances in all aspects of our modern life, including smart healthcare system, intelligent transportation infrastructure, etc \cite{...
2,121,713,845,797
arxiv
\section{Gravitational wave and underground facilities} \label{sec:gw-underground} To detect a Gravitational Wave (GW) with high signal-to-noise ratio, locating the interferometric detector underground is an effective way to avoid and filtering noise sources caused by human activities and meteorological phenomenon. F...
2,121,713,845,798
arxiv
\section*{Do tumors grow stochastically or hierarchically?} Two main models have been used in the past to describe tumor development: in the stochastic clonal evolution model \citep{Nowell1976}, each cells can be tumorigenic and sustain tumor growth, while according to the cancer stem cell (CSC) theory \citep{bonnet199...
2,121,713,845,799
arxiv
\section{Introduction} Liver cancer is one of the leading causes of cancer-induced death, which poses a serious risk to human health~\cite{el2020epidemiology}. Accurate liver tumor segmentation (LiTS) is a vital prerequisite for liver cancer diagnosis and treatment, which helps to increase the five-year survival rate. ...
2,121,713,845,800
arxiv
\section{Introduction} \subsection{Main results} Throughout the paper, we work over an algebraically closed field $\mathbb{K}$ of characteristic zero. Let $\mathbb{G}_{a}=(\mathbb{K},+)$ be the additive group of the field and $\mathbb{G}_{a}^{n}=\mathbb{G}_{a} \times \mathbb{G}_{a} \times ... \times \mathbb{G}_{a}$($n$...
2,121,713,845,801
arxiv
\section{Introduction} At high redshift, the intergalactic medium (IGM) contains the majority of baryons in the Universe \citep[]{petitjeanal93,Fukugita}, is highly ionised by the UV-background (UVB) produced by galaxies and QSOs \citep[]{GunnandPeterson} at least since redshift $z\sim 6$ \citep[]{Fan06, Becker07}, b...
2,121,713,845,802
arxiv
\section{Problem Statement} \label{sec:problem} Protecting machine learning from adversarial attacks is of paramount importance~\cite{vorobeychik2018adversarial,joseph2018adversarial,zhu2018optimal}. To do so one much first understand various types of adversarial attacks. Data poisoning is a type of attack where an at...
2,121,713,845,803
arxiv
\section*{Acknowledgments} We thank B. VanSaders and J. Kim for useful discussions. We thank T. Gandhi for useful discussions, and help fabricating the particles. This research was supported by the National Science Foundation through Grant No. DMR-2104733. The experiments utilized the shared experimental facilities at...
2,121,713,845,804
arxiv
\section{Motivation} \label{sec:motivation} Quantum chromodynamics (QCD) is a theory that is chirally symmetric in the limit of massless quarks. Chiral symmetry and its spontaneous breaking play an important role in QCD phenomenology. Many observables depend strongly on the chiral properties of QCD. When one studies QC...
2,121,713,845,805
arxiv
\section*{Nomenclature} \begin{IEEEdescription}[\IEEEusemathlabelsep\IEEEsetlabelwidth{$Y^s = g^s-$}] \item [{$N$}] - The set of nodes \item [{$E$, $E^R$}] - The set of {\em from} and {\em to} branches \item [{$G$}] - The set of generators \item [{$L$}] - The set of loads \item [{$H$}] - The set of bu...
2,121,713,845,806
arxiv
\section{Introduction} Image segmentation approaches rarely provide measures of \mn{segmentation label uncertainty.} In fact, most existing and probabilistically-motivated segmentation approaches only compute \mn{the} \emph{maximum a posteriori} (MAP) \mn{solution}~\cite{kolmogorov2004,li2009,bresson2007,cremers2007...
2,121,713,845,807
arxiv
\section{Introduction} \label{sec:intro} Extensions of the SM often include one or more additional abelian gauge symmetries beside the Standard Model $U(1)_Y$ hypercharge. Compelling motivation for these extensions arises from grand unified theories (GUT) and from string theory. The phenomenology of new abelian gauge ...
2,121,713,845,808
arxiv
\section{Introduction} The study of face numbers of convex polytopes is one of the main themes in algebraic and geometric combinatorics and has attracted a lot of attention during the last decades. It has been of great interest to completely characterize the possible face numbers of simplicial polytopes and to find su...
2,121,713,845,809
arxiv
\subsection{General lowest-order pre-big bang equations} \label{sec2.1} In this section we write down the classical equations of motion of string gravity at lowest order both in the $\alpha'$ and in the string-loop expansion. Such an approximation should be valid at early enough times since, in the pre-big bang scenari...
2,121,713,845,810
arxiv
\section{Introduction} The flavor structure of the nucleon sea can provide new insight on the nature of QCD at the confinement scale. Perturbative QCD predicts a largely flavor symmetric $\bar u, \bar d, \bar s$ sea, as the $g \to Q \bar Q$ process, in which a gluon split into a quark antiquark pair ($Q \bar...
