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541,165,882,656
arxiv
\section{Introduction} In \cite{Zilber05peACF0}, the second author introducted a class of exponential fields he called \emph{pseudo-exponential fields}, as the class of models $\tuple{F;+,\cdot,\exp}$ of the following axioms. \begin{description} \item[1. ELA-field] $F$ is an algebraically closed field of characteris...
541,165,882,657
arxiv
\section{Introduction} Coloring the vertices or edges of a graph $G$ in order to distinguish neighboring objects is fundamental to graph theory. While typical coloring problems color the same objects that they aim to distinguish, it is natural to consider how edge-colorings can distinguish neighboring vertices. For an...
541,165,882,658
arxiv
\section{Introduction} Direct reciprocity is a fundamental mechanism to promote the evolution of cooperation \cite{nowak2006five,barfuss2020caring,hilbe2017memory,su2019evolutionary,li2020evolution,nowak2004emergence,wu2017coevolutionary,wu2018coevolutionary,van2012emergence,akccay2018collapse,pinheiro2014evolution}. R...
541,165,882,659
arxiv
\section*{Acknowledgments} The authors acknowledge the law students Michael Rasmussen and Martyna Glaz at Fordham University who worked as annotators to make the development of this corpus possible. This work was supported in part by National Science Foundation Grant OAC 1920462. Any opinions, findings, conclusions, or...
541,165,882,660
arxiv
\section{Introduction} Out-of-distribution (OOD) detection \cite{Yang2021GeneralizedOD}, i.e. identifying data samples that do not belong to the training distribution, is a task that is receiving an increasing amount of attention in the domain of deep learning \citep{Liang2018EnhancingTR,Liu2020EnergybasedOD,Du2022VOSL...
541,165,882,661
arxiv
\section{Introduction} \label{section:introduction} \IEEEPARstart{R}{obust} control methods for systems with unknown disturbances must take into account worst-case disturbance bounds in order to guarantee satisfaction of hard constraints on system states and control inputs~\cite{Mayne2000auto}. However, for problems wi...
541,165,882,662
arxiv
\section{INTRODUCTION} A precise determination of Cabibbo Kobayashi Maskawa (CKM) matrix elements \cite{ckm} is the most important goal of the forthcoming $B$-factories \cite{B-fact}, CLEO-III, KEK-B, SLAC-B, HERA-B, LHC-B. Their precise values are urgently needed for analyzing CP-violation and for testing the Standar...
541,165,882,663
arxiv
\section{Introduction} Wireless data traffic is predicted to continue its exponential growth in the coming years, mainly driven by the proliferation of mobile devices with increased processing and display capabilities, and the explosion of available online contents. Current wireless architecture is widely acknowledged ...
541,165,882,664
arxiv
\section{Introduction} \label{sec:Intro1} Modern condensed matter physics have stemmed from translational symmetry analysis, which determines the transport properties of waves according to the band structure, following the Bloch theorem, which is applicable to any periodic system. Thus, bandgaps related to the period...
541,165,882,665
arxiv
\section{Introduction} For over forty years the study of black hole thermodynamics has remained an active field of inquiry. Of particular interest are the thermodynamics of Anti de Sitter (AdS) black holes which, through proposed gauge/gravity dualities, represent the holographic duals of strongly coupled conformal f...
541,165,882,666
arxiv
\section{Introduction} \label{intro} Molecular clouds in their vast complexity hold the key to understanding the early stages of the star formation process. Magnetic fields and turbulence are the two main mechanisms that dictate the structural, dynamical and evolutionary properties of these clouds, through their com...
541,165,882,667
arxiv
\section{Introduction}\label{sec:intro} \begin{comment} Exponential families are important subjects of study in the field of information geometry and are often used for Bayes inference because they have conjugate priors, which have been well studied \cite{diaconis-ylvisoker}. By definition, there are infinitely...
541,165,882,668
arxiv
\section{Introduction} Solar system comets are currently stored in two main reservoirs, namely the Oort Cloud and the Kuiper Belt, having different dynamical histories and physical properties. The bodies contained in these reservoirs can be scattered to the inner solar system by various gravitational processes. The Sc...
