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\section{Introduction} Let $G$ be a simple undirected graph with the \textit{vertex set} $V(G)$ and the \textit{edge set} $E(G)$. A vertex with degree one is called a \textit{pendant vertex}. The distance between the vertices $u$ and $v$ in graph $G$ is denoted by $d_G(u,v)$. A cycle $C$ is called \textit{chordless} if... | b7c40b41b7eedaa408f87d154284a1aba126589c |
\section{Principle of nano strain-amplifier} \begin{figure*}[t!] \centering \includegraphics[width=5.4in]{Fig1} \vspace{-0.5em} \caption{Schematic sketches of nanowire strain sensors. (a)(b) Conventional non-released and released NW structure; (c)(d) The proposed nano strain-amplifier and its simplified physical model.... | 1b77ae9f541b19668cc96624c7ec0f83945284e2 |
\section{Introduction}\label{intro} Gas has a fundamental role in shaping the evolution of galaxies, through its accretion on to massive haloes, cooling and subsequent fuelling of star formation, to the triggering of extreme luminous activity around super massive black holes. Determining how the physical state of gas i... | 467d37196f1b4f439bbd55a25dd550222fb466db |
\section{Introduction} Given $\rho>0$, we consider the problem \begin{equation}\label{eq:main_prob_U} \begin{cases} -\Delta U + \lambda U = |U|^{p-1}U & \text{in }\Omega,\smallskip\\ \int_\Omega U^2\,dx = \rho, \quad U=0 & \text{on }\partial\Omega, \end{cases} \end{equation} where $\Omega\subset{\mathbb{R}}^N$ is a Lip... | bdfca2090653522b89d9415dc698595c4bfce1ec |
\section{Introduction} \label{sec:intro} Despite the immense popularity and availability of online video content via outlets such as Youtube and Facebook, most work on object detection focuses on static images. Given the breakthroughs of deep convolutional neural networks for detecting objects in static images, the app... | 0139d272d2b2af4606ec78c8e956da717b63bad8 |
\section{Introduction} The wave-particle duality is an alternative statement of the complementarity principle, and it establishes the relation between \ankb{corpuscular and undulatory}{the corpuscular and the ondulatory} nature of quantum entities \cite{Bohr1928}. It can be illustrated in a two-way interferometer, wher... | ef6fecbf91bf23ce97668d9e0f68279d16e146af |
\section{#1}\setcounter{equation}{0}} \newcommand{\subsect}[1]{\subsection{#1}} \renewcommand{\theequation}{\arabic{section}.\arabic{equation}} \font\mbn=msbm10 scaled \magstep1 \font\mbs=msbm7 scaled \magstep1 \font\mbss=msbm5 scaled \magstep1 \newfam\mbff \textfont\mbff=\mbn \scriptfont\mbff=\mbs \scriptscriptfont\mb... | 12790d44df56e9367af1706e5d4b7a67a1df785f |
\section{Introduction} \label{sec:introduction} In recent years there has been a resurgence of interest in the properties of metastable states, due mostly to the studies of the jammed states of hard sphere systems; see for reviews Refs. \onlinecite{charbonneau16, baule16}. There are many topics to study, including for ... | 3935b10ebd2ab44f820e6d8233731be14a55d558 |
\section{Introduction} \label{sec:intro} The production of hadrons and jets at a future Electron Ion Collider (EIC) will play a central role in understanding the structure of the protons and nuclei which comprise the visible matter in the universe. Measurements of inclusive jet and hadron production with transversely p... | 417ff865a9cbac3a94a3b3975ec2721852d90a63 |
\section{Introduction} \label{sec:intro} Compact stars have a large number of pulsation modes that have been extensively studied since the seminal work of Chandrasekhar on radial oscillations \cite{APJ140:417:1964,PRL12:114:1964}. In general, these modes are very difficult to observe in the electromagnetic spectrum; th... | 1c5ca046551cfa4aa819c11109c3debac9a8e52b |
\section{Introduction} Ultra-cold molecules can play important roles in studies of many-body quantum physics~\cite{pupillo2008cold}, quantum logic operations~\cite{demille2002quantum}, and ultra-cold chemistry~\cite{ni2010dipolar}. In our recent studies of LiRb, motivated largely by its large permanent dipole moment~\c... | d95635bc08fd14ade0a89cf08420e98ffd0f6b8b |
\section{Introduction}\label{sec:introduction} The use of GPS for localizing sensor nodes in a sensor network is considered to be excessively expensive and wasteful, also in some cases intractable, \cite{bul:00,bis:06}. Instead many solutions for the localization problem tend to use inter-sensor distance or range measu... | d8a5e808b3b90b0513cf0c72dcfd2e3df48814d2 |
