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\section{Introduction}
Evolution algebras were introduced by Tian in his book \cite{T1} (see also \cite{TV}) to model the self reproduction process in non-Mendelian genetics. As shown in \cite{T1}, the theory of evolution algebras is connected to many areas of Mathematics, like, for example, graph theory, group theory... | proofpile-arXiv_065-3842 | {
"file_path": "/home/ubuntu/dolma-v1_7/algebraic-stack-train-0000.json.gz"
} |
\section{Introduction}
The most studied example of quantum field theory in curved spacetime is probably the theory of a scalar field in de Sitter space. Indeed the model is simple enough to be solved analytically and therefore the properties of the field can be studied in detail. In particular the thermal properties of... | proofpile-arXiv_065-6373 | {
"file_path": "/home/ubuntu/dolma-v1_7/algebraic-stack-train-0000.json.gz"
} |
\section{Introduction}
Fifth generation (5G) communication networks will likely adopt \ac{mm-wave} and massive \ac{MIMO} technologies, thanks to a number of favorable properties. In particular, operating at carrier frequencies beyond 30 GHz, with large available bandwidths, \ac{mm-wave} can provide extremely high data... | proofpile-arXiv_065-7442 | {
"file_path": "/home/ubuntu/dolma-v1_7/algebraic-stack-train-0000.json.gz"
} |
\section{Introduction}
One of the most intriguing and mysterious objects in the Universe is the black hole. This area of research is now in the forefront ever since the black holes have been observationally identified using gravitational wave astronomy. The study of black holes is now considered mainstream and astrop... | proofpile-arXiv_065-9775 | {
"file_path": "/home/ubuntu/dolma-v1_7/algebraic-stack-train-0000.json.gz"
} |
\section*{Abstract}
{\bf
The abstract is in boldface, and should fit in 8 lines.
It should be written in a clear and accessible style, emphasizing the context, the problem(s) studied, the methods used, the results obtained, the conclusions reached, and the outlook. You can add a table contents, recommended if your pape... | proofpile-arXiv_065-10081 | {
"file_path": "/home/ubuntu/dolma-v1_7/algebraic-stack-train-0000.json.gz"
} |
\section{\label{sec:introduction}Introduction}
Imagining oneself attempting to swim in a pool of viscous honey, it is not hard to anticipate that, because of the high fluid viscosity, our usual swimming strategy consisting of imparting momentum to the surrounding fluid will not be effective. The world microorganisms i... | proofpile-arXiv_065-10753 | {
"file_path": "/home/ubuntu/dolma-v1_7/algebraic-stack-train-0000.json.gz"
} |
\section{Introduction}
There is extensive experimental evidence, eg.\ in Refs.~\cite{Adams:2005dq,Adare:2008ab}, that a hot and strongly interacting medium is formed in high-energy heavy-ion collisions.
It is expected that color screening of the quark-antiquark binding potential within such a medium would render qua... | proofpile-arXiv_065-11401 | {
"file_path": "/home/ubuntu/dolma-v1_7/algebraic-stack-train-0000.json.gz"
} |
\section{\label{sec:Introduction} Introduction}
{
As the temperature is increased, strongly interacting matter undergoes
a transition to a state with different properties than the vacuum at zero
temperature.
Deconfinement of gluons and quarks, restoration of chiral symmetry and
screening of color charges are the ke... | proofpile-arXiv_065-14643 | {
"file_path": "/home/ubuntu/dolma-v1_7/algebraic-stack-train-0000.json.gz"
} |
\section{Introduction}
\setcounter{equation}{0}
\renewcommand{\mathcal X}{{X}}
\newcommand{{T}}{{T}}
\newcommand{{Y}}{{Y}}
In this paper, we study a family of spheres with
constant mean curvature (CMC)
in the Riemannian Heisenberg group $H^1$. We introduce in $H^1$ two
real parameters
that can be used to deform ... | proofpile-arXiv_066-681 | {
"file_path": "/home/ubuntu/dolma-v1_7/algebraic-stack-train-0000.json.gz"
} |
\section{Introduction}
For a metric space $(X,d)$ with a notion of volume and boundary, an isoperimetric inequality gives a lower bound on the boundary of a set of fixed volume. Ideally, for any fixed volume, it produces a set of that volume with minimal boundary. The most well-known isoperimetric inequality stat... | proofpile-arXiv_066-1310 | {
"file_path": "/home/ubuntu/dolma-v1_7/algebraic-stack-train-0000.json.gz"
} |
\section{Introduction}
Let $A$ be a Banach algebra and let $\varphi \colon A\times A\to\mathbb{C}$ be a continuous bilinear functional satisfying
\begin{equation}\label{B}
a,b\in A, \ [a,b]=0 \ \ \Longrightarrow \ \ \varphi(a,b)=0
\end{equation}
(here and subsequently, $[a,b]$ stands for the commutator $ab - ba$).
Thi... | proofpile-arXiv_066-2843 | {
"file_path": "/home/ubuntu/dolma-v1_7/algebraic-stack-train-0000.json.gz"
} |
\section{Introduction} \label{Introduction}
Blue Straggler Stars (BSS) are intriguing objects found in diverse environments such as globular clusters \citep{sandage53, fusi92, sarajedini93}, open clusters \citep{johnson55,burbidge58,sandage62,al95}, OB associations \citep{mathys87}, Galactic fields \citep{preston00}, ... | proofpile-arXiv_066-3259 | {
"file_path": "/home/ubuntu/dolma-v1_7/algebraic-stack-train-0000.json.gz"
} |
\section{Acknowledgements}
This work was partially supported by Innovate UK grant 133549: \textit{Intelligent Situational Awareness Platform}, and by EPSRC grant EP/R033722/1: \textit{Trust in Human-Machine Partnerships}. Also, this work is partially supported by the Autonomous Province of Trento in the scope of L.P.... | proofpile-arXiv_066-3465 | {
"file_path": "/home/ubuntu/dolma-v1_7/algebraic-stack-train-0000.json.gz"
} |
\section{Introduction}
A \emph{quadrature formula} for integration with respect to the \emph{weight function} $\rho\colon\Omega\mapsto\real$ takes the form
\begin{equation}\label{eq:quadrature}
\int_{\Omega}f(t)\rho(t)d{t}\approx \sum_{k=1}^{K}w_k f(t_k).
