arxiv_id stringlengths 0 16 | text stringlengths 10 1.65M |
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2205.15082 | \section{Introduction}
Consider a scalar, autonomous ordinary differential equation (ODE) of the form
\begin{equation}\label{eq:ode}
\begin{split}
\frac{dX}{dt}(t) &= a(X(t)) \qquad \text{for } t > 0, \\
X(0) &= 0
\end{split}
\end{equation}
where \( a\from{\mathbb R} \rightarrow {\mathbb R} \) is Borel measurab... |
2205.15013 | \section{Definitions and Basic Identities}
Let the coefficient of a power series be defined as:
\begin{equation}
[q^n] \sum_{k=0}^{\infty} a_k q^k = a_n
\end{equation}
Let $P(n)$ be the number of integer partitions of $n$, and let $P(n,m)$ be the
number of integer partitions of $n$ into exactly $m$ parts.
Let $P(n,m,... |
2205.15024 | \section{Counterexample}\label{sec:counterexample}
\begin{thm} \label{thm:mainTheorem}
Let $\textup{R}_8$ be the dihedral quandle of order $8$. Then
\begin{displaymath}
\left|\Delta^2\left(\textup{R}_8\right)/\Delta^3\left(\textup{R}_8\right)\right|= 16.
\end{displaymath}
\end{thm}
\noindent From... |
2205.15032 | \section{Introduction}
By a finite partially ordered set (poset) \(I\) of size \(n\) we mean a pair \(I=(\{1,\ldots,n\}, \preceq_I)\), where \(\preceq_I\) is a reflexive, antisymmetric and transitive binary relation. Every poset \(I\) is uniquely determined by its \textit{incidence matrix}
\[
C_{I} = [c_{ij}] \in... |
2302.11221 | \section{\protect\bigskip \textbf{Introduction}}
We know that the Mac Donald polynomials and their particular cases can be
represented as analogs with \ one or two parameters of the usual symmetric
functions. A large number of papers continue to be published on the subject
giving rise to various analogues of symmetric... |
2205.14924 | \section{Introduction}
\subsection{Background}
Denote by $ \|\cdot\| $ the distance to the nearest integer. The famous Dirichlet Theorem asserts that for any real numbers $ x\in[0,1] $ and $ N\ge 1 $, there exists a positive integer $ n $ such that
\begin{equation}\label{eq:Dirichlet's theorem}
\|nx\|<\frac{1}... |
2302.12183 | \section{Introduction}
Fractional calculus is nowadays a well consolidated field of research
with many applications in various areas of knowledge, which is interesting
and important as it presents more refined results that are in line with reality
\cite{Sousa,Sousa1,Sousa3,Sousa4,Sousa5,Oliveira,Podlubny,Kilbas,La... |
2302.12079 | \section{Introduction}
Let $C$ be a germ of complex plane curve singularity with \(r\geq 1\) branches. Campillo, Delgado and Kiyek \cite{CDKmanuscr} attached a series
\[
P_C(\underline{t})=P_C(t_1,\ldots, t_r)=\frac{\displaystyle\prod_{i=1}^r (t_i-1) \cdot\bigg(\displaystyle\sum_{\underline{w} \in \mathbb{Z}^r_{\geq... |
2302.12082 | \section{Introduction}
A random matrix is a matrix whose entries are random variables. As
eigenvalues of a matrix are continuous functions of its entries, so
the eigenvalues of a random matrix are random variables.
A random $N\times N$ matrix has the Jacobi $\beta$-Ensemble (J$\betaup$E) distribution
if a joint probab... |
2302.12062 | \section{Introduction}
The quantum dilogarithm is a $q$-series with many remarkable properties \cite{Z}, including the famous five-term identity \cite{FK}. Cluster algebra theory and wall-crossing of motivic invariants of quivers have led to vast generalizations of such dilogarithm identities \cite{K}.\\[1ex]
In th... |
2302.12153 | \section{$4$-term relations}\label{s1}
In 1990, V.~Vassiliev~\cite{V90} introduced the notion of finite type
knot invariant and associated to any knot invariant of order at most~$n$
a function on chord diagrams with~$n$ chords. He showed that any such
function satisfies $4$-term relations. In 1993, M.~Kontsevich~\cit... |
2302.12166 | \section{Introduction}
In porous media flow models in geophysical applications, the porosity of the medium is often treated as a static quantity. This assumption, however, need not always be justified due to the ability of rocks to deform by compaction.
