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\section{Introduction}
\subsection{Curvature-dimension conditions and Li-Yau inequalities}
The $\Gamma$-calculus of Bakry and \'Emery is nowadays known as a powerful theory at the interface of analysis, geometry and probability theory. The central role is played by the curvature-dimension condition $CD(\kappa,d)$, whic... | {
"timestamp": "2022-01-13T02:23:43",
"yymm": "2201",
"arxiv_id": "2201.04564",
"language": "en",
"url": "https://arxiv.org/abs/2201.04564"
} |
\section{Introduction}
Consider the following first-order singularly perturbed differential equation:
\eqntag{\label{211211103217}
\hbar \del_x f = \FF (x, \hbar, f)
\fullstop{,}
}
where $\FF$ is an $\NN$-dimensional holomorphic vector function of a single complex variable $x$, a small complex perturbation parameter ... | {
"timestamp": "2022-01-13T02:21:57",
"yymm": "2201",
"arxiv_id": "2201.04526",
"language": "en",
"url": "https://arxiv.org/abs/2201.04526"
} |
\section{Introduction}
Manifolds \emph{with density}, or \emph{weighted} manifolds, have long appeared in mathematics.
A weighted manifold is a Riemannian manifold $(M,g)$ endowed with a function $f:M\to \mathbb{R}$, defining the measure $e^{-f}dV_g$.
After being introduced by Lichnerowicz in \cite{lic1,lic2}, more ... | {
"timestamp": "2022-01-13T02:19:13",
"yymm": "2201",
"arxiv_id": "2201.04475",
"language": "en",
"url": "https://arxiv.org/abs/2201.04475"
} |
\section{Introduction}
We study the \textit{best arm identification (BAI) with a fixed budget} in stochastic multi-armed bandit (MAB) problems. The goal is to identify an arm that has the highest expected reward with the smallest failure probability under a fixed number of rounds, called a \textit{budget}.
\citep{Bubec... | {
"timestamp": "2022-02-14T02:15:31",
"yymm": "2201",
"arxiv_id": "2201.04469",
"language": "en",
"url": "https://arxiv.org/abs/2201.04469"
} |
\section{Introduction}
\label{instroduction}
\label{sec:sample1}
Over the last few years, deep learning techniques have started to become increasingly popular, introducing new and exciting challenges. One of the main challenges and obstacles in the training of deep neural networks is the need for datasets containin... | {
"timestamp": "2022-01-13T02:18:35",
"yymm": "2201",
"arxiv_id": "2201.04449",
"language": "en",
"url": "https://arxiv.org/abs/2201.04449"
} |
\section{Introduction}
\label{Introduction}
Phase transition is the key concept in condensed matter and statistical physics \cite{SSachdev}. In general, the quantum phase transitions in equilibrium case always signify that the ground-state properties of the quantum many-body systems have changed, in particular, the cor... | {
"timestamp": "2022-01-13T02:17:40",
"yymm": "2201",
"arxiv_id": "2201.04430",
"language": "en",
"url": "https://arxiv.org/abs/2201.04430"
} |
\section{Two-step Projection}
\label{sec:thm1-proof}
\setcounter{theorem}{0}
\begin{theorem}
For any arbitrary vector $\bm \delta \in {\mathbb{R}}^m$, its projection onto the region defined by the intersection of the norm-bounded and zero-mean constraints is equivalent to the projection first onto the zero-mean hyp... | {
"timestamp": "2022-01-14T02:11:05",
"yymm": "2201",
"arxiv_id": "2201.04397",
"language": "en",
"url": "https://arxiv.org/abs/2201.04397"
} |
\subsection*{Acknowledgments}
We thank Matteo Baggioli and Mary Thomson for useful suggestions.
A.Z. acknowledges financial support from US Army Research Office, contract nr. W911NF-19-2-0055.
\bibliographystyle{apsrev4-2}
| {
"timestamp": "2022-01-13T02:22:46",
"yymm": "2201",
"arxiv_id": "2201.04541",
"language": "en",
"url": "https://arxiv.org/abs/2201.04541"
} |
\section{Introduction}
The direct detections of gravitational waves (GWs) from binary black holes \cite{LIGOScientific:2016aoc} and a binary neutron star inspiral \cite{LIGOScientific:2017vwq} by the LIGO and Virgo collaborations have opened a new window for exploring our Universe and the theory of gravity.
