url stringlengths 31 38 | title stringlengths 7 229 | abstract stringlengths 44 2.87k | text stringlengths 319 2.51M | meta dict |
|---|---|---|---|---|
https://arxiv.org/abs/1102.2350 | The best possible upper bound on the probability of undetected error for linear codes of full support | There is a known best possible upper bound on the probability of undetected error for linear codes. The $[n,k;q]$ codes with probability of undetected error meeting the bound have support of size $k$ only. In this note, linear codes of full support ($=n$) are studied. A best possible upper bound on the probability of u... | \section*{Upper bounds on $P_{\rm ue}(C,p)$ for linear codes $C$}
Let $n\ge k \ge 1$. An $[n,k;q]$ code is a linear code of length $n$ and dimension $k$ over the field $F_q$ of $q$ elements.
For an $[n,k;q]$ code $C$, the probability of undetected error $P_{\rm ue}(C,p)$ is the probability that a
codeword is cha... | {
"timestamp": "2011-02-14T02:01:34",
"yymm": "1102",
"arxiv_id": "1102.2350",
"language": "en",
"url": "https://arxiv.org/abs/1102.2350",
"abstract": "There is a known best possible upper bound on the probability of undetected error for linear codes. The $[n,k;q]$ codes with probability of undetected error... |
https://arxiv.org/abs/1703.09595 | Notes on Pointed Gromov-Hausdorff Convergence | The present article addresses to everyone who starts working with (pointed) Gromov-Hausdorff convergence. In the major part, both Gromov-Hausdorff convergence of compact and of pointed metric spaces are introduced and investigated. Moreover, the relation of sublimits occurring with pointed Gromov-Hausdorff convergence ... | \section{The compact case}\label{sec:GH-cpt}
Given a metric space, an interesting question is
whether it is possible to assign each two subsets a distance
such that this distance in turn defines a metric.
In \cite[Chapter VIII §6]{hausdorff}, Hausdorff answered this question
by describing what nowadays is called the... | {
"timestamp": "2017-03-29T02:08:54",
"yymm": "1703",
"arxiv_id": "1703.09595",
"language": "en",
"url": "https://arxiv.org/abs/1703.09595",
"abstract": "The present article addresses to everyone who starts working with (pointed) Gromov-Hausdorff convergence. In the major part, both Gromov-Hausdorff converg... |
https://arxiv.org/abs/2208.07781 | Note on the pinned distance problem over finite fields | Let F_q be a finite field with odd q elements. In this article, we prove that if E \subseteq \mathbb F_q^d, d\ge 2, and |E|\ge q, then there exists a set Y \subseteq \mathbb F_q^d with |Y|\sim q^d$ such that for all y\in Y, the number of distances between the point y and the set E is similar to the size of the finite f... | \section{Introduction}
Let $\mathbb F_q^d$ be the $d$-dimensional vector space over the finite field $\mathbb F_q$ with $q$ elements.
In 2005, Iosevich and Rudnev \cite{IR07} initially posed and studied an analogue of the Falconer distance problem over finite fields.
They asked for the minimal exponent $\alpha>0$ suc... | {
"timestamp": "2022-08-17T02:15:19",
"yymm": "2208",
"arxiv_id": "2208.07781",
"language": "en",
"url": "https://arxiv.org/abs/2208.07781",
"abstract": "Let F_q be a finite field with odd q elements. In this article, we prove that if E \\subseteq \\mathbb F_q^d, d\\ge 2, and |E|\\ge q, then there exists a ... |
https://arxiv.org/abs/0812.0456 | The existence of thick triangulations -- an "elementary" proof | We provide an alternative, simpler proof of the existence of thick triangulations for noncompact $\mathcal{C}^1$ manifolds. Moreover, this proof is simpler than the original one given in \cite{pe}, since it mainly uses tools of elementary differential topology. The role played by curvatures in this construction is also... | \section{Introduction}
The existence of the so called ``thick'' or ``fat'' triangulations
is an important both in Pure Mathematics, in Differential Geometry
(where it plays a crucial role in the computation of curvatures for
piecewise-flat approximations of smooth Riemannian manifolds, with
applications to Regge Calcu... | {
"timestamp": "2008-12-02T10:41:26",
"yymm": "0812",
"arxiv_id": "0812.0456",
"language": "en",
"url": "https://arxiv.org/abs/0812.0456",
"abstract": "We provide an alternative, simpler proof of the existence of thick triangulations for noncompact $\\mathcal{C}^1$ manifolds. Moreover, this proof is simpler... |
https://arxiv.org/abs/1807.06170 | Learning Convex Partitions and Computing Game-theoretic Equilibria from Best Response Queries | Suppose that an $m$-simplex is partitioned into $n$ convex regions having disjoint interiors and distinct labels, and we may learn the label of any point by querying it. The learning objective is to know, for any point in the simplex, a label that occurs within some distance $\epsilon$ from that point. We present two a... | \section{Introduction}\label{sec:introduction}
The computation of game-theoretic equilibria is a topic of long-standing interest in the algorithmic and AI communities. This includes computation in the ``classical'' setting of complete information about a game, as well as settings of partial information, communication-... | {
"timestamp": "2019-04-10T02:19:27",
"yymm": "1807",
"arxiv_id": "1807.06170",
"language": "en",
"url": "https://arxiv.org/abs/1807.06170",
"abstract": "Suppose that an $m$-simplex is partitioned into $n$ convex regions having disjoint interiors and distinct labels, and we may learn the label of any point ... |
https://arxiv.org/abs/2109.14559 | Asymptotic profiles of zero points of solutions to the heat equation | In this paper, we consider the asymptotic profiles of zero points for the spatial variable of the solutions to the heat equation. By giving suitable conditions for the initial data, we prove the existence of zero points by extending the high-order asymptotic expansion theory for the heat equation. This reveals a previo... | \section{Introduction}
We consider a Cauchy problem
\be\label{eq:main}
\begin{cases}
\dfrac{\partial u}{\partial t}=\dfrac{\partial^2 u}{\partial x^2} \quad (t>0,\ x\in\bR), \vspace{3mm}\\
u(0,x)=f(x) \quad (x\in\bR),
\end{cases}
\ee
where $u=u(t,x)\in\bR\ (t>0,x\in\bR)$ and $f\in L^1(\bR)\cap L^{\infty}(\bR)$.
Throug... | {
"timestamp": "2021-10-04T02:12:26",
"yymm": "2109",
"arxiv_id": "2109.14559",
"language": "en",
"url": "https://arxiv.org/abs/2109.14559",
"abstract": "In this paper, we consider the asymptotic profiles of zero points for the spatial variable of the solutions to the heat equation. By giving suitable condi... |
https://arxiv.org/abs/2201.08062 | A stabilizer-free $C^0$ weak Galerkin method for the biharmonic equations | In this article, we present and analyze a stabilizer-free $C^0$ weak Galerkin (SF-C0WG) method for solving the biharmonic problem. The SF-C0WG method is formulated in terms of cell unknowns which are $C^0$ continuous piecewise polynomials of degree $k+2$ with $k\geq 0$ and in terms of face unknowns which are discontinu... | \section{Introduction}
We consider the biharmonic equation of the form
\begin{subequations}
\begin{eqnarray}
\Delta^2 u&=&f,\quad \mbox{in}\;\Omega,\label{pde}\\
u&=&g_D,\quad\mbox{on}\;\Gamma,\label{pde-bc1}\\
\frac{\partial u}{\partial
\bm{n}}&=&g_N, \quad\mbox{on}\;\Gamma,\label{pde-bc2}
\end{eqnarray}
\end{subequa... | {
"timestamp": "2022-01-21T02:12:25",
"yymm": "2201",
"arxiv_id": "2201.08062",
"language": "en",
"url": "https://arxiv.org/abs/2201.08062",
"abstract": "In this article, we present and analyze a stabilizer-free $C^0$ weak Galerkin (SF-C0WG) method for solving the biharmonic problem. The SF-C0WG method is f... |
https://arxiv.org/abs/1507.02654 | Ranges of Unitary Divisor Functions | For any real $t$, the unitary divisor function $\sigma_t^*$ is the multiplicative arithmetic function defined by $\sigma_t^*(p^{\alpha})=1+p^{\alpha t}$ for all primes $p$ and positive integers $\alpha$. Let $\overline{\sigma_t^*(\mathbb N)}$ denote the topological closure of the range $\sigma_t^*$. We calculate an exp... | \section{Introduction}
For any $c\in\mathbb C$, the divisor function $\sigma_c$ is defined by $\sigma_c(n)=\sum_{d\mid n}d^c$. Divisor functions, especially $\sigma_1,\sigma_0$, and $\sigma_{-1}$, are among the most extensively-studied arithmetic functions \cite{Apostol, Hardy, Mitrinovic}. For example, two very class... | {
"timestamp": "2017-06-26T02:03:17",
"yymm": "1507",
"arxiv_id": "1507.02654",
"language": "en",
"url": "https://arxiv.org/abs/1507.02654",
"abstract": "For any real $t$, the unitary divisor function $\\sigma_t^*$ is the multiplicative arithmetic function defined by $\\sigma_t^*(p^{\\alpha})=1+p^{\\alpha t... |
https://arxiv.org/abs/2209.03722 | Percolation on High-dimensional Product Graphs | We consider percolation on high-dimensional product graphs, where the base graphs are regular and of bounded order. In the subcritical regime, we show that typically the largest component is of order logarithmic in the number of vertices. In the supercritical regime, our main result recovers the sharp asymptotic of the... | \section{Introduction}
\subsection{Background and motivation}
In 1960, Erd\H{o}s and R\'enyi \cite{ER60} discovered the following fundamental phenomenon: the component structure of the binomial random graph $G(d+1,p)$\footnote{As we mainly consider $d$-regular graphs, we use the slightly unusual notation of $G(d+1,p)$ ... | {
"timestamp": "2022-09-09T02:13:05",
"yymm": "2209",
"arxiv_id": "2209.03722",
"language": "en",
"url": "https://arxiv.org/abs/2209.03722",
"abstract": "We consider percolation on high-dimensional product graphs, where the base graphs are regular and of bounded order. In the subcritical regime, we show tha... |
https://arxiv.org/abs/1602.03865 | Higher signature Delaunay decompositions | A Delaunay decomposition is a cell decomposition in R^d for which each cell is inscribed in a Euclidean ball which is empty of all other vertices. This article introduces a generalization of the Delaunay decomposition in which the Euclidean balls in the empty ball condition are replaced by other families of regions bou... | \section{Introduction}
Let $X$ be a finite set of points in Euclidean space $\mathbb R^d$ of dimension $d \geq 2$. A cell decomposition of the convex hull $\mathrm{CH}(X)$ of $X$ is called a \emph{Delaunay decomposition} for $X$ if it satisfies the \emph{empty ball condition:} each cell of the decomposition is inscribe... | {
"timestamp": "2016-02-12T02:13:13",
"yymm": "1602",
"arxiv_id": "1602.03865",
"language": "en",
"url": "https://arxiv.org/abs/1602.03865",
"abstract": "A Delaunay decomposition is a cell decomposition in R^d for which each cell is inscribed in a Euclidean ball which is empty of all other vertices. This ar... |
https://arxiv.org/abs/2011.01291 | Singularity of sparse random matrices: simple proofs | Consider a random $n\times n$ zero-one matrix with "density" $p$, sampled according to one of the following two models: either every entry is independently taken to be one with probability $p$ (the "Bernoulli" model), or each row is independently uniformly sampled from the set of all length-$n$ zero-one vectors with ex... | \section{Introduction}
Let $M$ be an $n\times n$ random matrix with i.i.d.\ $\Ber(p)$
entries (meaning that each entry $M_{ij}$ satisfies $\Pr(M_{ij}=1)=p$
and $\Pr(M_{ij}=0)=1-p$). It is a famous theorem of Koml\'os\ \cite{Kom67,Kom68}
that for $p=1/2$ a random Bernoulli matrix is \emph{asymptotically
almost surely} ... | {
"timestamp": "2020-11-04T02:02:26",
"yymm": "2011",
"arxiv_id": "2011.01291",
"language": "en",
"url": "https://arxiv.org/abs/2011.01291",
"abstract": "Consider a random $n\\times n$ zero-one matrix with \"density\" $p$, sampled according to one of the following two models: either every entry is independe... |
https://arxiv.org/abs/1408.0602 | Extremal problems on shadows and hypercuts in simplicial complexes | Let $F$ be an $n$-vertex forest. We say that an edge $e\notin F$ is in the shadow of $F$ if $F\cup\{e\}$ contains a cycle. It is easy to see that if $F$ is "almost a tree", that is, it has $n-2$ edges, then at least $\lfloor\frac{n^2}{4}\rfloor$ edges are in its shadow and this is tight. Equivalently, the largest numbe... | \section{Introduction}
This article is part of an ongoing research effort to bridge
between graph theory and topology (see, e.g.~\cite{kalai, sum_complex,DNRR,lin_mesh,bab_kah,farber,gromov,lubotzky}).