In certain cases, the interaction of porosity and pressure can le... |
2302.13218 | \section{Introduction}
We consider the one-dimensional Schr\"{o}dinger equation with a finite number
of $\delta$-interactions
\begin{equation}
-y^{\prime\prime}+\left( q(x)+\sum_{k=1}^{N}\alpha_{k}\delta(x-x_{k})\right)
y=\lambda y,\quad0<x<b,\;\lambda\in\mathbb{C},\label{Schrwithdelta}%
\end{equation}
where $q\in L_... |
2302.13237 | \section{Introduction}
Task mapping in modern high performance parallel computers can be modeled as a graph embedding problem.
Let $G(V,E)$ be a simple and connected graph with vertex set $V(G)$ and edge set $E(G)$.
Graph embedding\cite{BCHRS1998,AS2015,ALDS2021} is an
ordered pair $<f,P_f>$ of injective mapping betwe... |
2302.13186 | \section{}
\begin{abstract}
\noindent We count the number of ways to build paths, stars, cycles, and complete graphs as a sequence of vertices and edges, where each edge follows both of its endpoints. The problem was considered 50 years ago by Stanley but the explicit sequences corresponding to graph families seem to ... |
2302.13249 | \section{Introduction}
Over the past two decades, 3d $\mathcal N=4$ mirror symmetry has attracted a lot
of attentions from both physicians and mathematicians (see, for example,
\cite{BFN,BDG,N} and references therein). It is also closely related
to the theory of \textit{symplectic duality} of Braden et al. \cite{BPW... |
2302.13260 | \section{Introduction}
\subsection{Background}
In \cite{HNY}, He-Nie-Yu studies the affine Deligne-Lusztig varieties with finite Coxeter parts. They study such types of varieties using the Deligne-Lusztig reduction method from \cite{DL76} and carefully investigating the reduction path. In the approach, they establish... |
2302.13606 | \subsubsection{}}
\def\begin{gather*}{\begin{gather*}}
\def\end{gather*}{\end{gather*}}
\def\begin{question}{\begin{question}}
\def\end{question}{\end{question}}
\def\on{rank}{\on{rank}}
\newcommand{V_{-1}}{V_{-1}}
\newcommand{V_{-2}}{V_{-2}}
\newcommand{{\stackrel{\scriptscriptstyle{1}}{\rho}}{}}{{\stackrel{\scripts... |
2302.13716 | \section{Introduction}
Consider a non-elementary hyperbolic group $\Gamma$ endowed with an invariant metric $d$, satisfying some regularity assumptions, acting by measure class preserving transformations on its Gromov boundary $(\partial \Gamma,\nu_{d})$ equipped with $\nu_{d}$ the so-called Patterson-Sullivan measur... |
2302.13708 | \section{Introduction} \label{sec:Intro}
Let $X$ be an $M\times N$ matrix; we assume that $\frac{M}{N}$ converges to a limit $\phi$ as both $M$ and $N$ tend to $\infty$ (although this may be relaxed). Let
\begin{equation}
\Sigma = VDV^*, \quad V = \begin{pmatrix} \mid & & \mid \\ \mathbf{v}_1 & \dots & \mathbf{v}... |
2302.13758 | \section{Introduction}
An important problem in modern number theory is to construct $p$-adic $L$-functions of automorphic representations, in particular due to the arithmetic applications they provide. In \cite{pollack2011}, Pollack and Stevens gave a construction of $p$-adic $L$-functions of modular forms using the t... |
2302.13588 | \section{Introduction}
\addtocontents{toc}{\protect\setcounter{tocdepth}{1}}
Let $A = \Bbbk[x_1, \cdots, x_n]$ over an algebraically closed field $\Bbbk$ of characteristic 0, and $G \subseteq \text{Aut}_{\text{gr}}(A)$ be a finite subgroup. It is natural to ask: what properties, and particularly what homological proper... |
2206.14088 | \section{Introduction}
This article considers range theorems for the Poisson transform on Riemannian symmetric spaces $Z$ in the context of horospherical complex geometry.
