url stringlengths 31 38 | title stringlengths 7 229 | abstract stringlengths 44 2.87k | text stringlengths 319 2.51M | meta dict |
|---|---|---|---|---|
https://arxiv.org/abs/2209.05976 | Local boundedness for $p$-Laplacian with degenerate coefficients | We study local boundedness for subsolutions of nonlinear nonuniformly elliptic equations whose prototype is given by $\nabla \cdot (\lambda |\nabla u|^{p-2}\nabla u)=0$, where the variable coefficient $0\leq\lambda$ and its inverse $\lambda^{-1}$ are allowed to be unbounded. Assuming certain integrability conditions on... | \section{Introduction}
In this note, we study local boundedness of weak (sub)solutions of non-uniformly elliptic quasi-linear equations of the form
\begin{equation}\label{eq}
\nabla \cdot a(x,\nabla u)=0\qquad\mbox{in $\Omega$},
\end{equation}
where $\Omega\subset\R^d$ with $d\geq2$ and $a:\Omega\times\R^d\to\R^d$ is ... | {
"timestamp": "2022-09-14T02:22:56",
"yymm": "2209",
"arxiv_id": "2209.05976",
"language": "en",
"url": "https://arxiv.org/abs/2209.05976",
"abstract": "We study local boundedness for subsolutions of nonlinear nonuniformly elliptic equations whose prototype is given by $\\nabla \\cdot (\\lambda |\\nabla u|... |
https://arxiv.org/abs/2110.08670 | Upper Bounds on Resolvent Degree via Sylvester's Obliteration Algorithm | For each $n$, let RD$(n)$ denote the minimum $d$ for which there exists a formula for the general polynomial of degree $n$ in algebraic functions of at most $d$ variables. In this paper, we recover an algorithm of Sylvester for determining non-zero solutions of systems of homogeneous polynomials, which we present from ... | \section{Introduction}\label{sec:Introduction}
A classical problem in mathematics is to determine the roots of a general degree $n$ polynomial in one variable in terms of its coefficients. Modern work on this problem centers around resolvent degree, an invariant whose ideas permeate classical work, but was not formally... | {
"timestamp": "2021-10-19T02:15:38",
"yymm": "2110",
"arxiv_id": "2110.08670",
"language": "en",
"url": "https://arxiv.org/abs/2110.08670",
"abstract": "For each $n$, let RD$(n)$ denote the minimum $d$ for which there exists a formula for the general polynomial of degree $n$ in algebraic functions of at mo... |
https://arxiv.org/abs/1408.1262 | Theta rank, levelness, and matroid minors | The Theta rank of a finite point configuration $V$ is the maximal degree necessary for a sum-of-squares representation of a non-negative linear function on $V$. This is an important invariant for polynomial optimization that is in general hard to determine. We study the Theta rank and levelness, a related discrete-geom... | \section{Introduction}
\label{sec:intro}
Let $V$ be a configuration of finitely many points in $\R^n$. A linear
function $\ell(\x) = \delta - \langle c, \x \rangle$ which is non-negative on
$V$ is called $\mathbf{k}$\Defn{-sos} with respect to $V$ if there exist polynomials
$h_1,\ldots,h_s\in \mathbb{R}[x_1,\ldots , x... | {
"timestamp": "2015-09-09T02:11:44",
"yymm": "1408",
"arxiv_id": "1408.1262",
"language": "en",
"url": "https://arxiv.org/abs/1408.1262",
"abstract": "The Theta rank of a finite point configuration $V$ is the maximal degree necessary for a sum-of-squares representation of a non-negative linear function on ... |
https://arxiv.org/abs/1501.00430 | The Unimodality Conjecture for cubical polytopes | Although the Unimodality Conjecture holds for some certain classes of cubical polytopes (e.g. cubes, capped cubical polytopes, neighborly cubical polytopes), it fails for cubical polytopes in general. A 12-dimensional cubical polytope with non-unimodal face vector is constructed by using capping operations over a neigh... | \section{Introduction}
The vector $\textbf{a}=(a_0,\ldots, a_{d-1})$ is called \textit{unimodal} if for some (not necessarily unique) index $i$, $(a_0,\ldots, a_i)$ is non-decreasing and $(a_i,\ldots, a_{d-1})$ is non-increasing. If that is the case, we say that the unimodal vector $\textbf{a}$ \textit{peaks} at $i... | {
"timestamp": "2015-01-07T02:04:26",
"yymm": "1501",
"arxiv_id": "1501.00430",
"language": "en",
"url": "https://arxiv.org/abs/1501.00430",
"abstract": "Although the Unimodality Conjecture holds for some certain classes of cubical polytopes (e.g. cubes, capped cubical polytopes, neighborly cubical polytope... |
https://arxiv.org/abs/2205.03487 | Twist monomials of binary delta-matroids | Recently, we introduced the twist polynomials of delta-matroids and gave a characterization of even normal binary delta-matroids whose twist polynomials have only one term and posed a problem: what would happen for odd binary delta-matroids? In this paper, we show that a normal binary delta-matroid whose twist polynomi... | \section{Introduction}
The partial dual with respect to a subset $A$ of edges of a ribbon graph $G$ was introduced by Chmutov \cite{CG} in connection with the Jones-Kauffman and Bollob\'{a}s-Riordan polynomials. In 2020, Gross, Mansour and Tucker \cite{GMT} introduced the partial duality polynomial of a ribbon graph, ... | {
"timestamp": "2022-05-10T02:04:37",
"yymm": "2205",
"arxiv_id": "2205.03487",
"language": "en",
"url": "https://arxiv.org/abs/2205.03487",
"abstract": "Recently, we introduced the twist polynomials of delta-matroids and gave a characterization of even normal binary delta-matroids whose twist polynomials h... |
https://arxiv.org/abs/1410.8753 | Refined Upper Bounds on Stopping Redundancy of Binary Linear Codes | The $l$-th stopping redundancy $\rho_l(\mathcal C)$ of the binary $[n, k, d]$ code $\mathcal C$, $1 \le l \le d$, is defined as the minimum number of rows in the parity-check matrix of $\mathcal C$, such that the smallest stopping set is of size at least $l$. The stopping redundancy $\rho(\mathcal C)$ is defined as $\r... | \section{Introduction}
\emph{Stopping sets} are a known cause of failures of message-passing decoders, when applied to binary linear codes on a binary erasure
channel~\cite{di2002finite}. Small stopping sets are especially harmful, as they have higher probability of causing the damage.
Stopping sets, however, ar... | {
"timestamp": "2015-03-02T02:10:50",
"yymm": "1410",
"arxiv_id": "1410.8753",
"language": "en",
"url": "https://arxiv.org/abs/1410.8753",
"abstract": "The $l$-th stopping redundancy $\\rho_l(\\mathcal C)$ of the binary $[n, k, d]$ code $\\mathcal C$, $1 \\le l \\le d$, is defined as the minimum number of r... |
https://arxiv.org/abs/1312.3437 | On the growth of a Coxeter group | For a Coxeter system $(W,S)$ let $a_n^{(W,S)}$ be the cardinality of the sphere of radius $n$ in the Cayley graph of $W$ with respect to the standard generating set $S$. It is shown that, if $(W,S)\preceq(W',S')$ then $a_n^{(W,S)}\leq a_n^{(W',S')}$ for all $n\in \mathbb{N}_0$, where $\preceq$ is a suitable partial ord... |
\section*{Introduction}
The growth of finitely generated groups has been the subject of intensive investigations (cf.~\cite{grigorchuk--bppg,grigorchuk--dgfggtim}, \cite{grigorchuk-delaharpe--prgesgt}, \cite{delaharpe--tggt}) and led to ground-breaking results, e.g., M.~Gromov showed that a finitely generated group ha... | {
"timestamp": "2015-04-01T02:06:44",
"yymm": "1312",
"arxiv_id": "1312.3437",
"language": "en",
"url": "https://arxiv.org/abs/1312.3437",
"abstract": "For a Coxeter system $(W,S)$ let $a_n^{(W,S)}$ be the cardinality of the sphere of radius $n$ in the Cayley graph of $W$ with respect to the standard genera... |
https://arxiv.org/abs/1606.01809 | Syzygy bundles and the weak Lefschetz property of almost complete intersections | Deciding the presence of the weak Lefschetz property often is a challenging problem. In this work an in-depth study is carried out in the case of Artinian monomial ideals with four generators in three variables. We use a connection to lozenge tilings to describe semistability of the syzygy bundle of such an ideal, to d... | \section{Introduction} \label{sec:intro}
The \emph{weak Lefschetz property} for a standard graded Artinian algebra $A$ over a field $K$ is a natural property. It says that there is a linear form $\ell \in A$ such that the multiplication map $\times \ell : [A]_i \rightarrow [A]_{i+1}$ has maximal rank for all $i$ (i.... | {
"timestamp": "2016-06-07T02:19:28",
"yymm": "1606",
"arxiv_id": "1606.01809",
"language": "en",
"url": "https://arxiv.org/abs/1606.01809",
"abstract": "Deciding the presence of the weak Lefschetz property often is a challenging problem. In this work an in-depth study is carried out in the case of Artinian... |
https://arxiv.org/abs/1701.06760 | On the dense Preferential Attachment Graph models and their graphon induced counterpart | Letting $\mathcal{M}$ denote the space of finite measures on $\mathbb{N}$, and $\mu_\lambda\in\mathcal{M}$ denote the Poisson distribution with parameter $\lambda$, the function $W:[0,1]^2\to\mathcal{M}$ given by \[ W(x,y)=\mu_{c\log x\log y} \] is called the PAG graphon with density $c$. It is known that this is the l... | \section{Introduction}
Preferential attachment graphs (PAGs) form a group of random growing graph models that have been studied for a long time \cite{barabasi, durrett, frieze}. The main motivation is modelling randomly evolving large real-world networks, like online and offline social networks, the internet, or bi... | {
"timestamp": "2017-01-25T02:03:59",
"yymm": "1701",
"arxiv_id": "1701.06760",
"language": "en",
"url": "https://arxiv.org/abs/1701.06760",
"abstract": "Letting $\\mathcal{M}$ denote the space of finite measures on $\\mathbb{N}$, and $\\mu_\\lambda\\in\\mathcal{M}$ denote the Poisson distribution with para... |
https://arxiv.org/abs/1802.04851 | KdV is wellposed in $H^{-1}$ | We prove global well-posedness of the Korteweg--de Vries equation for initial data in the space $H^{-1}(R)$. This is sharp in the class of $H^{s}(R)$ spaces. Even local well-posedness was previously unknown for $s<-3/4$. The proof is based on the introduction of a new method of general applicability for the study of lo... | \section{Introduction}
The Korteweg--de Vries equation
\begin{align}\label{KdV}\tag{KdV}
\frac{d\ }{dt} q = - q''' + 6qq'
\end{align}
was derived in \cite{KdV1895} to explain the observation of solitary waves in a shallow channel of water. Specifically, they sought to definitively settle (to use their words) the deb... | {
"timestamp": "2019-04-29T02:20:12",
"yymm": "1802",
"arxiv_id": "1802.04851",
"language": "en",
"url": "https://arxiv.org/abs/1802.04851",
"abstract": "We prove global well-posedness of the Korteweg--de Vries equation for initial data in the space $H^{-1}(R)$. This is sharp in the class of $H^{s}(R)$ spac... |
https://arxiv.org/abs/hep-th/9603103 | Quasi-Exactly Solvable Potentials on the Line and Orthogonal Polynomials | In this paper we show that a quasi-exactly solvable (normalizable or periodic) one-dimensional Hamiltonian satisfying very mild conditions defines a family of weakly orthogonal polynomials which obey a three-term recursion relation. In particular, we prove that (normalizable) exactly-solvable one-dimensional systems ar... | \section{qes}, we explain in \section{rr} how to construct the weakly
orthogonal polynomial system associated to each of the normal forms
of a one-dimensional \qes. Hamiltonian listed in \rf{GKOnorm}, \rf{GKO}.