2,121,713,845,811
arxiv
\section{Introduction} An incompressible fluid flow is described by the governing equations, as \begin{subequations} \label{1} \begin{equation} \frac{\partial u_i}{\partial x_i} = 0, \label{1a} \end{equation} \begin{equation} \rho \frac{\partial u_i}{\partial t} + \rho u_j \frac{\partial u_i}{\partial x_...
2,121,713,845,812
arxiv
\section{Introduction} \begin{figure}[t] \begin{center} \scriptsize \scalebox{1}{ \includegraphics[width=1\linewidth]{figures/overview_0909.pdf} } \end{center} \vspace{-2mm} \caption{Overview. We propose to incorporate visual scene graph in VL model's pre-training, fine-tuning and conventional Transformer's st...
2,121,713,845,813
arxiv
\section{Introduction} Tunneling is one of the most intriguing phenomenon in quantum mechanics and tunneling time doubly so. Quantum time concepts in general were developed in connection with collisions or scattering in three dimensions (3D) and tunneling in one dimension (1D). Both these times in 3D and 1D are essen...
2,121,713,845,814
arxiv
\section{Main Results and Their Context} We start by formulating the main results of this paper. Let $\Lambda\subset \R^2$ be a lattice, i.e. a discrete cocompact subgroup of $\R^2$, satisfying condition $\text{A}_\Lambda<1$, where $\text{A}_\Lambda$ denotes the area of the fundamental domain of $\Lambda$. For a ...
2,121,713,845,815
arxiv
\section{Longitudinal resistance $R_{xx}$ as a function of the Hall bar length} The gate dependence of $R_{xx}$ was measured at zero magnetic field for several Hall bars with lengths $L$ ranging from 1 to 40 $\mu$m keeping the aspect ratio constant. All the Hall bars considered in this section were fabricated from sam...
2,121,713,845,816
arxiv
\section{Introduction} One of the interesting features of $\mathcal{N}{=}\,4$ supersymmetric mechanics is its relation with the Witten--Dijkgraaf--Verlinde--Verlinde (WDVV) equations \cite{WDVV}. The most natural appearance of the WDVV equations is seen at the component level. As was first demonstrated in \cite{Wyl...
2,121,713,845,817
arxiv
\section{Introduction} Proteins participate in essentially all biological processes and play critical roles for an organism. The structures of proteins are highly correlated to their functions in the biological processes. Determining the protein structures to understand their functions can bring considerable contrib...
2,121,713,845,818
arxiv
\section{Introduction} Cano and D\'iaz \cite{Diaz1, Diaz2} have recently explored a novel method of obtaining continuous analogues of discrete objects such as binomial coefficients and Catalan numbers. First, they realized these discrete quantities as the number of certain \textbf{lattice paths}. Next, they considered...
2,121,713,845,819
arxiv
\section{Introduction} The study of traffic flow has uncovered some interesting phenomena such as the propagation of nonlinear density waves representing congestion. To determine traffic behaviour, a variety of modelling techniques are used, which include the application of car following, cellular automation, gas kinet...
2,121,713,845,820
arxiv
\section{Introduction} The great success of the kinetic gas theory, which has essentially contributed to the acceptance of the particle nature of the microcosmos, was the connection between the macroscopic thermodynamic observables pressure $P$ and volume $V$ (of the container/ heat bath) with the statistical mean kin...
2,121,713,845,821
arxiv
\section{Introduction} Noncollinear magnetic textures, such as magnetic domain walls, vortices, bubbles, and skyrmions are currently the subject of intense research. New concepts allowing efficient manipulation of these objects at the nanoscale, fuel unrelenting interest in this topic. Owing to the relatively weak co...
2,121,713,845,822
arxiv
\section{Introduction} Radiative recombination of carriers is a major loss mechanism in many semiconductors. Long carrier lifetimes are desirable for collection of carriers in charge transport devices and for the observation of excited-state physics in general. In most solid-state materials, the radiative recombinatio...
2,121,713,845,823
arxiv
\section{Basic notions} \label{sec: introduction} This section pedagogically introduces the concept of compact Wannier states, and serves as a basis for all further derivations. \subsection{Real space construction} We begin by constructing compact trial states for an obstructed atomic insulator (OAI) in real space. T...
2,121,713,845,824
arxiv
\section{Introduction} Let $\mathbb{k}^n(\mathbb{C})$ be the complex projective space of dimension $n$ endowed with its Fubini-Study metric. For $q=0,1,\ldots,n$, we denote by $\zeta_q$ the zeta function of the Laplace operator $\Delta_q$ associated to the Fubini-Study metric and acting on $A^{0,q}(\mathbb{k}^n(\...
2,121,713,845,825
arxiv
\section{Introduction} Channel estimation plays a critical role in future mobile communications systems, e.g., \cite{RuPeLaLaMaEdTu13,ArDeAxMo14,SaRa16}. The \ac{mse} minimizing channel estimator is known as \ac{cme}. Computing the \ac{cme} in closed form requires analytic knowledge of the channel \ac{pdf}. Even if t...