We assume that $Z$ is of non-compact type and let $G$ be the semisimple Lie group of isometries of $Z$. Then $Z$ is homogeneous for $G$ and ident... |
2206.14174 | \section{Introduction}
In this paper we continue our long running programme to identify (up to conjugacy) all the finitely many arithmetic lattices $\Gamma$ in the group of orientation preserving isometries of hyperbolic $3$-space $Isom^+(\mathbb H^3)\cong PSL(2,\mathbb C)$ generated by two elements of finite order $p... |
2205.03965 | \section{Introduction}
Graph Ramsey theory is currently among the most active areas in combinatorics. Two of the main parameters in the theory are Ramsey number and size Ramsey number, which are defined as follows. Given two graphs $G_1$ and $G_2$, we write $G\to (G_1,G_2)$ if for any edge colouring of $G$ such that ea... |
2205.03922 | \section*{References}}
\usepackage{lineno}
\usepackage[colorlinks,linkcolor={blue}]{hyperref}
\modulolinenumbers[5]
\usepackage{amsfonts}
\usepackage{graphicx}
\usepackage{amsmath}
\usepackage{graphicx}
\usepackage{amssymb, nicefrac}
\usepackage{mathtools}
\DeclarePairedDelimiter{\setof}{\{}{\}}
\DeclarePairedDe... |
2205.03928 | \part{title}
\usepackage{amsmath,amsthm,amssymb,amscd}
\newcommand{\mathcal E}{\mathcal E}
\newtheorem{theorem}{Theorem}[section]
\newtheorem{lemma}[theorem]{Lemma}
\newtheorem{proposition}[theorem]{Proposition}
\newtheorem{result}[theorem]{Result}
\newtheorem{corollary}[theorem]{Corollary}
\theoremstyle{definition}
\n... |
2205.02634 | \section{Introduction}
Let $G = (V,E)$ be a graph with vertex set $V$ and edge set $E$. Throughout this paper, we consider graphs without loops and directed edges.
For each vertex $v\in V$, the set $N(v)=\{u\in V | uv \in E\}$ refers to the open neighbourhood of $v$ and the set $N[v]=N(v)\cup \{v\}$ refers to the cl... |
2205.02578 | \section{Introduction}\label{Section1}
Let $G$ be a finite group, and let $\chi$ be a character of $G$. We define the field of values of $\chi$ as
$$\mathbb{Q}(\chi)=\mathbb{Q}(\chi(g)|g \in G).$$
We also define
$$f(G)=\max_{F/\mathbb{Q}}|\{\chi \in \operatorname{Irr}(G)|\mathbb{Q}(\chi)=F\}|.$$
In \cite... |
2205.14255 | \section{Introduction}
The Graph Minor Theorem of Robertson and Seymour~\cite{RS} implies that
any minor closed graph property $\mathcal{P}$ is characterized by a finite
set of obstructions. For example, planarity is
determined by $K_5$ and $K_{3,3}$ \cite{K,W} while
linkless embeddability has
seven obstructions, k... |
2302.11932 | \section{Introduction}\label{sec:intro}
For $n \ge 2$ let $\mathcal{I}_n$ denote the set of all irreducible degree $n$ polynomials in ${\mathbb F}_{2}[x]$, and let $\text{Tr}_n: {\mathbb F}_{2^n} \rightarrow {\mathbb F}_2: \alpha \mapsto \alpha + \alpha^2 + \alpha^{2^2} + \cdots + \alpha^{2^{n-1}}$ denote the absolut... |
2302.12035 | \section{Introduction}
Classical orthogonal polynomials (Hermite, Laguerre, Jacobi, and Bessel) have been characterized using different approaches. For instance, they can be characterized in terms of differential equations \cite{B29}, their derivatives (\cite{Hahn35,Krall36}), structure relations (\cite{ASC72,Ger40, ... |
2302.11964 | \section{Introduction}
Let $(M, g)$ be a smooth compact connected Riemannian manifold on dimension $n \ge 2$ with smooth boundary $\Sigma$. The Steklov problem on $(M, g)$ consists in finding the real numbers $\sigma$ and the harmonic functions $f : M \longrightarrow \mathbb{R}$ such that $\partial_\nu f=\sigma f$ on... |
2205.08453 | \subsection*{Organization}
\end{section}
\begin{section}{Preliminaries}
In this section we recall notions of sectional category and topological complexity; we refer to
\cite{BasGRT14, CohFW21, CohFW, Far03, Gar19, Rud10, Sva66} for more information.