Like the polynomial system introduced in \rf{BenDun}, this system
always satisfies a three-term recursion rel... | {
"timestamp": "1996-03-15T11:55:13",
"yymm": "9603",
"arxiv_id": "hep-th/9603103",
"language": "en",
"url": "https://arxiv.org/abs/hep-th/9603103",
"abstract": "In this paper we show that a quasi-exactly solvable (normalizable or periodic) one-dimensional Hamiltonian satisfying very mild conditions defines... |
https://arxiv.org/abs/1104.2882 | Minimum Weight Cycles and Triangles: Equivalences and Algorithms | We consider the fundamental algorithmic problem of finding a cycle of minimum weight in a weighted graph. In particular, we show that the minimum weight cycle problem in an undirected n-node graph with edge weights in {1,...,M} or in a directed n-node graph with edge weights in {-M,..., M} and no negative cycles can be... | \section{Introduction}
We consider the algorithmic problem of finding a minimum weight cycle (i.e., weighted girth) in weighted directed and undirected graphs. Surprisingly, although the problem is very fundamental, the state of the art for it dates back to a seminal paper by Itai and Rodeh~\cite{Clique1}, first pre... | {
"timestamp": "2011-04-15T02:03:26",
"yymm": "1104",
"arxiv_id": "1104.2882",
"language": "en",
"url": "https://arxiv.org/abs/1104.2882",
"abstract": "We consider the fundamental algorithmic problem of finding a cycle of minimum weight in a weighted graph. In particular, we show that the minimum weight cyc... |
https://arxiv.org/abs/1609.07631 | A note on the Gaussian curvature on noncompact surfaces | We give a short proof of the following fact. Let $\Sigma$ be a connected, finitely connected, noncompact manifold without boundary. If $g$ is a complete Riemannian metric on $\Sigma$ whose Gaussian curvature $K$ is nonnegative at infinity, then $K$ must be integrable. In particular, we obtain a new short proof of the f... | \section{Introduction}
In~\cite{RosSto94}, J.Rosenberg and S.Stolz conjectured that a closed manifold $X$ admits a metric of positive scalar curvature when the cylinder $X\times\mathbb{R}$ admits a \emph{complete} metric of positive scalar curvature.
When $X$ is one-dimensional, this conjecture corresponds to the state... | {
"timestamp": "2016-12-02T02:08:30",
"yymm": "1609",
"arxiv_id": "1609.07631",
"language": "en",
"url": "https://arxiv.org/abs/1609.07631",
"abstract": "We give a short proof of the following fact. Let $\\Sigma$ be a connected, finitely connected, noncompact manifold without boundary. If $g$ is a complete ... |
https://arxiv.org/abs/1708.05407 | The $6\times 6$ grid is $4$-path-pairable | Let $G=P_6\Box P_6$ be the $6\times 6$ grid, the Cartesian product of two paths of six vertices. Let $T$ be the set of eight distinct vertices of $G$, called terminals, and assume that $T$ is partitioned into four terminal pairs $\{s_i,t_i\}$, $1\leq i\leq 4$. We prove that $G$ is $4$-path-pairable, that is, for every ... | \section{Introduction}
For $k$ fixed, a graph $G$ is {\it $k$-path-pairable}, if for any set of $k$ disjoint pairs of vertices, $s_i,t_i$, $1\leq i\leq k$, there exist pairwise edge-disjoint $s_i,t_i$-paths in $G$. The {\it path-pairability number}, denoted $pp(G)$, is the largest $k$ such that $G$ is $k$-path-pairab... | {
"timestamp": "2017-08-21T02:00:35",
"yymm": "1708",
"arxiv_id": "1708.05407",
"language": "en",
"url": "https://arxiv.org/abs/1708.05407",
"abstract": "Let $G=P_6\\Box P_6$ be the $6\\times 6$ grid, the Cartesian product of two paths of six vertices. Let $T$ be the set of eight distinct vertices of $G$, c... |
https://arxiv.org/abs/2103.04766 | The size of Betti tables of edge ideals arising from bipartite graphs | Let $\operatorname{pd}(I(G))$ and $\operatorname{reg}(I(G))$ respectively denote the projective dimension and the regularity of the edge ideal $I(G)$ of a graph $G$. For any positive integer $n$, we determine all pairs $(\operatorname{pd}(I(G)),\, \operatorname{reg}(I(G)))$ as $G$ ranges over all connected bipartite gr... | \section{Introduction}
Let $G$ be a finite simple graph with the vertex set $V(G)=\{x_1,\dots ,x_n\}$. Let $S=\Bbbk[x_1,\dots ,x_n]$ be the polynomial ring in $n$ variables over a field $\Bbbk$. The \textit{edge ideal} of $G$, denoted by $I(G)$, is the monomial ideal generated by the monomials $x_ix_j$ such that $\{x_i... | {
"timestamp": "2021-03-09T02:40:24",
"yymm": "2103",
"arxiv_id": "2103.04766",
"language": "en",
"url": "https://arxiv.org/abs/2103.04766",
"abstract": "Let $\\operatorname{pd}(I(G))$ and $\\operatorname{reg}(I(G))$ respectively denote the projective dimension and the regularity of the edge ideal $I(G)$ of... |
https://arxiv.org/abs/1602.02210 | Classification accuracy as a proxy for two sample testing | When data analysts train a classifier and check if its accuracy is significantly different from chance, they are implicitly performing a two-sample test. We investigate the statistical properties of this flexible approach in the high-dimensional setting. We prove two results that hold for all classifiers in any dimensi... | \section{Introduction}
The recent popularity of machine learning has resulted in the extensive teaching and use of \textit{prediction} in theoretical and applied communities and the relative lack of awareness or popularity of the topic of Neyman-Pearson style \textit{hypothesis testing} in the computer science and rel... | {
"timestamp": "2016-02-09T02:02:12",
"yymm": "1602",
"arxiv_id": "1602.02210",
"language": "en",
"url": "https://arxiv.org/abs/1602.02210",
"abstract": "When data analysts train a classifier and check if its accuracy is significantly different from chance, they are implicitly performing a two-sample test. ... |
https://arxiv.org/abs/2211.10499 | Fundamental groups of reduced suspensions are locally free | In this paper, we analyze the fundamental group $\pi_1(\Sigma X,\overline{x_0})$ of the reduced suspension $\Sigma X$ where $(X,x_0)$ is an arbitrary based Hausdorff space. We show that $\pi_1(\Sigma X,\overline{x_0})$ is canonically isomorphic to a direct limit $\varinjlim_{A\in\mathscr{P}}\pi_1(\Sigma A,\overline{x_0... | \section{Introduction}
When a based space $(X,x_0)$ is well-pointed, i.e. the inclusion $\{x_0\}\to X$ is a cofibration, the reduced suspension $\Sigma X$ with canonical basepoint $\overline x_0$ is homotopy equivalent to the unreduced suspension $SX$ and it follows that $\pi_1(\Sigma X,\overline x_0)$ is free on the ... | {
"timestamp": "2022-11-22T02:01:28",
"yymm": "2211",
"arxiv_id": "2211.10499",
"language": "en",
"url": "https://arxiv.org/abs/2211.10499",
"abstract": "In this paper, we analyze the fundamental group $\\pi_1(\\Sigma X,\\overline{x_0})$ of the reduced suspension $\\Sigma X$ where $(X,x_0)$ is an arbitrary ... |
https://arxiv.org/abs/1710.10616 | $k$-Foldability of Words | We extend results regarding a combinatorial model introduced by Black, Drellich, and Tymoczko (2017+) which generalizes the folding of the RNA molecule in biology. Consider a word on alphabet $\{A_1, \overline{A}_1, \ldots, A_m, \overline{A}_m\}$ in which $\overline{A}_i$ is called the complement of $A_i$. A word $w$ i... | \section{Introduction}
The molecule ribonucleic acid (RNA) consists of a single strand of the four nucleotides adenine, uracil, cytosine, and guanine. In short, RNA is representable by finite sequences (or words) from the alphabet $A$, $U$, $C$, and $G$, lending itself to combinatorial study. In contrast to the double... | {
"timestamp": "2017-10-31T01:10:23",
"yymm": "1710",
"arxiv_id": "1710.10616",
"language": "en",
"url": "https://arxiv.org/abs/1710.10616",
"abstract": "We extend results regarding a combinatorial model introduced by Black, Drellich, and Tymoczko (2017+) which generalizes the folding of the RNA molecule in... |
https://arxiv.org/abs/2206.02995 | Strong cospectrality in trees | We prove that no tree contains a set of three vertices which are pairwise strongly cospectral. This answers a question raised by Godsil and Smith in 2017. | \section{Introduction}\label{intro}
Let $G$ be a finite simple graph and $A$ its adjacency matrix. A continuous-time quantum walk can be defined having $G$ as an underlying graph, and in certain models where no external interference exists, all properties of the walk are determined by the spectrum of $A$. A desirable ... | {