\end{equation}
The weight function $\rho$ is a strictly p... | proofpile-arXiv_066-4168 | {
"file_path": "/home/ubuntu/dolma-v1_7/algebraic-stack-train-0000.json.gz"
} |
proofpile-arXiv_066-5352 | {
"file_path": "/home/ubuntu/dolma-v1_7/algebraic-stack-train-0000.json.gz"
} | |
\section{Introduction}
\begin{flushleft}
{\footnotesize We might characterize today's breakdown of
industrial or ``Second Wave"\\
society as a civilizational ``bifurcation", and the rise
of a more differentiated, \\
``Third Wave" society as a leap to new
``dissipative structures" on a world scale.\\
And, if we accept... | proofpile-arXiv_066-7472 | {
"file_path": "/home/ubuntu/dolma-v1_7/algebraic-stack-train-0000.json.gz"
} |
\section{Introduction}
Sunspot groups are formed when magnetic flux tubes rise, likely from the tachocline between the convection and radiation zones \citep{1982A&A...113...99V}. Precisely how they form and the details of their ascent are invisible to observers. However, patterns of sunspot surface activity offer clu... | proofpile-arXiv_066-8423 | {
"file_path": "/home/ubuntu/dolma-v1_7/algebraic-stack-train-0000.json.gz"
} |
\section{The CMS Collaboration \label{app:collab}}\begin{sloppypar}\hyphenpenalty=5000\widowpenalty=500\clubpenalty=5000\input{TOP-20-007-authorlist.tex}\end{sloppypar}
\end{document}
| proofpile-arXiv_066-11147 | {
"file_path": "/home/ubuntu/dolma-v1_7/algebraic-stack-train-0000.json.gz"
} |
\section{Introduction}
Throughout the present paper, all rings are assumed to be commutative and noetherian.
Let $R$ be a ring, $I$ an ideal of $R$, and $M$ a finitely generated $R$-module.
The asymptotic behavior of the quotient modules $M/I^n M$ of $M$ for large integers $n$ is one of the most classical subjects... | proofpile-arXiv_066-11790 | {
"file_path": "/home/ubuntu/dolma-v1_7/algebraic-stack-train-0000.json.gz"
} |
\section{Introduction}
\label{secintro}
A basic tenet of modern cosmology is the idea that the present
large-scale structure the Universe originated by the gravitational
growth of small matter inhomogeneities. These initial density
fluctuations are thought to be imprinted in a universe dominated by
collisionless dark ... | proofpile-arXiv_066-12356 | {
"file_path": "/home/ubuntu/dolma-v1_7/algebraic-stack-train-0000.json.gz"
} |
\section{Introduction}
The Partite Lemma is immensely useful in structural Ramsey theory (for example it is used in \cite{2}, \cite{3}, \cite{10}, \cite{5}, \cite{6}, and \cite{11}). This lemma was discovered by Ne\v{s}et\v{r}il and R\"{o}dl in \cite{2}, \cite{3}, and \cite{10}. In \cite{6} Solecki gave a dual versi... | proofpile-arXiv_066-12918 | {
"file_path": "/home/ubuntu/dolma-v1_7/algebraic-stack-train-0000.json.gz"
} |
\section{Introduction}
\label{sec:1}
Consider the following kinetic equation for the one-particle distribution function $f(x,v,t)$,
\begin{equation}
\label{BGK}
(\partial_t f+ v\cdot \nabla_x f) (x,v,t) = \lambda(\varrho) \big(\varrho(x,t) M_f (x,v,t)-f(x,v,t)\big)\,,
\end{equation}
where
\[
M_f(x,v,t) = \frac 1 {(2 \... | proofpile-arXiv_067-329 | {
"file_path": "/home/ubuntu/dolma-v1_7/algebraic-stack-train-0000.json.gz"
} |
\section{Introduction}
\label{intro}
Patient clinical records typically contain longitudinal data about patients' health status, diseases, conducted tests and response to treatments. Analysing such information can prove of immense value not only for clinical practice, but also for the organisation and management of... | proofpile-arXiv_067-929 | {
"file_path": "/home/ubuntu/dolma-v1_7/algebraic-stack-train-0000.json.gz"
} |
\section{Introduction}
Sparsifying transforms \cite{SparseRep} allow efficient representation of data when a data-dependent overcomplete dictionary is available. Overcomplete dictionaries are useful in image processing \cite{DictImageDenosing, DictAstronomicalImageDenoising, DictDeblurr}, speech processing \cite{Spee... | proofpile-arXiv_067-932 | {
"file_path": "/home/ubuntu/dolma-v1_7/algebraic-stack-train-0000.json.gz"
} |
\section{\setcounter{equation}{0}\oldsection}
\renewcommand\thesection{\arabic{section}}
\renewcommand\theequation{\thesection.\arabic{equation}}
\allowdisplaybreaks
\def\it{Proof.}\rm\quad{\it{Proof.}\rm\quad}
\DeclareMathOperator*{\Cat}{\mathbf{Cat}}
\newcommand\ww{\bm {w}}
\newcommand\bb{\bm b}
\newcommand\vv{\bm v... | proofpile-arXiv_067-2268 | {
"file_path": "/home/ubuntu/dolma-v1_7/algebraic-stack-train-0000.json.gz"
} |
\section{Introduction}
The study of collective excitations
in finite systems originated in Nuclear Physics and subsequently
were carried out in free atoms and metal clusters as well.