\subsection*{Sectional category}
Let $p: E \to B$ be a Hurewi... |
2205.06223 | \section{Introduction}\label{section-introduction}
Stern's sequence $(a(n))_{n \geq 0}$, defined by the recurrence relations
$$ a(2n) = a(n), \quad a(2n+1) = a(n)+a(n+1),$$
for $n \geq 0$, and initial values $a(0) = 0$, $a(1) = 1$,
has been studied for over 150 years. It was introduced by Stern in 1858 \cite{Ste... |
2302.12947 | \section{Introduction}
In this paper, we discuss the following two (intersection) numbers defined as values of residue integrals.
\begin{defi}
\ba
&&w(\sigma_{(N-k)d+j-1}({\cal O}_{h^{N-2-j}}){\cal O}_{h^{0}})_{0,2}:=\no\\
&&\frac{1}{(2 \pi \sqrt{-1})^{d+1}} \oint_{C_{0}} \frac{dz_{0}}{(z_{0})^{N}} \oint_{C_{1}} \... |
2302.12942 | \section{Introduction}\label{s:intro}
A \emph{Latin rectangle} is an $n \times m$ matrix, with $n \leq m$, on $m$ symbols such that each symbol occurs at most once in each row and column. A \emph{Latin square} is a square Latin rectangle. Let $L$ be a Latin square with symbol set $S$. We will index the rows and colu... |
2302.12905 | \section{Introduction}
\hskip .5cm Throughout this paper, $R$ will be an associative ring with identity, and all modules will be, unless otherwise specified, unital left $R$-modules. When right $R$-modules need to be used, they will be denoted as $M_R$, while in these cases left $R$-modules will be denoted by ... |
1904.02546 | \section{Introduction}\label{s:intro}
\IEEEPARstart{F}{ortran} has a long history in scientific programming and is
still in common use today~\cite{decyk2007fortran} in application codes for
climate science \cite{e3sm}, weather forecasting \cite{um}, chemical
looping reactors \cite{mfix}, plasma physics, and other fiel... |
2203.08369 | \section{Introduction}\label{sec:Inc}
\def{\rm d} {{\rm d}}
Vaccination is critical for the prevention and control of infectious diseases, there are more than 20 life-threatening diseases could be prevented by vaccines up to now.
Vaccinators can achieve immunity by having the immune system recognize foreign substances,... |
1412.8018 | \section{introduction}\label{intro}
Stability of linear time-varying (LTV) systems has been a topic of significant interest in a wide range of disciplines including but not restricting to mathematical modeling and control of dynamical systems,~\cite{rosenbrook1963stability,1100529,1084637,Ilchmann1987157,tsakalis1993li... |
2201.03214 | \section{Introduction}
\IEEEPARstart{C}{yber}
security of multi-agent systems and distributed algorithms has become an important research area in systems control in the last decade. For multi-agent systems, consensus is one of the fundamental problems \cite{bullo2009distributed}, \cite{Lynch}.
Based on consensus ... |
1805.01300 | \section{Introduction}
Conformal field theory{~\cite{francesco_conformal_1999}} (CFT) has become the center of much interest during the past decades. Due to its powerful nature in two dimensions, it has been widely applied to study the universal behavior at the critical points of two-dimensional statistical systems an... |
1805.01212 | \section{Introduction}
The Bianchi IX Universe~\cite{Landau:1980,Misner:1973} is the most
interesting among the Bianchi models. In fact, like the Bianchi type
VIII, it is the most general allowed by the homogeneity constraint,
but unlike the former, it admits an isotropic limit, naturally reached
during its evolution ... |
2105.01469 | \section{Introduction}
We are interested in counting (or uniformly sampling) vertices of a polytope defined by linear inequalities $Ax\leq b$. In particular we concentrate on the sort of polytopes that arise in the study of computational optimisation problems: integral polytopes (convex hulls of finite subsets of $... |
2108.10794 | \section{Introduction}\label{sec:intro}
Laughlin wavefunctions
\[
\Psi_p(z_1,\dots , z_N) \propto \prod_{1\leq j < k \leq N } (z_j-z_k)^{p+2} \, \prod_{j=1}^N \exp\left( - \frac{|z_j|^2}{2\ell^2}\right) ,
\]
describe the ground-state properties of highly correlated quantum systems such as quantum Hall systems \cite{... |
2206.09150 | \section{The Complete Proof of Lemma \ref{Lemma_Complexity}}\label{Appendix_A}
\textbf{Lemma 4.7} (restated) Under event $\mathcal{E}_{0,c} \land \mathcal{E}_{1,c} \land \mathcal{E}_{2,c}$, a base arm $i$ will not be pulled if $N_i(t) \ge {98\operatornamewithlimits{width} C(t)L_2(t) \over \Delta_{i,c}^2}$.