"timestamp": "2022-06-08T02:07:50",
"yymm": "2206",
"arxiv_id": "2206.02995",
"language": "en",
"url": "https://arxiv.org/abs/2206.02995",
"abstract": "We prove that no tree contains a set of three vertices which are pairwise strongly cospectral. This answers a question raised by Godsil and Smith in 2017.... |
https://arxiv.org/abs/1102.5065 | On $(\le k)$-edges, crossings, and halving lines of geometric drawings of $K_n$ | Let $P$ be a set of points in general position in the plane. Join all pairs of points in $P$ with straight line segments. The number of segment-crossings in such a drawing, denoted by $\crg(P)$, is the \emph{rectilinear crossing number} of $P$. A \emph{halving line} of $P$ is a line passing though two points of $P$ tha... | \section{Introduction}
We consider three important well-known problems in Combinatorial
Geometry: the rectilinear crossing number, the maximum number of
halving lines, and the minimum number of $(\leq k) $-edges of
complete geometric graphs on $n$ vertices. All point sets in this
paper are in the plane, finite, and in... | {
"timestamp": "2011-03-17T01:02:06",
"yymm": "1102",
"arxiv_id": "1102.5065",
"language": "en",
"url": "https://arxiv.org/abs/1102.5065",
"abstract": "Let $P$ be a set of points in general position in the plane. Join all pairs of points in $P$ with straight line segments. The number of segment-crossings in... |
https://arxiv.org/abs/2103.00531 | Sensitivity of low-rank matrix recovery | We characterize the first-order sensitivity of approximately recovering a low-rank matrix from linear measurements, a standard problem in compressed sensing. A special case covered by our analysis is approximating an incomplete matrix by a low-rank matrix. We give an algorithm for computing the associated condition num... | \section{Introduction} \label{sec_introduction}
Compressed sensing \cite{CRT2006, Donoho2006,DE2011,EK2012,FR2013} is a general methodology for recovering an unknown but structured signal $y \in \mathbb{R}^k$ from a measurement $a = L(y) \in \mathbb{R}^\ell$, where $\ell$ can be much smaller than $k$ and $L$ is a sens... | {
"timestamp": "2021-03-02T02:27:18",
"yymm": "2103",
"arxiv_id": "2103.00531",
"language": "en",
"url": "https://arxiv.org/abs/2103.00531",
"abstract": "We characterize the first-order sensitivity of approximately recovering a low-rank matrix from linear measurements, a standard problem in compressed sensi... |
https://arxiv.org/abs/math/0702301 | Information-theoretic limits on sparsity recovery in the high-dimensional and noisy setting | The problem of recovering the sparsity pattern of a fixed but unknown vector $\beta^* \in \real^p based on a set of $n$ noisy observations arises in a variety of settings, including subset selection in regression, graphical model selection, signal denoising, compressive sensing, and constructive approximation. Of inter... | \section{Introduction}
Suppose that we are given a set of $\ensuremath{n}$ observations of a fixed
but unknown vector $\ensuremath{\beta^*} \in \real^\mdim$. In a variety of
settings, it is known \emph{a priori} that the vector $\ensuremath{\beta^*}$ is
sparse, meaning that its support set $\ensuremath{S}$---corres... | {
"timestamp": "2007-02-20T07:47:11",
"yymm": "0702",
"arxiv_id": "math/0702301",
"language": "en",
"url": "https://arxiv.org/abs/math/0702301",
"abstract": "The problem of recovering the sparsity pattern of a fixed but unknown vector $\\beta^* \\in \\real^p based on a set of $n$ noisy observations arises i... |
https://arxiv.org/abs/2108.09962 | Fractional Helly theorem for Cartesian products of convex sets | Helly's theorem and its variants show that for a family of convex sets in Euclidean space, local intersection patterns influence global intersection patterns. A classical result of Eckhoff in 1988 provided an optimal fractional Helly theorem for axis-aligned boxes, which are Cartesian products of line segments. Answeri... | \section{Introduction}
A family of non-empty sets is {\em intersecting} if all sets within have an element in common. Let $\mathcal{F}$ be a (possibly infinite) family of non-empty sets.
The {\em Helly number} of $\mathcal{F}$ is the minimal size of a subfamily $\mathcal{H}$ such that every proper subfamily of $\mathca... | {
"timestamp": "2021-08-31T02:31:01",
"yymm": "2108",
"arxiv_id": "2108.09962",
"language": "en",
"url": "https://arxiv.org/abs/2108.09962",
"abstract": "Helly's theorem and its variants show that for a family of convex sets in Euclidean space, local intersection patterns influence global intersection patte... |
https://arxiv.org/abs/math/0510603 | Approximation by smooth functions with no critical points on separable Banach spaces | We characterize the class of separable Banach spaces $X$ such that for every continuous function $f:X\to\mathbb{R}$ and for every continuous function $\epsilon:X\to\mathbb(0,+\infty)$ there exists a $C^1$ smooth function $g:X\to\mathbb{R}$ for which $|f(x)-g(x)|\leq\epsilon(x)$ and $g'(x)\neq 0$ for all $x\in X$ (that ... | \section[Introduction and main results]{Introduction and main results}
The Morse-Sard theorem \cite{Sard1, Sard2} states that if
$f:\mathbb{R}^{n}\longrightarrow \mathbb{R}^{m}$ is a $C^r$ smooth
function, with $r>\max\{n-m, 0\}$, and $C_{f}$ is the set of
critical points of $f$, then the set of critical values $f(C_{... | {
"timestamp": "2005-10-27T16:27:41",
"yymm": "0510",
"arxiv_id": "math/0510603",
"language": "en",
"url": "https://arxiv.org/abs/math/0510603",
"abstract": "We characterize the class of separable Banach spaces $X$ such that for every continuous function $f:X\\to\\mathbb{R}$ and for every continuous functio... |
https://arxiv.org/abs/2109.09580 | G-invariant Spin Structures on Spheres | We examine which of the compact connected Lie groups that act transitively on spheres of different dimensions leave the unique spin structure of the sphere invariant. We study the notion of invariance of a spin structure and prove this classification in two different ways; through examining the differential of the acti... | \section*{Introduction}
Given a Lie group $G$ acting on a manifold $M$, it is a natural question to ask which structures of the manifold are preserved by $G$. For example, if $M$ is orientable, then connected Lie groups always preserve an orientation. However, if we consider that $M$ admits spin structures (which can ... | {
"timestamp": "2021-09-21T02:39:32",
"yymm": "2109",
"arxiv_id": "2109.09580",
"language": "en",
"url": "https://arxiv.org/abs/2109.09580",
"abstract": "We examine which of the compact connected Lie groups that act transitively on spheres of different dimensions leave the unique spin structure of the spher... |
https://arxiv.org/abs/1809.02162 | Escaping Saddle Points in Constrained Optimization | In this paper, we study the problem of escaping from saddle points in smooth nonconvex optimization problems subject to a convex set $\mathcal{C}$. We propose a generic framework that yields convergence to a second-order stationary point of the problem, if the convex set $\mathcal{C}$ is simple for a quadratic objectiv... |
\subsubsection{#1}\vspace{-3\baselineskip}\color{black}\bigskip{\noindent \bf \thesubsubsection. #1.}}
\newcommand{\myparagraph}[1]{\needspace{1\baselineskip}\medskip\noindent {\it #1.}}
\newcommand{\myparagraphtc}[1]{\needspace{1\baselineskip}\medskip\noindent {\it #1.}\addcontentsline{toc}{subsubsection}{\qquad\qq... | {
"timestamp": "2018-10-10T02:05:26",
"yymm": "1809",
"arxiv_id": "1809.02162",
"language": "en",
"url": "https://arxiv.org/abs/1809.02162",
"abstract": "In this paper, we study the problem of escaping from saddle points in smooth nonconvex optimization problems subject to a convex set $\\mathcal{C}$. We pr... |
https://arxiv.org/abs/1106.2944 | Matroids and log-concavity | We show that f-vectors of matroid complexes of realisable matroids are log-concave. This was conjectured by Mason in 1972. Our proof uses the recent result by Huh and Katz who showed that the coefficients of the characteristic polynomial of a realisable matroid form a log-concave sequence. We also discuss the relations... | \section{Introduction}
Let $M=(E,\Delta)$ be a matroid of rank $r$. $E$ denotes the ground set and $\Delta \subseteq 2^E$
denotes the matroid complex, \ie the abstract simplicial complex of independent sets.