Recently, ... | {
"timestamp": "2022-01-13T02:23:23",
"yymm": "2201",
"arxiv_id": "2201.04552",
"language": "en",
"url": "https://arxiv.org/abs/2201.04552"
} |
\section{Introduction}
\label{sectI}
In recent years the focus of exoplanet research has shifted from the
mere detection to their detailed characterization.
The detailed characterization requires accurate determinations of
their masses, radii and studies of their atmospheres. As up to now,
transiting exoplanets ar... | {
"timestamp": "2022-01-13T02:16:26",
"yymm": "2201",
"arxiv_id": "2201.04413",
"language": "en",
"url": "https://arxiv.org/abs/2201.04413"
} |
\section{INTRODUCTION} \label{sec:intro}
The inhomogeneous complex nature of the quiet Sun (QS) is predominantly due to the presence of a large variety of small-scale magnetic features. It is believed that these small-scale magnetic features are essentially the sources of magnetic energy, which can be dissipated to hea... | {
"timestamp": "2022-01-13T02:18:46",
"yymm": "2201",
"arxiv_id": "2201.04459",
"language": "en",
"url": "https://arxiv.org/abs/2201.04459"
} |
\section*{Appendix for ``OCSampler: Compressing Videos to One Clip with Single-step Sampling''}
\input{supp/baselines}
\input{supp/implementation}
\input{supp/localization}
\input{supp/per_class}
\input{supp/strategy}
\input{supp/instance}
\begin{figure}[t]
\centering
\resizebox{\columnwidth}{!}{\inclu... | {
"timestamp": "2022-01-13T02:15:36",
"yymm": "2201",
"arxiv_id": "2201.04388",
"language": "en",
"url": "https://arxiv.org/abs/2201.04388"
} |
\section{Introduction}
In this work we study the spectral properties of a non-local self-adjoint operator $\cal L$ in $L_2(\mathds{R}^d)$ of the form
\begin{equation}\label{intro-1}
\cL u = \cA u+ V u, \qquad (\cA u)(x): = \int\limits_{\mathds{R}^d} a(x-y) u(y) \, dy,
\end{equation}
where $\cA$ is a convolution... | {
"timestamp": "2022-01-13T02:21:15",
"yymm": "2201",
"arxiv_id": "2201.04511",
"language": "en",
"url": "https://arxiv.org/abs/2201.04511"
} |
\section{Introduction}
In the context of continuum methods for the study of nonperturbative QCD~\cite{Roberts:1994dr,Alkofer:2000wg,Maris:2003vk,Pawlowski:2005xe,Fischer:2006ub,Aguilar:2006gr,Aguilar:2008xm,Boucaud:2008ky,Binosi:2009qm,Campagnari:2010wc,Pennington:2011xs,Vandersickel:2012tz,Serreau:2012cg,Cloet:2013... | {
"timestamp": "2022-01-13T02:18:39",
"yymm": "2201",
"arxiv_id": "2201.04451",
"language": "en",
"url": "https://arxiv.org/abs/2201.04451"
} |
\section*{Acknowledgments}
L. Beir\~ao da Veiga was partially supported by the italian PRIN 2017
grant “Virtual Element Methods: Analysis and Applications” and the
PRIN 2020 grant “Advanced polyhedral discretisations of heterogeneous
PDEs for multiphysics problems”.
Both these supports are gratefully acknowledged.
L... | {
"timestamp": "2022-01-13T02:16:40",
"yymm": "2201",
"arxiv_id": "2201.04417",
"language": "en",
"url": "https://arxiv.org/abs/2201.04417"
} |
\section{TODO}
\section{Introduction}
As machine learning begins moving into sensitive predictions tasks, it becomes critical to ensure the fair performance of prediction models. Naively trained machine learning systems can replicate biases present in their training data, resulting in unfair outcomes that can accent... | {
"timestamp": "2022-01-13T02:18:48",
"yymm": "2201",
"arxiv_id": "2201.04461",
"language": "en",
"url": "https://arxiv.org/abs/2201.04461"
} |
\section{Introduction}
\subsection{History}
Floquet theory indicates that a nonautonomous $T$-periodic linear system of differential equations can be reducible to a corresponding autonomous linear system of differential equations by a periodic Lyapunov transformation \cite{d8}.