This research program starts from the observation that a graph can be viewed as a $1$-dimensional simplicial comple... | {
"timestamp": "2015-11-13T02:07:07",
"yymm": "1408",
"arxiv_id": "1408.0602",
"language": "en",
"url": "https://arxiv.org/abs/1408.0602",
"abstract": "Let $F$ be an $n$-vertex forest. We say that an edge $e\\notin F$ is in the shadow of $F$ if $F\\cup\\{e\\}$ contains a cycle. It is easy to see that if $F$... |
https://arxiv.org/abs/1708.05041 | Total Forcing and Zero Forcing in Claw-Free Cubic Graphs | A dynamic coloring of the vertices of a graph $G$ starts with an initial subset $S$ of colored vertices, with all remaining vertices being non-colored. At each discrete time interval, a colored vertex with exactly one non-colored neighbor forces this non-colored neighbor to be colored. The initial set $S$ is called a f... | \section{Introduction}
A dynamic coloring of the vertices in a graph is a coloring of the vertex set which may change, or propagate, throughout the vertices during discrete time intervals. Of the dynamic colorings, the notion of \emph{forcing sets} (\emph{zero forcing sets}), and the associated graph invariant known a... | {
"timestamp": "2017-08-18T02:01:08",
"yymm": "1708",
"arxiv_id": "1708.05041",
"language": "en",
"url": "https://arxiv.org/abs/1708.05041",
"abstract": "A dynamic coloring of the vertices of a graph $G$ starts with an initial subset $S$ of colored vertices, with all remaining vertices being non-colored. At... |
https://arxiv.org/abs/1810.02437 | Permutation graphs and the Abelian sandpile model, tiered trees and non-ambiguous binary trees | A permutation graph is a graph whose edges are given by inversions of a permutation. We study the Abelian sandpile model (ASM) on such graphs. We exhibit a bijection between recurrent configurations of the ASM on permutation graphs and the tiered trees introduced by Dugan et al. [10]. This bijection allows certain para... | \section{Introduction}\label{sec:intro}
In the Abelian sandpile model (ASM) on a graph, each vertex has a number of ``grains''. If a vertex has at least as many grains as its degree is then it can be toppled, donating one grain to each of its neighbors. If a (nonempty) sequence of topplings from a configuration $c$ of... | {
"timestamp": "2018-10-08T02:03:25",
"yymm": "1810",
"arxiv_id": "1810.02437",
"language": "en",
"url": "https://arxiv.org/abs/1810.02437",
"abstract": "A permutation graph is a graph whose edges are given by inversions of a permutation. We study the Abelian sandpile model (ASM) on such graphs. We exhibit ... |
https://arxiv.org/abs/2203.07518 | Erdős--Szekeres-type problems in the real projective plane | We consider point sets in the real projective plane $\mathbb{R}P^2$ and explore variants of classical extremal problems about planar point sets in this setting, with a main focus on Erdős--Szekeres-type problems.We provide asymptotically tight bounds for a variant of the Erdős--Szekeres theorem about point sets in conv... | \section{Introduction}
\label{sec:introduction}
\subsection{Erd\H{o}s-Szekeres-type results in the Euclidean plane}
Throughout the whole paper, we consider each set $S$ of points from the Euclidean plane $\mathbb{R}^2$ to be finite and in \emph{general position}, that is, no three points of $S$ lie on a common line.... | {
"timestamp": "2022-03-16T01:07:29",
"yymm": "2203",
"arxiv_id": "2203.07518",
"language": "en",
"url": "https://arxiv.org/abs/2203.07518",
"abstract": "We consider point sets in the real projective plane $\\mathbb{R}P^2$ and explore variants of classical extremal problems about planar point sets in this s... |
https://arxiv.org/abs/1802.02381 | The $b$-branching problem in digraphs | In this paper, we introduce the concept of $b$-branchings in digraphs, which is a generalization of branchings serving as a counterpart of $b$-matchings. Here $b$ is a positive integer vector on the vertex set of a digraph, and a $b$-branching is defined as a common independent set of two matroids defined by $b$: an ar... | \section{Introduction}
\label{SECintro}
Since the pioneering work of Edmonds \cite{Edm70,Edm79},
the importance of
{\em matroid intersection} has been well appreciated.
A special class of matroid intersection is
\emph{branchings} (or \emph{arborescences}) in digraphs.
Branchings have several good proper... | {
"timestamp": "2018-02-08T02:06:48",
"yymm": "1802",
"arxiv_id": "1802.02381",
"language": "en",
"url": "https://arxiv.org/abs/1802.02381",
"abstract": "In this paper, we introduce the concept of $b$-branchings in digraphs, which is a generalization of branchings serving as a counterpart of $b$-matchings. ... |
https://arxiv.org/abs/1906.00105 | A Lipschitz Matrix for Parameter Reduction in Computational Science | We introduce the Lipschitz matrix: a generalization of the scalar Lipschitz constant for functions with many inputs. Among the Lipschitz matrices compatible a particular function, we choose the smallest such matrix in the Frobenius norm to encode the structure of this function. The Lipschitz matrix then provides a func... |
\section*{Acknowledgements}
The authors would like to thank Akil Narayan for suggesting the
counter example to maximum uncertainty designs in~\cref{sec:design:uncertainty}
and Drew Kouri for pointing us to the randomized algorithms for Voronoi vertex sampling.
\section{Background\label{sec:background}}
Here w... | {
"timestamp": "2019-06-04T02:03:35",
"yymm": "1906",
"arxiv_id": "1906.00105",
"language": "en",
"url": "https://arxiv.org/abs/1906.00105",
"abstract": "We introduce the Lipschitz matrix: a generalization of the scalar Lipschitz constant for functions with many inputs. Among the Lipschitz matrices compatib... |
https://arxiv.org/abs/2207.13638 | A Simple and Elegant Mathematical Formulation for the Acyclic DAG Partitioning Problem | This work addresses the NP-Hard problem of acyclic directed acyclic graph (DAG) partitioning problem. The acyclic partitioning problem is defined as partitioning the vertex set of a given directed acyclic graph into disjoint and collectively exhaustive subsets (parts). Parts are to be assigned such that the total sum o... | \section{Introduction}
\label{sec.intro}
Graph partitioning has been an active area of research for several decades, and is an essential
technique for
data and computation distribution for efficient computation~\cite{kaku:98:metis,Catalyurek99,HENDRICKSON20001519}.
A graph partitioning problem is, in general, defined ... | {
"timestamp": "2022-07-28T02:18:57",
"yymm": "2207",
"arxiv_id": "2207.13638",
"language": "en",
"url": "https://arxiv.org/abs/2207.13638",
"abstract": "This work addresses the NP-Hard problem of acyclic directed acyclic graph (DAG) partitioning problem. The acyclic partitioning problem is defined as parti... |
https://arxiv.org/abs/1607.08712 | Signal Recovery in Uncorrelated and Correlated Dictionaries Using Orthogonal Least Squares | Though the method of least squares has been used for a long time in solving signal processing problems, in the recent field of sparse recovery from compressed measurements, this method has not been given much attention. In this paper we show that a method in the least squares family, known in the literature as Orthogon... | \section{Introduction}
\lettrine[findent=2pt]{\textbf{C}}{}OMPRESSED SENSING (CS) \cite{eldar2012compressed} has led to a new paradigm in signal processing. Compressed sensing provides a novel way of acquiring a sparse signal $\bm{x} \in \mathbb{R}^{N}$ such that $\|x\|_{0} \le K$ with very few number of linear measur... | {
"timestamp": "2016-08-01T02:05:48",
"yymm": "1607",
"arxiv_id": "1607.08712",
"language": "en",
"url": "https://arxiv.org/abs/1607.08712",
"abstract": "Though the method of least squares has been used for a long time in solving signal processing problems, in the recent field of sparse recovery from compre... |
https://arxiv.org/abs/2211.07559 | Lagrangian intersections and cuplength in generalised cohomology | We find lower bounds on the number of intersection points between two relatively exact Hamiltonian isotopic Lagrangians. The bounds are given in terms of the cuplength of the Lagrangian in various multiplicative generalised cohomology theories. The intersection of the Lagrangians need not be transverse, however, we req... | \section{Two examples}\label{Examples}
Let
$$\Sp(n) := \normalfont\text{Sp}(2n;\mathbb{C})\cap U(2n)$$ be the \emph{compact symplectic group}. It is a compact simply-connected Lie group of dimension $n(2n+1)$. The zero section defines a Lagrangian embedding $\Sp(n)\hookrightarrow T^*\Sp(n)$, where we endow $T^*\Sp(n)$... | {
"timestamp": "2022-11-15T02:31:51",
"yymm": "2211",
"arxiv_id": "2211.07559",
"language": "en",
"url": "https://arxiv.org/abs/2211.07559",
"abstract": "We find lower bounds on the number of intersection points between two relatively exact Hamiltonian isotopic Lagrangians. The bounds are given in terms of ... |
https://arxiv.org/abs/1802.09039 | Flag bundles, Segre polynomials and push-forwards | In this note, we give Gysin formulas for partial flag bundles for the classical groups. We then give Gysin formulas for Schubert varieties in Grassmann bundles, including isotropic ones. All these formulas are proved in a rather uniform way by using the step-by-step construction of flag bundles and the Gysin formula fo... | \section{Introduction}
\label{se:intro}
Let \(E\to X\) be a vector bundle of rank \(n\) on a variety \(X\) over an algebraically closed field.
Let \(\pi\colon\mathbf{F}}\def\P{\mathbf{P}}\def\G{\mathbf{G}(E)\to X\) be the bundle of flags of subspaces of dimensions \(1,2,\dots, n-1\) in the fibers of \(E\to X\).
The fl... | {
"timestamp": "2018-02-27T02:11:08",
"yymm": "1802",
"arxiv_id": "1802.09039",
"language": "en",
"url": "https://arxiv.org/abs/1802.09039",
"abstract": "In this note, we give Gysin formulas for partial flag bundles for the classical groups. We then give Gysin formulas for Schubert varieties in Grassmann bu... |
https://arxiv.org/abs/1807.06283 | Tropical Fano Schemes | We define a tropical version $\F_d(\trop X)$ of the Fano Scheme $\F_d(X)$ of a projective variety $X\subseteq \mathbb P^n$ and prove that $\F_d(\trop X)$ is the support of a polyhedral complex contained in $\trop \Grp(d,n)$. In general $\trop \F_d(X)\subseteq \F_d(\trop X)$ but we construct linear spaces $L$ such that ... | \section{Introduction}
The classical Fano scheme of a projective variety $X\subseteq \mathbb P^n$ is the fine moduli space parametrising linear spaces contained in $X$. It is denoted by $\F_d(X)$, with $d$ the dimension of the linear spaces, and is a subscheme of the Grassmannian
$\Grp(d,n)$ of $d-$dimensional s... | {
"timestamp": "2019-04-05T02:18:43",
"yymm": "1807",
"arxiv_id": "1807.06283",
"language": "en",
"url": "https://arxiv.org/abs/1807.06283",
"abstract": "We define a tropical version $\\F_d(\\trop X)$ of the Fano Scheme $\\F_d(X)$ of a projective variety $X\\subseteq \\mathbb P^n$ and prove that $\\F_d(\\tr... |
https://arxiv.org/abs/2009.09440 | The Significance Filter, the Winner's Curse and the Need to Shrink | The "significance filter" refers to focusing exclusively on statistically significant results. Since frequentist properties such as unbiasedness and coverage are valid only before the data have been observed, there are no guarantees if we condition on significance. In fact, the significance filter leads to overestimati... | \section{Introduction}
The long-standing debate about the role of statistical significance in research \cite{rozeboom1960fallacy}, \cite{meehl1978theoretical} has recently intensified \cite{wasserstein2016asa},\cite{benjamin2018redefine},\cite{wasserstein2019moving},\cite{mcshane2019abandon},\cite{amrhein2018remove} a... | {
"timestamp": "2020-09-22T02:17:00",
"yymm": "2009",
"arxiv_id": "2009.09440",
"language": "en",
"url": "https://arxiv.org/abs/2009.09440",
"abstract": "The \"significance filter\" refers to focusing exclusively on statistically significant results. Since frequentist properties such as unbiasedness and cov... |
https://arxiv.org/abs/0809.4561 | Stable string operations are trivial | We show that in closed string topology and in open-closed string topology with one $D$-brane, higher genus stable string operations are trivial. This is a consequence of Harer's stability theorem and related stability results on the homology of mapping class groups of surfaces with boundaries. In fact, this vanishing r... | \section{Introduction}
Let $M$ be a closed oriented smooth $d$ dimensional manifold and let $LM$ be the loop space consisting of continuous maps from $S^1$ into $M$. In this paper, we use (co)homology with integral coefficients unless otherwise stated, except in section 4. Chas and Sullivan \cite{CS} showed that the... | {
"timestamp": "2008-09-26T10:42:43",
"yymm": "0809",
"arxiv_id": "0809.4561",
"language": "en",
"url": "https://arxiv.org/abs/0809.4561",
"abstract": "We show that in closed string topology and in open-closed string topology with one $D$-brane, higher genus stable string operations are trivial. This is a c... |
https://arxiv.org/abs/1502.04200 | Gaps in the Milnor-Moore spectral sequence and the Hilali conjecture | In his study of Halperin's toral-rank conjecture, M. R. Hilali conjectured that for any simply connected rationally elliptic space $X$, one must have $dim\pi_*(X)\otimes \mathbb{Q} \leq dimH^*(X,\mathbb{Q})$. Let $(\Lambda V, d)$ denote a Sullivan minimal model of $X$ and $d_k$ the first non-zero homogeneous part of th... | \section[#1]{\centering #1}}
\newcommand{\mathop{.}}{\mathop{.}}
\newcommand{\expo}[2]{#1^{#2}}
\author{Youssef Rami}
\address{D\'epartement de Math\'ematiques \& Informatique,\\
Universit\'e My Ismail, B. P. 11 201 Zitoune, Mekn\`es, Morocco,}
\email{yousfoumadan@gmail.com}
\title
{Gaps in the Milnor-Moore spectr... | {
"timestamp": "2015-03-31T02:12:14",
"yymm": "1502",
"arxiv_id": "1502.04200",
"language": "en",
"url": "https://arxiv.org/abs/1502.04200",
"abstract": "In his study of Halperin's toral-rank conjecture, M. R. Hilali conjectured that for any simply connected rationally elliptic space $X$, one must have $dim... |
https://arxiv.org/abs/1907.12312 | Unimodular covers of 3-dimensional parallelepipeds and Cayley sums | We show that the following classes of lattice polytopes have unimodular covers, in dimension three: the class of parallelepipeds, the class of centrally symmetric polytopes, and the class of Cayley sums $\text{Cay}(P,Q)$ where the normal fan of $Q$ refines that of $P$. This improves results of Beck et al.~(2018) and Ha... | \section{Introduction}
A lattice polytope $P\subset \ensuremath{\mathbb{R}}^d$ has the \emph{integer decomposition property} if for every positive integer $n$, every lattice point $p \in nP\cap \ensuremath{\mathbb{Z}}^d$ can be written as a sum of $n$ lattice points in $P$. We abbreviate this by saying that ``$P$ is... | {
"timestamp": "2019-07-30T02:24:19",
"yymm": "1907",
"arxiv_id": "1907.12312",
"language": "en",
"url": "https://arxiv.org/abs/1907.12312",
"abstract": "We show that the following classes of lattice polytopes have unimodular covers, in dimension three: the class of parallelepipeds, the class of centrally s... |
https://arxiv.org/abs/1210.2953 | Characterization of Differentiable Copulas | This paper proposes a new class of copulas which characterize the set of all twice continuously differentiable copulas. We show that our proposed new class of copulas is a new generalized copula family that include not only asymmetric copulas but also all smooth copula families available in the current literature. Spea... | \section{Introduction}
Recently, a study of dependence by using copulas has been getting more attention in the areas of finance, actuarial science, biomedical studies and engineering because a copula function does not require a normal distribution and independent, identical distribution assumptions. Furthermore, the i... | {
"timestamp": "2012-10-11T02:07:28",
"yymm": "1210",
"arxiv_id": "1210.2953",
"language": "en",
"url": "https://arxiv.org/abs/1210.2953",
"abstract": "This paper proposes a new class of copulas which characterize the set of all twice continuously differentiable copulas. We show that our proposed new class ... |
https://arxiv.org/abs/1409.8229 | Geometry and stability of tautological bundles on Hilbert schemes of points | The purpose of this paper is to explore the geometry and establish the slope stability of tautological vector bundles on Hilbert schemes of points on smooth surfaces. By establishing stability in general we complete a series of results of Schlickewei and Wandel who proved the slope stability of these vector bundles for... | \section*{Introduction}
The purpose of this paper is to explore the geometry of tautological bundles on Hilbert schemes of smooth surfaces and to establish the slope stability of these bundles.