Let $f=(f_0,\ldots, f_r)$ be the $f$-vector of $\Delta$, \ie $f_i$ is the number of sets of cardinality $i$
i... | {
"timestamp": "2011-08-22T02:01:23",
"yymm": "1106",
"arxiv_id": "1106.2944",
"language": "en",
"url": "https://arxiv.org/abs/1106.2944",
"abstract": "We show that f-vectors of matroid complexes of realisable matroids are log-concave. This was conjectured by Mason in 1972. Our proof uses the recent result ... |
https://arxiv.org/abs/2001.10770 | Array Codes for Functional PIR and Batch Codes | A functional PIR array code is a coding scheme which encodes some $s$ information bits into a $t\times m$ array such that every linear combination of the $s$ information bits has $k$ mutually disjoint recovering sets. Every recovering set consists of some of the array's columns while it is allowed to read at most $\ell... | \section{Introduction}\label{sec:intro}
\renewcommand{\baselinestretch}{1}\normalsize
\emph{Private information retrieval (PIR) codes} and {batch codes} are families of codes which have several applications such as PIR protocols~\cite{BIKR02,CKGS98,DvirGopi16_1,FVY15,G04,Y10}, erasure codes in distributed storage syste... | {
"timestamp": "2020-09-02T02:10:58",
"yymm": "2001",
"arxiv_id": "2001.10770",
"language": "en",
"url": "https://arxiv.org/abs/2001.10770",
"abstract": "A functional PIR array code is a coding scheme which encodes some $s$ information bits into a $t\\times m$ array such that every linear combination of the... |
https://arxiv.org/abs/0910.4987 | Optimal bounds for the colored Tverberg problem | We prove a "Tverberg type" multiple intersection theorem. It strengthens the prime case of the original Tverberg theorem from 1966, as well as the topological Tverberg theorem of Barany et al. (1980), by adding color constraints. It also provides an improved bound for the (topological) colored Tverberg problem of Baran... | \section{Introduction}
Tverberg's theorem from 1966 \cite{Tverberg-1} \cite[Sect.~8.3]{mat-1}
claims that any family of $(d+1)(r-1)+1$ points in $\R^d$ can
be partitioned into $r$ sets whose convex hulls
intersect; a look at the codimensions of intersections shows that
the number $(d+1)(r-1)+1$ of points is minimal fo... | {
"timestamp": "2009-11-19T15:25:31",
"yymm": "0910",
"arxiv_id": "0910.4987",
"language": "en",
"url": "https://arxiv.org/abs/0910.4987",
"abstract": "We prove a \"Tverberg type\" multiple intersection theorem. It strengthens the prime case of the original Tverberg theorem from 1966, as well as the topolog... |
https://arxiv.org/abs/1710.04705 | On smooth square-free numbers in arithmetic progressions | A. Booker and C. Pomerance (2017) have shown that any residue class modulo a prime $p\ge 11$ can be represented by a positive $p$-smooth square-free integer $s = p^{O(\log p)}$ with all prime factors up to $p$ and conjectured that in fact one can find such $s$ with $s = p^{O(1)}$. Using bounds on double Kloosterman sum... | \section{Introduction and main results}
\subsection{Motivation}
We recall that an integer $n$ is called {\it $y$-smooth\/} if all prime divisors
of $n$ do not exceed $y$, and is called {\it square-free\/} if it is not divisible by
a square of a prime.
Following Booker and Pomerance~\cite{BoPom}, for a prime $p $ w... | {
"timestamp": "2018-06-12T02:14:11",
"yymm": "1710",
"arxiv_id": "1710.04705",
"language": "en",
"url": "https://arxiv.org/abs/1710.04705",
"abstract": "A. Booker and C. Pomerance (2017) have shown that any residue class modulo a prime $p\\ge 11$ can be represented by a positive $p$-smooth square-free inte... |
https://arxiv.org/abs/1807.03663 | Orbits of monomials and factorization into products of linear forms | This paper is devoted to the factorization of multivariate polynomials into products of linear forms, a problem which has applications to differential algebra, to the resolution of systems of polynomial equations and to Waring decomposition (i.e., decomposition in sums of d-th powers of linear forms; this problem is al... | \section{Introduction}
The main contribution of this paper is a simple algorithm which determines
whether an input polynomial $f(x_1,\ldots,x_n)$ has a factorization of the form
\begin{equation} \label{problem}
f(x)=l_1(x)^{\alpha_1} \cdots l_n(x)^{\alpha_n}
\end{equation}
where the linear forms $l_i$ are linearly in... | {
"timestamp": "2018-07-11T02:09:47",
"yymm": "1807",
"arxiv_id": "1807.03663",
"language": "en",
"url": "https://arxiv.org/abs/1807.03663",
"abstract": "This paper is devoted to the factorization of multivariate polynomials into products of linear forms, a problem which has applications to differential alg... |
https://arxiv.org/abs/1609.09565 | Analysis of Exact and Approximated Epidemic Models over Complex Networks | We study the spread of discrete-time epidemics over arbitrary networks for well-known propagation models, namely SIS (susceptible-infected-susceptible), SIR (susceptible-infected-recovered), SIRS (susceptible-infected-recovered-susceptible) and SIV (susceptible-infected-vaccinated). Such epidemics are described by $2^n... | \section{Introduction}\label{sec:introduction}}
\IEEEPARstart{E}{pidemic} models have been extensively studied since a first mathematical formulation was introduced in 1927 by Kermack and McKendrick \cite{kermack1927contribution}. Though initially proposed to understand the spread of contagious diseases \cite{baile... | {
"timestamp": "2016-10-03T02:01:27",
"yymm": "1609",
"arxiv_id": "1609.09565",
"language": "en",
"url": "https://arxiv.org/abs/1609.09565",
"abstract": "We study the spread of discrete-time epidemics over arbitrary networks for well-known propagation models, namely SIS (susceptible-infected-susceptible), S... |
https://arxiv.org/abs/2109.09242 | Renormalisation of the two-dimensional border-collision normal form | We study the two-dimensional border-collision normal form (a four-parameter family of continuous, piecewise-linear maps on $\mathbb{R}^2$) in the robust chaos parameter region of [S. Banerjee, J.A. Yorke, C. Grebogi, Robust Chaos, Phys. Rev. Lett. 80(14):3049--3052, 1998]. We use renormalisation to partition this regio... | \section{Introduction}
\label{sec:intro}
\setcounter{equation}{0}
Piecewise-linear maps can exhibit complicated dynamics
yet are relatively amenable to an exact analysis.
For this reason they provide a useful tool for us to explore complex aspects of dynamical systems, such as chaos.
They arise as approximation... | {
"timestamp": "2021-09-21T02:26:17",
"yymm": "2109",
"arxiv_id": "2109.09242",
"language": "en",
"url": "https://arxiv.org/abs/2109.09242",
"abstract": "We study the two-dimensional border-collision normal form (a four-parameter family of continuous, piecewise-linear maps on $\\mathbb{R}^2$) in the robust ... |
https://arxiv.org/abs/1612.04443 | Indivisibility of class numbers of imaginary quadratic fields | We quantify a recent theorem of Wiles on class numbers of imaginary quadratic fields by proving an estimate for the number of negative fundamental discriminants down to -X whose class numbers are indivisible by a given prime and whose imaginary quadratic fields satisfy any given set of local conditions. This estimate m... | \section{Introduction}
Ideal class numbers of imaginary quadratic fields have been studied since Gauss, who conjectured that for any given $h$, there are only finitely many negative fundamental discriminants $D$ such that $h(D) = h$. The history of Gauss' Conjecture is rich. The conjecture was shown to be true by work ... | {
"timestamp": "2017-11-07T02:12:16",
"yymm": "1612",
"arxiv_id": "1612.04443",
"language": "en",
"url": "https://arxiv.org/abs/1612.04443",
"abstract": "We quantify a recent theorem of Wiles on class numbers of imaginary quadratic fields by proving an estimate for the number of negative fundamental discrim... |
https://arxiv.org/abs/1211.5384 | Superfast solution of linear convolutional Volterra equations using QTT approximation | We address a linear fractional differential equation and develop effective solution methods using algorithms for inversion of triangular Toeplitz matrices and the recently proposed QTT format. The inverses of such matrices can be computed by the divide and conquer and modified Bini's algorithms, for which we present th... | \section{Introduction}
Equations involving derivatives of fractional order are of great importance, due to their role in mathematical models applied in mechanics, biochemistry, electrical engineering, medicine, etc., see~\cite{diethelm-1997,CapMain1,FreedDiet1}.