\section{Introduction} Quantum theory of gravity is one of the most sought-after goals in physics. Despite continuous efforts to tackle this important problem, resulting in interesting proposals such as superstring theory and loop quantum gravity, there is still no clear sign of the theory of quantum gravity \cite{Giul... | 3a890d61b35aff2fdcf6bc715cfb6957a8a2cb8c |
\part{Background} \bigskip \addcontentsline{toc}{section}{1. Preliminaries} \textbf{\S 1. Preliminaries} \stepcounter{section} \bigskip The prerequisites for reading this paper are a background of one year of graduate level study in set theory, a working knowledge of forcing, and some basic familiarity with proper forc... | 6e964ae3be26a56c939b5985e33af46f1e30cd66 |
\section{Introduction} The concept of synchronistion is based on the adjustment of rhythms of oscillating systems due to their interaction \cite{pikovsky01}. Synchronisation phenomenon was recognised by Huygens in the 17th century, time when he performed experiments to understand this phenomenon \cite{bennett02}. To da... | 1ba0a8c597a5b6ee0830ca23c5b9ab8ce3b62efd |
\subsection{Power} \noindent PMTs that meet the required specifications in terms of pulse rise time, dark current and counting rates, and quantum efficiency require applied high voltages (HV) between $1-2.5$~kV and have maximum current ratings of $0.2-0.5$~mA. For the detector design using 12 read-out channels per modu... | a5fd2f310d6714cde82b7c04bb3e6f796c5aae70 |
\section{Introduction Throughout this paper, let $R$ denote a commutative Noetherian ring with identity and ${\mathfrak a}$ a proper ideal of $R$. For any non-zero $R$-module $M$, the ith local cohomology module of $M$ is defined as $$H^{i}_{{\mathfrak a}}(M):=\lim_{\underset{n\geq 1}{\longrightarrow}} \operatorname{Ex... | 2f59f7879be9c80f1df4909ebccace08db257c28 |
\section{Introduction} To write high-quality program code for a Multi-Processor System-on-Chip (MPSoC), software developers must fully understand how their code will be executed on-chip. Debugging and tracing tools can help developers to gain this understanding. They are a keyhole through which developers can peek and ... | c06ec0f30465dd21ff3ea5027d2bbfa652a2e3e5 |
\section{Introduction} \label{sec:intro} The Type~Ia supernova (SN~Ia) SN~2011fe was discovered on 2011 August 24, just 11~hr after explosion \citep{nugent11}. It is among the nearest ($\sim 6.9$~Mpc) and youngest ($\sim 11$~hr) SNe~Ia ever discovered. Extensive spectroscopic and photometric studies of SN~2011fe indica... | d18a74adc6f563a5494f9cf0ee38af9746eada63 |
\section{High-field instability from spin-wave theory} In the asymptotic high-field limit all spins are aligned along the field axis. Magnon excitations are suppressed by a large energy gap. By lowering the field strength the magnon gap decreases and eventually vanishes at some critical field strength $h_{\mathrm{c}0}$... | 185e9f90d93d078196d46d0c79174714237f3669 |
\section{Introduction} The black hole information puzzle is the puzzle of whether black hole formation and evaporation is unitary, and debate on this issue has continued for more than 36 years \cite{Page:1993up, Giddings:2006sj, Mathur:2008wi}, since Hawking radiation was discovered \cite{Hawking:1974sw}. Hawking origi... | c7dfc98266d9a9c36e71efeb0e655803ef3a7190 |
\section{Results} The actuation concept consists of two elements. First, the conversion of rotation into time-reversible translation is achieved by each particle separately, hence, a single-particle problem. Second, the breaking of the time reversibility arises from the interaction between the particles in a cluster. I... | 5410a4b3a1b09f1912adf6ec69edc991a5231d5d |
\section{Introduction} Currents of spin angular momentum play a central role in the field of spintronics. Significant contributions have been made by spin currents, such as control of magnetizations by spin transfer torque,\citep{PhysRevLett.84.3149,demidov2011control,berger1996emission,ralph2008spin} transmission of e... | 842d24bc33ac769220affce1ce229e3d0c36375b |
\section{Introduction}\label{introduction} \setcounter{equation}{0} \numberwithin{equation}{section} In the present paper, we consider the equation \begin{equation}\label{1.1} -y''(x)+q(x)y(x )=f(x),\quad x\in \mathbb R \end{equation} where $f\in L_p^{\loc}(\mathbb R)$, $p\in[1,\infty)$ and \begin{equation}\label{1.2} ... | 7c6ec6b07f6e9cc57c84968ebb95269aa2395b34 |
\section{Introduction} Spectral embedding methods are based on analyzing Markov chains on a high-dimensional data set $\left\{x_i\right\}_{i=1}^{n} \subset \mathbb{R}^d$. There are a variety of different methods, see e.g. Belkin \& Niyogi \cite{belk}, Coifman \& Lafon \cite{coif1}, Coifman \& Maggioni \cite{coif2}, Don... | 48196a99e6c64a2673a380447e415ed30b20c95a |