Let $S$ be a smooth complex projective surface, and denote by $\hns{n}{S}$ the Hilbert scheme parametrizing length $n$ subsc... | {
"timestamp": "2015-06-30T02:11:29",
"yymm": "1409",
"arxiv_id": "1409.8229",
"language": "en",
"url": "https://arxiv.org/abs/1409.8229",
"abstract": "The purpose of this paper is to explore the geometry and establish the slope stability of tautological vector bundles on Hilbert schemes of points on smooth... |
https://arxiv.org/abs/1304.0428 | Convex and subharmonic functions on graphs | We explore the relationship between convex and subharmonic functions on discrete sets. Our principal concern is to determine the setting in which a convex function is necessarily subharmonic. We initially consider the primary notions of convexity on graphs and show that more structure is needed to establish the desired... | \section{Introduction}
Classical analysis provides several equivalent definitions of a convex function, which have led to several non-equivalent concepts of a convex function on a graph. As an interesting alternative, there appears to be a consensus on how to define subharmonic functions on graphs. In the real varia... | {
"timestamp": "2013-04-02T02:08:19",
"yymm": "1304",
"arxiv_id": "1304.0428",
"language": "en",
"url": "https://arxiv.org/abs/1304.0428",
"abstract": "We explore the relationship between convex and subharmonic functions on discrete sets. Our principal concern is to determine the setting in which a convex f... |
https://arxiv.org/abs/1805.05417 | Hamiltonian systems: symbolical, numerical and graphical study | Hamiltonian dynamical systems can be studied from a variety of viewpoints. Our intention in this paper is to show some examples of usage of two Maxima packages for symbolical and numerical analysis (\texttt{pdynamics} and \texttt{poincare}, respectively), along with the set of scripts \KeTCindy\ for obtaining the \LaTe... |
\section{Introduction}
For simplicity, we will consider Hamiltonians defined on the symplectic manifold
$\mathbb{R}^{2n}$, with coordinates $(q^j,p_j)$ ($1\leq j\leq n$), endowed with
the canonical form $w=\mathrm{d}p_j\wedge \mathrm{d}q^j$, and the induced Poisson bracket
on $\mathcal{C}^\infty (\mathbb{R}... | {
"timestamp": "2018-05-16T02:02:12",
"yymm": "1805",
"arxiv_id": "1805.05417",
"language": "en",
"url": "https://arxiv.org/abs/1805.05417",
"abstract": "Hamiltonian dynamical systems can be studied from a variety of viewpoints. Our intention in this paper is to show some examples of usage of two Maxima pac... |
https://arxiv.org/abs/2103.10758 | Intermediate spaces, Gaussian probabilities and exponential tightness | Let us consider a Gaussian probability on a Banach space. We prove the existence of an intermediate Banach space between the space where the Gaussian measure lives and its RKHS. Such a space has full probability and a compact embedding. This extends what happens with Wiener measure, where the intermediate space can be ... | \section{Introduction}
Let $E=\cl C_0([0,T],\mathbb{R}^m)$ be the space of continuous $\mathbb{R}^m$-valued paths starting at $0$ and endowed with the sup norm and let $\mu$ be the Wiener measure on it. It is well known that the Reproducing Kernel Hilbert Space (RKHS) of this Gaussian probability is the space $\cl H=H^... | {
"timestamp": "2021-03-22T01:17:02",
"yymm": "2103",
"arxiv_id": "2103.10758",
"language": "en",
"url": "https://arxiv.org/abs/2103.10758",
"abstract": "Let us consider a Gaussian probability on a Banach space. We prove the existence of an intermediate Banach space between the space where the Gaussian meas... |
https://arxiv.org/abs/1301.1107 | Spectral Condition-Number Estimation of Large Sparse Matrices | We describe a randomized Krylov-subspace method for estimating the spectral condition number of a real matrix A or indicating that it is numerically rank deficient. The main difficulty in estimating the condition number is the estimation of the smallest singular value \sigma_{\min} of A. Our method estimates this value... | \section{Introduction}
Estimating the smallest singular value $\sigma_{\min}$ of a matrix
is difficult. Dense SVD algorithms can approximate $\sigma_{\min}$
well and their running time is predictable, but they are also slow.
Furthermore, dense SVD algorithms require space that is proportional
to $mn$ when the ma... | {
"timestamp": "2013-01-08T02:04:04",
"yymm": "1301",
"arxiv_id": "1301.1107",
"language": "en",
"url": "https://arxiv.org/abs/1301.1107",
"abstract": "We describe a randomized Krylov-subspace method for estimating the spectral condition number of a real matrix A or indicating that it is numerically rank de... |
https://arxiv.org/abs/2009.12989 | Tree densities in sparse graph classes | What is the maximum number of copies of a fixed forest $T$ in an $n$-vertex graph in a graph class $\mathcal{G}$ as $n\to \infty$? We answer this question for a variety of sparse graph classes $\mathcal{G}$. In particular, we show that the answer is $\Theta(n^{\alpha_d(T)})$ where $\alpha_d(T)$ is the size of the large... | \section{Introduction}
Many classical theorems in extremal graph theory concern the maximum number of copies of a fixed graph $H$ in an $n$-vertex graph\footnote{All graphs in this paper are undirected, finite, and simple, unless stated otherwise. Let $\mathbb{N}:=\{1,2,\dots\}$ and $\mathbb{N}_0:=\mathbb{N}\cup\{0\}... | {
"timestamp": "2021-07-06T02:28:40",
"yymm": "2009",
"arxiv_id": "2009.12989",
"language": "en",
"url": "https://arxiv.org/abs/2009.12989",
"abstract": "What is the maximum number of copies of a fixed forest $T$ in an $n$-vertex graph in a graph class $\\mathcal{G}$ as $n\\to \\infty$? We answer this quest... |
https://arxiv.org/abs/1907.09046 | Fujita's conjecture for quasi-elliptic surfaces | We show that Fujita's conjecture is true for quasi-elliptic surfaces. Explicitly, for any quasi-elliptic surface $X$ and an ample line bundle $A$ on $X$, we have $K_X + tA$ is base point free for $t \geq 3$ and is very ample for $t \geq 4$. | \section{Introduction}
Let $X$ be a smooth projective variety and $A$ be an ample line bundle.
The classical problem is to understand whether the adjoint linear system $K_X+A$ is base point free or very ample.
Thanks to Serre's theorem, we know that $K_X+mA$ is very ample for $m$ sufficiently large,
and there is a g... | {
"timestamp": "2019-07-23T02:14:26",
"yymm": "1907",
"arxiv_id": "1907.09046",
"language": "en",
"url": "https://arxiv.org/abs/1907.09046",
"abstract": "We show that Fujita's conjecture is true for quasi-elliptic surfaces. Explicitly, for any quasi-elliptic surface $X$ and an ample line bundle $A$ on $X$, ... |
https://arxiv.org/abs/0811.1075 | Resolution Trees with Lemmas: Resolution Refinements that Characterize DLL Algorithms with Clause Learning | Resolution refinements called w-resolution trees with lemmas (WRTL) and with input lemmas (WRTI) are introduced. Dag-like resolution is equivalent to both WRTL and WRTI when there is no regularity condition. For regular proofs, an exponential separation between regular dag-like resolution and both regular WRTL and regu... |
\section{A Lower Bound for RTLW with short lemmas}
\label{sec:smlem}
In this section we prove a lower bound showing that learning only
short clauses does not help a DLL algorithm for certain hard formulas.
The proof system corresponding to DLL algorithms with learning
restricted to clauses of length $k$... | {
"timestamp": "2008-12-05T11:34:34",
"yymm": "0811",
"arxiv_id": "0811.1075",
"language": "en",
"url": "https://arxiv.org/abs/0811.1075",
"abstract": "Resolution refinements called w-resolution trees with lemmas (WRTL) and with input lemmas (WRTI) are introduced. Dag-like resolution is equivalent to both W... |
https://arxiv.org/abs/1807.11675 | The V-monoid of a weighted Leavitt path algebra | We compute the $V$-monoid of a weighted Leavitt path algebra of a row-finite weighted graph, correcting a wrong computation of the $V$-monoid that exists in the literature. Further we show that the description of $K_0$ of a weighted Leavitt path algebra that exists in the literature is correct (although the computation... | \section{Introduction}
The weighted Leavitt path algebras (wLpas) were introduced by R. Hazrat in \cite{hazrat13}. They generalise the Leavitt path algebras (Lpas). While the Lpas only embrace Leavitt's algebras $L_K(1,1+k)$ where $K$ is a field and $k\geq 0$, the wLpas embrace all of Leavitt's algebras $L_K(n,n+k)$ wh... | {
"timestamp": "2018-08-01T02:06:32",
"yymm": "1807",
"arxiv_id": "1807.11675",
"language": "en",
"url": "https://arxiv.org/abs/1807.11675",
"abstract": "We compute the $V$-monoid of a weighted Leavitt path algebra of a row-finite weighted graph, correcting a wrong computation of the $V$-monoid that exists ... |
https://arxiv.org/abs/0910.0096 | Gröbner-Shirshov bases for Coxeter groups I | A conjecture of Gröbner-Shirshov basis of any Coxeter group has proposed by L.A. Bokut and L.-S. Shiao \cite{bs01}. In this paper, we give an example to show that the conjecture is not true in general. We list all possible nontrivial inclusion compositions when we deal with the general cases of the Coxeter groups. We g... | \section{Introduction}
Let $M=\|m_{ij}\|_{n\times n}$ be a symmetric $n\times n$ matrix
such that $m_{ii}=1,\ 2\leq m_{ij}\leq\infty$. The Coxeter group
$W=W(M)$ is defined by the generators $s_1,\cdots, s_n$ and the
defining relations $(s_is_j)^{m_{ij}}=1$.