In this paper we present a superfast algorithm for the nu... | {
"timestamp": "2012-11-26T02:02:59",
"yymm": "1211",
"arxiv_id": "1211.5384",
"language": "en",
"url": "https://arxiv.org/abs/1211.5384",
"abstract": "We address a linear fractional differential equation and develop effective solution methods using algorithms for inversion of triangular Toeplitz matrices a... |
https://arxiv.org/abs/0807.0779 | The complex Busemann-Petty problem for arbitrary measures | The complex Busemann-Petty problem asks whether origin symmetric convex bodies in C^n with smaller central hyperplane sections necessarily have smaller volume. The answer is affirmative if n\leq 3 and negative if n\geq 4. In this article we show that the answer remains the same if the volume is replaced by an "almost" ... | \section{Introduction}
In 1956 the Busemann-Petty problem was posed (see [BP]), asking the following question:
suppose that $K$ and $L$ are two origin symmetric convex bodies in $\mathbb{R}^n$ such that for every $\xi \in S^{n-1},$
$$\mbox{\rm Vol}_{n-1}\bigl(K\cap \xi^{\perp}\bigr) \leq \mbox{\rm Vol}_{n-1}\bigl(L\... | {
"timestamp": "2008-07-04T17:25:27",
"yymm": "0807",
"arxiv_id": "0807.0779",
"language": "en",
"url": "https://arxiv.org/abs/0807.0779",
"abstract": "The complex Busemann-Petty problem asks whether origin symmetric convex bodies in C^n with smaller central hyperplane sections necessarily have smaller volu... |
https://arxiv.org/abs/2110.06488 | The Convex Geometry of Backpropagation: Neural Network Gradient Flows Converge to Extreme Points of the Dual Convex Program | We study non-convex subgradient flows for training two-layer ReLU neural networks from a convex geometry and duality perspective. We characterize the implicit bias of unregularized non-convex gradient flow as convex regularization of an equivalent convex model. We then show that the limit points of non-convex subgradie... |
\section{Introduction}
Neural networks (NNs) exhibit remarkable empirical performance in various machine learning tasks. However, a full characterization of the optimization and generalization properties of NNs is far from complete. Non-linear operations inherent to the structure of NNs, over-parameterization and the ... | {
"timestamp": "2021-10-14T02:10:42",
"yymm": "2110",
"arxiv_id": "2110.06488",
"language": "en",
"url": "https://arxiv.org/abs/2110.06488",
"abstract": "We study non-convex subgradient flows for training two-layer ReLU neural networks from a convex geometry and duality perspective. We characterize the impl... |
https://arxiv.org/abs/1011.5460 | Quantum Walks on Regular Graphs and Eigenvalues | We study the transition matrix of a quantum walk on strongly regular graphs. It is proposed by Emms, Hancock, Severini and Wilson in 2006, that the spectrum of $S^+(U^3)$, a matrix based on the amplitudes of walks in the quantum walk, distinguishes strongly regular graphs. We find the eigenvalues of $S^+(U)$ and $S^+(U... | \section{Introduction}
A discrete-time quantum walk is a quantum process on a graph whose state vector is governed by a matrix, called the transition matrix. In \cite{ESWH, EHSW06} Emms, Severini, Wilson and Hancock propose that the quantum walk transition matrix can be used to distinguish between non-isomorphic graph... | {
"timestamp": "2011-07-28T02:04:12",
"yymm": "1011",
"arxiv_id": "1011.5460",
"language": "en",
"url": "https://arxiv.org/abs/1011.5460",
"abstract": "We study the transition matrix of a quantum walk on strongly regular graphs. It is proposed by Emms, Hancock, Severini and Wilson in 2006, that the spectrum... |
https://arxiv.org/abs/2107.13443 | On fractional version of oriented coloring | We introduce the fractional version of oriented coloring and initiate its study. We prove some basic results and study the parameter for directed cycles and sparse planar graphs. In particular, we show that for every $\epsilon > 0$, there exists an integer $g_{\epsilon} \geq 12$ such that any oriented planar graph havi... | \section{Introduction}
``It is possible to go to a graph theory conference and to ask oneself, at the end of every talk,
what is the fractional analogue?'' - Scheinermann and Ullman~\cite{scheinermann2008fgt} made this remark in the preface of their book on fractional graph theory. Considering the popularity of studyin... | {
"timestamp": "2021-07-29T02:23:38",
"yymm": "2107",
"arxiv_id": "2107.13443",
"language": "en",
"url": "https://arxiv.org/abs/2107.13443",
"abstract": "We introduce the fractional version of oriented coloring and initiate its study. We prove some basic results and study the parameter for directed cycles a... |
https://arxiv.org/abs/2011.14299 | A characterization of $X$ for which spaces $C_p(X)$ are distinguished and its applications | We prove that the locally convex space $C_{p}(X)$ of continuous real-valued functions on a Tychonoff space $X$ equipped with the topology of pointwise convergence is distinguished if and only if $X$ is a $\Delta$-space in the sense of \cite {Knight}. As an application of this characterization theorem we obtain the foll... | \section{Introduction}\label{intro}
Following J. Dieudonn\'{e} and
L. Schwartz \cite{dieudonne} a locally convex space (lcs) $E$ is called \emph{distinguished} if every bounded subset of the bidual of $E$
in the weak$^{*}$-topology is contained in the closure of the weak$^{*}$-topology of some bounded subset ... | {
"timestamp": "2020-12-01T02:18:30",
"yymm": "2011",
"arxiv_id": "2011.14299",
"language": "en",
"url": "https://arxiv.org/abs/2011.14299",
"abstract": "We prove that the locally convex space $C_{p}(X)$ of continuous real-valued functions on a Tychonoff space $X$ equipped with the topology of pointwise con... |
https://arxiv.org/abs/2004.09093 | The Number of Singular Fibers in Hyperelliptic Lefschetz Fibrations | We consider complex surfaces, viewed as smooth $4$-dimensional manifolds, that admit hyperelliptic Lefschetz fibrations over the $2$-sphere. In this paper, we show that the minimal number of singular fibers of such fibrations is equal to $2g+4$ for even $g\geq4$. For odd $g\geq7$, we show that the number is greater tha... | \section{Introduction}
Donaldson and Gompf's results (\cite{Don.1}, \cite{Don.2}, \cite{Go} and \cite{GS}) give the relation between symplectic $4$-manifolds and Lefschetz fibrations, which are a fibering of a $4$-manifold by surfaces, with a finite number of singularities of a prescribed type. Donaldson proved that ev... | {
"timestamp": "2020-04-21T02:22:49",
"yymm": "2004",
"arxiv_id": "2004.09093",
"language": "en",
"url": "https://arxiv.org/abs/2004.09093",
"abstract": "We consider complex surfaces, viewed as smooth $4$-dimensional manifolds, that admit hyperelliptic Lefschetz fibrations over the $2$-sphere. In this paper... |
https://arxiv.org/abs/1707.01308 | Measuring heavy-tailedness of distributions | Different questions related with analysis of extreme values and outliers arise frequently in practice. To exclude extremal observations and outliers is not a good decision because they contain important information about the observed distribution. The difficulties with their usage are usually related to the estimation ... | \section{INTRODUCTION}
More than 90 years scientists look for appropriate way for handling outliers. \cite{irwin1925criterion}, \cite{mckay1935distribution}, \cite{nair1948distribution} and \cite{dixon1950analysis, dixon1953processing} consider them mainly with respect to the deviations of the distribution of the m... | {
"timestamp": "2017-07-06T02:04:02",
"yymm": "1707",
"arxiv_id": "1707.01308",
"language": "en",
"url": "https://arxiv.org/abs/1707.01308",
"abstract": "Different questions related with analysis of extreme values and outliers arise frequently in practice. To exclude extremal observations and outliers is no... |
https://arxiv.org/abs/1412.4271 | Multi-Context Models for Reasoning under Partial Knowledge: Generative Process and Inference Grammar | Arriving at the complete probabilistic knowledge of a domain, i.e., learning how all variables interact, is indeed a demanding task. In reality, settings often arise for which an individual merely possesses partial knowledge of the domain, and yet, is expected to give adequate answers to a variety of posed queries. Tha... | \section*{\centerline{APPENDIX}}
\subsubsection*{A-I $\mathcal{I}_{non-scale}^\ast$: A short version of $\mathcal{I}^\ast$ without scale-invariance property}
\label{A-I}
$\mathcal{I}^\ast$ aims at minimally parameterizing the information contained in an MCM so that the posed inter-contextual query can be stated as an L... | {