\section{Introduction}\label{sintro} \section{Background: CUR and low-rank approximation}\label{sbcgr} {\em Low-rank approximation} of an $m\times n$ matrix $W$ having a small numerical rank $r$, that is, having a well-conditioned rank-$r$ matrix nearby, is one of the most fundamental problems of numerical linear algeb... | ff44ea6d25a77da54b74b5060a441c09c58b4dfa |
\section{Introduction} NGC 4660 is an E5 elliptical galaxy with a strong incrusted disk component, and has frequently been used as a `classic' example of this type of galaxy. As such it has appeared frequently in the literature. It is located in the Virgo cluster, and has been identified as a member of the nearest comp... | daee9918f4f93de04946c46745d1c314288d3d3e |
\section*{Supplemental Material} In this Supplemental Material, we provide more numerical data for the ground-state entanglement entropy and entanglement spectrum. \subsection*{Ground-state entanglement entropy} In the main text, we have discussed the ground-state entanglement entropy $S(\overline{\rho})$ obtained by a... | 5fab997cf8b27e973a64a061be0aa50cb3e2044f |
\section{Introduction} The shallow water equations (Saint-Venant \cite{Saint-Venant1871}) are a common $(d - 1)$ approximation to the $d$--dimensional Navier-Stokes equations to model incompressible, free surface flows. Due to the ability of high-order Galerkin methods to keep dissipation and dispersion errors low (Ain... | d53bbf469ca04bb5fbd7062a450cba2c00479b10 |
\section{Introduction and Summary of Results} The problem of admissible functional-classes has been of recent interest in the context of higher-spin (HS) theories \cite{Vasiliev:1990en}. In particular, in \cite{Kessel:2015kna,Boulanger:2015ova} the quadratic interaction term sourcing Fronsdal's equations was extracted ... | 9b897dee32341df521b91e8a88f9d2b9a04e562f |
\section{Introduction} \blfootnote{ % % % % \hspace{-0.65cm} This work is licensed under a Creative Commons Attribution 4.0 International License. License details: \url{http://creativecommons.org/licenses/by/4.0/} } Argumentation mining is a relatively new challenge in corpus-based discourse analysis that involves auto... | 03df1d25322bbd4914a5768042c64fe6efc97101 |
\section{Menger co-analytic groups} We shall assume all spaces are completely regular. \begin{defn} A topological space is \textbf{analytic} if it is a continuous image of $\mathbb{P}$, the space of irrationals. A space is \textbf{Lusin} if it is an injective continuous image of $\mathbb{P}$. (This is the terminology o... | ff4a6df1a52f4891034852c14c652312e4fea285 |
\section{Introduction} There are many open questions regarding the strength and geometry of the magnetic field in radio galaxies and their relation to other properties of the radio source. The observed degree of polarization depends on the intrinsic properties, such as the regularity and orientation of the source magne... | 31ec072526eada9187ae9e5d9bca9e7b1fe6f89c |
\section{Introduction}\label{sec:intro} The constraint satisfaction problem (CSP) provides a framework in which it is possible to express, in a natural way, many combinatorial problems encountered in computer science and AI~\cite{Cohen06:handbook,Creignou01:book,Feder98:monotone}. An instance of the CSP consists of a s... | 3831f5d43651b93443f7b97153ed8ff9384f90a1 |
\section{Introduction} \label{sec:Introduction} Topological insulators (TIs) form a class of materials with unique properties, associated with a non-trivial topology of their quasiparticle band structure (for a review, see Refs.~\cite{Zhang:rev, Hasan-Kane:rev, Hasan-Moore:rev, Ando:rev}). The key feature of two-dimens... | bcd73857a29c93a81082cd2b5634975a37343c29 |
\section{Gibbs' Canonical Ensemble} From Gibbs' 1902 text {\it Elementary Principles in Statistical Mechanics}, page 183 : \begin{quotation} ``If a system of a great number of degrees of freedom is microcanonically distributed in phase, any very small part of it may be regarded as canonically distributed.'' \end{quotat... | 4df0043dbd096d6c69998163b90855e98340756c |
\section{Introduction} In recent decades acoustic techniques in solid state physics demonstrate serious progress, especially by moving to previously unattainable high-frequency band, up to a terahertz frequencies \cite{ps-ultrasonics}. Considerable efforts in this direction, called often picosecond ultrasonics, are sti... | fe9f0cbedace3b1bc230475543afbb1bc2881730 |