A conjecture of Gr\"{o}bner-Shirshov basis of any Coxeter ... | {
"timestamp": "2009-10-01T09:11:02",
"yymm": "0910",
"arxiv_id": "0910.0096",
"language": "en",
"url": "https://arxiv.org/abs/0910.0096",
"abstract": "A conjecture of Gröbner-Shirshov basis of any Coxeter group has proposed by L.A. Bokut and L.-S. Shiao \\cite{bs01}. In this paper, we give an example to sh... |
https://arxiv.org/abs/2104.01965 | AuTO: A Framework for Automatic differentiation in Topology Optimization | A critical step in topology optimization (TO) is finding sensitivities. Manual derivation and implementation of the sensitivities can be quite laborious and error-prone, especially for non-trivial objectives, constraints and material models. An alternate approach is to utilize automatic differentiation (AD). While AD h... | \section{Introduction}
\label{sec:introduction}
\paragraph{} Fueled by improvements in manufacturing capabilities and computational modeling, the field of topology optimization (TO) has witnessed tremendous growth in recent years. To further accelerate the development of TO, we consider here automating a critical step ... | {
"timestamp": "2021-04-06T02:38:38",
"yymm": "2104",
"arxiv_id": "2104.01965",
"language": "en",
"url": "https://arxiv.org/abs/2104.01965",
"abstract": "A critical step in topology optimization (TO) is finding sensitivities. Manual derivation and implementation of the sensitivities can be quite laborious a... |
https://arxiv.org/abs/2111.05386 | Computing Area-Optimal Simple Polygonizations | We consider methods for finding a simple polygon of minimum (Min-Area) or maximum (Max-Area) possible area for a given set of points in the plane. Both problems are known to be NP-hard; at the center of the recent CG Challenge, practical methods have received considerable attention. However, previous methods focused on... | \section{Introduction}
\label{sec:introduction}
While the classic geometric Traveling Salesman Problem (TSP) is to find a (simple)
polygon with a given set of vertices that has shortest perimeter, it is natural
to look for a simple polygon with a given set of vertices that minimizes
another basic geometric measure: th... | {
"timestamp": "2021-11-11T02:01:28",
"yymm": "2111",
"arxiv_id": "2111.05386",
"language": "en",
"url": "https://arxiv.org/abs/2111.05386",
"abstract": "We consider methods for finding a simple polygon of minimum (Min-Area) or maximum (Max-Area) possible area for a given set of points in the plane. Both pr... |
https://arxiv.org/abs/1408.4895 | Simple Parametrization Methods for Generating Adomian Polynomials | In this paper, we discuss two simple parametrization methods for calculating Adomian polynomials for several nonlinear operators, which utilize the orthogonality of functions einx, where n is an integer. Some important properties of Adomian polynomials are also discussed and illustrated with examples. These methods req... | \section{Introduction}
The Adomian decomposition method (ADM) \cite{Adomian1986,Adomian1989,Adomian1994} provides an analytical approximate solution for nonlinear functional equation in terms of a rapidly converging series, without linearization, perturbation or discretization. Consider a functional equation
\begin{eq... | {
"timestamp": "2014-08-22T02:04:00",
"yymm": "1408",
"arxiv_id": "1408.4895",
"language": "en",
"url": "https://arxiv.org/abs/1408.4895",
"abstract": "In this paper, we discuss two simple parametrization methods for calculating Adomian polynomials for several nonlinear operators, which utilize the orthogon... |
https://arxiv.org/abs/1109.4019 | Tate-Hochschild homology and cohomology of Frobenius algebras | We study Tate-Hochschild homology and cohomology for a two-sided Noetherian Gorenstein algebra. These (co)homology groups are defined for all degrees, non-negative as well as negative, and they agree with the usual Hochschild (co)homology groups for all degrees larger than the injective dimension of the algebra. We pro... | \section{Introduction}\label{intro}
Hochschild cohomology was introduced by Hochschild in \cite{Hochschild1, Hochschild2} as a tool for
studying the structure of associative algebras. A bit later, Tate introduced a cohomology theory based on complete resolutions, which consequently defined cohomology in all degrees, p... | {
"timestamp": "2011-10-10T02:01:53",
"yymm": "1109",
"arxiv_id": "1109.4019",
"language": "en",
"url": "https://arxiv.org/abs/1109.4019",
"abstract": "We study Tate-Hochschild homology and cohomology for a two-sided Noetherian Gorenstein algebra. These (co)homology groups are defined for all degrees, non-n... |
https://arxiv.org/abs/1808.00885 | Kodaira dimensions of almost complex manifolds I | This is the first of a series of papers, in which we study the plurigenera, the Kodaira dimension and more generally the Iitaka dimension on compact almost complex manifolds.Based on the Hodge theory on almost complex manifolds, we introduce the plurigenera, Kodaira dimension and Iitaka dimension on compact almost comp... | \section{Introduction}
The Iitaka dimension for a holomorphic line bundle $L$ over a compact complex manifold is a numerical invariant to measure the size of the space of holomorphic sections. It could be equivalently defined as the growth rate of the dimension of the space $H^0(X, L^{\otimes d})$, or the maximal image... | {
"timestamp": "2020-04-28T02:30:04",
"yymm": "1808",
"arxiv_id": "1808.00885",
"language": "en",
"url": "https://arxiv.org/abs/1808.00885",
"abstract": "This is the first of a series of papers, in which we study the plurigenera, the Kodaira dimension and more generally the Iitaka dimension on compact almos... |
https://arxiv.org/abs/math/0510552 | Betti Numbers and Degree Bounds for Some Linked Zero-Schemes | In their paper on multiplicity bounds (1998), Herzog and Srinivasan study the relationship between the graded Betti numbers of a homogeneous ideal I in a polynomial ring R and the degree of I. For certain classes of ideals, they prove a bound on the degree in terms of the largest and smallest Betti numbers, generalizin... | \section{Introduction}\label{sec:one}
Let $R$ be a polynomial ring over a field $\mathbb{K}$, and let $I$ be a
homogeneous ideal. Then the module $R/I$ admits a finite minimal graded
free resolution over $R$:
\begin{center}
$ \mathbb{F}: \mbox{ }\cdots \rightarrow \bigoplus\limits_{j \in
J_2} R(-d_{2,j}) \rightar... | {
"timestamp": "2005-10-26T13:00:10",
"yymm": "0510",
"arxiv_id": "math/0510552",
"language": "en",
"url": "https://arxiv.org/abs/math/0510552",
"abstract": "In their paper on multiplicity bounds (1998), Herzog and Srinivasan study the relationship between the graded Betti numbers of a homogeneous ideal I i... |
https://arxiv.org/abs/1106.4598 | Inverse problems for Jacobi operators II: Mass perturbations of semi-infinite mass-spring systems | We consider an inverse spectral problem for infinite linear mass-spring systems with different configurations obtained by changing the first mass. We give results on the reconstruction of the system from the spectra of two configurations. Necessary and sufficient conditions for two real sequences to be the spectra of t... | \section{Introduction}
\label{sec:intro}
In this work we treat the two spectra inverse problem for Jacobi
operators in $l_2(\mathbb{N})$. The Jacobi operators considered here are
obtained from each other by a particular kind of rank-two
perturbation. The special form of the perturbation has a physical
motivation; it is... | {
"timestamp": "2013-01-14T02:00:44",
"yymm": "1106",
"arxiv_id": "1106.4598",
"language": "en",
"url": "https://arxiv.org/abs/1106.4598",
"abstract": "We consider an inverse spectral problem for infinite linear mass-spring systems with different configurations obtained by changing the first mass. We give r... |
https://arxiv.org/abs/1202.3066 | Sets computing the symmetric tensor rank | Let n_d denote the degree d Veronese embedding of a projective space P^r. For any symmetric tensor P, the 'symmetric tensor rank' sr(P) is the minimal cardinality of a subset A of P^r, such that n_d(A) spans P. Let S(P) be the space of all subsets A of P^r, such that n_d(A) computes sr(P). Here we classify all P in P^n... | \section{Introduction}\label{S1}
Let $\nu _d: \mathbb {P}^r \to \mathbb {P}^N$, $N:= \binom{r+d}{r}-1$,
denote the degree $d$ Veronese embedding of $\mathbb {P}^r$.
Set $X_{r,d}:= \nu _d(\mathbb {P}^r)$.
For any $P\in \mathbb {P}^N$, the {\emph {symmetric rank}} or {\emph
{symmetric tensor rank}} or, just, the {\em... | {
"timestamp": "2012-02-15T02:03:08",
"yymm": "1202",
"arxiv_id": "1202.3066",
"language": "en",
"url": "https://arxiv.org/abs/1202.3066",
"abstract": "Let n_d denote the degree d Veronese embedding of a projective space P^r. For any symmetric tensor P, the 'symmetric tensor rank' sr(P) is the minimal cardi... |
https://arxiv.org/abs/2209.10309 | On the Existential Fragments of Local First-Order Logics with Data | We study first-order logic over unordered structures whose elements carry a finite number of data values from an infinite domain which can be compared wrt. equality. As the satisfiability problem for this logic is undecidable in general, in a previous work, we have introduced a family of local fragments that restrict q... | \subsection{Preliminary results: 0 and 1 data values}
We introduce two preliminary results we shall use in this
section to obtain new decidability results. First, note that
formulas in $\ndFO{0}{\Sigma}$ (i.e. where no data is considered)
correspond to first order logic formulas with a set of predicates and
equality t... | {
"timestamp": "2022-09-22T02:15:54",
"yymm": "2209",
"arxiv_id": "2209.10309",
"language": "en",
"url": "https://arxiv.org/abs/2209.10309",
"abstract": "We study first-order logic over unordered structures whose elements carry a finite number of data values from an infinite domain which can be compared wrt... |
https://arxiv.org/abs/1612.06706 | The Coulomb potential in quantum mechanics revisited | The procedure commonly used in textbooks for determining the eigenvalues and eigenstates for a particle in an attractive Coulomb potential is not symmetric in the way the boundary conditions at $r=0$ and $r \rightarrow \infty$ are considered. We highlight this fact by solving a model for the Coulomb potential with a cu... | \section{introduction}
The solution of the quantum mechanical problem of determining the energy levels of a (bound) particle in the presence of
an attractive Coulomb potential, i.e. the hydrogen atom with centre-of-mass coordinate removed, was a spectacular achievement by
Schr\"odinger, published in the same paper in... | {
"timestamp": "2016-12-21T02:06:33",
"yymm": "1612",
"arxiv_id": "1612.06706",
"language": "en",
"url": "https://arxiv.org/abs/1612.06706",
"abstract": "The procedure commonly used in textbooks for determining the eigenvalues and eigenstates for a particle in an attractive Coulomb potential is not symmetri... |
https://arxiv.org/abs/1110.2554 | Stable Birational Equivalence and Geometric Chevalley-Warning | We propose a 'geometric Chevalley-Warning' conjecture, that is a motivic extension of the Chevalley-Warning theorem in number theory. It is equivalent to a particular case of a recent conjecture of F. Brown and O.Schnetz. In this paper, we show the conjecture is true for linear hyperplane arrangements, quadratic and si... | \section{introduction}
Let ${\mathbb{F}}_q$ be the finite field of $q$ elements with $q$ a prime power. The Chevalley-Warning theorem states that the number of solutions in ${\mathbb{F}}_q$ of a system of polynomial equations with $n$ variables is divisible by $q$, provided that the sum of the degrees of these polynom... | {
"timestamp": "2011-10-13T02:01:21",
"yymm": "1110",
"arxiv_id": "1110.2554",
"language": "en",
"url": "https://arxiv.org/abs/1110.2554",
"abstract": "We propose a 'geometric Chevalley-Warning' conjecture, that is a motivic extension of the Chevalley-Warning theorem in number theory. It is equivalent to a ... |
https://arxiv.org/abs/1408.0673 | Geometric structure for the principal series of a split reductive $p$-adic group with connected centre | Let $\mathcal{G}$ be a split reductive $p$-adic group with connected centre. We show that each Bernstein block in the principal series of $\mathcal{G}$ admits a definite geometric structure, namely that of an extended quotient. For the Iwahori-spherical block, this extended quotient has the form $T//W$ where $T$ is a m... | \section{Introduction}
Let ${\mathcal G}$ be a split reductive $p$-adic group with connected centre, \
and let $G = {\mathcal G}^\vee$ denote the Langlands dual group. Then $G$ is a complex reductive group.
Let $T$ be a maximal torus in $G$ and let $W$ be the common Weyl group of ${\mathcal G}$ and $G$.