Floquet theory is a powerful
too... | {
"timestamp": "2022-03-29T02:05:56",
"yymm": "2201",
"arxiv_id": "2201.04447",
"language": "en",
"url": "https://arxiv.org/abs/2201.04447"
} |
\section{Introduction}
We consider supervised learning using deep neural networks. Let $(X_1,Y_1),...,(X_n,Y_n)$ be $n$ i.i.d. observed pairs in $\mathcal{X} \times \mathcal{Y}$ with input space $\mathcal{X}$ and output space $\mathcal{Y}$. Write $f(\cdot;\mathcal{A}): \mathcal{X} \to \mathcal{Y}$ for a function gener... | {
"timestamp": "2022-01-13T02:23:06",
"yymm": "2201",
"arxiv_id": "2201.04545",
"language": "en",
"url": "https://arxiv.org/abs/2201.04545"
} |
\section*{Plain Language Summary}
Previous studies of the reflectance spectra of Uranus and Neptune have concentrated on individual, narrow wavelength regions and the conclusions have been difficult to compare with each other. Here, we analyse a combined set of observations from three different instruments covering the... | {
"timestamp": "2022-01-13T02:21:38",
"yymm": "2201",
"arxiv_id": "2201.04516",
"language": "en",
"url": "https://arxiv.org/abs/2201.04516"
} |
\section{Introduction} \label{sec1}
\begin{figure*}[t]
\includegraphics[width=0.90 \textwidth]{setup27.pdf}
\caption{A comparison of three general schemes to achieve an enhancement in estimating an unknown parameter $\varphi$. (a) Classical scheme consisting of independent and uncorrelated systems where each probe i... | {
"timestamp": "2022-01-13T02:16:26",
"yymm": "2201",
"arxiv_id": "2201.04412",
"language": "en",
"url": "https://arxiv.org/abs/2201.04412"
} |
\section{Derivation of the MPC prediction matrices} \label{appendix:MPC}
This appendix concerns the derivation of the MPC prediction matrices, which are used to describe the evolution of the states and output over the prediction horizon. Remember the relations $t(0|k)=t(k) \in \mathbb{R}_{\geq0}$, $\olsi{x}(0|k)=\olsi{... | {
"timestamp": "2022-01-13T02:23:08",
"yymm": "2201",
"arxiv_id": "2201.04550",
"language": "en",
"url": "https://arxiv.org/abs/2201.04550"
} |
\section{Introduction and main results}
The remarkably versatile experimental conditions of cold atoms physics allow to emulate several condensed matter phenomena in a well-controlled fashion. A very interesting direction is to simulate the effect of an external magnetic field on a coherent matter wave, in analogy w... | {
"timestamp": "2022-01-13T02:16:42",
"yymm": "2201",
"arxiv_id": "2201.04418",
"language": "en",
"url": "https://arxiv.org/abs/2201.04418"
} |
\section{Introduction} \label{sec:introduction}
In light of the on-going COVID-19 pandemic, the understanding of how \sloppy{virus-containing droplets exhaled during respiratory events (e.g., when coughing, sneezing or talking)} travel in the surrounding environment has gained considerable importance~\cite{bahl2020air... | {
"timestamp": "2022-01-13T02:23:38",
"yymm": "2201",
"arxiv_id": "2201.04556",
"language": "en",
"url": "https://arxiv.org/abs/2201.04556"
} |
\section{Introduction}
\label{sec:intro}
Identifying the nature of dark matter (DM) and dark energy (DE), the two dominant components of the Universe, is among the most pressing issues in physics~\citep[for a review see e.g.][]{Sahni:2004ai}. State-of-the-art strategies for probing the microphysical nature of DM are n... | {
"timestamp": "2022-03-09T02:16:32",
"yymm": "2201",
"arxiv_id": "2201.04528",
"language": "en",
"url": "https://arxiv.org/abs/2201.04528"
} |
\section{Introduction}
\IEEEPARstart{C}{hronic} obstructive pulmonary disease (COPD) is one of the most prevalent lung diseases and a leading cause of chronic morbidity and mortality worldwide \cite{adeloye2015global}. Airway narrowing and remodeling are typical COPD characteristics. Therefore, assessing airway remodel... | {
"timestamp": "2022-01-13T02:22:18",
"yymm": "2201",
"arxiv_id": "2201.04532",
"language": "en",
"url": "https://arxiv.org/abs/2201.04532"
} |
\section{Introduction}
AI models have greatly improved their classification accuracy primarily due to the power and flexibility of DNNs. While original efforts focused on image related classification problems, their application domain has extended to various diverse areas such as healthcare assistive technologies, natu... | {
"timestamp": "2022-01-13T02:23:42",
"yymm": "2201",
"arxiv_id": "2201.04562",
"language": "en",
"url": "https://arxiv.org/abs/2201.04562"
} |
\section{Introduction}
In nuclear physics we use transparent models not only to understand the
observed characteristics of nuclear spectra and dynamics but also to
provide checks and guidance on the complex computer codes that produce
the quantitative theory of their properties.