It is understood that in case of atomic nuclei, the coherent
motion of shell nucleons driven
by a sufficiently confining s... | proofpile-arXiv_067-2836 | {
"file_path": "/home/ubuntu/dolma-v1_7/algebraic-stack-train-0000.json.gz"
} |
\section{Introduction}
The discoveries presented in this paper are motivated by deep-seated and
long-standing problems in machine learning and statistics. In this article,
I\ will formulate the problem of learning unknown, linear and quadratic
discriminant functions from data as a locus problem, thereby formulati... | proofpile-arXiv_067-4720 | {
"file_path": "/home/ubuntu/dolma-v1_7/algebraic-stack-train-0000.json.gz"
} |
\section{Introduction}
An ultraluminous X-ray source (ULX) is an off-nuclear point-like source whose X-ray
luminosity exceeds $ 10^{39} \,\rm erg\,s^{-1}$ \citep[see][for a review]{kfr17}.
It is generally believed that such a source is an X-ray binary (XRB) powered by accretion
onto a compact object. An intermediate... | proofpile-arXiv_067-6859 | {
"file_path": "/home/ubuntu/dolma-v1_7/algebraic-stack-train-0000.json.gz"
} |
\section*{Introduction}
Let $R$ be a $d$-dimensional standard graded $K$-domain over a perfect field $K$ of characteristic $p>0$ which is $F$-finite. For every finitely generated $R$-module $M$ and every natural number $e$ we denote by $F^{e*}(M)=M\otimes_R\! ^eR$, the $e$-th iteration of the Frobenius functor given by... | proofpile-arXiv_067-7854 | {
"file_path": "/home/ubuntu/dolma-v1_7/algebraic-stack-train-0000.json.gz"
} |
\section{Introduction}
Galaxy mergers are central to the widely accepted hierarchical structure formation paradigm \citep{toomre72}. Because most massive galaxies harbor a massive black hole \citep[MBH;][]{Kormendy1995}, mergers should produce binary MBHs \citep{begelman80}. In rarer situations, triple MBHs may form w... | proofpile-arXiv_067-9252 | {
"file_path": "/home/ubuntu/dolma-v1_7/algebraic-stack-train-0000.json.gz"
} |
\section{Introduction}
The primary task of a communication network architect is
to provision as well as utilize network resources efficiently
to satisfy the demands imposed on it. The main algorithmic
problem is that of allocating or scheduling resources among
various entities or data units, e.g. packets, flows, that
... | proofpile-arXiv_067-9697 | {
"file_path": "/home/ubuntu/dolma-v1_7/algebraic-stack-train-0000.json.gz"
} |
\section{Introduction}
Current technology (robotic and otherwise) falls well short of a human's ability to perceive the world using vision. A nearly limitless range of applications would be facilitated by successful embodied object recognition (i.e., the ability of a mobile platform to perform human-like visual scene... | proofpile-arXiv_067-9931 | {
"file_path": "/home/ubuntu/dolma-v1_7/algebraic-stack-train-0000.json.gz"
} |
\section{Introduction}
Experimental physicists often need to recognize objects, count them, follow them and characterise them. \citet{perrin} had to count colloids by hand to establish the sedimentation-diffusion equilibrium. Nowadays computer vision algorithms are used routinely in the lab to track hundreds of thousa... | proofpile-arXiv_067-10684 | {
"file_path": "/home/ubuntu/dolma-v1_7/algebraic-stack-train-0000.json.gz"
} |
\section{Introduction}
\label{sec:intro}
Let $\Gamma$ be a countable group and let $S$ be a finite symmetric subset of $\Gamma$. The \textbf{co-spectral radius} of a subgroup $H\subset \Gamma$ (with respect to $S$) is defined as the norm of the operator $M\colon L^2(\Gamma/H)\to L^2(\Gamma/H)$:
\[ M\phi(\gamma H)=\frac... | proofpile-arXiv_067-11453 | {
"file_path": "/home/ubuntu/dolma-v1_7/algebraic-stack-train-0000.json.gz"
} |
\section{Introduction}
\label{intro}
Establishing the microscopic nature of Dark Matter (DM) is one of the central, open questions in cosmology and particle physics. In the context of cold nonbaryonic DM, the prevailing paradigm is based on weakly interacting massive particles (WIMPs), and extensive theoretical and ex... | proofpile-arXiv_067-13882 | {
"file_path": "/home/ubuntu/dolma-v1_7/algebraic-stack-train-0000.json.gz"
} |
\subsubsection*{\bibname}}
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\usepackage{graphicx}
\usepackage{amsmath,amsfonts,amssymb,amsthm,bbm}
\usepackage[pagebackref]{hyperref}
\hypersetup{
colorlinks=true,
linkcolor=royalB... | proofpile-arXiv_068-139 | {
"file_path": "/home/ubuntu/dolma-v1_7/algebraic-stack-train-0000.json.gz"
} |
\section{Introduction}
\label{section:1}
Theories of distributive justice hold that justice can be measured (in part) in terms of the fair distribution of benefits and burdens across people in society.
These theories help us (i.e., community members, researchers, and policymakers) to know both what justice is and how ... | proofpile-arXiv_068-238 | {
"file_path": "/home/ubuntu/dolma-v1_7/algebraic-stack-train-0000.json.gz"
} |
\section{Introduction}
\label{Intro}
A classifier usually makes predictions for a test sample by selecting the class label with the highest predicted probability. Such a strategy is insufficient to meet the growing interest in characterizing the prediction reliability in real applications such as medical diagnosis \ci... | proofpile-arXiv_068-1070 | {
"file_path": "/home/ubuntu/dolma-v1_7/algebraic-stack-train-0000.json.gz"
} |
\section{Introduction}
Polarization of an elastic or an electromagnetic wave
refers to the vector-valued amplitude in the high-frequency regime.