\begin{pr... |
2301.04800 | \section{Introduction} \label{intro}
Trees of complete graphs with random edge weights are important from both theoretical and practical perspectives. For independent and identically distributed (i.i.d.) edge weights with a common cumulative distribution function (cdf)~\(F(.)\) that varies linearly close to zero,... |
2301.06009 | \section{Introduction}
Although deep neural networks have recently been contributing to state-of-the-art advances in various areas \cite{Krizhevsky:2012:ICD:2999134.2999257, hinton2012deep, DBLP:journals/corr/SutskeverVL14},
such models are often black-box, and therefore may not be deemed appropriate in situations wher... |
1904.10852 | \section{Introduction}
The study of Schubert varieties and their singularities is a field where topology, algebraic geometry, and representation theory meet. An effective strategy to study Schubert varieties is assigning characteristic classes to them. However, the most natural characteristic class, the fundamental c... |
1904.10746 | \section{Introduction and discussion}
The spontaneous breaking of supersymmetry is one of the most challenging aspects of realistic model building within String Theory and Supergravity.
The phenomenon itself,
in four-dimensional N=1 supergravity,
is well-understood and there are various models that can describe t... |
1910.07799 | \section{Introduction}
%
%
%
Label placement is an important step in map production, both manual and automatic, and it can require up to 50 percent of the total map production time for manually created maps~\cite{yoeli1972}. Imhof's 1975 statement ``Good form and placing of type make the good map. Poor, sloppy, a... |
1910.07750 | \section{Introduction}
A numbering is a surjective mapping $\gamma :\omega \rightarrow S$
from the natural numbers $\omega$ to a set $S$.
The theory of numberings was started by Ershov in a series of
papers, beginning with \cite{Ershov} and \cite{Ershov2}.
Ershov studied the computability-theoretic properti... |
2104.00385 | \section{Introduction}
\label{sec:introduction}
In the last decade, the tasks (or objects) required of robots have become steadily more complex.
For such next-generation robot control problems, traditional model-based control like~\cite{kobayashi2018unified} seems to reach its limit due to the difficulty of modeling c... |
2110.12487 | \section{Abstract}
Many quantum programs require circuits for addition, subtraction and logical operations. These circuits may be packaged within routines known as oracles. However, oracles can be tedious to code with current frameworks. To solve this problem the author developed Higher-Level Oracle Description Langua... |
2108.11640 | \section{Introduction}
When analysing mathematical models of biological systems, we often aim to reverse engineer the parameters of the model
by fitting to observed data. The Bayesian formalism provides a principled way to perform parameter inference that quantifies our uncertainty in the model parameters \citep[se... |
2204.05610 | \subsection{Appendices}
\section{Method Detail}
\subsection{Disentangler BERT Learning Detail} \label{appendix:method}
We initialize $\mathcal{F}$ with two pre-trained BERT. In the unsupervised initialization stage we only train the BERT$^{\alpha}$, then in the reinforcement learning stage, we fix the parameters of ... |
1501.03653 | \section{Introduction}
The diffusion is anomalous when the variance rises with time slower or faster than linearly and
the density distribution differs from the normal distribution.
This means that the central limit theorem is violated. One can expect that the theorem is not valid
for transport processes if memory ... |
1501.03570 | \section{Introduction}
\label{intro}
The emergence of collective motion of living things, such as insects, birds, slime molds, bacteria
and fish is a fascinating far-from-equilibrium phenomenon which has attracted a great deal of cross-disciplinary attention
\cite{vicsek_zafeiris_12}.
The study of these systems falls... |
1501.03909 | \section{Introduction}
What does dynamical systems theory contribute to our understanding of matter?
To a large extent, the royal road to gain an understanding of fluids or solids has been statistical mechanics.
Based on interaction potentials obtained from experiments and quantum mechanical simulations,
sophistic... |
2201.09786 | \section{Selection of key technologies for aerial recharging}
Aerial recharging of \gls{iot} nodes raises significant challenges in terms of both the charging itself, which needs to be in a short time, and the localization of the node by the \gls{uav}.