"timestamp": "2015-06-19T02:15:22",
"yymm": "1412",
"arxiv_id": "1412.4271",
"language": "en",
"url": "https://arxiv.org/abs/1412.4271",
"abstract": "Arriving at the complete probabilistic knowledge of a domain, i.e., learning how all variables interact, is indeed a demanding task. In reality, settings of... |
https://arxiv.org/abs/1811.02399 | Subspaces that can and cannot be the kernel of a bounded operator on a Banach space | Given a Banach space $E$, we ask which closed subspaces may be realised as the kernel of a bounded operator $E \rightarrow E$. We prove some positive results which imply in particular that when $E$ is separable every closed subspace is a kernel. Moreover, we show that there exists a Banach space $E$ which contains a cl... | \section{Introduction}
\noindent
In this note we address the following natural question: given a Banach space $E$, which of its closed linear subspaces $F$ are the kernel of some bounded linear operator $E \rightarrow E$? We shall begin by showing that if either $E/F$ is separable, or $F$ is separable and $E$ has the... | {
"timestamp": "2018-11-30T02:12:09",
"yymm": "1811",
"arxiv_id": "1811.02399",
"language": "en",
"url": "https://arxiv.org/abs/1811.02399",
"abstract": "Given a Banach space $E$, we ask which closed subspaces may be realised as the kernel of a bounded operator $E \\rightarrow E$. We prove some positive res... |
https://arxiv.org/abs/2103.11432 | Results and questions on matchings in groups and vector subspaces of fields | A matching from a finite subset $A$ of an abelian group to another subset $B$ is a bijection $f:A\rightarrow B$ with the property that $a+f(a)$ never lies in $A$. A matching is called acyclic if it is uniquely determined by its multiplicity function. Motivated by a question of E. K. Wakeford on canonical forms for symm... | \section{Introduction}
The notion of matchings in abelian groups was introduced by Fan and Losonczy in \cite{MR1371651} in order to generalize a geometric property of lattices in Euclidean space. The study of acyclic matchings was motivated by an old problem of Wakeford concerning canonical forms for symmetric tensor... | {
"timestamp": "2021-03-23T01:20:42",
"yymm": "2103",
"arxiv_id": "2103.11432",
"language": "en",
"url": "https://arxiv.org/abs/2103.11432",
"abstract": "A matching from a finite subset $A$ of an abelian group to another subset $B$ is a bijection $f:A\\rightarrow B$ with the property that $a+f(a)$ never lie... |
https://arxiv.org/abs/1405.6587 | On the grid Ramsey problem and related questions | The Hales--Jewett theorem is one of the pillars of Ramsey theory, from which many other results follow. A celebrated theorem of Shelah says that Hales--Jewett numbers are primitive recursive. A key tool used in his proof, now known as the cube lemma, has become famous in its own right. In its simplest form, this lemma ... | \section{Introduction}
\label{sec:intro}
Ramsey theory refers to a large body of deep results in mathematics whose underlying philosophy is captured succinctly by the statement that ``Every large system contains a large well-organized subsystem.'' This is an area in which a great variety of techniques from many branc... | {
"timestamp": "2014-09-23T02:08:35",
"yymm": "1405",
"arxiv_id": "1405.6587",
"language": "en",
"url": "https://arxiv.org/abs/1405.6587",
"abstract": "The Hales--Jewett theorem is one of the pillars of Ramsey theory, from which many other results follow. A celebrated theorem of Shelah says that Hales--Jewe... |
https://arxiv.org/abs/1805.09312 | Ergodicity of Iwasawa continued fractions via markable hyperbolic geodesics | We prove the convergence and ergodicity of a wide class of real and higher-dimensional continued fraction algorithms, including folded and $\alpha$-type variants of complex, quaternionic, octonionic, and Heisenberg continued fractions, which we combine under the framework of Iwasawa continued fractions. The proof is ba... | \section{Introduction}
Regular continued fractions (CFs) represent the fractional part $x-\floor{x}$ of a real number as a descending iterated fraction $\frac{1}{a_1+\frac{1}{a_2+\cdots}}$ with positive integer coefficients. Other real CF algorithms adjust the notion of inversion (e.g., backward CFs), floor function (e... | {
"timestamp": "2018-05-24T02:14:55",
"yymm": "1805",
"arxiv_id": "1805.09312",
"language": "en",
"url": "https://arxiv.org/abs/1805.09312",
"abstract": "We prove the convergence and ergodicity of a wide class of real and higher-dimensional continued fraction algorithms, including folded and $\\alpha$-type ... |
https://arxiv.org/abs/2002.00921 | Repeated patterns in proper colourings | For a fixed graph $H$, what is the smallest number of colours $C$ such that there is a proper edge-colouring of the complete graph $K_n$ with $C$ colours containing no two vertex-disjoint colour-isomorphic copies, or repeats, of $H$? We study this function and its generalisation to more than two copies using a variety ... | \section{Introduction} \label{sec:intro}
A considerable body of recent work in extremal combinatorics is devoted to the study of rainbow patterns in proper edge-colourings of complete graphs. To mention two such results (amongst many~\cite{BaPoSu, BePoSu, CoPe, EhGlJo, GaRaWaWo, GlJo, GlKuMoOs, KeYe, KiKuKuOs, MoPoSu,... | {
"timestamp": "2021-06-28T02:16:06",
"yymm": "2002",
"arxiv_id": "2002.00921",
"language": "en",
"url": "https://arxiv.org/abs/2002.00921",
"abstract": "For a fixed graph $H$, what is the smallest number of colours $C$ such that there is a proper edge-colouring of the complete graph $K_n$ with $C$ colours ... |
https://arxiv.org/abs/0903.3068 | Long-time asymptotics for fully nonlinear homogeneous parabolic equations | We study the long-time asymptotics of solutions of the uniformly parabolic equation \[ u_t + F(D^2u) = 0 \quad {in} \R^n\times \R_+, \] for a positively homogeneous operator $F$, subject to the initial condition $u(x,0) = g(x)$, under the assumption that $g$ does not change sign and possesses sufficient decay at infini... | \section{Introduction and main results}
The connection between the scaling invariance of the mathematical expressions for certain physical laws and the asymptotic behavior of physical phenomena is of fundamental importance to the study of mechanics. In this work, we have in mind the study of self-similar solutions of ... | {
"timestamp": "2009-09-25T08:13:52",
"yymm": "0903",
"arxiv_id": "0903.3068",
"language": "en",
"url": "https://arxiv.org/abs/0903.3068",
"abstract": "We study the long-time asymptotics of solutions of the uniformly parabolic equation \\[ u_t + F(D^2u) = 0 \\quad {in} \\R^n\\times \\R_+, \\] for a positive... |
https://arxiv.org/abs/1008.3854 | Asymptotics of the maximal and the typical dimensions of isotypic components of tensor representations of the symmetric group | Vershik and Kerov gave asymptotical bounds for the maximal and the typical dimensions of irreducible representations of symmetric groups $S_n$. It was conjectured by G. Olshanski that the maximal and the typical dimensions of the isotypic components of tensor representations of the symmetric group admit similar asympto... | \section{Introduction}
For $n\in\mathbb{N}$, let $S_n$ be the symmetric group on $n$ letters. The complex finite dimensional irreducible representations of $S_n$ are parametrized by the set of partitions of $n$, or equivalently by the set $\mathbb{Y}^n$ of Young diagrams with $n$ cells. Since each irreducible repres... | {
"timestamp": "2011-10-21T02:04:04",
"yymm": "1008",
"arxiv_id": "1008.3854",
"language": "en",
"url": "https://arxiv.org/abs/1008.3854",
"abstract": "Vershik and Kerov gave asymptotical bounds for the maximal and the typical dimensions of irreducible representations of symmetric groups $S_n$. It was conje... |
https://arxiv.org/abs/2101.07560 | A doubly relaxed minimal-norm Gauss-Newton method for underdetermined nonlinear least-squares problems | When a physical system is modeled by a nonlinear function, the unknown parameters can be estimated by fitting experimental observations by a least-squares approach. Newton's method and its variants are often used to solve problems of this type. In this paper, we are concerned with the computation of the minimal-norm so... | \section{Introduction}\label{intro}
Let us assume that $F(\bm{x})=[F_1(\bm{x}),\ldots,F_m(\bm{x})]^T$
is a nonlinear twice continuously Frech\'et-differentiable
function with values in ${\mathbb{R}}^m$, for any $\bm{x}\in{\mathbb{R}}^n$.