Extending methods of geometrical optics, microlocal analysis applies to prove
well-posedness of propagation of polarizations along rays broken by
reflection and transmission ... | proofpile-arXiv_068-1565 | {
"file_path": "/home/ubuntu/dolma-v1_7/algebraic-stack-train-0000.json.gz"
} |
\section{Introduction}
As the use of machine learning (ML) models across industry and society has grown dramatically in recent years,
so too have concerns about the privacy of personal data that is used in training such models. It is well-documented that ML models may leak sensitive, confidential data, e.g. via model ... | proofpile-arXiv_068-2900 | {
"file_path": "/home/ubuntu/dolma-v1_7/algebraic-stack-train-0000.json.gz"
} |
\subsection{The transformation rules}
\label{subsec:Rules}
First, we introduce the following notion of a {\it stratification} for a set of clauses.
Let $\mathbb N$ denote the set of the natural numbers.
A \emph{level mapping} is a
function~$\ell\!:\mathit{Pred}\!\rightarrow\!\mathbb{N}$. For every predicate $... | proofpile-arXiv_068-4592 | {
"file_path": "/home/ubuntu/dolma-v1_7/algebraic-stack-train-0000.json.gz"
} |
\section{Introduction}
\label{sec:introduction}
Historical photographs provide a valuable source of information for researchers in several fields of science. Alone the photographs of the two World Wars have been analyzed in archaeology \cite{WW_archaeology,WW_archaeologyII}, war history \cite{WW_ypres_salient,WW_warhis... | proofpile-arXiv_068-4818 | {
"file_path": "/home/ubuntu/dolma-v1_7/algebraic-stack-train-0000.json.gz"
} |
\section{Introduction}
Given a simple, connected graph $G$, the graph associahedron $\KG$ is a convex polytope whose face poset is based on the connected subgraphs of $G$ \cite{cd}. For special examples of graphs, the graph associahedra become well-known, sometimes classical polytopes. For instance, when $G$ is a pa... | proofpile-arXiv_068-5416 | {
"file_path": "/home/ubuntu/dolma-v1_7/algebraic-stack-train-0000.json.gz"
} |
\section{Introduction}
Let $G$ be a simple graph, that is, no loops or multiple edges. We write $V(G)$ for the vertex set of $G$ and $\delta(G)$ for the minimum degree of $G$. An \emph{edge-coloured graph} is a graph in which each edge is assigned a colour. We say such an edge-coloured $G$ is \emph{proper} if no t... | proofpile-arXiv_068-7170 | {
"file_path": "/home/ubuntu/dolma-v1_7/algebraic-stack-train-0000.json.gz"
} |
\section{I. Introduction}
The so-called Generalized Uncertainty Principle (GUP) it is an immediate way to realize the old intuition about the existence of a fundamental minimal scale. In fact, a natural (Planckian) cut-off length has, in some (not yet understood) sense, to appears as soon as the smooth picture of the ... | proofpile-arXiv_068-7918 | {
"file_path": "/home/ubuntu/dolma-v1_7/algebraic-stack-train-0000.json.gz"
} |
\section{Introduction}
\label{intro}
In recent years computer simulations are becoming an ever more important tool to study a large spectrum of physical problems, a trend supported by the increasing processor throughput and advances in the parallel computing research.
Nonetheless, while the constraint due to the cost... | proofpile-arXiv_068-10304 | {
"file_path": "/home/ubuntu/dolma-v1_7/algebraic-stack-train-0000.json.gz"
} |
\section{INTRODUCTION}\label{Section 1}
Nabla Laplace transform is a powerful tool to convert a discrete time signal, which is a sequence of real or complex numbers, into a complex frequency domain representation \cite{Hein:2011PAMJ}. Similar to the classic $Z$ transform, it can be considered as a discrete time general... | proofpile-arXiv_068-10312 | {
"file_path": "/home/ubuntu/dolma-v1_7/algebraic-stack-train-0000.json.gz"
} |
\section{Qualitative Results}
\section{Conclusion}
\label{sec:conclude}
In this paper, we presented a simple, efficient, and powerful pooling scheme -- SVM pooling -- for video representation learning. We cast the pooling problem in a multiple instance learning framework, and seek to learn useful decision bou... | proofpile-arXiv_068-10465 | {
"file_path": "/home/ubuntu/dolma-v1_7/algebraic-stack-train-0000.json.gz"
} |
\section{Introduction}
With the swift progress in computer vision, surveillance systems using static cameras are promising technologies for advanced tasks such as behavior analysis \mbox{\cite{Zhang2020}}, object segmentation \mbox{\cite{Ammar2020}} and motion analysis \cite{Park2018}, \cite{Bilge2017}. Among their var... | proofpile-arXiv_068-10951 | {
"file_path": "/home/ubuntu/dolma-v1_7/algebraic-stack-train-0000.json.gz"
} |
\section{Introduction}\label{Sec:intro}
Fractional differential equations (FDEs) are a generalization of the classical ordinary and partial differential equations, in which the order of differentiation is permitted to be any real (or even complex) number, not only a natural number.