541,165,882,669
arxiv
\section{Introduction}\label{sec:intro} All graphs in this paper are simple and undirected. We wish to prove a theorem analogous to the following theorems. (For missing definitions in the following, please refer to the referenced papers.) \begin{description} \item[Ramsey's theorem] \itshape \raggedright Every suff...
541,165,882,670
arxiv
\section{Introduction} Asymptotic freedom~\cite{Gross:1973id,Politzer:1973fx} is one of the signatures of non-Abelian gauge theories. At short distances, the coupling is small and perturbation theory can be successfully used to compute observables. By dimensional transmutation, a scale is generated (of mass dimension 1...
541,165,882,671
arxiv
\section{Introduction} \label{sec:intro} The rank statistic tests play an important role in univariate non-parametric statistics. If one attempts to generalize the rank tests to the multivariate case, the problem of defining a multivariate order statistic will occur. It is not clear how to define a multivariate order o...
541,165,882,672
arxiv
\section{Introduction} \hspace{0.5cm} The recent interest in pentaquark baryons has been inspired by the experimental discovery of $\Theta^+(1540)$ whose quark composition is $uudd\bar{s}$. We will not address the experimental situation. It is summarized by T. Nakano in his plenary talk during this conference~\ci...
541,165,882,673
arxiv
\section{Introduction}\label{sec:intro} The light scalar mesons, $\sigma(600)$, $\kappa(800)$, $f_0(980)$ and $a_0(980)$, have been intensively discussed for many years~\cite{Amsler:2004ps,Bugg:2004xu,Klempt:2007cp}. However, their nature is still not fully understood~\cite{Caprini:2005zr,Hatsuda:1994pi,Oller:1997ti,...
541,165,882,674
arxiv
\section[Intuition]{Intuition} Quantum Computing is a fascinating new field at the intersection of computer science, mathematics and physics. This field studies how to harness some of the strange aspects of quantum physics for use in computer science. Many of the texts to this field require knowledge of a large cor...
541,165,882,675
arxiv
\section{Language networks: applications} \label{sec:app} Complex networks have been used to model a wide range of applications~\cite{battiston2020networks}. Particularly, this model have been used also to analyze and classify texts. From the theoretical perspective, complex networks have been used to analyze many asp...
541,165,882,676
arxiv
\section{Introduction}\label{sec:a} A heavy quarkonium, or any other hadronic state, immersed into Quark-Gluon Plasma (QGP) dissociates as a result of the Debye screening \cite{Matsui:1986dk,Mocsy:2013syh} and induction of the imaginary part of the potential \cite{Digal:2001ue,Wong:2004zr,Mocsy:2005qw,Alberico:2006vw,...
541,165,882,677
arxiv
\section{Introduction} Quantum systems can feature non-classical correlations which have become an intrinsic part of quantum physics \cite{Einstein1935}. In particular, entanglement has been a subject of intensive research \cite{Horodecki1996,Horodecki2009}. In general, a multipartite system is entangled if it cannot ...
541,165,882,678
arxiv
\section{Introduction} The filtering of hidden processes from noisy observations is an important and routine problem arising in many applications. The basic problem is to derive an optimal online estimator for an unobserved `signal' process $X$ evolving randomly in time, from observations of another process $Y$ whos...
541,165,882,679
arxiv
\section{Introduction} With the massive data readily available in the digital and information era, advanced statistical learning methodologies for analysis of big data are in high demand. Traditional statistical methods are often used to discover the general rule of the population. However, in many applications we are...
541,165,882,680
arxiv
\section{Introduction} The emergence of ride-hailing platforms, led by companies such as DiDi, Uber, and Lyft, has revolutionized the way that personal mobility needs are met. As urban populations continue to grow in world's largest markets \cite{chinastats2019,michigan2019mod}, the current modes of transportation are ...
541,165,882,681
arxiv
\section{Introduction} Individuals' spatial organisation plays a central role in the formation and stability of ecosystems \cite{ecology}. Researchers have shown that three strains of bacteria \textit{Escherichia coli} - whose cyclic dominance is described by the rock-paper-scissors game rules - survive only if the int...
