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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... |
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