In the following, we elaborate on the potential technological opti... |
2108.09877 | \section{Introduction}\label{sec:introduction}
\subsection{Background}
Finding a complete and consistent theory that reconciles Quantum Mechanics (QM) and General Relativity (GR) has been an elusive goal since the very first attempts \cite{bronstein1936kvantovanie} made during the `miracle decades' of theoretical phys... |
2103.05671 | \section{Introduction}
\label{sec:intro}
The interaction between a many-body quantum system
and its environment can give rise to exotic and
counterintuitive out-of-equilibrium behavior.
One of the most intriguing is the so-called quantum Zeno
effect~\cite{degasperis-1974,misra-1977,facchi-2002}:
As a consequence... |
1807.01145 | \section{Introduction}
The KArlsruhe Research Accelerator (KARA) is the storage ring of the accelerator test facility and synchrotron light source of the Karlsruhe Institute of Technology (KIT) in Germany.
A special short-bunch operation mode at \unit[1.3]{GeV} allows the reduction of the momentum compaction factor an... |
2106.02727 | \section{Introduction}
In life testing, progressively type-II censored order statistics serve to model component lifetimes in experiments, where upon each failure a pre-fixed number of intact components are removed; see, e.g., \cite{BalAgg2000,BalCra2014}. Such withdrawals of operating components may be part of the exp... |
0904.1589 | \section{Introduction}\label{sec:intro}
Counts of galaxy clusters are a potentially very powerful technique to probe
dark energy and the accelerating universe (e.g.\ \cite{FTH,sah09,mar06,voi05,pie03,bat03,ros02,hai01,hol01}). The idea
is an old one: count clusters as a function of redshift (and, potentially,
mass), ... |
0904.2388 | \section{Introduction}
M82 is a nearby \citep[3.6 Mpc based on a Cepheid distance to M81
by][]{FreedmanHughesMadore1994} irregular (I0) galaxy with a very
active starburst in its nuclear region. It harbors many bright supernova
remnants in its central region, which have been studied extensively
for decades
\citep{Muxl... |
0904.1575 | \section{Introduction}
\label{sec:introduction}
\setcounter{equation}{0}
The first measurements of the Sun's rotation rate were obtained by careful
tracking of the location of sunspots. In fact, in 1611, shortly after the
invention of the telescope, independent observations of the motion of sunspots
across the solar d... |
1710.00190 | \section{Introduction and motivation}
This work was conceived and carried out in the context of a task to reduce
respondent burden in a mental health study. We were interested in a range of outcome
variables, and our analytical goal was fitting regression models to explain the mental health outcomes.
The instrument c... |
1710.00321 | \section{Introduction}
Let $A \in \mathbb{Z}^{d \times n}$ be the integral matrix. Its $ij$-th element is
denoted by $A_{i\,j}$, $A_{i\,*}$ is $i$-th row of $A$, and $A_{*\,j}$ is $j$-th column of $A$. The set of integer values started from a value $i$ and finished on $j$ is denoted by the symbol $i:j = \{i,i+1,\dots... |
1710.00044 | \section{Introduction}\label{sec:introduction}
Metasurfaces are engineered subwavelengthly thin $\left(\delta/\lambda_0\ll 1\right)$ materials consisting of a two-dimensional array of scattering particles. In the most general case, they are bianisotropic and nonperiodic~\cite{Kuester_AveragTransCond_2003, Karim_ms_susc... |
1710.00097 | \section{Introduction}
In \cite{FS}, Fuchs and Salce proved the equivalence of nine conditions for modules over commutative rings $R$ with perfect ring of quotients $Q$. The aim of this paper is to show that the equivalence of seven of their conditions also holds for noncommutative right and left Ore rings $R$ for wh... |
1007.2672 | \section{Introduction}
\label{sec:Intro}
An interesting resolution of the gauge hierarchy problem is offered by
warped models based on the original Randall-Sundrum (RS) geometry
\cite{RS} which is a slice of the 5D Anti de Sitter (AdS$_5$)
spacetime. This geometry, characterized by a curvature scale $k$, is
bounded b... |
1907.04918 | \section{Introduction and Preliminaries}
Throughout this paper, $\mathbb{N}$ denotes the set of natural numbers. Bakhtin \cite{3} and Czerwik \cite{4} generalized the concept of metric spaces and introduced the notion of $b$-metric spaces as follows:
\begin{definition}
\emph{Let $X$ be a nonempty set. A $b$-metric is a... |
2205.14892 | \section{Introduction}\label{sec:introduction}
Traditionally, machine learning treats the world as \textit{closed} and \textit{static} space. In particular for classification, domain data is assumed to comprise pre-defined classes with stationary class-conditional distributions. Also datasets to fit models before depl... |
2205.14887 | \section{Introduction}
\IEEEPARstart
{H}{yperspectral} (HS) imaging aims to capture the continuous electromagnetic spectrum of real-world scenes/objects. Benefiting from such dense spectral resolution, HS images are widely applied in numerous areas, such as agriculture \cite{park2015hyperspectral,lu2020recent}, milit... |
1208.6492 | \section{Introduction}
The nuclear symmetry energy plays an important role in the properties of nuclei and neutron stars~\cite{Latti2001,Latti2004,Stein2005,Anna2006,Yakov2004}. To a good approximantion, it can be written as
\begin{equation}
E_{sym}=S(\rho)\delta^2.