541,165,882,682
arxiv
\section{Introduction} Modern remote sensing techniques allow recording enormous amounts of spatial data, including geographical, natural resources, land use, and environmental remote sensing images, which need efficient (preferably real-time) processing~\cite{Rossi94,Foster08}. Such processing involves the reconstru...
541,165,882,683
arxiv
\section{Introduction} A cognitive model is a computational model of human learning and problem-solving which can be used to predict human behavior and performance on the modeled problems. In this paper, we consider cognitive models in the context of intelligent tutoring systems. A cognitive model that matches student ...
541,165,882,684
arxiv
\section{Introduction}\label{sec:intro} At least ninety countries around the world implement Freedom of Information (FOI) acts, i.e. laws that state that information that is produced by the governments or public bodies must be made available, or \textit{opened}, to the public~\citep{peled2010constitutional}, for exampl...
541,165,882,685
arxiv
\section{Using multiple models}
541,165,882,686
arxiv
\section{Introduction} The demand for higher rates already exceeds today the supply of rates and thus resulting in a spectrum deficit. This is mainly due to an exclusive bandwidth allocation to each user. Hence, each user communicates over its own bandwidth without neither causing interference to other users ...
541,165,882,687
arxiv
\section{Precise Performance Analysis}\label{pr_analysis} \subsection{Technical Assumptions}\label{ass_not} The asymptotic predictions derived in this paper are based on the following technical assumptions. \begin{enumerate}[label=\text{A.\arabic*}] \item \label{itm:data_Gauss} The data vectors $\lbrace \va_i \rbrace_...
541,165,882,688
arxiv
\section{Introduction} Progress in fundamental physics is dependent on the identification of underlying symmetries such as general coordinate invariance or gauge invariance. The gauge symmetries appearing in the highly successful Standard Model (SM) of particles and interactions is based on Cartan-Lie Algebras a...
541,165,882,689
arxiv
\section*{Introduction} \setcounter{equation}{0} \renewcommandA.\arabic{equation}{0.\arabic{equation}} \medskip Let $\{\,v^{(i)}\,,\,i=1,\ldots ,n\,\}$ be a "barycentric basis" in a Cartan subalgebra ${\frak h} \subset sl(n)\,.\,$ Viewed as operators in the $n$-dimensional complex space $V = {\Bbb C}^n\,,\, v^{(i)}\,...
541,165,882,690
arxiv
\section{Introduction} The simulation of high-frequency electromagnetic problems is often carried out in frequency domain. This choice is motivated by the linearity of the underlying governing equations and an implicit assumption that the source signal can be decomposed in the Fourier basis. However, the solution o...
541,165,882,691
arxiv
\section{Introduction} \label{intro} Keyphrase extraction is concerned with automatically extracting a set of representative phrases from a document that concisely summarize its content \citep{hasan+ng2014}. There exist both supervised and unsupervised keyphrase extraction methods. Unsupervised methods are popular ...
541,165,882,692
arxiv
\section{Introduction} Recommender systems (RSs) are now widely employed in various web services such as online shopping, video-on-demand, and even web APIs \cite{Qi2020a} to increase sales or improve user experience. The dominant paradigm of RSs is collaborative filtering (CF) that suggests relevant items to users acc...
541,165,882,693
arxiv
\section{Introduction} \label{sec:introduction} The development of better information retrieval systems is driven by how improvements are measured. The design of test collections and evaluation metrics that started with the Cranfield paradigm in the early 1960s allowed researchers to analyze the quality of different r...
541,165,882,694
arxiv
\section{Introduction} \par Starting from the works of Gaspard and Rice \cite{gaspard}, chaotic scattering was found to be ubiquitous. A large amount of work has been done on potential scattering ({\it i.e.} scattering of an elementary particle on fixed potential centers) \cite{bleher,bleher2,troll,brandis}, but a...