For a given $\bm{b}\in{\mathbb{R}}^m$, we consider the nonlinear least-squares da... | {
"timestamp": "2021-09-20T02:17:02",
"yymm": "2101",
"arxiv_id": "2101.07560",
"language": "en",
"url": "https://arxiv.org/abs/2101.07560",
"abstract": "When a physical system is modeled by a nonlinear function, the unknown parameters can be estimated by fitting experimental observations by a least-squares... |
https://arxiv.org/abs/1205.2128 | Anisotropic regularity and optimal rates of convergence for the Finite Element Method on three dimensional polyhedral domains | We consider the model Poisson problem $-\Delta u = f \in \Omega$, $u = g$ on $\pa \Omega$, where $ \Omega $ is a bounded polyhedral domain in $\RR^n$. The objective of the paper is twofold. The first objective is to review the well posedness and the regularity of our model problem using appropriate weighted spaces for ... | \section*{Introduction}
Let $\Omega \subset \RR^n$ be an open, bounded set. Consider the
boundary value problem
\begin{equation}\label{eq.BVP}
\begin{cases} \; \Delta u = f & \text{ in }\Omega
\\ u\vert_{\pa \Omega} = g, & \text{ on } \Omega,
\end{cases}
\end{equation}
defined on a bounded domain $\Omega \su... | {
"timestamp": "2012-05-11T02:00:51",
"yymm": "1205",
"arxiv_id": "1205.2128",
"language": "en",
"url": "https://arxiv.org/abs/1205.2128",
"abstract": "We consider the model Poisson problem $-\\Delta u = f \\in \\Omega$, $u = g$ on $\\pa \\Omega$, where $ \\Omega $ is a bounded polyhedral domain in $\\RR^n$... |
https://arxiv.org/abs/1106.1022 | Bohman-Frieze processes at criticality and emergence of the giant component | The evolution of the usual Erdős-Rényi random graph model on n vertices can be described as follows: At time 0 start with the empty graph, with n vertices and no edges. Now at each time k, choose 2 vertices uniformly at random and attach an edge between these two vertices. Let \bfG_n(k) be the graph obtained at step k.... | \section{Introduction}
\section{Introduction}
\label{sec-int}
Random graph models of various systems in the real world have witnessed a tremendous growth in the last decade. The availability of a large amount of empirical data on real world networks and systems such as road and rail networks, bio-chemical networks, so... | {
"timestamp": "2011-06-09T02:03:02",
"yymm": "1106",
"arxiv_id": "1106.1022",
"language": "en",
"url": "https://arxiv.org/abs/1106.1022",
"abstract": "The evolution of the usual Erdős-Rényi random graph model on n vertices can be described as follows: At time 0 start with the empty graph, with n vertices a... |
https://arxiv.org/abs/1311.0892 | Equidistribution of polynomial sequences in function fields, with applications | We prove a function field analog of Weyl's classical theorem on equidistribution of polynomial sequences. Our result covers the case in which the degree of the polynomial is greater than or equal to the characteristic of the field, which is a natural barrier when applying the Weyl differencing process to function field... | \section{Introduction} \label{sec:intro}
Equidistribution theory started with Weyl's seminal paper
\cite{weyl2}. We recall that a sequence $(a_{n})_{n=1}^{\infty}$ of real numbers is
said to be \textit{equidistributed} $(\mod 1)$ if for any interval
$[\alpha,\beta] \subset [0,1)$, we have
\[\lim_{N \rightarrow \inft... | {
"timestamp": "2013-11-06T02:00:47",
"yymm": "1311",
"arxiv_id": "1311.0892",
"language": "en",
"url": "https://arxiv.org/abs/1311.0892",
"abstract": "We prove a function field analog of Weyl's classical theorem on equidistribution of polynomial sequences. Our result covers the case in which the degree of ... |
https://arxiv.org/abs/1207.3750 | Use of MAX-CUT for Ramsey Arrowing of Triangles | In 1967, Erdős and Hajnal asked the question: Does there exist a $K_4$-free graph that is not the union of two triangle-free graphs? Finding such a graph involves solving a special case of the classical Ramsey arrowing operation. Folkman proved the existence of these graphs in 1970, and they are now called Folkman grap... | \section{Introduction}
Given a simple graph $G$, we write $G \rightarrow (a_1,\dots,a_k)^e$ and say that $G$
\emph{arrows} $(a_1,\dots,a_k)^e$ if for every edge $k$-coloring of $G$, a
monochromatic $K_{a_i}$ is forced for some color $i \in
\{1,\dots,k\}$. Likewise, for graphs $F$ and $H$, $G\rightarrow (F,H)^e$ if for ... | {
"timestamp": "2013-03-22T01:00:58",
"yymm": "1207",
"arxiv_id": "1207.3750",
"language": "en",
"url": "https://arxiv.org/abs/1207.3750",
"abstract": "In 1967, Erdős and Hajnal asked the question: Does there exist a $K_4$-free graph that is not the union of two triangle-free graphs? Finding such a graph in... |
https://arxiv.org/abs/2202.04551 | Shortest Paths without a Map, but with an Entropic Regularizer | In a 1989 paper titled "shortest paths without a map", Papadimitriou and Yannakakis introduced an online model of searching in a weighted layered graph for a target node, while attempting to minimize the total length of the path traversed by the searcher. This problem, later called layered graph traversal, is parametri... | \section{Introduction}
\paragraph{Our results.}
In this paper we present a randomized $O(k^2)$-competitive online algorithm
for width $k$ layered graph traversal. The problem, whose history is discussed
in detail below, is an online version of the conventional shortest path problem
(see~\cite{Sch12}), and of Bellman's... | {
"timestamp": "2022-02-10T02:24:38",
"yymm": "2202",
"arxiv_id": "2202.04551",
"language": "en",
"url": "https://arxiv.org/abs/2202.04551",
"abstract": "In a 1989 paper titled \"shortest paths without a map\", Papadimitriou and Yannakakis introduced an online model of searching in a weighted layered graph ... |
https://arxiv.org/abs/1510.06353 | Localization of Quantum States and Landscape Functions | Eigenfunctions in inhomogeneous media can have strong localization properties. Filoche \& Mayboroda showed that the function $u$ solving $(-\Delta + V)u = 1$ controls the behavior of eigenfunctions $(-\Delta + V)\phi = \lambda\phi$ via the inequality $$|\phi(x)| \leq \lambda u(x) \|\phi\|_{L^{\infty}}.$$ This inequalit... | \section{Introduction}
\subsection{The Landscape function.} It is well known that physical systems comprised of inhomogeneous materials can exhibit peculiar vibration properties: let $\Omega \in \mathbb{R}^n$ be open, bounded and
\begin{align*}
(-\Delta + V)\phi = \lambda \phi \qquad \mbox{in~}\Omega ~\mbox{with Diric... | {
"timestamp": "2015-10-22T02:12:23",
"yymm": "1510",
"arxiv_id": "1510.06353",
"language": "en",
"url": "https://arxiv.org/abs/1510.06353",
"abstract": "Eigenfunctions in inhomogeneous media can have strong localization properties. Filoche \\& Mayboroda showed that the function $u$ solving $(-\\Delta + V)u... |
https://arxiv.org/abs/1002.0519 | Coincidence isometries of a shifted square lattice | We consider the coincidence problem for the square lattice that is translated by an arbitrary vector. General results are obtained about the set of coincidence isometries and the coincidence site lattices of a shifted square lattice by identifying the square lattice with the ring of Gaussian integers. To illustrate the... | \section{Introduction}
The sublattice of finite index formed by the points of intersection of a lattice and a rotated copy of the same lattice is called a coincidence site lattice or CSL. It was Friedel
in 1911 who first recognized the use of CSLs in describing and classifying grain boundaries in crystals \cite{Fr}... | {
"timestamp": "2010-02-02T16:55:10",
"yymm": "1002",
"arxiv_id": "1002.0519",
"language": "en",
"url": "https://arxiv.org/abs/1002.0519",
"abstract": "We consider the coincidence problem for the square lattice that is translated by an arbitrary vector. General results are obtained about the set of coincide... |
https://arxiv.org/abs/2205.12249 | Competitive Algorithms for Block-Aware Caching | We study the block-aware caching problem, a generalization of classic caching in which fetching (or evicting) pages from the same block incurs the same cost as fetching (or evicting) just one page from the block. Given a cache of size $k$, and a sequence of requests from $n$ pages partitioned into given blocks of size ... |
\section{Appendix}
\label{sec:appendix}
\subsection{Deferred Proofs}
\label{sec:extra_proofs}
\betaoff*
\begin{proof}
Consider the following instance. For any $\bsize$, let $n = 2\bsize^2$ pages be organized into $2\bsize$ blocks of size $\bsize$. Let $P$ be the first $\bsize$ blocks and $Q$ be the second $\bsi... | {
"timestamp": "2022-05-25T02:25:25",
"yymm": "2205",
"arxiv_id": "2205.12249",
"language": "en",
"url": "https://arxiv.org/abs/2205.12249",
"abstract": "We study the block-aware caching problem, a generalization of classic caching in which fetching (or evicting) pages from the same block incurs the same co... |
https://arxiv.org/abs/cs/0702113 | Fast Computation of Small Cuts via Cycle Space Sampling | We describe a new sampling-based method to determine cuts in an undirected graph. For a graph (V, E), its cycle space is the family of all subsets of E that have even degree at each vertex. We prove that with high probability, sampling the cycle space identifies the cuts of a graph. This leads to simple new linear-time... | \section{Introduction}\label{sec:intro}
Let $\ensuremath{G} = (V, E)$ be a connected undirected graph. A part of $\ensuremath{G}$
is said to be a \emph{cut} if, after deleting it from $\ensuremath{G}$, the
remaining graph is disconnected. We use the following terminology:
\begin{itemize}
\item A \emph{cut vertex} is a ... | {
"timestamp": "2010-07-22T02:01:11",
"yymm": "0702",
"arxiv_id": "cs/0702113",
"language": "en",
"url": "https://arxiv.org/abs/cs/0702113",
"abstract": "We describe a new sampling-based method to determine cuts in an undirected graph. For a graph (V, E), its cycle space is the family of all subsets of E th... |
https://arxiv.org/abs/1301.6469 | Weighted Fejér Constants and Fekete Sets | We give the connections among the Fekete sets, the zeros of orthogonal polynomials, $1(w)$-normal point systems, and the nodes of a stable and most economical interpolatory process via the Fejér contants. Finally the convergence of a weighted Grünwald interpolation is proved. | \section{Introduction}
L. Fej\'er introduced the so-called Hermite-Fej\'er interpolatory process, and in 1934 he gave the definition of normal- and $\varrho$-normal system of nodes for which the Hermite-Fej\'er interpolation is a positive interpolatory process. The surprising nice convergence properties of Lagrange, H... | {
"timestamp": "2013-01-29T02:03:37",
"yymm": "1301",
"arxiv_id": "1301.6469",
"language": "en",
"url": "https://arxiv.org/abs/1301.6469",
"abstract": "We give the connections among the Fekete sets, the zeros of orthogonal polynomials, $1(w)$-normal point systems, and the nodes of a stable and most economic... |
https://arxiv.org/abs/1009.3637 | Lines on projective varieties and applications | The first part of this note contains a review of basic properties of the variety of lines contained in an embedded projective variety and passing through a general point. In particular we provide a detailed proof that for varieties defined by quadratic equations the base locus of the projective second fundamental form ... | \section*{Introduction}
The {\it principle} that the Hilbert scheme of
lines contained in a (smooth) projective
variety $X\subset{\mathbb P}^N$ and passing through a (general) point can inherit intrinsic and extrinsic geometrical properties
of the variety, has emerged recently. This principle allowed
to attack some... | {
"timestamp": "2011-05-06T02:02:41",
"yymm": "1009",
"arxiv_id": "1009.3637",
"language": "en",
"url": "https://arxiv.org/abs/1009.3637",
"abstract": "The first part of this note contains a review of basic properties of the variety of lines contained in an embedded projective variety and passing through a ... |
https://arxiv.org/abs/0903.0840 | Real loci of based loop groups | Let $(G,K)$ be a Riemannian symmetric pair of maximal rank, where $G$ is a compact simply connected Lie group and $K$ the fixed point set of an involutive automorphism $\sigma$. This induces an involutive automorphism $\tau$ of the based loop space $\Omega(G)$. There exists a maximal torus $T\subset G$ such that the ca... | \section{Introduction}
Let $G$ be a compact connected simply connected Lie group.