FDEs containing not only on... | proofpile-arXiv_068-12647 | {
"file_path": "/home/ubuntu/dolma-v1_7/algebraic-stack-train-0000.json.gz"
} |
\section{Introduction} \label{sec:intro}
Solar flares are the largest explosive events that occur around the surface of the Sun. This phenomenon is caused by the reconnection of magnetic field lines above sun spots and produces electromagnetic radiation from radio to $\gamma$-rays~\citep{1974IAUS...57..105K}. Solar f... | proofpile-arXiv_068-13314 | {
"file_path": "/home/ubuntu/dolma-v1_7/algebraic-stack-train-0000.json.gz"
} |
\section{Introduction}\label{SecIntroduction}
Neutral particles can emulate the dynamics of electrons in the presence of magnetic fields through the engineering of artificial gauge fields \cite{Dalibard2011,Goldman2014}. In the well-known Aharonov-Bohm effect \cite{Aharonov1959,Wu1975}, a charged particle performing a... | proofpile-arXiv_068-13759 | {
"file_path": "/home/ubuntu/dolma-v1_7/algebraic-stack-train-0000.json.gz"
} |
\section{Introduction}
Ever since the first exorcism of Maxwell's demon \cite{Szil29a}, determining
how much energetic input a particular computation requires has been a
broadly-appreciated theoretical question. In the current century, however, the
question has taken on a markedly practical bent; a familiar example i... | proofpile-arXiv_069-1019 | {
"file_path": "/home/ubuntu/dolma-v1_7/algebraic-stack-train-0000.json.gz"
} |
\section{INTRODUCTION}
The study of extragalactic radio jets is an important area in astrophysics. In
radio loud sources, jets contribute a large fraction of the total radiated
power, and sustain the formation of energetic kiloparsec scale lobes. While
observational properties of jets are widely differentiated, they ... | proofpile-arXiv_069-1992 | {
"file_path": "/home/ubuntu/dolma-v1_7/algebraic-stack-train-0000.json.gz"
} |
\section{Introduction} \label{sec:intro}
The Sun is the most well-studied star and serves as a benchmark for our understanding of stellar physics. High resolution spectra of the Sun have been essential references for a variety of stellar and planetary studies that strive to understand atomic physics processes in the so... | proofpile-arXiv_069-3420 | {
"file_path": "/home/ubuntu/dolma-v1_7/algebraic-stack-train-0000.json.gz"
} |
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{.7\linespacing} {\fontsize{13}{14}\selectfont\bfseries\centering}}
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\renewcommand\theequation{\thesection.\arabic{equation}}
\@addtoreset{equati... | proofpile-arXiv_069-3439 | {
"file_path": "/home/ubuntu/dolma-v1_7/algebraic-stack-train-0000.json.gz"
} |
\section{Introduction}
Millimeter-wave (mmWave) technologies have played an important role in 5G communication systems. Compared to the microwave, the mmWave can achieve a large system capacity and security performance \cite{b1}. However, the blockage issue needs to be tackled before the commercial application of mmWav... | proofpile-arXiv_069-4916 | {
"file_path": "/home/ubuntu/dolma-v1_7/algebraic-stack-train-0000.json.gz"
} |
\section{Introduction}
Let $X$ be a (finite dimensional) locally compact Hausdorff space and $B$ a $C\sp*$-aglebra. We are concerned with the projection lifting problem from the corona algebra to the multiplier algebra of a $C\sp*$-algebra of the form $C(X)\otimes B$. An earlier result in this direction is that of W.... | proofpile-arXiv_069-5839 | {
"file_path": "/home/ubuntu/dolma-v1_7/algebraic-stack-train-0000.json.gz"
} |
\section*{Overview}
Throughout this note we shall consider a Young function $\Phi$ with the following properties. Given $r\geq 1$ and $\delta\geq 0$, we say that a Young function $\Phi$ belongs to the family $\mathfrak{F}_{r,\delta}$ if it is submultiplicative, has lower type $r$ and satisfies the condition
\[\fra... | proofpile-arXiv_069-5923 | {
"file_path": "/home/ubuntu/dolma-v1_7/algebraic-stack-train-0000.json.gz"
} |
\section{Introduction}
It has now been over a decade since the publication of the theoretical
works of S. A. Mikhailov on the low-frequency (\textit{intraband})
nonlinear response of the monolayer of graphene to an external electric
field \citep{mikhailov2007,mikhailov2008}, which marked the birth
of the study of nonl... | proofpile-arXiv_069-6189 | {
"file_path": "/home/ubuntu/dolma-v1_7/algebraic-stack-train-0000.json.gz"
} |
\section{Introduction}
\begin{figure}[t]
\centering
\includegraphics[width=8cm]{global_framework.pdf}
\caption{Illustration of the RL-LTV algorithm framework. An RL is employed to solve a item-level MDP and provides a policy optimizing item long-term rewards (LTV). The policy score is combined with CTR ranking ... | proofpile-arXiv_069-7565 | {
"file_path": "/home/ubuntu/dolma-v1_7/algebraic-stack-train-0000.json.gz"
} |
\section{Introduction}
\input{sections/introduction}
\section{Background: an overview of BBR and BBRv2}
\input{sections/background}
\section{A Deep Dive into BBRv2}
\input{sections/measurement}
\section{Design and implementation of BBRv2+}
\input{sections/motivation-arch}
\section{Evaluation of BBRv2+}
\input{sec... | proofpile-arXiv_069-7665 | {
"file_path": "/home/ubuntu/dolma-v1_7/algebraic-stack-train-0000.json.gz"
} |
\section{Introduction}
In the American system of democracy, local representatives from a state are elected to the national House of Representatives in direct local elections, held in districts of (roughly) equal population. These Congressional districts of a state are redrawn every 10 years, following the decennial ce... | proofpile-arXiv_069-8720 | {
"file_path": "/home/ubuntu/dolma-v1_7/algebraic-stack-train-0000.json.gz"
} |
\section{Introduction and Summary of Results:}
Traditionally, the analysis of information processing systems is
based on a certain modelling of the process that generates the
observed data (e.g an ergodic process). Based on this a-priori
model, a processor (e.g. a compression algorithm, a classifier, etc)
is then opt... | proofpile-arXiv_069-14225 | {
"file_path": "/home/ubuntu/dolma-v1_7/algebraic-stack-train-0000.json.gz"
} |
\section{Introduction}
In the last five years we have witnessed a renaissance
of charm spectroscopy. Several new charmed states have been
observed, using data samples collected by so-called
$B$-factories i.e. $e^+e^-$ storage rings dedicated to the
studies of CP violation in the sector of the beauty quark.