541,165,882,695
arxiv
\section{Introduction} Gravitating equilibrium structures must satisfy the Jeans equations, however these are generally difficult to solve - especially for multi-component or flattened systems. One of the main difficulties is that there is no clear connection between the density and the components of the velocity d...
541,165,882,696
arxiv
\section{Introduction} Learning-based controllers are becoming increasingly relevant for robotics applications \cite{Scholkopf2007, Gillula2012, Fisac2019, Rana2021}. As a result, a steady increase in methods that allow a system to safely learn its dynamics has been noticed. Such methods provide safety guarantees while...
541,165,882,697
arxiv
\section{Introduction} \label{section:introduction} Classification is a simple but important task that has numerous applications in a variety of domains such as computer vision or security. A traditional assumption that is used in the design of classification algorithms is that the input data is generated without kno...
541,165,882,698
arxiv
\section{Introduction}\label{sec:Intro} \noindent The Circular Law states that the empirical spectral distribution of a non-Hermitian random matrix with i.i.d.\ entries converges to the uniform distribution on the complex disc as the size of the matrix tends to infinity. Interestingly, for the product of $m$ independen...
541,165,882,699
arxiv
\section{Introduction\label{sec:Introduction}} \Ac{MIMO} systems represent a key technology in wireless communications, as they can substantially improve both the reliability and the data rate \cite{goldsmith2005wireless}. For a \ac{MIMO} system with channel state information available at the transmitter, the pre...
541,165,882,700
arxiv
\section{INTRODUCTION} The study of hydrogen interaction with metals has gained an increased interest in the last decade~\cite{Okamoto,Poulain,Bartczak,Khanna,Musaev,Mainardi,Kumar}. The use of metal and semiconductor clusters as components of nanodevices, the development of cluster-based materials and the catalytic p...
541,165,882,701
arxiv
\section{Introduction} The definition of the adjoint of a closed graph linear operator, not necessarily having dense domain of definition, encounters the uninviting observation that it is multi-valued. A natural way to circumvent this obstacle is to accept multi-valued operators whose graph is simply a linear subspace....
541,165,882,702
arxiv
\section{ Introduction } Spatially localized topological configurations in nonlinear field theories are solutions with localized energy density that attain topological profile and propagate freely in time without loosing form. Solitons, for instance, maintain their form even after scattering, but there are other loca...
541,165,882,703
arxiv
\section{Introduction}\label{I} \noindent Loop Quantum Gravity (LQG) \cite{Ashtekar:2004eh,Rovelli:2004tv,Thiemann:2007zz} is an attempt of background independent quantization of Einsteinian gravity. The theory cast in the first order formalism may be reshuffled --- in the original proposal by Ashtekar --- in terms of...
541,165,882,704
arxiv
\section{Introduction}\label{SecIntroduction} Experimental and empirical studies suggest that decision makers often behave in a time-inconsistent manner, with individuals acting impatiently in the current moment whilst planning to act patiently in the future\footnote{In economics, \cite{str1955} first observed that non...
541,165,882,705
arxiv
\section{Introduction} Unmanned aerial vehicles (UAVs), also known as drones, have become prevalent in recent years and are getting integrated into the daily operations across industries. Reliable and long-range connectivity with ground pilots through wireless communications is of great importance to provide stable ...
541,165,882,706
arxiv
\section{Introduction} The light gravitino is one of the most motivated candidate of dark matter in the supersymmetric theories, since the gravitino is the unique and the inevitable prediction of supergravity. If the gravitino were in the thermal bath in early universe the observed dark matter density, $\Omega...
541,165,882,707
arxiv
\section{Introduction} The phenomenon of ``sub-pulse drifting'', i.e., the systematic variation in position and intensity of sub-pulses, was noticed \citep{DC68} soon after the discovery of pulsars. Ruderman \& Sutherland (1975; hereafter R\&S) suggested this regular modulation to be a manifestation of a carousel of ``...
541,165,882,708
arxiv
\section{Introduction}\label{sec:introduction} In the field of solving Partial Differential Equations (PDEs), methods can be generally divided into (semi-)analytical methods and numerical methods. Analytical methods include the method of separation of variables \cite{churchill1963fourier}, integral transforms \cite{ba...