\end{equation}
where $\delta=(\rho_n-\rho_p)/(\r... |
1208.6166 | \section{Introduction}
The notion of a transmutation operator relating two linear differential
operators was introduced in 1938 by J. Delsarte \cite{Delsarte} and nowadays
represents a widely used tool in the theory of linear differential equations
(see, e.g., \cite{BegehrGilbert}, \cite{Carroll}, \cite{LevitanInverse... |
1801.09377 | \section{Introduction}
Linear response theory (LRT) has been a cornerstone of statistical mechanics ever since its introduction in the 1960s. When valid, it allows us to express the average of some observable when subjected to small perturbations from an unperturbed state -- the system's so called {\em{response}} -- e... |
1902.00978 | \section{Introduction}
We say that a permutation on $n$ symbols has a descent at position $i$ if $\pi(i) > \pi(i+1)$, and we let $d(\pi)$ denote the number of descents of $\pi$. For example. the permutation $1\underline{4}32\underline{6}5$ has descents at positions $2$ and $5$, and has $d(\pi)=2$. Descents appear in n... |
2107.12492 | \section{Introduction}
\label{sec:intro}
\input{sections/introduction.tex}
\section{Methodology}
\label{sect:method}
\input{sections/method.tex}
\section{Experimental Validations}
\label{sect:results}
\input{sections/results.tex}
\section{Conclusion}
\label{sect:conc}
\input{sections/conclusion.tex}
\bibliographystyle{... |
2107.12416 | \section{Introduction}
Zeroth-order optimization (ZOO) algorithms solve optimization problems with implicit function information by estimating gradients via zeroth-order observation (function evaluations) at judiciously chosen points \cite{Spall05}. They have been extensively employed as model-free reinforcement learn... |
1511.06698 | \section{Introduction}
\label{intro_Bugaev}
The hadron resonance gas model (HRGM) \cite{Andronic:05} is traditionally used to extract the parameters of chemical freeze-out (CFO) from the measured hadronic yields. Its version with the multicomponent hard-core repulsion
\cite{Oliinychenko:12,HRGM:13,SFO:13}
allowed on... |
2109.12021 | \section{Introduction} \label{sec:intro}
Prefetching is a well-studied speculation technique that predicts the addresses of long-latency memory requests and fetches the corresponding data from main memory to on-chip caches before the \rbc{program executing on the processor} demands it.