We can f... | {
"timestamp": "2016-04-13T02:12:11",
"yymm": "1408",
"arxiv_id": "1408.0673",
"language": "en",
"url": "https://arxiv.org/abs/1408.0673",
"abstract": "Let $\\mathcal{G}$ be a split reductive $p$-adic group with connected centre. We show that each Bernstein block in the principal series of $\\mathcal{G}$ ad... |
https://arxiv.org/abs/2009.05124 | Tiered Random Matching Markets: Rank is Proportional to Popularity | We study the stable marriage problem in two-sided markets with randomly generated preferences. We consider agents on each side divided into a constant number of "soft tiers", which intuitively indicate the quality of the agent. Specifically, every agent within a tier has the same public score, and agents on each side h... | \section{Introduction}
\label{sectionIntroduction}
The theory of stable matching, initiated by~\cite{gale1962college}, has led to a deep understanding of two-sided matching markets and inspired successful real-world market designs. Examples of such markets include marriage markets, online dating, assigning students ... | {
"timestamp": "2021-01-14T02:03:29",
"yymm": "2009",
"arxiv_id": "2009.05124",
"language": "en",
"url": "https://arxiv.org/abs/2009.05124",
"abstract": "We study the stable marriage problem in two-sided markets with randomly generated preferences. We consider agents on each side divided into a constant num... |
https://arxiv.org/abs/0902.4899 | New results on the lower central series quotients of a free associative algebra | We continue the study of the lower central series and its associated graded components for a free associative algebra with n generators, as initiated by B. Feigin and B. Shoikhet. We establish a linear bound on the degree of tensor field modules appearing in the Jordan-Hoelder series of each graded component, which is ... | \section{Introduction and results}
In this paper we consider the free associative algebra\footnote{over $\mathbb{C}$, or any field of characteristic zero} $A:=A_n$ on generators $x_1,\ldots, x_n$, for $n\geq 2$, and its lower central series filtration: $L_1=A, L_{m+1}=[A,L_m]$. The corresponding associated graded Li... | {
"timestamp": "2009-02-27T23:19:42",
"yymm": "0902",
"arxiv_id": "0902.4899",
"language": "en",
"url": "https://arxiv.org/abs/0902.4899",
"abstract": "We continue the study of the lower central series and its associated graded components for a free associative algebra with n generators, as initiated by B. ... |
https://arxiv.org/abs/0902.4682 | Lectures on Jacques Herbrand as a Logician | We give some lectures on the work on formal logic of Jacques Herbrand, and sketch his life and his influence on automated theorem proving. The intended audience ranges from students interested in logic over historians to logicians. Besides the well-known correction of Herbrand's False Lemma by Goedel and Dreben, we als... |
\section{\Firstsectionname}%
\label{sec:preface}%
Regarding the work on formal logic of \herbrandname\ \herbrandlifetime,
our following lectures will provide a lot of useful information for the
student interested in logic
as well as a few surprising insights for the experts in the fields
of history and logic.
As \... | {
"timestamp": "2009-05-12T21:09:44",
"yymm": "0902",
"arxiv_id": "0902.4682",
"language": "en",
"url": "https://arxiv.org/abs/0902.4682",
"abstract": "We give some lectures on the work on formal logic of Jacques Herbrand, and sketch his life and his influence on automated theorem proving. The intended audi... |
https://arxiv.org/abs/2007.11383 | A correction term for the asymptotic scaling of drag in flat-plate turbulent boundary layers | An asymptotic scaling law for drag in flat-plate turbulent boundary layers has been proposed [Dixit SA, Gupta A, Choudhary H, Singh AK and Prabhakaran T. Asymptotic scaling of drag in flat-plate turbulent boundary layers. Phys. Fluids Vol. 32, 041702 (2020)]. In this paper we suggest to amend the scaling law by using a... | \section{Introduction}
In \cite{dixit_a}, an asymptotic (high Reynolds number) scaling law for drag in zero-pressure-gradient (ZPG) flow has been derived based on an approximation of $M$, the kinematic momentum rate through the boundary layer:
\begin{equation}
\label{eq:dixit_asymp}
M = \int_0^{\delta} U^2 {\rm d}z... | {
"timestamp": "2021-04-07T02:10:37",
"yymm": "2007",
"arxiv_id": "2007.11383",
"language": "en",
"url": "https://arxiv.org/abs/2007.11383",
"abstract": "An asymptotic scaling law for drag in flat-plate turbulent boundary layers has been proposed [Dixit SA, Gupta A, Choudhary H, Singh AK and Prabhakaran T. ... |
https://arxiv.org/abs/1902.07919 | Finite element method for radially symmetric solution of a multidimensional semilinear heat equation | This study aims to present the error and numerical blow up analyses of a finite element method for computing the radially symmetric solutions of semilinear heat equations. In particular, this study establishes optimal order error estimates in $L^\infty$ and weighted $L^2$ norms for the symmetric and nonsymmetric formul... | \section{Introduction}
This study \ek{was conducted} to investigate the convergence \tn{property} of finite element method (FEM) applied to a parabolic equation with singular coefficients for the function $u=u(x,t)$, $x\in\overline{I}=[0,1]$\ek{,} and $t\ge 0$, as expressed in
\begin{subequations}
\label{eq:1}
\begin{... | {
"timestamp": "2019-08-28T02:18:34",
"yymm": "1902",
"arxiv_id": "1902.07919",
"language": "en",
"url": "https://arxiv.org/abs/1902.07919",
"abstract": "This study aims to present the error and numerical blow up analyses of a finite element method for computing the radially symmetric solutions of semilinea... |
https://arxiv.org/abs/1205.5983 | Abelian ideals of a Borel subalgebra and root systems | Let $g$ be a simple Lie algebra and $Ab$ the poset of non-trivial abelian ideals of a fixed Borel subalgebra of $g$. In 2003 (IMRN, no.35, 1889--1913), we constructed a partition of $Ab$ into the subposets $Ab_\mu$, parameterised by the long positive roots of $g$, and established some properties of these subposets. In ... | \section*{Introduction}
\noindent
Let $\g$ be a complex simple Lie algebra with a triangular decomposition
$\g=\ut\oplus\te\oplus \ut^-$. Here $\te$ is a fixed Cartan subalgebra and $\be=\ut\oplus\te$
is a fixed Borel subalgebra. Accordingly, $\Delta$ is the set of roots of $(\g,\te)$, $\Delta^+$
is the set of posit... | {
"timestamp": "2012-05-29T02:01:50",
"yymm": "1205",
"arxiv_id": "1205.5983",
"language": "en",
"url": "https://arxiv.org/abs/1205.5983",
"abstract": "Let $g$ be a simple Lie algebra and $Ab$ the poset of non-trivial abelian ideals of a fixed Borel subalgebra of $g$. In 2003 (IMRN, no.35, 1889--1913), we c... |
https://arxiv.org/abs/0805.3795 | Approximating with Gaussians | Linear combinations of translations of a single Gaussian, e^{-x^2}, are shown to be dense in L^2(R). Two algorithms for determining the coefficients for the approximations are given, using orthogonal Hermite functions and least squares. Taking the Fourier transform of this result shows low-frequency trigonometric serie... | \section{Linear combinations of Gaussians with a single variance are dense in
$L^{2}$}
$L^{2}\left( \mathbb{R}\right) $ denotes the space of square integrable
functions $f:\mathbb{R}\rightarrow\mathbb{R}$ with norm $\left\| f\right\|
_{2}:=\sqrt{\int_{\mathbb{R}}\left| f\left( x\right) \right| ^{2}dx}$. We
use ... | {
"timestamp": "2008-05-26T15:16:49",
"yymm": "0805",
"arxiv_id": "0805.3795",
"language": "en",
"url": "https://arxiv.org/abs/0805.3795",
"abstract": "Linear combinations of translations of a single Gaussian, e^{-x^2}, are shown to be dense in L^2(R). Two algorithms for determining the coefficients for the... |
https://arxiv.org/abs/1108.3479 | The semicircle law for matrices with independent diagonals | We investigate the spectral distribution of random matrix ensembles with correlated entries. We consider symmetric matrices with real valued entries and stochastically independent diagonals. Along the diagonals the entries may be correlated. We show that under sufficiently nice moment conditions the empirical eigenvalu... | \section{Introduction}
Large-dimensional random matrices are, among others, of interest in statistics and in theoretical physics, in particular when studying the properties of atoms with heavy
nuclei. One of the most interesting and best studied questions, has been to investigate the properties of the eigenvalues of r... | {
"timestamp": "2011-08-23T02:02:41",
"yymm": "1108",
"arxiv_id": "1108.3479",
"language": "en",
"url": "https://arxiv.org/abs/1108.3479",
"abstract": "We investigate the spectral distribution of random matrix ensembles with correlated entries. We consider symmetric matrices with real valued entries and sto... |
https://arxiv.org/abs/1608.06086 | Power of Two as sums of Three Pell Numbers | In this paper, we find all the solutions of the Diophantine equation $P_\ell + P_m +P_n=2^a$, in nonnegative integer variables $(n,m,\ell, a)$ where $P_k$ is the $k$-th term of the Pell sequence $\{P_n\}_{n\ge 0}$ given by $P_0=0$, $P_1=1$ and $P_{n+1}=2P_{n}+ P_{n-1}$ for all $n\geq 1$. | \section{Introduction}
\noindent The Pell sequence $\{P_n\}_{n\ge 0}$ is the binary reccurent sequence given by $P_0=0$, $P_1=1$ and $P_{n+1}=2P_{n}+ P_{n-1}$ for all $n\geq 0$. There are many papers in the literature dealing with Diophantine equations obtained by asking that
members of some fixed binary recurrence seq... | {
"timestamp": "2016-08-23T02:07:48",
"yymm": "1608",
"arxiv_id": "1608.06086",
"language": "en",
"url": "https://arxiv.org/abs/1608.06086",
"abstract": "In this paper, we find all the solutions of the Diophantine equation $P_\\ell + P_m +P_n=2^a$, in nonnegative integer variables $(n,m,\\ell, a)$ where $P_... |
https://arxiv.org/abs/2006.03639 | Topological charges and conservation laws involving an arbitrary function of time for dynamical PDEs | Dynamical PDEs that have a spatial divergence form possess conservation laws that involve an arbitrary function of time. In one spatial dimension, such conservation laws are shown to describe the presence of an $x$-independent source/sink; in two and more spatial dimensions, they are shown to describe a topological cha... | \section{Introduction}\label{sec:intro}
Many dynamical PDEs have the form of a spatial divergence.
In one spatial dimension, the simplest such form consists of
\begin{equation}\label{1D.eqn}
u_{tx} = D_x F(t,x,u,u_x,u_{xx},\ldots)
\end{equation}
with $D$ denoting a total derivative.
A prominent physical example is
... | {
"timestamp": "2020-12-29T02:09:29",
"yymm": "2006",
"arxiv_id": "2006.03639",
"language": "en",
"url": "https://arxiv.org/abs/2006.03639",
"abstract": "Dynamical PDEs that have a spatial divergence form possess conservation laws that involve an arbitrary function of time. In one spatial dimension, such co... |
https://arxiv.org/abs/1705.01973 | Evolving Affine Evolutoids | The envelope of straight lines affine normal to a plane curve C is its affine evolute; the envelope of the affine lines tangent to C is the original curve, together with the entire affine tangent line at each inflexion of C. In this paper, we consider plane curves without inflexions. We use some techniques of singulari... | \section{Introduction}
\label{intro}
Let $\gamma$ be a plane curve, which we shall assume closed, smooth and without affine inflexions. The {\it envelope} of a family of lines is formed by intersections of infinitesimal consecutive lines or equivalently a curve tangent to all the lines. For example, the envelope of th... | {
"timestamp": "2017-05-08T02:00:54",
"yymm": "1705",
"arxiv_id": "1705.01973",
"language": "en",
"url": "https://arxiv.org/abs/1705.01973",
"abstract": "The envelope of straight lines affine normal to a plane curve C is its affine evolute; the envelope of the affine lines tangent to C is the original curve... |
https://arxiv.org/abs/1912.11518 | Fluctuations of the spectrum in rotationally invariant random matrix ensembles | We investigate traces of powers of random matrices whose distributions are invariant under rotations (with respect to the Hilbert--Schmidt inner product) within a real-linear subspace of the space of $n\times n$ matrices. The matrices we consider may be real or complex, and Hermitian, antihermitian, or general. We use ... | \section{Introduction}
The limiting behavior of the eigenvalues of random matrices is a
central problem in modern probability, with applications and
connections in statistics, physics, and beyond. The eigenvalues of
the classical ensembles have been studied extensively, and much is
known. However, there are many oth... | {
"timestamp": "2020-06-24T02:06:12",
"yymm": "1912",
"arxiv_id": "1912.11518",
"language": "en",
"url": "https://arxiv.org/abs/1912.11518",
"abstract": "We investigate traces of powers of random matrices whose distributions are invariant under rotations (with respect to the Hilbert--Schmidt inner product) ... |
https://arxiv.org/abs/1509.05304 | On a magnetic characterization of spectral minimal partitions | Given a bounded open set $\Omega$ in $ \mathbb R^n$ (or in a Riemannian manifold) and a partition of $\Omega$ by $k$ open sets $D_j$, we consider the quantity $\max_j \lambda(D_j)$ where $\lambda(D_j)$ is the ground state energy of the Dirichlet realization of the Laplacian in $D_j$. If we denote by $ \mathfrak L_k(\Om... | \section{Introduction}\label{Section1}
\subsection{Main definitions}
We consider mainly the Dirichlet Laplacian in a bounded
domain $\Omega\subset \mathbb R^2$.