541,165,882,709
arxiv
\section{Experimental methods} \label{sec_methods} \subsection{Setup} \label{sec_setup} \subsubsection{Sample} \label{sec_sample} The heterostructure of the wafer used in this work, which has been used in previous studies \cite{Stockill2016, Ethier-Majcher2017, Huthmacher2018, Bodey2019, Gangloff2020}, is depicted sch...
541,165,882,710
arxiv
\section{Introduction.} Since its discovery, in 1980, the quantum Hall (QH) effect \cite{Klitzing} has been a very rich source of interesting problems related to topological and correlation effects in condensed matter systems. The QH effect is observed in two-dimensional electron gases\cite{Datta} (2DEG) exposed to ...
541,165,882,711
arxiv
\section{Introduction} The first set of data (OPERA-1), released on 23 September 2011 by OPERA team, suggested that the muon neutrino could propagate at a speed $v$ larger than of light \cite{opera}. In OPERA experiment, the energetic muonic neutrinos ($\nu_\mu$), mainly produced in the decay, $\pi^{(\pm)} \rightarrow...
541,165,882,712
arxiv
\section{Introduction} \label{sec:introduction} In many situations, phases of many-body quantum systems are stable under weak static, or ``quenched,'' disorder in the presence of a gap, and the disorder average of certain quantities can be calculated in a related clean system via either the replica trick or supersymm...
541,165,882,713
arxiv
\section*{Abstract} For high-dimensional classification Fishers rule performs poorly due to noise from estimation of the covariance matrix. \cite{Fan} introduced the ROAD classifier that puts an $L_1$-constraint on the classification vector. In their Theorem 1 \cite{Fan} show that the ROAD classifier asymptoticall...
541,165,882,714
arxiv
\section{Introduction} Consider the general nonlinear integer minimization problem in standard form, \begin{equation}\label{NIM} \min\,\left\{f(x)\ :\ x\in\Z^n\,,\ Ax=b\,,\ l\leq x\leq u\right\}, \end{equation} with $A\in\Z^{m\times n}$, $b\in\Z^m$, $l,u\in\Z_{\infty}^n$ with $\Z_{\infty}:=\Z\uplus\{\pm\infty\...
541,165,882,715
arxiv
\section{Introduction} Let $\mathcal{D}$ be a dyadic lattice. Recall that a collection $\mathcal{S}$ of cubes in $\mathcal{D}$ is said to be sparse if the following holds, uniformly over $P\in\mathcal{D}$: $\abs{\cup_{Q\in\mathcal{S}:S\subset P}Q} \leq \frac{1}{2}\abs{P}$. This implies that the following holds, unifo...
541,165,882,716
arxiv
\section{Modularity as intrinsic disentanglement} \begin{figure} \newcommand{.65}{.65} \centering \begin{subfigure}{.26\textwidth} \input{comDiagDisent} \vspace*{-.3cm} \subcaption{\label{fig:commDiag}} \end{subfigure} \hfill \begin{subfigure}{.23\textwidth} \begin{tikzpicture} \GraphInit[vstyle=Normal] ...
541,165,882,717
arxiv
\section{Introduction } \begin{figure}[t] \centering \includegraphics[width=0.5\textwidth]{images/Drosophila_sketch.pdf} \caption{ Mechanics and growth arrest of the \textit{Drosophila} wing disc. (\textbf{A}) Sketch of \textit{Drosophila} wing disc. The center of the pouch (dashed region) is in compression, the re...
541,165,882,718
arxiv
\section{Introduction} With the proliferation of mobile devices, an increasing amount of population data is being collected, and there is a growing demand for their use. Currently, we can quickly find out how many people are staying in Tokyo, Japan, at any given time or place. These data can be useful in a wide range ...
541,165,882,719
arxiv
\section{Introduction} \begin{figure}[tb] \centering \includegraphics[width=\textwidth]{figs/NA61_setup.pdf} \caption[]{% Schematic layout of the NA61\slash SHINE\xspace detector system~\capcite{bib:NA61_facility} (horizontal cut in the beam plane, not to scale). Also outlined are the coordinate syste...