These m... | proofpile-arXiv_069-14248 | {
"file_path": "/home/ubuntu/dolma-v1_7/algebraic-stack-train-0000.json.gz"
} |
\section{Introduction}
The existence of long-lived vortices in accretion discs was first proposed by \cite{W44} in a model of planet formation. This idea was reintroduced by \cite{BS95} to accelerate the formation of planetesimals through a dust trapping process. Moreover, large scale vortices can lead to a significant... | proofpile-arXiv_069-15828 | {
"file_path": "/home/ubuntu/dolma-v1_7/algebraic-stack-train-0000.json.gz"
} |
\section{Introduction}\label{sec:intro}
The magnetorotational instability (MRI, \citealp{BH91}) is considered the
most promising mechanism for triggering turbulence and transporting angular momentum
in accretion disks. The properties of the MRI depend on magnetic field geometry. Without
external field, the MRI serves ... | 5eba3c0b59dcf679978abf33c66b50a7f63cc632 | {
"file_path": "/home/ubuntu/dolma-v1_7/arxiv-0016.json.gz"
} |
\section{Introduction}
\label{sec:intro}
V838 Monocerotis (henceforth V$838$ Mon) is a dramatic stellar object: in 2002, it brightened nine magnitudes during three outbursts \citep{Brown2002,Goranskii2002}, experienced a variety of distinctive optical and infrared (IR) changes \citep{Wisniewski2003,Lynch2004,Rushton200... | e381532d789668ef5fc170bc284427f7f40213ee | {
"file_path": "/home/ubuntu/dolma-v1_7/arxiv-0016.json.gz"
} |
\section{Introduction}
Highest weight categories were first introduced in \cite{CPS88} with the purpose of axiomatizing certain phenomena arising naturally in the representation theory of complex semisimple Lie algebras. This prompted the definition of a quasi-hereditary algebra (see \cite{Scott87}), which was shown b... | 77995f6026756476650f093eb6df2eb0f90b3cb9 | {
"file_path": "/home/ubuntu/dolma-v1_7/arxiv-0016.json.gz"
} |
\section{}
\section{Introduction}
The concept of fault diameter of Cartesian product graphs was first described in \cite{1}, but the upper bound was wrong,
as shown by Xu, Xu and Hou who provided a small counter example and corrected the mistake \cite{0}.
More precisely, denote by $\mathcal{D}^V_{a }(G)$ the ... | 56d74dd34cdf699151d38b9e9bf751da8169412f | {
"file_path": "/home/ubuntu/dolma-v1_7/arxiv-0016.json.gz"
} |
\section{Introduction and main results }\label{csw-sec1}
Let $\mathbb{R}^{n}
$ denote the $n$-dimensional Euclidean space, where
$n\geq2$. For $a=(a_{1},\ldots,a_{n})$ and
$x=(x_{1},\ldots,x_{n})\in\mathbb{R}^{n}$, we define the
inner product $\langle \cdot ,\cdot \rangle$ by $\langle
x,a\rangle=x_{1}a_{1}+\cdots+x_{... | 89e14879130d3119b80a559b543c0965d9baa8a8 | {
"file_path": "/home/ubuntu/dolma-v1_7/arxiv-0016.json.gz"
} |
\section{Introduction}
\label{sec:introduction}
Visual Place Recognition (VPR) is a well known problem in Robotics and
Computer Vision~\cite{lowry-place-recognition-survey-2016} and
represents a building block of several applications in Robotics.
These range from Localization and Navigation to Simultaneous Localizatio... | 01b560c6acdbe8296fa7b443d243fa7d800ab60d | {
"file_path": "/home/ubuntu/dolma-v1_7/arxiv-0016.json.gz"
} |
\section{Introduction}
One of the joys of working in a metric space is that the closure of a set coincides with its \textit{sequential closure}. In particular, if $X$ is a metric space, $A$ is a subset of $X$, and $b$ is in the closure of $A$, then there exists a sequence of elements in $A$ which converges to $b$. In... | 8e5fd2e6b0b96f94a42a291146753ff58b176445 | {
"file_path": "/home/ubuntu/dolma-v1_7/arxiv-0016.json.gz"
} |
\section{\bf Introduction}
\label{s:intro}
The investigation of strange particle production in neutral current,
deep inelastic scattering (DIS) interactions could provide information
about the $s$-quarks in
the nucleon, about the boson-gluon fusion process and, above all, the parton
fragmentation process.
Strange part... | 2951c2e1f80b2e5aa7de35b9a1d504aabf42f429 | {
"file_path": "/home/ubuntu/dolma-v1_7/arxiv-0016.json.gz"
} |
\section{Introduction}
Starting from Gromov's uniqueness theorem on fillings of $(S^3,\xi_{\rm std})$ \cite{MR809718} and the Eliashberg-Floer-McDuff theorem \cite{MR1091622} on fillings of $(S^{2n-1},\xi_{\rm std})$, understanding the uniqueness of exact fillings of some contact manifolds has been a fundamental and i... | 72715c36dd65682c69402e37bf32240ab1b2a7a8 | {
"file_path": "/home/ubuntu/dolma-v1_7/arxiv-0016.json.gz"
} |
\section{Introduction}
Recently the problem of superconductivity near the boundaries of a Bardeen–Cooper–Schrieffer (BCS) superconductor was revisited. The original calculations in BCS theory \cite{de1964boundary,de1966superconductivity,CdGM_Coherence,CdGM_french,abrikosov1965concerning}
came to the conclusion that the... | 68ffd2d6365a953ec45cd3803cd4342fae82a986 | {
"file_path": "/home/ubuntu/dolma-v1_7/arxiv-0016.json.gz"
} |
\section{Introduction}\label{intro}
The Oxford English Dictionary records three different meanings of the
noun {\em wake}:
\begin{itemize}
\item a trail of disturbed water or air left by the passage of a ship
or aircraft;
\item a watch or vigil held beside the body of someone who has died;
\item (especially in ... | 2c307e63af383d587827b31db64f3aab8dbe288f | {
"file_path": "/home/ubuntu/dolma-v1_7/arxiv-0016.json.gz"
} |
\section*{Introduction}
In this paper we consider the notion of the Weyl filtration dimension
and good filtration dimension of modules for a linear algebraic group.