We would like to analyze the relations between the nodal domains
of the real-valued eigenfunctions of this Laplacian and the partitions of
$\Omega$
by ... | {
"timestamp": "2015-09-18T02:11:12",
"yymm": "1509",
"arxiv_id": "1509.05304",
"language": "en",
"url": "https://arxiv.org/abs/1509.05304",
"abstract": "Given a bounded open set $\\Omega$ in $ \\mathbb R^n$ (or in a Riemannian manifold) and a partition of $\\Omega$ by $k$ open sets $D_j$, we consider the q... |
https://arxiv.org/abs/1111.3454 | Permanents of heavy-tailed random matrices with positive elements | We study the asymptotic behavior of permanents of $n \times n$ random matrices $A$ with positive entries. We assume that $A$ has either i.i.d. entries or is a symmetric matrix with the i.i.d. upper triangle. Under the assumption that elements have power law decaying tails, we prove a strong law of large numbers for $\l... | \section{Introduction}
The permanent of an $m \times n$ matrix $A$ (height $m$ and width $n$) satisfying $m \leq n$ is defined as
\[
\perm A = \sum_{\pi \in S_{m,n}} \prod_{i=1}^n a_{i,\pi(i)},
\]
where $S_{m,n}$ is the set of one-to-one functions from $[m]=\{1,\dots,m\}$ to $[n]=\{1,\dots,n\}$. When $m=n$, that is wh... | {
"timestamp": "2011-11-16T02:01:13",
"yymm": "1111",
"arxiv_id": "1111.3454",
"language": "en",
"url": "https://arxiv.org/abs/1111.3454",
"abstract": "We study the asymptotic behavior of permanents of $n \\times n$ random matrices $A$ with positive entries. We assume that $A$ has either i.i.d. entries or i... |
https://arxiv.org/abs/2005.12909 | $Δ$-critical graphs with a vertex of degree 2 | Let $G$ be a simple graph with maximum degree $\Delta$. A classic result of Vizing shows that $\chi'(G)$, the chromatic index of $G$, is either $\Delta$ or $\Delta+1$. We say $G$ is of \emph{Class 1} if $\chi'(G)=\Delta$, and is of \emph{Class 2} otherwise. A graph $G$ is \emph{$\Delta$-critical} if $\chi'(G)=\Delta+1$... | \section{Introduction}
For two integer $p,q$ with $q\ge p$, we use $[p,q]$ to denote the set of all integer between $p$
and $q$, inclusively.
We consider only simple graphs. Let $G$ be a graph with maximum degree $\Delta(G)=\Delta$. We denote by $V(G)$ and $E(G)$ the vertex set and edge set of $G$, respectively.... | {
"timestamp": "2020-05-28T02:00:12",
"yymm": "2005",
"arxiv_id": "2005.12909",
"language": "en",
"url": "https://arxiv.org/abs/2005.12909",
"abstract": "Let $G$ be a simple graph with maximum degree $\\Delta$. A classic result of Vizing shows that $\\chi'(G)$, the chromatic index of $G$, is either $\\Delta... |
https://arxiv.org/abs/math/9703215 | On the zeros of the Hahn-Exton q-Bessel function and associated q-Lommel polynomials | For the Bessel function \begin{equation} \label{bessel} J_{\nu}(z) = \sum\limits_{k=0}^{\infty} \frac{(-1)^k \left( \frac{z}{2} \right)^{\nu+2k}}{k! \Gamma(\nu+1+k)} \end{equation} there exist several $q$-analogues. The oldest $q$-analogues of the Bessel function were introduced by F. H. Jackson at the beginning of thi... | \section{Introduction}
\markboth{\hfill{\sc Preprint}\hfill}{\hfill{\sc Preprint}\hfill}
\pagestyle{myheadings}
\def4.\arabic{equation}{1.\arabic{equation}}
\setcounter{equation}{0}
For the Bessel function
\begin{equation}
\label{bessel} J_{\nu}(z) = \sum\limits_{k=0}^{\infty}
\frac{(-1)^k \left( \frac{z}{2} \right)... | {
"timestamp": "1998-09-11T06:38:22",
"yymm": "9703",
"arxiv_id": "math/9703215",
"language": "en",
"url": "https://arxiv.org/abs/math/9703215",
"abstract": "For the Bessel function \\begin{equation} \\label{bessel} J_{\\nu}(z) = \\sum\\limits_{k=0}^{\\infty} \\frac{(-1)^k \\left( \\frac{z}{2} \\right)^{\\n... |
https://arxiv.org/abs/1901.04855 | Linear inequalities in primes | In this paper we prove an asymptotic formula for the number of solutions in prime numbers to systems of simultaneous linear inequalities with algebraic coefficients. For $m$ simultaneous inequalities we require at least $m+2$ variables, improving upon existing methods, which generically require at least $2m+1$ variable... | \section{Introduction}
\label{section introduction}
Fourier analysis is a vital tool in the study of diophantine problems. In recent years, however, new tools have been developed which can prove asymptotic formulae for the number of solutions to certain systems even when the Fourier-analytic approach is not known to su... | {
"timestamp": "2019-10-22T02:11:24",
"yymm": "1901",
"arxiv_id": "1901.04855",
"language": "en",
"url": "https://arxiv.org/abs/1901.04855",
"abstract": "In this paper we prove an asymptotic formula for the number of solutions in prime numbers to systems of simultaneous linear inequalities with algebraic co... |
https://arxiv.org/abs/1610.09791 | The arc length of a random lemniscate | A polynomial lemniscate is a curve in the complex plane defined by $\{z \in \mathbb{C}:|p(z)|=t\}$. Erdös, Herzog, and Piranian posed the extremal problem of determining the maximum length of a lemniscate $\Lambda=\{ z \in \mathbb{C}:|p(z)|=1\}$ when $p$ is a monic polynomial of degree $n$. In this paper, we study the ... | \section{Introduction}
A (polynomial) lemniscate is a curve defined in the complex plane by the equation $|p(z)| = t$,
where $p$ is a polynomial.
If the degree of $p$ is $n,$ then from the conjugation-invariant equation $p(z) \overline{p(z)} = t^2$,
it is apparent that the lemniscate is a real algebraic curve of degre... | {
"timestamp": "2017-02-02T02:02:53",
"yymm": "1610",
"arxiv_id": "1610.09791",
"language": "en",
"url": "https://arxiv.org/abs/1610.09791",
"abstract": "A polynomial lemniscate is a curve in the complex plane defined by $\\{z \\in \\mathbb{C}:|p(z)|=t\\}$. Erdös, Herzog, and Piranian posed the extremal pro... |
https://arxiv.org/abs/math/0703921 | Sparse Hypergraphs and Pebble Game Algorithms | A hypergraph $G=(V,E)$ is $(k,\ell)$-sparse if no subset $V'\subset V$ spans more than $k|V'|-\ell$ hyperedges. We characterize $(k,\ell)$-sparse hypergraphs in terms of graph theoretic, matroidal and algorithmic properties. We extend several well-known theorems of Haas, Lov{á}sz, Nash-Williams, Tutte, and White and Wh... | \section{Introduction \labelsec{introduction}}
The focus of this paper is on $(k,\ell)$-sparse hypergraphs. A
hypergraph (or set system) is a pair $G=(V,E)$ with {\bf vertices}
$V$, $n=|V|$ and {\bf edges} $E$ which are subsets of $V$ (multiple
edges are allowed). If all the edges have exactly two vertices, $G$
is a ... | {
"timestamp": "2007-03-30T16:15:00",
"yymm": "0703",
"arxiv_id": "math/0703921",
"language": "en",
"url": "https://arxiv.org/abs/math/0703921",
"abstract": "A hypergraph $G=(V,E)$ is $(k,\\ell)$-sparse if no subset $V'\\subset V$ spans more than $k|V'|-\\ell$ hyperedges. We characterize $(k,\\ell)$-sparse ... |
https://arxiv.org/abs/1908.05650 | The maximum number of points in the cross-polytope that form a packing set of a scaled cross-polytope | The problem of finding the largest number of points in the unit cross-polytope such that the $l_{1}$-distance between any two distinct points is at least $2r$ is investigated for $r\in\left(1-\frac{1}{n},1\right]$ in dimensions $\geq2$ and for $r\in\left(\frac{1}{2},1\right]$ in dimension $3$. For the $n$-dimensional c... | \section{Introduction}
Let $K$ and $L$ be origin-symmetric convex sets in $\mathbb{R}^{n}$
with nonempty interiors. A set $D\subset\mathbb{R}^{n}$ is a (translative)
packing set for $K$ if, for all distinct $\mathbf{x},\mathbf{y}\in D$,
\[
\left(\mathbf{x}+\inter K\right)\cap\left(\mathbf{y}+\inter K\right)=\emptyset.... | {
"timestamp": "2019-08-16T02:13:20",
"yymm": "1908",
"arxiv_id": "1908.05650",
"language": "en",
"url": "https://arxiv.org/abs/1908.05650",
"abstract": "The problem of finding the largest number of points in the unit cross-polytope such that the $l_{1}$-distance between any two distinct points is at least ... |
https://arxiv.org/abs/1008.0266 | Dilation properties for weighted modulation spaces | In this paper we give a sharp estimate on the norm of the scaling operator $U_{\lambda}f(x)=f(\lambda x)$ acting on the weighted modulation spaces $\M{p,q}{s,t}(\R^{d})$. In particular, we recover and extend recent results by Sugimoto and Tomita in the unweighted case. As an application of our results, we estimate the ... | \section{Introduction}\label{intro}
The modulation spaces were introduced
by H.~Feichtinger \cite{Fei83}, by
imposing integrability conditions on
the short-time Fourier transform (STFT)
of tempered distributions. More
specifically, for $x, \omega \in
\mathbb{R}^{d}$, we let $M_\omega$ and $T_x$
denote the operators of ... | {
"timestamp": "2010-08-03T02:02:51",
"yymm": "1008",
"arxiv_id": "1008.0266",
"language": "en",
"url": "https://arxiv.org/abs/1008.0266",
"abstract": "In this paper we give a sharp estimate on the norm of the scaling operator $U_{\\lambda}f(x)=f(\\lambda x)$ acting on the weighted modulation spaces $\\M{p,... |
https://arxiv.org/abs/1305.2856 | On the flag curvature of invariant Randers metrics | In the present paper, the flag curvature of invariant Randers metrics on homogeneous spaces and Lie groups is studied. We first give an explicit formula for the flag curvature of invariant Randers metrics arising from invariant Riemannian metrics on homogeneous spaces and, in special case, Lie groups. We then study Ran... | \section{Introduction}
The geometry of invariant structures on homogeneous spaces is one
of the interesting subjects in differential geometry. Invariant
metrics are of these invariant structures. K. Nomizu studied many
interesting properties of invariant Riemannian metrics and the
existence and properties of invariant ... | {
"timestamp": "2013-05-14T02:04:11",
"yymm": "1305",
"arxiv_id": "1305.2856",
"language": "en",
"url": "https://arxiv.org/abs/1305.2856",
"abstract": "In the present paper, the flag curvature of invariant Randers metrics on homogeneous spaces and Lie groups is studied. We first give an explicit formula for... |
https://arxiv.org/abs/1501.03053 | Random Triangle Theory with Geometry and Applications | What is the probability that a random triangle is acute? We explore this old question from a modern viewpoint, taking into account linear algebra, shape theory, numerical analysis, random matrix theory, the Hopf fibration, and much much more. One of the best distributions of random triangles takes all six vertex coordi... | \section{Introduction}
Triangles live on a hemisphere and are linked to 2 by 2 matrices.
The familiar triangle is seen in a different light. New understanding
and new applications come from its connections to the modern developments of random matrix theory.
You may never look at a triangle the same way again.
We began... | {
"timestamp": "2015-01-14T02:12:41",
"yymm": "1501",
"arxiv_id": "1501.03053",
"language": "en",
"url": "https://arxiv.org/abs/1501.03053",
"abstract": "What is the probability that a random triangle is acute? We explore this old question from a modern viewpoint, taking into account linear algebra, shape t... |
https://arxiv.org/abs/2204.02201 | On the size distribution of Levenshtein balls with radius one | The fixed length Levenshtein (FLL) distance between two words $\mathbf{x,y} \in \mathbb{Z}_m^n$ is the smallest integer $t$ such that $\mathbf{x}$ can be transformed to $\mathbf{y}$ by $t$ insertions and $t$ deletions. The size of a ball in FLL metric is a fundamental but challenging problem. Very recently, Bar-Lev, Et... | \section{Introduction}
The \emph{Levenshtein distance} ({also known as {\em edit distance}}) between two words is the smallest number of deletions and insertions needed to transform one word to {the other}.
This {is a metric used for codes correcting synchronization errors}. The theory of {coding with respect to Leven... | {
"timestamp": "2022-04-06T02:26:40",
"yymm": "2204",
"arxiv_id": "2204.02201",
"language": "en",
"url": "https://arxiv.org/abs/2204.02201",
"abstract": "The fixed length Levenshtein (FLL) distance between two words $\\mathbf{x,y} \\in \\mathbb{Z}_m^n$ is the smallest integer $t$ such that $\\mathbf{x}$ can... |
https://arxiv.org/abs/2007.09874 | A Note on Stabbing Convex Bodies with Points, Lines, and Flats | $\newcommand{\eps}{\varepsilon}\newcommand{\tldO}{\widetilde{O}}$Consider the problem of constructing weak $\eps$-nets where the stabbing elements are lines or $k$-flats instead of points. We study this problem in the simplest setting where it is still interesting -- namely, the uniform measure of volume over the hyper... | \section{Introduction}
\myparagraph{Range spaces and $\varepsilon$-nets.} %
A \emphi{range space} is a pair $\RangeSpace = (\Ground, \Ranges)$,
where $\Ground$ is the \emphi{ground set} (finite or infinite) and
$\Ranges$ is a (finite or infinite) family of subsets of $\Ground$.
The elements of $\Ranges$ are \emphi{ra... | {
"timestamp": "2020-12-07T02:24:55",
"yymm": "2007",
"arxiv_id": "2007.09874",
"language": "en",
"url": "https://arxiv.org/abs/2007.09874",
"abstract": "$\\newcommand{\\eps}{\\varepsilon}\\newcommand{\\tldO}{\\widetilde{O}}$Consider the problem of constructing weak $\\eps$-nets where the stabbing elements ... |
https://arxiv.org/abs/1312.6344 | Relation Between Surface Codes and Hypermap-Homology Quantum Codes | Recently, a new class of quantum codes based on hypermaps were proposed. These codes are obtained from embeddings of hypergraphs as opposed to surface codes which are obtained from the embeddings of graphs. It is natural to compare these two classes of codes and their relation to each other. In this context two related... | \section{Introduction}
Surface codes, proposed by Kitaev \cite{kitaev03}, are an extremely appealing class of codes for fault tolerant quantum computation \cite{dennis02,raussen07}. They have been generalized in various directions \cite{bravyi98,bullock07,bombin07b,bombin07,bombin06,tillich09, zemor09}.