541,165,882,720
arxiv
\section{Introduction}\label{sec:intro} \subsection*{Formulation of the problem and presentation of results} By \emph{densities} we understand non-negative, non-zero functions $f \in L^1(\R^d)$, $d \geq 1$ (we assume that $\R^d$ is equipped with the Lebesgue measure). The $n$-fold convolution of a density $f$ is ...
541,165,882,721
arxiv
\section{Introduction} The discovery of superconductivity in the iron-based pnictides \cite{Kamihara08} provided a new class of compounds to the high temperature superconductor (HTS) family. Three main groups of these iron-based superconductors are intensively studied: the $R$FeAsO compounds with $R$ = La-Gd ('1111'),...
541,165,882,722
arxiv
\section{Introduction} \label{sec:intro} The clustering of galaxies provides a window not only to the formation of inhomogeneities in the early universe but also onto the physics of galaxy formation. Galaxies with different properties cluster differently \citep{hubble36,zwicky68,davis76,dressler80,postman84,hamilton8...
541,165,882,723
arxiv
\section{Introduction} An open Riemann surface $X$ is said to be (potential-theoretically) hyperbolic if it admits a non-constant negative subharmonic function, and parabolic if it does not. Consider the on-diagonal Bergman kernel $K(z)|dz|^2$, the logarithmic capacity $c_{\beta}(z)|dz|$, and the analytic capacity...
541,165,882,724
arxiv
\section{Introduction} A domain in $\CC^n$ is a connected open set. If $\Omega$ is a domain, then we let $\hbox{Aut}\, (\Omega)$ denote the group (under the binary operation of composition of mappings) of biholomorphic self-maps of $\Omega$. When $\Omega$ is a bounded domain, $\hbox{Aut}\, (\Omega)$ is a real ...
541,165,882,725
arxiv
\section{Introduction} 1SWASP~J024743.37$-$251549.2 (WASP\,0247$-$25 hereafter) is one of several million bright stars ($8\la V \la 13$) that have been observed by the Wide Angle Search for Planets, (WASP, \citealt{2006PASP..118.1407P}). \citet{2011MNRAS.418.1156M} showed that this eclipsing binary star contains ...
541,165,882,726
arxiv
\section{Introduction} Quantum gravity is changing everything we know about space and time by defying intuitive notions we have about them. It has the potential of becoming one of the strongest theories defining the physical relations, matter and cosmology by combining quantum mechanics and general relativity. ...
541,165,882,727
arxiv
\section{Introduction} Hole-doped perovskite manganites $R_{1-x}A_x$MnO$_3$, where $R$ is a rare-earth ($R=$ La, Nd, Pr) and $A$ is an alkaline-earth atom ($A=$ Sr, Ba, Ca) have attracted much attention because they exhibit remarkable physical properties such as colossal magnetoresistance and complex elect...
541,165,882,728
arxiv
\section{Introduction} \label{sec:intro} Pixel-wise labeling is labor-intensive \cite{cordts2016cityscapes}. Lots of research have been dedicated to supervising a semantic segmentation model with weaker forms of supervision than pixel-wise labelings, such as scribbles~\cite{tang2018normalized}, points~\cite{b...
541,165,882,729
arxiv
\section{Introduction} Knowledge graphs (KGs) provide a structured and transparent form of information representation and lie at the core of popular Semantic Web technologies. They are utilized as a source of truth in a variety of downstream tasks (e.g., information extraction~\cite{DBLP:journals/semweb/Martinez-Rodri...
541,165,882,730
arxiv
\section{Introduction}\label{s:introduction} The rise in the importance of the web browser in modern society has been accompanied by an increase in the sensitivity of the information the browser processes. Consequently, browsers have become targets of attacks aiming to extract or gain control of users' private informa...
541,165,882,731
arxiv
\section{Introduction} \label{intro} Recent gravitational waves detection confirms the existence of binary black holes systems. Actually because of the enormous emission of gravitational radiation provided by the interaction of black hole pairs, this will be the most abundant and relevant source of gravitational wav...