These concepts were first introduced by Friedlander and
Parshall~\cite{fripar} and may be considered a variation of the notion
of projective dimension and ... | 120dd35cddfa6cb4477fda73ce32c53dccc61ed7 | {
"file_path": "/home/ubuntu/dolma-v1_7/arxiv-0016.json.gz"
} |
\section{Introduction}
RNA takes part in a variety of important cellular activities, including
protein synthesis, intron splicing, gene silencing, and genome rearrangement
(Lee et al., 2002; Mochizuki et al., 2002; Gratias \& Betermier, 2003; Yang
et al., 2003). Considering the extensive functional repertoire of RNA
m... | bd5fb7c00c1460ab484b72c57da142a6f7e84d51 | {
"file_path": "/home/ubuntu/dolma-v1_7/arxiv-0016.json.gz"
} |
\section{Introduction}
Synchronization of chaotic systems has been explored extensively in recent years~\cite{Piko01}.
In addition to complete synchronization between two identical chaotic systems~\cite{Fuji83}, various notions of chaotic synchronization have evolved~\cite{Piko01}.
Among them, the concept of {\it gene... | dddf1dace8080d081daf306c85885facb1466dc3 | {
"file_path": "/home/ubuntu/dolma-v1_7/arxiv-0016.json.gz"
} |
\section{Introduction}
The spatial behavior of accelerated expansion of universe has captured much attention in the modern generation of cosmology and astrophysics
\cite{1, 2}. Recent evolutions in this era of cosmology have exposed new concepts to acquaint the critical and observational innovations for this accelera... | c8babf0102639fd129a1659f049749da180d9b26 | {
"file_path": "/home/ubuntu/dolma-v1_7/arxiv-0016.json.gz"
} |
\section{Introduction}
Entanglement is a unique feature of a quantum system and entanglement entropy, defined through the von Neumann entropy
(vNE) measure, is one of the most widely used quantitative measures of entanglement.
\cite{Osborne2002,Calabrese2004,Vidal2004,Kopp2007} Consider a composite system that can be p... | 8892060ac15a18c1055b81b27e574d02e3ff8f26 | {
"file_path": "/home/ubuntu/dolma-v1_7/arxiv-0016.json.gz"
} |
\section{The overlap operator and the sign function at nonzero quark chemical potential}
\label{sec:sign}
The overlap Dirac operator \cite{Narayanan:1994gw,Neuberger:1997fp}
provides an exact solution of the Ginsparg-Wilson relation and hence
implements chiral symmetry in lattice QCD even at finite lattice spacing.
At... | 75e8686545baab64487bccc383f7d43b7d2a9afa | {
"file_path": "/home/ubuntu/dolma-v1_7/arxiv-0016.json.gz"
} |
\section{Introduction}
\label{sec:introduction}
The general properties of the 90 cm sky are not very well known and even less is known at VLBI resolution. Previous snapshot surveys at these wavelengths have only targeted the brightest sources and were plagued by poor sensitivity, radio interference and limited coheren... | 56d2281642bd4a50e135e4eeb203640b6b4d59dc | {
"file_path": "/home/ubuntu/dolma-v1_7/arxiv-0016.json.gz"
} |
\section{Introduction}
The AdS/CFT correspondence \cite{MGW} has more and more revealed the deep
relations between the $\mathcal{N}=4$ super Yang-Mills (SYM) theory
and the string theory in $AdS_5\times S^5$, where classical string
solutions play an important role \cite{GKP,AT,JP}. The energies of
classical strings ... | 047afb7b6f772b533c958fad81005938eb156e3d | {
"file_path": "/home/ubuntu/dolma-v1_7/arxiv-0016.json.gz"
} |
\section{Introduction}
\label{sec:intro}
The theory of group actions on $\Lambda$-trees goes back to early 1960's. Lyndon introduced abstract
length functions on groups \cite{Lyndon:1963}, axiomatizing Nielsen cancellation method; he initiated
the study of groups with real valued length functions. Chiswell related s... | e619e47dc92e8744fc1d7033e0f81ddf6ea97131 | {
"file_path": "/home/ubuntu/dolma-v1_7/arxiv-0016.json.gz"
} |
\section{Introduction}\label{Sintro}
The \emph{product formula} in algebraic number theory states that, given an algebraic number $x \ne 0$ in a number field $K$,
the product of $|x|$ as $|\cdot|$ ranges over all
inequivalent absolute values of $K$ (appropriately normalized) is equal to $1$. In logarithmic form, the ... | e3fecc15d719da52fbbb03be9f7212653bb0d29f | {
"file_path": "/home/ubuntu/dolma-v1_7/arxiv-0016.json.gz"
} |
\section{introduction}
In the present paper, we prove an explicit coproduct formula
for quantum groups $U_q(\mathfrak{g}),$ where
$\mathfrak{g}=\mathfrak{sp}_{2n}$ or $\mathfrak{g}=\mathfrak{so}_{2n}$
are simple Lie algebras of type $C,$ $D$ respectively.