\section{Introduction} \label{sec:intro} Atmospheric metals are not expected to be present in isolated white dwarfs (WDs) with effective temperatures below $\sim25,000$ K. At these temperatures, radiative forces become too weak \citep{chayer95} to significantly counteract the quick gravitational settling that sinks mat... | f059ade8ca1b6c7457fa8310cb89acd964da485d |
\section{Introduction} In his book ``Proximal Flows''~\cite[Section~\RNum{2}.3, p.\ 19]{glasner1976proximal} Glasner defines the notion of a {\em strongly amenable group}: A group is strongly amenable if each of its proximal actions on a compact space has a fixed point. A continuous action $G \curvearrowright X$ of a t... | 307a7516e620bdb53ec72d9db06c57a1b2448573 |
\section{Introduction} \label{sec:1} The influence of social groups in pedestrian dynamics, especially in evacuation scenarios, is an area of recent interest, see e.g. \cite{mueller2,mueller} and other contributions in these proceedings. The situations that are considered are widespread and well-known in everyday life.... | e446ef41a60af69ad04b265c37552ed3922672e1 |
\section{Introduction} \label{sec:intro} Policy search algorithms based on supervised learning from a computational or human ``teacher'' have gained prominence in recent years due to their ability to optimize complex policies for autonomous flight \cite{rmswd-lmruc-13}, video game playing \cite{rgb-rilsp-11,gsllw-amcts... | b2626f3873b25d41c2de31c91c507e7e8082993f |
\section{Introduction} Spatio--temporal models are widely used by practitioners. Explaining economic, environmental, social, or biological phenomena, such as peer influence, neighbourhood effects, contagion, epidemics, interdependent preferences, climate change, and so on, are only some of the interesting applications ... | c2084d91152fccc47f8e0c5b3c965e679a0d55ea |
\section*{Abstract}{\small Here is considered the full evolution of a spherical supernova remnant. We start by calculating the early time ejecta-dominated stage and continue through the different phases of interaction with the circumstellar medium, and end with the dissipation and merger phase. The physical connection ... | ea26d50ef9855d66aef5d2296d47fb43cf42e00c |
\section{Introduction} The purpose of this paper is to provide a convenient operadic framework for the cumulants of free probability theory. In~\cite{DrummondColeParkTerilla:HPTI,DrummondColeParkTerilla:HPTII}, the author and his collaborators described an operadic framework for so-called Boolean and classical cumulant... | ba21779ca4df037124955b1d43a715e5c701dcfa |
\section{Introduction} The Navier-Stokes equations (NSEs) represent a formulation of the Newton's laws of motion for a continuous distribution of matter in a fluid state, characterized by an inability to support shear stresses, see \cite{Doering-Gibbon}. The NSEs allow to determine the velocity field and the pressure o... | c119738c8140213d35cc0c262585ef2842765f45 |
\section{Introduction} Germanium is widely used as a detector material in experiments searching for a rare process like the interaction of weakly interacting massive particles (WIMPs)~\cite{dmreview}. It is possible to build detectors with very good energy resolution based on the measurement of the ionization produced ... | d1c27e8f8bf8c3fc658b94c78ecb9ad84b736d71 |
\section{Introduction.} Katz \cite[5.3.1]{Katz90ESDE} discovered that the hypergeometric $\sD$-modules on $\bA^1_{\bC}\setminus\{0\}$ can be described as the multiplicative convolution of hypergeometric $\sD$-modules of rank one. Precisely speaking, Katz proved the statement (ii) in the following theorem (the statement... | 8b38a56a8d3dfec99cda595719feed3583d351f9 |
\section{Introduction} Many problems, particularly in combinatorics, reduce to asking whether some graph with a given property exists, or alternatively, asking how many such non-isomorphic graphs exist. Such graph search and graph enumeration problems are notoriously difficult, in no small part due to the extremely lar... | 461c005ff63aee7aa7a74b332faadbc07ca57726 |
\section{\label{intro}Introduction} The ``instanton calculus'' is a common approach for studying the non-perturbative semiclassical effects in gauge theories and sigma models. One of the first and perhaps the best known illustration of this approach is the $O(3)$ Non-Linear Sigma Model (NLSM) in two dimensions, where m... | 50d97946ad5e25c8d148a3d665dd68f161cea3ba |
\section{Introduction} The motivation for this note was the observation that the basic recursion relation for the modified Bessel function $K$[1], $$K_0(z)+\left(\frac{2}{z}\right)K_1(z)=K_2(z)$$ can be expressed as the symmetry with respect to $m=0$ and $n=1$ of the sum $$\sum_{k=0}^n K_{k-m-1}(z)\left(\frac{z}{2}\rig... | 702ece0f7a9b408770cf6d81d20d81b11c11d0e5 |