541,165,882,732
arxiv
\section{Introduction}\label{S1} In the context of AdS/CFT \cite {Maldacena:1997re, Witten:1998qj}, the thermofield double (TFD) state plays a crucial role in exploring the intriguing connection between black hole physics and quantum information theory. The holographic dual of TFD state turns out to be essential to di...
541,165,882,733
arxiv
\section{Introduction} Game Theory (GT) has become an important analytical tool in solving Machine Learning (ML) problems; the idea of "gamification" has become popular in recent years \cite{wellman2006methods, lanctot2017unified} particularly in multi-agent systems research. Despite the importance of risk-aversion i...
541,165,882,734
arxiv
\section{Relationship between drainage and penetration depth}\label{appendA} The ordinary differential equation (ODE) for 1D flow problem using the Darcy flow model with a drainage term can be written as: \begin{equation}\label{append:eq1} K(\rho_e)\der{\,^2p}{s^2} = pH(\rho_e), \end{equation} where $K$, $p$, and $H$ a...
541,165,882,735
arxiv
\section{Introduction} A numerical approach based upon the split-operator method and the fast Fourier transform (SO-FFT) is widely used for the solution of equations of the form of time-dependent Schr\"odinger equation (TDSE). Such equations commonly appear in the consideration of the wide range of problems of a quan...
541,165,882,736
arxiv
\section{\label{sec:level1}Introduction} Although many types of chaos continue to evade analytic solutions, the assumption that no solvable chaotic dynamics exist has been broken by the discovery of hybrid (consisting of interdependent continuous time and discrete time states) chaotic systems that exhibit exact solutio...
541,165,882,737
arxiv
\section{Introduction} We are concerned with mesh sensitivity for the finite element (FE) solution of linear elliptic boundary value problems (BVPs). The finite element method is a well developed method that is widely used in scientific and engineering computation and has been studied extensively in the numerical anal...
541,165,882,738
arxiv
\section{Introduction} The stochastic Hamiltonian system is an important model of degenerate diffusion system, which has been investigated in \cite{GW,W2,WZ1,WZ,Z1}. In this paper we aim to study functional version of this model (see \cite{BWY}) in infinite dimension. Recently, Zvonkin type transforms have been used t...
541,165,882,739
arxiv
\section*{Introduction} Fluid mechanics and infinite dimensional geometry already share a long and common history. In 1966, Arnold \cite{Arnold} suggested to regard the space of velocity fields of an incompressible fluid as the Lie algebra of the infinite dimensional Lie group of volume preserving diffeomorphisms ...
541,165,882,740
arxiv
\section{Introduction} Gamma-ray bursts \citep[GRBs,][]{1973ApJ...182L..85K} are the most violent explosions in the Universe. They are characterized by a short flash of gamma-ray photons followed by a long lasting afterglow that can be observed at all wavelengths. They can be classified into two types based on the dur...
541,165,882,741
arxiv
\section{Introduction} The significance of solving a linear system of equations arises in a variety of areas, such as Numerical Analysis, Economics, Computational Biology, and even in high school education. Solving a linear system of equations is undoubtedly one of the most practical problems in numerous aspects of sc...
541,165,882,742
arxiv
\section{\label{sec:intro}Introduction} A combined quantum mechanical/molecular mechanical (QM/MM) method is a powerful computational tool for studying chemical reactions in solution and in biological systems.\cite{Warshel_Book,Cramer_Book} It treats a chemically active part of the entire system with accurate QM meth...
541,165,882,743
arxiv
\section{INTRODUCTION} The mechanism of color confinement is still one of the unsolved and challenging problems in particle physics. It is hard because it is a nonperturbative phenomenon and must be solved by nonperturbative techniques. Lattice gauge theory, as a numerical method, has been successful in predicting po...