Consider a Weyl basis of the Lie algebra $\mathfrak{g}... | 91d0cb23957d1f407b302c304a48aa640df1d35e | {
"file_path": "/home/ubuntu/dolma-v1_7/arxiv-0016.json.gz"
} |
\section{Introduction}
For more than two decades, Bose-Einstein condensates (BECs) have provided a fruitful experimental, computational, and theoretical testbed for investigating nonlinear phenomena. In the mean-field limit, a BEC is governed by the Gross-Pitaevskii (GP) equation \cite{book1}, which is a nonlinear Sc... | 202ebceab47ae899b696d13eb45125c8b55b5a89 | {
"file_path": "/home/ubuntu/dolma-v1_7/arxiv-0016.json.gz"
} |
\section{\label{sec:level1}Introduction}
In mid infrared regime ranging from 2 to 12 $\mu$m high power optical pulses have found their applications in near field microscopy or spectroscopy, mid infrared fiber sources, chemical sensing, biomedical surgeries, imaging and so on \cite{sanghera,ghosh1,sensor}. In this regi... | 90f02ffe96ee64d0a01316e5e154dd50a17835c3 | {
"file_path": "/home/ubuntu/dolma-v1_7/arxiv-0048.json.gz"
} |
\section{Recent PDF Updates - effect and treatment of LHC data}
\begin{wrapfigure}{r}{0.6\columnwidth}
\vspace{-0.4cm}
\centerline{\includegraphics[width=0.62\textwidth]{figures_Ratio-Boxes.png}}
\vspace{-0.3cm}
\caption{The CMS measurement of the $t/\bar t$ ratio in $t$-channel production, figure from
\cite{Khachatr... | cca1aaccf58689da362cd6ff0c84427d408ad615 | {
"file_path": "/home/ubuntu/dolma-v1_7/arxiv-0048.json.gz"
} |
\section*{Introduction}
Surfaces isogenous to a product of curves have been introduced by Catanese in \cite{Ca00}. Starting from that paper they have been studied extensively, in particular in the last years.
They provide an easy way to construct surfaces of general type with fixed geometrical invariants.
Moreover... | 89b3a25b8dd57a87b7984de0036b2e4f4bfbaae1 | {
"file_path": "/home/ubuntu/dolma-v1_7/arxiv-0048.json.gz"
} |
\section{Introduction}
Machine learning (ML) especially deep learning is playing an increasingly important role in artificial intelligence (AI), and has achieved great success in many domains and applications in the past decades.
For example, Convolutional Neural Networks (CNNs) can often achieve even higher accuracy ... | f0df580c2cbee89392595a3e4e3bd1f326da1269 | {
"file_path": "/home/ubuntu/dolma-v1_7/arxiv-0048.json.gz"
} |
\section{Introduction}
Pre-trained vision and language foundation models~\cite{clip,align} have shown encouraging results toward open-domain visual-concept matching.
Benefiting from prompt engineering~\cite{entailment,declaration}, where free-form text prompts are designed for specific task goals, those foundation mode... | 7c8d49e74cb3313d9b449deaed6498ec66628e74 | {
"file_path": "/home/ubuntu/dolma-v1_7/arxiv-0048.json.gz"
} |
\section{Introduction}
Quasi two-dimensional charge-transfer salts based on the organic molecule BEDT-TTF (where BEDT-TTF stands for bis-ethylenedithio-tetrathiafulvalene) provide a unique playground for studying the interaction of electronic and structural properties because they exhibit a rich phase diagram rangin... | d8c4e90daca19cbe668820bd15090d8c52b0f931 | {
"file_path": "/home/ubuntu/dolma-v1_7/arxiv-0048.json.gz"
} |
\section{Introduction}
The U.S. patent system contains around 10 million patents classified in about 500 main classes. However, some classes are much larger than others, some classes are much older than others, and more importantly none of these classes can be thought of as a once-and-for-all well defined entity. Due ... | a5e026a991e7df7920801d9445d627d9be5adffc | {
"file_path": "/home/ubuntu/dolma-v1_7/arxiv-0048.json.gz"
} |
\section{Introduction}
Neural sequence-to-sequence models with attention have become the \textit{de facto} methods for machine translation~\cite{bahdanau2014neural,vaswani2017attention}. NMT models require a large amount of parallel data to surpass the quality of phrase-based statistical models, and they are very sens... | eaec81f326f9178fde6e3bb20566c3124d924fd9 | {
"file_path": "/home/ubuntu/dolma-v1_7/arxiv-0048.json.gz"
} |
\section{Introduction}
Much of the past work on phonetic duration falls into three categories, aimed at gaining phonetic insight, improving the quality of TTS and improving the accuracy of ASR. In the first category, researchers have examined the extent to which certain phonetic factors have an influence on duratio... | 9e7ddb45d58a919f221389fc2e77221f44090474 | {
"file_path": "/home/ubuntu/dolma-v1_7/arxiv-0048.json.gz"
} |
\section{Introduction}
In the algorithmic field of computer science, we usually have an optimization problem at hand and a state-of-the-art or a straight-forward exhaustive search algorithm that solves it. The challenge is then to suggest a new algorithm with a better running time, storage or other feature. A different... | cc915ccabafcffc6ce8e6494dba47d996e9433b4 | {
"file_path": "/home/ubuntu/dolma-v1_7/arxiv-0048.json.gz"
} |
\section{Introduction}
As the deployment of 5G technology continues in different parts of the world, the research community has started focusing on the 6G systems and how this generation can revamp wireless networks. Avant-garde applications have already been defined for the life in 2030 and beyond, some of which are s... | be7198ee03e34620ccce12cf7af3276be0656a48 | {
"file_path": "/home/ubuntu/dolma-v1_7/arxiv-0048.json.gz"
} |
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