\section{Introduction} For decades, the microscopic process which causes a linear-in-temperature term in the electrical resistivity of pure ferromagnetic metals (Fe, Co and Ni) at low temperatures---which is clearly observed around liquid-helium temperatures \cite{Campbell,Volkenshtein}---has remained unclear. In this ... | e618a3994cacdcd915be6c81aa7aff50b5abc60a |
\section{Handling batch insertions} In this section, we study the dynamic DFS tree problem in the batch insertion setting. The goal of this section is to prove Theorem \ref{batch-ins}. Our algorithm basically follows the same framework for fully dynamic DFS proposed in \cite{baswana2016dynamic}. Since we are only inter... | 34973f407d5ca4e750c9372e7cee1f1af47f89b1 |
\section{Introduction} \label{section:Introduction} Since 2012, the focus of Galactic center (GC) observations has been set on investigating an infrared (IR) excess source detected by \cite{Gillessen2012} as a fast-moving object approaching the position of the central supermassive black hole (SMBH) of the Milky Way, Sa... | 287255ae470416fd57cbbc11d592576739e71a00 |
\section{Introduction} A concordance of observations support a universe whose energy budget is dominated by the unknown elements of dark energy (DE) and dark matter (DM), while baryonic matter occupies only around 5\% of the total energy \cite{concord1,concord2,wmap9,planck2013,planck2015}. Focusing on DM, all concrete... | b26025642b0a26f49d0c14cd2ade145b9ea460f9 |
\section*{References}} \usepackage{graphicx} \usepackage{amsmath} \usepackage{natbib} \usepackage{amssymb} \usepackage{amsthm} \usepackage{lineno} \usepackage{subfig} \usepackage{enumerate} \usepackage{fullpage} \usepackage{algorithm} \usepackage{algpseudocode} \usepackage{xcolor} \usepackage[colorinlistoftodos]{todono... | acfcf9ae15b9762d15d4cf273fb5b434dfd8a101 |
\section{Introduction} Optical remote sensing has made significant advances in recent years. Among these has been the deployment and wide-spread use of hyperspectral imagery on a variety of platforms (including manned and unmanned aircraft and satellites) for a wide variety of applications, ranging from environmental m... | 45ba93c295302d5ab9571db456ed48805d2172e7 |
\section*{\refname}% \@mkboth{\MakeUppercase\refname}{\MakeUppercase\refname}% \list{\@biblabel{\@arabic\c@enumiv}}% {\settowidth\labelwidth{\@biblabel{#1}}% \leftmargin\labelwidth \advance\leftmargin\labelsep \@openbib@code \usecounter{enumiv}% \let\p@enumiv\@empty \itemsep=0pt \parsep=0pt \leftmargin=\parindent \item... | ff93b19cf23f2c010c37ca986e573725d1d60754 |
\section{Introduction}\label{sec:intro} A useful representation of the occupied states in a periodic insulator is the Wannier function. Wannier functions (WFs) provide a localized real-space description of the extended Bloch states.~\cite{MLWFs-Review} In particular, WFs give a chemical picture of the bonding nature of... | 1d17908881d0423d55305dc62465e3e4f84bfac9 |
\section{Introduction} \label{sec:introduction} Inference of the underlying point sources in photon count maps is a recurring problem in astronomy. Potential challenges include poorly known backgrounds, detector noise, shot noise from faint or modeling degeneracies from overlapping point sources. The resulting symptom ... | ac91c1ed2afc0d0bef05a4fbab6b16f61d9756c9 |
\section{Introduction} A basic problem in Riemannian geometry is that of describing curvatures on a given manifold. Suppose that $(\Sigma,g)$ is a 2-dimensional compact Riemannian manifold without boundary, and $K$ is the Gaussian curvature on it. Let $\widetilde{g}=e^{2u}g$ be a metric conformal to $g$, where $u\in C^... | ccaf2bdbdea134ed38d947f8a0b77e33783f4a48 |
\section{Introduction} It is well known that a gas composed of bosonic atoms with repulsive interparticle interaction at appropriate values of density and temperature undergoes Bose-Einstein condensation (BEC), a phase transition which shares similarities to transitions to superfluid and superconductive states. Since t... | 7b579c13dd17bdcca3252d58b00171cbb934decd |
\section{Introduction} Cell-Free massive multiple-input multiple-output (MIMO) refers to a massive MIMO system \cite{MarzettaNonCooperative} where the base station antennas are geographically distributed \cite{NgoCF,MarzettaCF,Truong}. These antennas, called access points (APs) herein, simultaneously serve many users i... | a9b85c0df78f30693c2498d4c57fe32bdf0a3b3a |
\section*{Introduction} Carbon nanotubes (CNTs) are promising nanomaterials, which have been extensively studied by many researchers \cite{cnt1,cnt2,cnt3,cnt4,cnt5,cnt6,cnt7,cnt8,cnt9,cnt10,25,27,28,23,16}. Due to different combinations of structural variation, CNTs can exhibit a wide range of electronic and optical pr... | ec2123e1664f35ffb4af3470b792dcf9e5391c4c |