541,165,882,744
arxiv
\section{Introduction} \label{s.intro} \paragraph{1. Cadre} Soit $X$ une marche au hasard en environnement al\'eatoire sur la droite $\mathbb{Z}$ des entiers. Ainsi, $(E,{\cal E}, m)$ est un espace de probabilit\'e, $S:E\to E$ une bijection bime\-surable qui pr\'eserve $m$, et $p:E\to(0,1)$ une application mesurable. ...
541,165,882,745
arxiv
\section{Introduction} \label{sec:1} A chemical reaction network (CRN) is a finite set of reactions. It is a directed graph with reactant or product complexes as vertices, and reactions as arcs. A reaction vector of a reaction is the difference between the product and the reactant complexes. In addition, the stoichiome...
541,165,882,746
arxiv
\section{Introduction} \label{sec1} The Lugiato-Lefever equation is given by \cite{lugi87} \begin{equation} \mathrm{i} A_{\tau} = - A_{\xi\xi} - \frac{\mathrm{i}\alpha}{2} A - \frac{3\lambda}{2\omega} |A|^2 A + F,\quad \xi\in\mathbb{R},\,\tau\geq0, \label{NLSeq} \end{equation} which is nothing else but a damp...
541,165,882,747
arxiv
\section{Introduction} Due to the Internet of Things and Industry 4.0 trends in both consumer electronics and industrial applications, an increasing number of devices are wirelessly connected. Currently, most of these devices operate in the unlicensed 2.4\,GHz \ac{ISM} band, and each new one is an additional competit...
541,165,882,748
arxiv
\section{Introduction} \label{sec:intro} The diversity in the internal structure of halos, such as those that host galaxy clusters, is not only a function of the fundamental physics -- nature of dark energy models, the sum of neutrino masses, non-Gaussian primordial fluctuations, the nature of gravity, and astrophysics...
541,165,882,749
arxiv
\section{Introduction} The questions \emph{``What is a proof?''} and \emph{``When are two proofs the same?''} are fundamental for proof theory. But for the most prominent logic, Boolean (or classical) propositional logic, we still have no satisfactory answers. This is not only embarrassing for proof theory itself, bu...
541,165,882,750
arxiv
\section{Introduction} \mlabel{sec:1} One of the core ideas of quantum theory is that the states of a quantum system correspond to one-dimensional subspaces of a complex Hilbert space~$\mathcal{H}$, i.e., the elements $[v] = {\mathbb C} v$, $v \not=0$, of its projective space ${\mathbb P}(\mathcal{H})$. This set...
541,165,882,751
arxiv
\section*{Abstract} We seek models for the genotype evolution of agricultural animals, animals involved in primary production processes. Classical models for genotype evolution have tended to be very simple in order that analytic methods may be employed in their study. Unfortunately these models fail to describe p...
541,165,882,752
arxiv
\section{Introduction} \subsection{Background} The run-time of many important algorithms in mathematics and computer science depend on how ``sparse'' the input data is. One such example is Lanczsos's algorithm \cite{Lan50} which can be used to compute a set of eigenvalues and eigenvectors of a matrix of size $n$ in $...
541,165,882,753
arxiv
\section{Introduction} Black holes are stationary vacuum solutions of Einstein's field equations. Despite the simplicity of these solutions, rotating black holes which are described by the Kerr metric appear to account for the numerous observations of astrophysical black holes with a remarkable accuracy. Furthermore, i...
541,165,882,754
arxiv
\section{Introduction} The variance-gamma (VG) distribution with parameters $r > 0$, $\theta \in \mathbb{R}$, $\sigma >0$, $\mu \in \mathbb{R}$ has probability density function \begin{equation}\label{vgdefn}p(x) = \frac{1}{\sigma\sqrt{\pi} \Gamma(\frac{r}{2})} \mathrm{e}^{\frac{\theta}{\sigma^2} (x-\mu)} \bigg(\frac{...
541,165,882,755
arxiv
\section{Introduction}Topological field theories were introduced by Schwarz \cite{Schwarz}, who related the Ray-Singer torsion to the partition function of a quantum field theory, and Witten \cite{Witten}, who introduced the so-called ``Witten index" and opened up a wide range of research lines in mathematics and physi...