Recently, a... | {
"timestamp": "2014-03-17T01:06:24",
"yymm": "1312",
"arxiv_id": "1312.6344",
"language": "en",
"url": "https://arxiv.org/abs/1312.6344",
"abstract": "Recently, a new class of quantum codes based on hypermaps were proposed. These codes are obtained from embeddings of hypergraphs as opposed to surface codes... |
https://arxiv.org/abs/2103.11420 | An inverse-type problem for cycles in local Cayley distance graphs | Let $E$ be a proper symmetric subset of $S^{d-1}$, and $C_{\mathbb{F}_q^d}(E)$ be the Cayley graph with the vertex set $\mathbb{F}_q^d$, and two vertices $x$ and $y$ are connected by an edge if $x-y\in E$. Let $k\ge 2$ be a positive integer. We show that for any $\alpha\in (0, 1)$, there exists $q(\alpha, k)$ large eno... | \section{Introduction}
Let $G$ be an abelian finite group and a symmetric set $E\subset G$. The Cayley graph $C_G(E)$ is defined as the graph with the vertex set $V=G$, and there is an edge from $x$ to $y$ if $y-x\in E$. Let $\mathbb{F}_q$ be a finite field of order $q$, where $q$ is a prime power. In this paper, we co... | {
"timestamp": "2021-03-23T01:20:03",
"yymm": "2103",
"arxiv_id": "2103.11420",
"language": "en",
"url": "https://arxiv.org/abs/2103.11420",
"abstract": "Let $E$ be a proper symmetric subset of $S^{d-1}$, and $C_{\\mathbb{F}_q^d}(E)$ be the Cayley graph with the vertex set $\\mathbb{F}_q^d$, and two vertice... |
https://arxiv.org/abs/2102.10358 | Mean dimension of product spaces: a fundamental formula | Mean dimension is a topological invariant of dynamical systems, which originates with Mikhail Gromov in 1999 and which was studied with deep applications around 2000 by Elon Lindenstrauss and Benjamin Weiss within the framework of amenable group actions. Let a countable discrete amenable group $G$ act continuously on c... | \section{Main result}
Mean dimension is a topological invariant of dynamical systems, which originates with Mikhail Gromov in 1999 and which was investigated with deep applications around 2000 by Elon Lindenstrauss and Benjamin Weiss within the framework of amenable group actions. The purpose of this paper is to establ... | {
"timestamp": "2022-11-22T02:09:19",
"yymm": "2102",
"arxiv_id": "2102.10358",
"language": "en",
"url": "https://arxiv.org/abs/2102.10358",
"abstract": "Mean dimension is a topological invariant of dynamical systems, which originates with Mikhail Gromov in 1999 and which was studied with deep applications ... |
https://arxiv.org/abs/1807.01667 | Equicontinuity of minimal sets for amenable group actions on dendrites | In this note, we show that if $G$ is an amenable group acting on a dendrite $X$, then the restriction of $G$ to any minimal set $K$ is equicontinuous, and $K$ is either finite or homeomorphic to the Cantor set. | \section{Introduction}
It is well known that every \tw{continuous} action of
\tw{a topological group}~$G$ on \tw{a compact metric space}~$X$
must have a minimal set~$K$. A natural
question is \tw{to ask}
what can \tw{be said} about the topology of~$K$,
and the dynamics of the subsystem~$(K, G)$.
The answer
to this ques... | {
"timestamp": "2020-06-29T02:08:21",
"yymm": "1807",
"arxiv_id": "1807.01667",
"language": "en",
"url": "https://arxiv.org/abs/1807.01667",
"abstract": "In this note, we show that if $G$ is an amenable group acting on a dendrite $X$, then the restriction of $G$ to any minimal set $K$ is equicontinuous, and... |
https://arxiv.org/abs/1611.05070 | Scaling Laws for Maximum Coloring of Random Geometric Graphs | We examine maximum vertex coloring of random geometric graphs, in an arbitrary but fixed dimension, with a constant number of colors. Since this problem is neither scale-invariant nor smooth, the usual methodology to obtain limit laws cannot be applied. We therefore leverage different concepts based on subadditivity to... | \section{Introduction}
\label{sec:intro}
We examine maximum coloring of random geometric graphs (RGGs),
in an arbitrary but fixed dimension~$d$, with a constant number
of colors.
The vertices of an RGG (whose spatial distribution will be defined below)
are embedded in an Euclidean space that is equipped with the $\ell... | {
"timestamp": "2016-11-17T02:00:34",
"yymm": "1611",
"arxiv_id": "1611.05070",
"language": "en",
"url": "https://arxiv.org/abs/1611.05070",
"abstract": "We examine maximum vertex coloring of random geometric graphs, in an arbitrary but fixed dimension, with a constant number of colors. Since this problem i... |
https://arxiv.org/abs/1603.01183 | Solving systems of polynomial inequalities with algebraic geometry methods | The goal of this paper is to provide computational tools able to find a solution of a system of polynomial inequalities. The set of inequalities is reformulated as a system of polynomial equations. Three different methods, two of which taken from the literature, are proposed to compute solutions of such a system. An ex... | \section{Introduction\label{sec:intro}}
In several control problems, it is needed to guarantee
the existence of real solutions, and, possibly, to compute one of them,
for a system of polynomial equalities or inequalities \cite{abdallah1995applications,henrion2005positive,chesi2010lmi}.
For instance, a solution of a ... | {
"timestamp": "2016-03-04T02:13:38",
"yymm": "1603",
"arxiv_id": "1603.01183",
"language": "en",
"url": "https://arxiv.org/abs/1603.01183",
"abstract": "The goal of this paper is to provide computational tools able to find a solution of a system of polynomial inequalities. The set of inequalities is reform... |
https://arxiv.org/abs/1504.01242 | Free divisors and rational cuspidal plane curves | A characterization of freeness for plane curves in terms of the Hilbert function of the associated Milnor algebra is given as well as many new examples of rational cuspidal curves which are free. Some stronger properties are stated as conjectures. | \section{Introduction} \label{sec:intro}
A (reduced) curve $C$ in the complex projective plane $\PP^2$ is called { \it free}, or a free divisor,
if the rank two vector bundle $T\langle C\rangle=Der(-logC)$ of logarithmic vector fields along $C$ splits as a direct sum of two line bundles on $\PP^2$. Note that $C$ i... | {
"timestamp": "2015-05-04T02:04:42",
"yymm": "1504",
"arxiv_id": "1504.01242",
"language": "en",
"url": "https://arxiv.org/abs/1504.01242",
"abstract": "A characterization of freeness for plane curves in terms of the Hilbert function of the associated Milnor algebra is given as well as many new examples of... |
https://arxiv.org/abs/1905.12306 | Effective viscosity of a polydispersed suspension | We compute the first order correction of the effective viscosity for a suspension containing solid particles with arbitrary shapes. We rewrite the computation as an homogenization problem for the Stokes equations in a perforated domain. Then, we extend the method of reflections to approximate the solution to the Stokes... | \section{Introduction}
When a viscous fluid transports solid particles, the particles modify in return the properties of the fluid. For instance, the rheological properties of the fluid are altered.
In his seminal paper \cite{Einstein}, Einstein addresses the computation of the effective viscosity of the mixture, hav... | {
"timestamp": "2019-05-30T02:13:35",
"yymm": "1905",
"arxiv_id": "1905.12306",
"language": "en",
"url": "https://arxiv.org/abs/1905.12306",
"abstract": "We compute the first order correction of the effective viscosity for a suspension containing solid particles with arbitrary shapes. We rewrite the computa... |
https://arxiv.org/abs/0912.3446 | Tight Lower Bounds on the Sizes of Symmetric Extensions of Permutahedra and Similar Results | It is well known that the permutahedron Pi_n has 2^n-2 facets. The Birkhoff polytope provides a symmetric extended formulation of Pi_n of size Theta(n^2). Recently, Goemans described a non-symmetric extended formulation of Pi_n of size Theta(n log(n)). In this paper, we prove that Omega(n^2) is a lower bound for the si... |
\section{Introduction}
Extended formulations of polyhedra have gained importance in the recent past, because this concept allows to represent a polyhedron by a higher-dimensional one with a simpler description.
To illustrate the power of extended formulations we take a look at the permutahedron~$\Pi_n\subseteq \ma... | {
"timestamp": "2011-01-25T02:02:30",
"yymm": "0912",
"arxiv_id": "0912.3446",
"language": "en",
"url": "https://arxiv.org/abs/0912.3446",
"abstract": "It is well known that the permutahedron Pi_n has 2^n-2 facets. The Birkhoff polytope provides a symmetric extended formulation of Pi_n of size Theta(n^2). R... |
https://arxiv.org/abs/1608.07762 | A class of Ramsey-extremal hypergraphs | In 1991, McKay and Radziszowski proved that, however each 3-subset of a 13-set is assigned one of two colours, there is some 4-subset whose four 3-subsets have the same colour. More than 25 years later, this remains the only non-trivial classical Ramsey number known for hypergraphs. In this article, we find all the ext... | \section{Introduction}\label{intro}
A colouring of all the $s$-subsets of an $n$-set with two
colours is called \textit{$R(j,k;s)$-good} if there is no $j$-subset
(of the $n$-set) containing only $s$-subsets of the first
colour, and no $k$-subset containing only $s$-subsets of the
second colour. (Note that it is the $... | {
"timestamp": "2016-08-30T02:03:15",
"yymm": "1608",
"arxiv_id": "1608.07762",
"language": "en",
"url": "https://arxiv.org/abs/1608.07762",
"abstract": "In 1991, McKay and Radziszowski proved that, however each 3-subset of a 13-set is assigned one of two colours, there is some 4-subset whose four 3-subsets... |
https://arxiv.org/abs/2003.04776 | Parallel Robust Computation of Generalized Eigenvectors of Matrix Pencils | In this paper we consider the problem of computing generalized eigenvectors of a matrix pencil in real Schur form. In exact arithmetic, this problem can be solved using substitution. In practice, substitution is vulnerable to floating-point overflow. The robust solvers xTGEVC in LAPACK prevent overflow by dynamically s... | \section{Introduction} \label{sec:introduction}
Let $A \in \R^{m \times m}$ and let $B \in \R^{m \times m}$. The matrix pencil $(A,B)$ consists of all matrices of the form $A - \lambda B$ where $\lambda \in \mathbb{C}$. The set of (generalized) eigenvalues of the matrix pencil $(A,B)$ is given by
\begin{equation}
\lam... | {
"timestamp": "2020-03-11T01:14:40",
"yymm": "2003",
"arxiv_id": "2003.04776",
"language": "en",
"url": "https://arxiv.org/abs/2003.04776",
"abstract": "In this paper we consider the problem of computing generalized eigenvectors of a matrix pencil in real Schur form. In exact arithmetic, this problem can b... |
https://arxiv.org/abs/1705.01646 | Recursive Integral Method with Cayley Transformation | Recently, a non-classical eigenvalue solver, called RIM, was proposed to compute (all) eigenvalues in a region on the complex plane. Without solving any eigenvalue problem, it tests if a region contains eigenvalues using an approximate spectral projection. Regions that contain eigenvalues are subdivided and tested recu... | \section{Introduction}
We consider the non-Hermitian eigenvalue problem
\begin{equation} \label{AxLambdaBx}
A x= \lambda B x,
\end{equation}
where $A$ and $B$ are $n\times n$ large sparse matrices. Here $B$ can be singular. Such eigenvalue problems arise in many scientific and engineering
applications \cite{GolubVorst... | {
"timestamp": "2017-05-05T02:02:00",
"yymm": "1705",
"arxiv_id": "1705.01646",
"language": "en",
"url": "https://arxiv.org/abs/1705.01646",
"abstract": "Recently, a non-classical eigenvalue solver, called RIM, was proposed to compute (all) eigenvalues in a region on the complex plane. Without solving any e... |
https://arxiv.org/abs/1912.06999 | Fixed-Time Extremum Seeking | We introduce a new class of extremum seeking controllers able to achieve fixed time convergence to the solution of optimization problems defined by static and dynamical systems. Unlike existing approaches in the literature, the convergence time of the proposed algorithms does not depend on the initial conditions and it... | \section{Introduction}
\label{Sec:introduction}
\PARstart{I}{n} several applications it is of interest to recursively minimize a particular cost function whose mathematical form is unknown and which is only accessible via measurements. For these types of problems, extremum seeking control (ESC) has shown to be a powerf... | {
"timestamp": "2019-12-17T02:12:23",
"yymm": "1912",
"arxiv_id": "1912.06999",
"language": "en",
"url": "https://arxiv.org/abs/1912.06999",
"abstract": "We introduce a new class of extremum seeking controllers able to achieve fixed time convergence to the solution of optimization problems defined by static... |
https://arxiv.org/abs/1611.06303 | Hilbert's Proof of His Irreducibility Theorem | Hilbert's Irreducibility Theorem is a cornerstone that joins areas of analysis and number theory. Both the genesis and genius of its proof involved combining real analysis and combinatorics. We try to expose the motivations that led Hilbert to this synthesis. Hilbert's famous Cube Lemma supplied fuel for the proof but ... | \section{Introduction.}
\label{sec:intro}
In 1892, David Hilbert
published what is
known today as \emph{Hilbert's irreducibility theorem}.