\section{Introduction} \label{intr} The frameworks of nonstationary nonperiodic and periodic wavelets are introduced and studied separately. The notion of nonstationary wavelet system is introduced independently by M.~Z.~Berkolayko, I.~Y.~Novikov \cite{BN} and by C.~de Boor, R.~DeVore, A.~Ron \cite{BDR}. In \cite{BN}, ... | 252379e632a62c2e5e4d2d4b4a5b2d2273214ec3 |
\section{Introduction} In this paper we consider the problem of finding the number of representations of the following quadratic forms in eight variables given by \begin{equation}\label{quad1} a_1x_1^2 + a_2 x_2^2 + a_3 x_3^2 + a_4 x_4^2 + b_1(x_5^2+x_5x_6 + x_6^2) + b_2(x_7^2+x_7x_8 + x_8^2), \end{equation} where the ... | d0819eb72ed67bc6b70ad623097618d7d680d039 |
\section{Introduction} Artificial neural networks are currently considered the state of the art in applications ranging from image classification, to speech recognition and even machine translation. However, little is understood about the process by which they are trained for supervised learning tasks. The problem of o... | 8b991deac18813db505269eef74924c02c11333b |
\section{Introduction} \subsection{Background and Importance} The minor planets orbiting beyond Neptune provide valuable insight on our solar system's formation and evolution, but they have only been studied since 1992 when the first Trans-Neptunian Object (TNO) after Pluto was discovered \citep{Luu1993}. Almost a quar... | 09724d78fabb82092f078405fbbf006bb4de8668 |
\section{Introduction} \label{sec:intro} The extraction of the transport properties of the strongly interacting medium created in heavy ion collision (HIC) experiments is currently a very active topic of research in the HIC community. The methods of relativistic hydrodynamics with minimal viscous correction have been q... | 0096a890f6b8d5115be38da0f72ecb222b6453b3 |
\section{Introduction} Observations have established the presence of magnetic field of various magnitudes and on various spatial scales in our universe. Galaxies such as Milky Wave contain regular magnetic fields of the order of $\mu$G, while coherent fields of the order of $100~\mu$G are detected in distant galaxies \... | 5f24b5927a023e8542f9f621e69759e4bb323094 |
\section{Introduction}\label{s1} In this paper, we consider distributed optimization problems where the goal is to minimize a sum of objective functions over a multi-agent network. Formally, we consider a decision variable,~$\mb{z}\in\mbb{R}^p$, and a strongly-connected network containing~$n$ agents, where each agent,~... | 0f25400f40b77edfa427d6c0b2cfd785aca148a2 |
\section{Introduction} \label{intro} Suitable models for the theory of computation and approximation are certain (quasi-)ordered sets, whose elements represent states of computation, knowledge or information, while the order abstractly describes refinement, improvement or temporal sequence. Let us briefly record the re... | 5d70cdcad4f6f6cc3f83289220a137ba17b24018 |
\section{I. \ Objective function used to correct the ZZ-error channel} Thanks to the isomorphism between SU(2) generators, $\sigma_X,\sigma_Y, \sigma_Z$, and the subgroup of SU(4) generators, $\sigma_{ZZ},\sigma_{ZX},\sigma_{IY}$, the right hand side of Eq. (11) can be expressed in a more tractable way as \begin{equati... | e0fc6263b2acf1dcdcec341879b91fa2489ba23b |
\section{Introduction} The combinatorial structure treated in this paper is a $2 \rightarrow 1$ directed hypergraph defined as follows. \begin{definition} A \emph{$2 \rightarrow 1$ directed hypergraph} is a pair $H = (V,E)$ where $V$ is a finite set of \emph{vertices} and the set of \emph{edges} $E$ is some subset of t... | 2b9759a1c56a44ff4776ae40175fecde3930f8aa |
\section{Introduction and Motivations}\label{sec:intro} The aim of the paper is to study a new notion of two-scale convergence\footnote{A deep bibliographic research, shows that the idea here presented is suggested in an paper (of the late seventies and so well before the introduction of the notion of two-scale converg... | 7913db4bc34326311360779d4714be05023eb0bf |
\section{Introduction} The study of hereditary properties of combinatorial structures is an important topic within the field of extremal combinatorics. Out of the many results in this line of research has emerged an pattern for how to prove approximate asymptotic enumeration and structure results. The aim of this paper... | a19e7cc772382c45e130c49c1e5e55a9877042a0 |