The Lipkin model is a typical exam... | {
"timestamp": "2022-03-08T02:20:01",
"yymm": "2201",
"arxiv_id": "2201.04495",
"language": "en",
"url": "https://arxiv.org/abs/2201.04495"
} |
\section{Introduction}
By the celebrated Stone duality, the category ${\sf BA}$ of boolean algebras is dually equivalent to the category ${\sf Stone}$ of Stone spaces (zero-dimensional compact Hausdorff spaces). The functor from ${\sf Stone}$ to ${\sf BA}$ associates with each Stone space $X$, the boolean algebra $\Cl... | {
"timestamp": "2022-01-13T02:17:20",
"yymm": "2201",
"arxiv_id": "2201.04423",
"language": "en",
"url": "https://arxiv.org/abs/2201.04423"
} |
\section{Introduction}
Entrywise functions of matrices preserving positive semi-definiteness has been a topic of active research. The long history of this field starts with the Schur product theorem (see \cite{HJ}), followed by the works of Schoenberg\cite{IS}, Rudin\cite{WR} and others. In particular, the study of en... | {
"timestamp": "2022-01-13T02:18:20",
"yymm": "2201",
"arxiv_id": "2201.04443",
"language": "en",
"url": "https://arxiv.org/abs/2201.04443"
} |
\section{Introduction}\label{s:intro}
For complex-valued functions on the hyperbolic plane that are simultaneously
eigenfunctions of the hyperbolic Laplacian and periodic in a horocycle
direction\footnote{We refer to Section~\ref{sec:setting} for precise
definitions. Using the upper half plane model~\eqref{eq:intr... | {
"timestamp": "2022-01-13T02:18:41",
"yymm": "2201",
"arxiv_id": "2201.04454",
"language": "en",
"url": "https://arxiv.org/abs/2201.04454"
} |
\section{Introduction}
Energy-optimal path planning on nonlinear spaces such as Riemannian manifolds has been an active field of interest in the last decades due to its numerous applications in manufacturing, aerospace technologies, and robotics \cite{blochgupta, hussein, ring}. It is often the case that the desired pa... | {
"timestamp": "2022-01-13T02:15:55",
"yymm": "2201",
"arxiv_id": "2201.04395",
"language": "en",
"url": "https://arxiv.org/abs/2201.04395"
} |
\section{Introduction}\label{sec:Introduction}
\captionsetup[figure]{labelfont={default},labelformat={default},labelsep=period,name={Fig.}} \captionsetup[table]{labelfont={default},labelformat={default},labelsep=newline,name={TABLE},textfont={sc},justification=centering}The\let\thefootnote\relax\footnotetext{Work fu... | {
"timestamp": "2022-01-13T02:19:08",
"yymm": "2201",
"arxiv_id": "2201.04472",
"language": "en",
"url": "https://arxiv.org/abs/2201.04472"
} |
\section{Introduction}
\noindent
In this paper, we consider the following nonlinear Schr\"{o}dinger equation
\begin{equation}\label{equ:double}
\begin{cases}
i\partial_tu+\Delta u+|u|^{\frac{4}{3}}u
+\mu\left(|x|^{-2}*|u|^2\right)u=0,\,\,t\in\mathbb{R},\,x\in\mathbb{R}^3,\\
u(0,x)=u_0(x)\in H^1(\mathbb{R}^3),
\end{case... | {
"timestamp": "2022-01-13T02:21:04",
"yymm": "2201",
"arxiv_id": "2201.04500",
"language": "en",
"url": "https://arxiv.org/abs/2201.04500"
} |
\section{Introduction}
Cell-free massive multiple-input multiple-output (MIMO) was introduced in \cite{Ngo2017} to overcome the inter-cell interference which is the main inherent limitation of cellular-based networks. In cell-free massive MIMO, many access points (APs) distributed
over the whole network serve many us... | {
"timestamp": "2022-01-13T02:18:17",
"yymm": "2201",
"arxiv_id": "2201.04440",
"language": "en",
"url": "https://arxiv.org/abs/2201.04440"
} |
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