We give his statement, using \emph{integral polynomial} to mean a polynomial in any number of variables whose coefficients are integers.
\begin{thm}
\label{irreducibility}
If $... | {
"timestamp": "2017-09-21T02:09:36",
"yymm": "1611",
"arxiv_id": "1611.06303",
"language": "en",
"url": "https://arxiv.org/abs/1611.06303",
"abstract": "Hilbert's Irreducibility Theorem is a cornerstone that joins areas of analysis and number theory. Both the genesis and genius of its proof involved combin... |
https://arxiv.org/abs/2008.04307 | Spectrum of twists of Cayley and Cayley sum graphs | Let $G$ be a finite group with $|G|\geq 4$ and $S$ be a subset of $G$. Given an automorphism $\sigma$ of $G$, the twisted Cayley graph $C(G, S)^\sigma$ (resp. the twisted Cayley sum graph $C_\Sigma(G, S)^\sigma$) is defined as the graph having $G$ as its set of vertices and the adjacent vertices of a vertex $g\in G$ ar... | \section{Introduction}
\subsection{Motivation}
The study of the spectrum of graphs is an important theme in the theory of expanders. It was remarked by Breuillard--Green--Guralnick--Tao that the eigenvalues of the normalised Laplacian operator of non-bipartite, finite Cayley graphs are bounded away from $2$ (see \cite[... | {
"timestamp": "2020-08-12T02:00:06",
"yymm": "2008",
"arxiv_id": "2008.04307",
"language": "en",
"url": "https://arxiv.org/abs/2008.04307",
"abstract": "Let $G$ be a finite group with $|G|\\geq 4$ and $S$ be a subset of $G$. Given an automorphism $\\sigma$ of $G$, the twisted Cayley graph $C(G, S)^\\sigma$... |
https://arxiv.org/abs/1802.04586 | Hamiltonicity in randomly perturbed hypergraphs | For integers $k\ge 3$ and $1\le \ell\le k-1$, we prove that for any $\alpha>0$, there exist $\epsilon>0$ and $C>0$ such that for sufficiently large $n\in (k-\ell)\mathbb{N}$, the union of a $k$-uniform hypergraph with minimum vertex degree $\alpha n^{k-1}$ and a binomial random $k$-uniform hypergraph $\mathbb{G}^{(k)}(... | \section{\@startsection{section}{1}%
\theoremstyle{plain}
\newtheorem{theorem}{Theorem}
\newtheoremstyle{note
{4pt
{4pt
{\sl
{
{\itshape
{.
{.5em
{
\theoremstyle{note}
\newtheorem{claim}{Claim}
\begin{document}
\title[Hamiltonicity in randomly perturbed hypergraphs]{Hamiltonicity in randomly... | {
"timestamp": "2019-11-19T02:01:43",
"yymm": "1802",
"arxiv_id": "1802.04586",
"language": "en",
"url": "https://arxiv.org/abs/1802.04586",
"abstract": "For integers $k\\ge 3$ and $1\\le \\ell\\le k-1$, we prove that for any $\\alpha>0$, there exist $\\epsilon>0$ and $C>0$ such that for sufficiently large ... |
https://arxiv.org/abs/1207.3933 | Bounds for approximate discrete tomography solutions | In earlier papers we have developed an algebraic theory of discrete tomography. In those papers the structure of the functions $f: A \to \{0,1\}$ and $f: A \to \mathbb{Z}$ having given line sums in certain directions have been analyzed. Here $A$ was a block in $\mathbb{Z}^n$ with sides parallel to the axes. In the pres... | \section{Introduction}
Let $n$ be a positive integer and let $A$ be a finite subset of $\mathbb{Z}^n$. If $f: A \to \mathbb{R}$, then the line sum of $f$ along the line $l=\underline{c}+t\underline{d}$ (with $\underline{c},\underline{d}\in \mathbb{Z}^n$, $\underline{d}\neq \underline{0}$ fixed and $t\in \mathbb{R}$ va... | {
"timestamp": "2012-07-18T02:02:47",
"yymm": "1207",
"arxiv_id": "1207.3933",
"language": "en",
"url": "https://arxiv.org/abs/1207.3933",
"abstract": "In earlier papers we have developed an algebraic theory of discrete tomography. In those papers the structure of the functions $f: A \\to \\{0,1\\}$ and $f:... |
https://arxiv.org/abs/2211.16874 | A survey on generalizations of Forelli's theorem and related pluripotential methods | We present a survey on recent developments of generalizations of Forelli's analyticity theorem and related pluripotential methods. | \section{Introduction}
When the higher-dimensional complex analysis began to emerge in the early 1900s, a natural concern was to establish criteria for the complex analyticity of functions of several complex variables. Then the study of analyticity theorems started with the following celebrated
\begin{theorem}[Hart... | {
"timestamp": "2022-12-01T02:12:08",
"yymm": "2211",
"arxiv_id": "2211.16874",
"language": "en",
"url": "https://arxiv.org/abs/2211.16874",
"abstract": "We present a survey on recent developments of generalizations of Forelli's analyticity theorem and related pluripotential methods.",
"subjects": "Comple... |
https://arxiv.org/abs/0811.2365 | Sturm and Sylvester algorithms revisited via tridiagonal determinantal representations | First, we show that Sturm algorithm and Sylvester algorithm, which compute the number of real roots of a given univariate polynomial, lead to two dual tridiagonal determinantal representations of the polynomial. Next, we show that the number of real roots of a polynomial given by a tridiagonal determinantal representat... | \section*{Introduction}
There are several methods to count the number of real roots of an univariate polynomial $p(x)\in{\Bbb R}[x]$ of degree $n$ (for details we refer to \cite{BPR}). Among them, the Sturm algorithm says that the number of real roots of $p(x)$ is equal to the number of Permanence minus the number of v... | {
"timestamp": "2008-11-14T16:49:56",
"yymm": "0811",
"arxiv_id": "0811.2365",
"language": "en",
"url": "https://arxiv.org/abs/0811.2365",
"abstract": "First, we show that Sturm algorithm and Sylvester algorithm, which compute the number of real roots of a given univariate polynomial, lead to two dual tridi... |
https://arxiv.org/abs/2206.07760 | Multiscale methods for signal selection in single-cell data | Analysis of single-cell transcriptomics often relies on clustering cells and then performing differential gene expression (DGE) to identify genes that vary between these clusters. These discrete analyses successfully determine cell types and markers; however, continuous variation within and between cell types may not b... | \section{Introduction}
Cells, the building blocks of life, are often classified into discrete cell types (e.g. liver, neuron, immune, or blood cells).
In modern experiments, cell type identification commonly relies on partitioning single cell RNA sequencing (scRNA-seq) data.
Differential gene expression (DGE) algorit... | {
"timestamp": "2022-06-17T02:01:03",
"yymm": "2206",
"arxiv_id": "2206.07760",
"language": "en",
"url": "https://arxiv.org/abs/2206.07760",
"abstract": "Analysis of single-cell transcriptomics often relies on clustering cells and then performing differential gene expression (DGE) to identify genes that var... |
https://arxiv.org/abs/2102.12937 | Sliding down over a horizontally moving semi-sphere | We studied the dynamics of an object sliding down on a semi-sphere with radius $R$. We consider the physical setup where the semi-sphere is free to move over a flat surface. For simplicity, we assume that all surfaces are friction-less. We analyze the values for the last contact angle $\theta^\star$, corresponding to t... | \section{Introduction}
In courses of Newtonian mechanics for engineers and physics students at undergraduate level, the concepts behind Newton's laws are key for understanding the kinematics of objects under the effects of forces. Indeed, in courses focuses on engineering, there is preference to solve problem using on... | {
"timestamp": "2022-03-07T02:04:39",
"yymm": "2102",
"arxiv_id": "2102.12937",
"language": "en",
"url": "https://arxiv.org/abs/2102.12937",
"abstract": "We studied the dynamics of an object sliding down on a semi-sphere with radius $R$. We consider the physical setup where the semi-sphere is free to move o... |
https://arxiv.org/abs/2302.14361 | Towards continuity: Universal frequency-preserving KAM persistence and remaining regularity | Beyond Hölder's type, this paper mainly concerns the persistence and remaining regularity of an individual frequency-preserving KAM torus in a finitely differentiable Hamiltonian system, even allows the non-integrable part being critical finitely smooth. To achieve this goal, besides investigating the Jackson approxima... | \section{Introduction}
The celebrated KAM theory, due to Kolmogorov and Arnold \cite{MR0068687,R-9,R-10,R-11}, Moser \cite{R-12,R-13}, mainly concerns the preservation of invariant tori of a Hamiltonian function $ H(y) $ under small perturbations (i.e., $H(y) \to H\left( {x,y,\varepsilon } \right) $ of freedom $ n \... | {
"timestamp": "2023-03-01T02:11:03",
"yymm": "2302",
"arxiv_id": "2302.14361",
"language": "en",
"url": "https://arxiv.org/abs/2302.14361",
"abstract": "Beyond Hölder's type, this paper mainly concerns the persistence and remaining regularity of an individual frequency-preserving KAM torus in a finitely di... |
https://arxiv.org/abs/1502.02966 | Quotient graphs for power graphs | In a previous paper of the first author a procedure was developed for counting the components of a graph through the knowledge of the components of its quotient graphs. We apply here that procedure to the proper power graph $\mathcal{P}_0(G)$ of a finite group $G$, finding a formula for the number $c(\mathcal{P}_0(G))$... | \section{\bf Introduction and main results}
\vskip 0.4 true cm
Kelarev and Quinn~\cite{kq} defined the directed power graph $\overrightarrow{P(S)}$ of a semigroup $S$ as the directed graph in which the set of vertices is $S$ and, for $x, y\in S$, there is an arc $(x,y)$ if $y=x^m$, for some $m\in\mathbb{N}$. The ... | {
"timestamp": "2016-07-22T02:10:20",
"yymm": "1502",
"arxiv_id": "1502.02966",
"language": "en",
"url": "https://arxiv.org/abs/1502.02966",
"abstract": "In a previous paper of the first author a procedure was developed for counting the components of a graph through the knowledge of the components of its qu... |
https://arxiv.org/abs/1710.06886 | Bounds for totally separable translative packings in the plane | A packing of translates of a convex domain in the Euclidean plane is said to be totally separable if any two packing elements can be separated by a line disjoint from the interior of every packing element. This notion was introduced by G. Fejes Tóth and L. Fejes Tóth (1973) and has attracted significant attention. In t... | \section{Introduction}\label{intro}
Our paper intends to bridge totally separable packings of discrete geometry and Oler's inequality of geometry of numbers. The concept of totally separable packings was introduced by G. Fejes T\'oth and L. Fejes T\'oth in \cite{FeFe} as follows. We say that a set of domains is totall... | {
"timestamp": "2017-10-20T02:00:32",
"yymm": "1710",
"arxiv_id": "1710.06886",
"language": "en",
"url": "https://arxiv.org/abs/1710.06886",
"abstract": "A packing of translates of a convex domain in the Euclidean plane is said to be totally separable if any two packing elements can be separated by a line d... |
https://arxiv.org/abs/2107.01881 | Robust Online Convex Optimization in the Presence of Outliers | We consider online convex optimization when a number k of data points are outliers that may be corrupted. We model this by introducing the notion of robust regret, which measures the regret only on rounds that are not outliers. The aim for the learner is to achieve small robust regret, without knowing where the outlier... | \section{Introduction}
Methods for online convex optimization (OCO) are designed to work even in
the presence of adversarially generated data
\citep{Hazan2016,ShalevShwartz,CesaBianchiLugosi2006}, but this is
only possible because strong boundedness assumptions are imposed on
the losses that limit the ... | {
"timestamp": "2021-07-06T02:31:20",
"yymm": "2107",
"arxiv_id": "2107.01881",
"language": "en",
"url": "https://arxiv.org/abs/2107.01881",
"abstract": "We consider online convex optimization when a number k of data points are outliers that may be corrupted. We model this by introducing the notion of robus... |
https://arxiv.org/abs/1303.2599 | Step by step categorification of the Jones polynomial in Kauffman's version | Given any diagram of a link, we define on the cube of Kauffman's states a "2-complex" whose homology is an invariant of the associated framed links, and such that the graded Euler characteristic reproduces the unnormalized Kauffman bracket. This includes a categorification of brackets skein relation. Then we incorporat... | \subsection*{Abstract}
Given any diagram of a link, we define on the cube of Kauffman's states a ``$2$-complex'' whose homology is an invariant of the associated framed links, and such that the graded Euler characteristic reproduces the unnormalized Kauffman bracket. This includes a categorification of brackets skein... | {
"timestamp": "2013-06-14T02:01:11",
"yymm": "1303",
"arxiv_id": "1303.2599",
"language": "en",
"url": "https://arxiv.org/abs/1303.2599",
"abstract": "Given any diagram of a link, we define on the cube of Kauffman's states a \"2-complex\" whose homology is an invariant of the associated framed links, and s... |
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