\section{Introduction} Let $(\Omega,{\cal F},\mathbb{F},\mathbb{P})$ be a complete filtered probability space on which a standard one-dimensional Brownian motion $\{W(t),t\ges0\}$ is defined such that $\mathbb{F}=\{{\cal F}_t\}_{t\ges0}$ is the natural filtration of $W(\cdot)$ augmented by all the $\mathbb{P}$-null set... | 8a749c78a0fac3cfd39a257c74f9c55d3c1664b5 |
\section{Introduction} \label{sec:introduction} Let $G$ be a simple graph without isolated vertices. If the edge set of a simple graph $K$ can be partitioned into edge sets of graphs each isomorphic to $G$, we say that there exists a {\em decomposition} of $K$ into $G$. In the case where $K$ is the complete graph $K_n$... | cbc85a15fa71c0f6eb113890e1e1f047d4cdcfee |
\section{Simple bounds for the needed embedding constants} \def\Alph{section}{\Alph{section}} The following theorem provides the best constant in the classical Sobolev inequality with critical exponents. \begin{theo}[T.~Aubin \cite{aubin1976} and G.~Talenti \cite{talenti1976}]\label{talentitheo} Let $u$ be any function... | c35deb6e25c2d4726086571871c372586524a4e9 |
\section{Introduction} \label{sec:introduction} Bioinformaticians define the $k$th-order de Bruijn graph for a string or set of strings to be the directed graph whose nodes are the distinct $k$-tuples in those strings and in which there is an edge from $u$ to $v$ if there is a \((k + 1)\)-tuple somewhere in those strin... | f11ef27323222b08c16b381c698b58d670f5722f |
\subsection*{Acknowledgements} A large number of people have supplied advice and encouragement on this project over a period of many years. The undergraduates from my Introductory VIGRE Research Group held in Fall 2010 at the University of Georgia and my student Darcy Chanin performed many calculations for genus 4, 5, ... | 685c5c179c71703dff362282218196092868cfde |
\section{Preliminaries and Problem Formulation} \label{sec:prelims} \label{sec2} \paragraph{Bipartite Graphs} A \textbf{bipartite graph} $G=(\mathcal{M},\mathcal{B},E)$ is a graph such that the vertices $\mathcal{M}\cup \mathcal{B}$ can be divided into two disjoint subsets, $\mathcal{M}$ and $\mathcal{B}$, and there ar... | 37b1241402dc2d669283f6b66eb4e2f5c59730bf |
\section{Introduction}\label{section1} The majority of stars are born in large clusters, and so, these sites are key to understanding the stellar contents of galaxies. Until recently the Milky Way was believed to be devoid of large young clusters. The realisation that our Galaxy harbours many young clusters with masses... | 1c07eb1032a3137098d691a20059a4bec8845aa0 |
\section{Introduction}\label{sc_intro} In this paper we discuss the application of a skewed-$t$ model suitable to capture skewness and kurtosis commonly present in insurance risks data. In particular, we introduce a Bayesian approach based on minimal informative prior distributions \citep{Villa:Walker:2014b} to estimat... | 10c719ed75e2abe1b9cd25954114801efe8c331d |
\section{Introduction} \label{introduction} For future fusion devices such as ITER, operating at least in a partially detached state is important for reducing the heat flux incident on the divertor to below engineering limits (10 $\text{MW/m}^2$) \cite{LOARTE2007NF}. Modelling for ITER demonstrates reduction of the pea... | 5fff69caf411dbd51f9742206d76b22d147dec26 |
\section{Introduction: classical configuration theorems} \label{intro} Projective configuration theorems are among the oldest and best known mathematical results. The next figures depict the famous theorems of Pappus, Desargues, Pascal, Brianchon, and Poncelet. \begin{figure}[hbtp] \centering \includegraphics[height=1.... | 5468cfb4c7702025bd5eb65395f5e9e81f8a552e |
\section{Introduction} \label{sec.intro} Random linear network coding (RNLC) is the process of constructing coded packets, which are random linear combinations of source packets over a finite field \cite{Ho06}. If $k$ source packets are considered, decoding at a receiving node starts after $k$ linearly independent code... | 7ab653d1273e1535ea384433140b5fb7976c2689 |
\section{Introduction} \label{Fsec.1} In this paper we will study the probability of the hitting time to a moving boundary. To state the main result, we need some notations on a Brownian motion. Let us call $P_{r,s}, r\in\mathbb{R}, s\geq 0$, the law on $\displaystyle C([s,\infty))$ of the Brownian motion $B_t$, $t\geq... | 9f30788dd903452d27e1d45966994dbec6ccc838 |
\section{Introduction} Representations $\rho:\pi_1(M)\rar G$ of the fundamental group of of a manifold $M$ inside a Lie group $G$ naturally arise as monodromies of $(G,G/H)$-geometric structures \`a la Ehresmann \cite{ehresmann:infinitesimales} \cite{ehresmann:locales} on $M$ (see also \cite{goldman:geometric-structure... | 7c7871cedea49617171941f63cecc55b2bb183f0 |