2,121,713,845,826
arxiv
\section{Introduction} \label{Introduction} People are likely to have an increasing difficulty in finding their favorite content effectively since extensive collections of video, audio, papers, art, etc. have been created both online and offline. For example, over hundreds of feature films and hundreds of thousands of...
2,121,713,845,827
arxiv
\section{Introduction} Parkinson's disease (PD) is one of the most widespread and most disabling neurodegenerative disorders; it adversely affects the structure and functions of brain areas resulting in a gradual cognitive, behavioral, and functional decline~\citep{ascherio2016epidemiology}. At present, there is no cur...
2,121,713,845,828
arxiv
\section{Introduction} Rationality of varieties of connected linear algebraic groups has been a topic of great interest. It is well known that in characteristic $0$ every such group variety is rational over the algebraic closure of its field of definition. However, rationality over the field of definition itself is a ...
2,121,713,845,829
arxiv
\section{Introduction} Maintaining cerebral blood flow is critical for adequate neuronal function \cite{Girouard2006,Iadecola2004}. Previous computational models of brain capillary networks have predicted that heterogeneous cerebral capillary flow patterns result in lower brain tissue partial oxygen pressures \cite{Je...
2,121,713,845,830
arxiv
\section{Introduction} Massive MIMO is currently drawing a lot of interest from both, academia and industry, due to the promise of full multiplexing gains with simple linear signal processing methods~\cite{rusek_scaling_2013}. This gain, it seems, is limited by the dimensionality bottleneck imposed by the fixed coher...
2,121,713,845,831
arxiv
\section{Introduction} Robustness is a key requirement when designing machine learning models and comes in various forms such as robustness to training set corruptions, missing feature values, and model misspecification In recent years, requiring robustness to {\em adversarial} or {\em test time} perturbations has b...
2,121,713,845,832
arxiv
\subsection{Few-Shot Learning} \label{rel_work:cls} Learning algorithms in few-shot learning can be divided broadly into two categories : \emph{Metric Learning} and \emph{Meta-Learning}. Metric learners \cite{matching-net, protonet, relation-net} learn generalizable feature representations from few-shot data, wh...
2,121,713,845,833
arxiv
\section{Introduction} Lattice Quantum Chromodynamics (QCD) provides a well-defined framework to directly calculate hadron form factors from the fundamental theory of strong interactions. Form factors characterize the internal structure of hadrons, including their magnetic moment, their size, and their charge density...
2,121,713,845,834
arxiv
\section{Introduction} Selling a single item to potential buyers is a popular problem in microeconomics, with amazing related discoveries during the last sixty years. In the most standard model, there are $n$ potential buyers (the agents), with private values for the item. The celebrated Vickrey auction~\cite{V61} is o...
2,121,713,845,835
arxiv
\part{Introduction, motivation and summary of the main results}\label{sec:part1} \section{Introduction}\label{sec:introduction} This work is concerned with the rigorous mathematical analysis of gravitational waves near infinity. In particular, it contains various dynamical constructions of physically motivated example ...
2,121,713,845,836
arxiv
\section{Introduction}\label{s:intro} In this fifth paper in the series of the discovery of isotopes, the discovery of the krypton isotopes is discussed. Previously, the discovery of cerium \cite{Gin09}, arsenic \cite{Sho09}, gold \cite{Sch09}, and tungsten \cite{Fri09} isotopes was discussed. The purpose of this seri...
2,121,713,845,837
arxiv
\section{The ALICE Collaboration} \begingroup \small \begin{flushleft} S.~Acharya\Irefn{org141}\And D.~Adamov\'{a}\Irefn{org95}\And A.~Adler\Irefn{org74}\And J.~Adolfsson\Irefn{org81}\And M.M.~Aggarwal\Irefn{org100}\And S.~Agha\Irefn{org14}\And G.~Aglieri Rinella\Irefn{org34}\And M.~Agnello\Irefn{org30}\And N.~...
2,121,713,845,838
arxiv
\section{Introduction} There are different ways to describe a permutation $\alpha: A\longrightarrow A$ of a set $A$ with $n$ elements, see for example the section "Permutation Statistics" in Stanley's book \cite{stanly}. First we "coordinatise" the set $A$ fixing a bijection $\beta: A\longrightarrow [n]=\{1,2,\ldo...
2,121,713,845,839
arxiv
\section{Introduction} \label{sec:intro} Federated Learning, first proposed in \citep{mcmahan2017communication}, has gradually evolved into a standard approach for large-scale machine learning \citep{kairouz2019advances,li2020federated}. In contrast to traditional machine learning paradigms which train a model on a pre...
2,121,713,845,840
arxiv
\section{Introduction} Evidence for a dark matter component of the Universe has been gathered over a broad range of physical scales in the past decades~\cite{Jungman:1995df,Bergstrom00}.~In the paradigm of Weakly Interacting Massive Particles (WIMPs) as a dark matter candidate, WIMPs are expected to interact with nucle...