\rbc{A program's repeated acces... |
1910.03260 | \section{Introduction}
In the present paper we offer a contribution to the general problem of understanding the interaction between energy and dissipation terms in variational approaches to gradient-flow type evolutions from the standpoint of minimizing movements (see also e.g.~\cite{donfremie,fle,flesav} for related w... |
1902.10138 | \section{Introduction}
The simplest form of Poincar\'e inequality in an open set $B\subset \rn n$ can be stated as follows: if $1\leq p<n$
there exists $C(B,p)>0$ such that for any
(say) smooth function $u$ on $\rn n$ there exists a constant $c_u$ such that
$$
\|u-c_u\|_{L^q(B)} \leq C(n,p)\,\|\nabla u\|_{L^p(B)} ... |
2208.06227 | \section*{Abstract}
{\bf
QCD predictions for final states with multiple jets in hadron collisions
make use of multi-jet merging methods, which allow one to combine
consistently the contributions from hard scattering matrix elements with different parton multiplicities and
parton showers. In this article I consider a... |
1812.04717 | \section*{Acknowledgments}
\vspace{-1mm}
This work is supported by the National Science Foundation grants CSR-1526237, TWC-1564009 and BD Spokes 1636879
\vspace{-2mm}
\bibliographystyle{ACM-Reference-Format}
\renewcommand*{\bibfont}{\footnotesize}
\section{Conclusion and Future Work}
\label{sec:Conclusion}
We prese... |
2208.07513 | \section*{Nomenclature}
\addcontentsline{toc}{section}{Nomenclature}
\subsection{Set and Indices}
\begin{IEEEdescription}[\IEEEusemathlabelsep\IEEEsetlabelwidth{$V_1,V_2,V_3$}]
\raggedright
\item[$\mathcal{I}, i$] Set and index of distribution bus, $i \in \mathcal{I}$
\item[$\ell =ij$] Distribution line connecting bu... |
2208.07621 | \section{Introduction}
Recent advances in quantum computing have been driving intense research in the development of quantum algorithms that offer significant advantage over their classical counterparts. In particular, quantum algorithms are used for studying interacting many-electron systems that fundamentally govern ... |
2208.07569 | \section{#1}}
\setcounter{footnote}{1}
\renewcommand{\theequation}{\arabic{section}.\arabic{equation}}
\newcommand{\stackrel{\rm def}{=}}{\stackrel{\rm def}{=}}
\newcommand{{\mathcal A}}{{\mathcal A}}
\newcommand{{\mathcal B}}{{\mathcal B}}
\newcommand{{\mathcal C}}{{\mathcal C}}
\newcommand{{\mathcal D}}{{\mathcal D}... |
2210.06978 | \section{Funding Disclosure}
This work was fully funded by NVIDIA.
\section{Continuous-Time Diffusion Models and Probability Flow ODE Sampling} \label{app:background_extended}
Here, we are providing additional background on denoising diffusion models (DDMs). In Sec.~\ref{sec:background}, we have introduced DDMs in the... |
2102.08366 | \section{Introduction}
Biomedical question-answering (QA) \yulan{aims to provide users with succinct answers given their queries by analysing a large-scale scientific literature.}
\yulan{It enables} clinicians, public health officials and end-users
to
\yulan{quickly} access the rapid flow of specialised knowledge cont... |
2202.02804 | \section{Introduction} \label{sec:intro}
Circumstellar disks around newly born stars evolve to be protoplanetary disks (PPDs) where planets are formed.
Recent interferometric observations revealed
directly the shape and the chemical structure
of PPDs \citep{Walsh:2015, Ansdell:2016, Johnston:2020}.
Near infrared obser... |
2104.11052 | \section{Introduction}
Millimeter-wave (mmWave) has been widely recognized as a key technology in future wireless communication systems, since the abundant bandwidth resources can significantly increase the throughput \cite{heath_JSTSP, GZ_WC}.
Moreover, to mitigate the severe propagation loss in the mmWave band, massi... |
2104.11021 | \section{INTRODUCTION} \label{intro}
Nowadays, perception is a crucial task for autonomous vehicles. Research in this field demands accurate sensors and
algorithms to perform safe and precise navigation. LiDAR stands as an ideal candidate to directly describe the scene geometry by a dense point cloud representation.
... |
1811.00890 | \section{Definitions and Proofs} \label{ap:proofs}
\subsection{Definitions}
\begin{definition}[Assigns-to set $\assset(S)$] \label{def:assset}
\assset(S) is the set that contains the names of global variables that have been assigned to within the statement S. It is defined recursively as follows: \vspace{-10pt}
\be... |
1304.6419 | \section{} |
1304.6407 | \section{Introduction}
\label{sec-intro}
Over the last few decades fundamental physics has been dominated by fine-tuning problems associated with the small scales of the cosmological constant, $\Lambda$, and the weak interactions, $v$. Small scales can arise from different origins: naturally from symmetries, or by ... |
1209.1508 | \section{Introduction}\label{sec1}
Consider the linear model
\begin{equation}
\label{model} Y = X \theta+ \varepsilon,
\end{equation}
where $X$ is a $n \times p$ matrix, $\theta\in\mathbb R^p$, potentially
$p>n$, and where $\varepsilon$ is a $n\times1$ vector consisting of
i.i.d. Gaussian noise independent of $... |
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