\section{Introduction} Magneto-hydrodynamics (MHD) forms the basis of large-scale description of physics of dense plasma in compact stars. A key quantity in the dissipative formulations of MHD is the conductivity of matter. It determines, for example, the dissipation of currents and therefore the decay of magnetic fiel... | 7da1a44fb55455b4defef399ac008ce28f41d342 |
\section{Introduction} A popular version of the third law of thermodynamics is that the entropy density of a physical system tends to zero in the $T \to 0$ limit\cite{mandl}. However, there is a class of theoretical models that violate this law\cite{fowler33,pauling,nagle66,lieb67,chow87,bramwell01,castelnovo08}:\ mode... | 0de96d7b73ce49baf4120f35a6fc772776e9cc0f |
\section{Introduction} The calculation of the transport properties of strongly coupled quantum theories is a challenging puzzle of interest to theorists working on a wide range of systems including ultra-cold Fermi gases at unitarity~\cite{Adams:2012th,Bulgac:2010dg}, heavy ion collisions~\cite{Adams:2012th,Bhalerao:20... | b555261b90153dda8c7183c0b453562be50a19f8 |
\section{Introduction}\label{sec:intro} The precise manipulation of nano and sub-nanoscale physical systems lies at the heart of the ongoing quantum revolution, by which new communication and information technologies are expected to emerge \cite{bib:natphot2009,bib:nature2010}. In this context, an amazing progress has ... | 1e3ffacba3892591a49facee33fb5eefba8dc145 |
\section{Introduction} The coupling of electronic and nuclear motions plays a significant role in many fascinating scientific phenomena, e.g., photoreactions \cite{photo1,photo2,photo3}, molecular electronics \cite{molel1,molel2,molel3}, and strong-field processes \cite{SFEN1,SFEN2,SFEN3,SFEN4,SFEN5}. In particular, th... | bb081fabeebb0fdb8e3d1f6ede6f2fa306b9e013 |
\section{Introduction} In robotics motion planning and control, one major challenge is to specify a high level task for a robot without specifying how to solve this task. For legged locomotion such a task include a goal position to reach or to manipulate an object without specifying gaits, contacts, balancing or other ... | 929a6a71f937242c2ee06aa7ed3e9864fff7437a |
\section{Introduction} The combinatorial structure treated in this paper is a $2 \rightarrow 1$ directed hypergraph defined as follows. \begin{definition} A \emph{$2 \rightarrow 1$ directed hypergraph} is a pair $H = (V,E)$ where $V$ is a finite set of \emph{vertices} and the set of \emph{edges} $E$ is some subset of t... | 4c4bb3a9f4dad4f9fcd9559dc34711ca86db1f7a |
\section{Introduction} \label{sec:Intro} Wireless communication, by its inherent broadcast nature, is vulnerable to eavesdropping by illegitimate receivers within communication range of the source. Wyner in \cite{075wyner}, for the first time, information-theoretically addressed the problem of secure communication in t... | 45dc3a242155cda7490ef1e2ab7c9d1e213c6b7c |
\section{Introduction} The process of particle creation from quantum vacuum because of moving boundaries or time-dependent properties of materials, commonly referred as the dynamical Casimir effect (DCE)\cite{1,2}, has been investigated since the pioneering works of Moore in 1970 \cite{moor}, who showed that photons wo... | 072bc831d00d069997282016e47c9ad44dc7dc1e |
\subsection{Logarithmic neural scales} Receptive fields that are evenly-spaced and of equal width on a logarithmic scale (Fig.~\ref{fig:FreeSimo}a, top) lead naturally to the Weber-Fechner perceptual law. A logarithmic scale implies several properties of the receptive fields (Fig.~\ref{fig:FreeSimo}a bottom). A logarit... | b219d0e4676240f880f1ec8d83cff1941ab1d7b6 |
\section{Introduction} Relativity theory, quantum theory, and information theory are fundamental blocks of theoretical physics \cite{peres2004}. The goal of theoretical physics is to describe and, to a certain extent, understand natural phenomena. Unfortunately, complex difficulties arise when one attempts to merge gen... | cdd2136e2fe55783e95f9757d2e68d2dd56b0897 |
\section{Introduction} The handwritten signature is a widely accepted means of authentication in government, legal, and commercial transactions. Signature verification systems aim to confirm the identity of a person based on their signature \cite{jain_introduction_2004}, that is, they classify signature samples as ``ge... | 490da31f8763b0a623c5c49a47d8963a66578df6 |
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