Consider the space
$$\Omega(G):=\{\gamma : S^1 \to G \ : \ \gamma \ {\rm of \ Sobolev \ class \ } H^1,
\gamma(1)=e\}$$ of all based loops in $G$ (here $S^1$ is the unit circle in the complex plane).
It is known that $\Omega(G)$ is an i... | {
"timestamp": "2009-09-11T22:26:31",
"yymm": "0903",
"arxiv_id": "0903.0840",
"language": "en",
"url": "https://arxiv.org/abs/0903.0840",
"abstract": "Let $(G,K)$ be a Riemannian symmetric pair of maximal rank, where $G$ is a compact simply connected Lie group and $K$ the fixed point set of an involutive a... |
https://arxiv.org/abs/2002.03001 | A Novel Evolution Strategy with Directional Gaussian Smoothing for Blackbox Optimization | We propose an improved evolution strategy (ES) using a novel nonlocal gradient operator for high-dimensional black-box optimization. Standard ES methods with $d$-dimensional Gaussian smoothing suffer from the curse of dimensionality due to the high variance of Monte Carlo (MC) based gradient estimators. To control the ... | \section{Introduction}
\label{sec:intro}
Evolution strategy (ES) is a type of evolutionary algorithms for black-box optimization, where we search for the optima of a $d$-dimensional loss function $F(\bm x)$ given access to only its function queries. This is motivated by several applications where the loss function's g... | {
"timestamp": "2020-06-15T02:02:14",
"yymm": "2002",
"arxiv_id": "2002.03001",
"language": "en",
"url": "https://arxiv.org/abs/2002.03001",
"abstract": "We propose an improved evolution strategy (ES) using a novel nonlocal gradient operator for high-dimensional black-box optimization. Standard ES methods w... |
https://arxiv.org/abs/2102.08052 | On a List Variant of the Multiplicative 1-2-3 Conjecture | The 1-2-3 Conjecture asks whether almost all graphs can be (edge-)labelled with $1,2,3$ so that no two adjacent vertices are incident to the same sum of labels. In the last decades, several aspects of this problem have been studied in literature, including more general versions and slight variations. Notable such varia... | \section{Introduction}
Let $G$ be a graph and $\ell$ be a \textit{$k$-labelling} of $G$, i.e., an assignment $\ell : E(G) \rightarrow \{1,\dots,k\}$ of labels $1,\dots,k$ to the edges of $G$.
For every vertex $v$ of $G$, one can compute, as a colour, the \textit{sum} $\sigma_\ell(v)$ of labels assigned by $\ell$ to th... | {
"timestamp": "2021-02-17T02:16:06",
"yymm": "2102",
"arxiv_id": "2102.08052",
"language": "en",
"url": "https://arxiv.org/abs/2102.08052",
"abstract": "The 1-2-3 Conjecture asks whether almost all graphs can be (edge-)labelled with $1,2,3$ so that no two adjacent vertices are incident to the same sum of l... |
https://arxiv.org/abs/1504.01721 | Rainbow connection in some digraphs | An edge-coloured graph $G$ is {\it rainbow connected} if any two vertices are connected by a path whose edges have distinct colours. This concept was introduced by Chartrand et al. in \cite{ch01}, and it was extended to oriented graphs by Dorbec et al. in \cite{DI}.In this paper we present some results regarding this e... | \section{Introduction}
Given a connected graph $G=(V(G), E(G))$, an edge-coloring of $G$ is called {\it rainbow connected} if for every pair of distinct vertices $u, v$ of $G$ there is a $uv$-path all whose edges received different colors. The {\it rainbow connectivity number of} $G$ is the minimum number $rc(G)$ su... | {
"timestamp": "2015-04-08T02:11:36",
"yymm": "1504",
"arxiv_id": "1504.01721",
"language": "en",
"url": "https://arxiv.org/abs/1504.01721",
"abstract": "An edge-coloured graph $G$ is {\\it rainbow connected} if any two vertices are connected by a path whose edges have distinct colours. This concept was int... |
https://arxiv.org/abs/2101.09711 | Testing for subsphericity when $n$ and $p$ are of different asymptotic order | We extend a classical test of subsphericity, based on the first two moments of the eigenvalues of the sample covariance matrix, to the high-dimensional regime where the signal eigenvalues of the covariance matrix diverge to infinity and either $p/n \rightarrow 0$ or $p/n \rightarrow \infty$. In the latter case we furth... | \section{Introduction}\label{sec:intro}
The objective of principal component analysis (PCA), and dimension reduction in general, is to extract a low-dimensional signal from noise-corrupted observed data. The most basic statistical model for the problem is as follows. Assume that $S_n$ is the sample covariance matrix o... | {
"timestamp": "2021-06-30T02:19:56",
"yymm": "2101",
"arxiv_id": "2101.09711",
"language": "en",
"url": "https://arxiv.org/abs/2101.09711",
"abstract": "We extend a classical test of subsphericity, based on the first two moments of the eigenvalues of the sample covariance matrix, to the high-dimensional re... |
https://arxiv.org/abs/1807.00393 | Adaptive Optimal Transport | An adaptive, adversarial methodology is developed for the optimal transport problem between two distributions $\mu$ and $\nu$, known only through a finite set of independent samples $(x_i)_{i=1..N}$ and $(y_j)_{j=1..M}$. The methodology automatically creates features that adapt to the data, thus avoiding reliance on a ... | \section*{\small Acknowledgments}
\end{center}
The authors would like to thank Yongxin Chen for connecting our variational formulation of the Kullback-Leibler divergence with the Donsker-Varadhan formula. This work has been partially supported by a grant from the Morse-Sloan Foundation. The work of Tabak was partially ... | {
"timestamp": "2019-02-20T02:03:10",
"yymm": "1807",
"arxiv_id": "1807.00393",
"language": "en",
"url": "https://arxiv.org/abs/1807.00393",
"abstract": "An adaptive, adversarial methodology is developed for the optimal transport problem between two distributions $\\mu$ and $\\nu$, known only through a fini... |
https://arxiv.org/abs/2212.12401 | Bakry-Émery curvature sharpness and curvature flow in finite weighted graphs. II. Implementation | In this second part of a sequence of two papers, we discuss the implementation of a curvature flow on weighted graphs based on the Bakry-Émery calculus. This flow can be adapted to preserve the Markovian property and its limits as time goes to infinity turn out to be curvature sharp weighted graphs. After reviewing som... | \section{Introduction}
This paper is concerned with computational aspects of a curvature flow on weighted graphs based on the Bakry-\'Emery calculus. This curvature flow was intoduced in our first paper \cite{CKLMPS-22}.
A \emph{weighted graph} in this paper is a finite simple mixed combinatorial graph $G=(V,E)$ wit... | {
"timestamp": "2022-12-26T02:12:39",
"yymm": "2212",
"arxiv_id": "2212.12401",
"language": "en",
"url": "https://arxiv.org/abs/2212.12401",
"abstract": "In this second part of a sequence of two papers, we discuss the implementation of a curvature flow on weighted graphs based on the Bakry-Émery calculus. T... |
https://arxiv.org/abs/math/0701629 | Linear spaces with a line-transitive point-imprimitive automorphism group and Fang-Li parameter gcd(k,r) at most eight | In 1991, Weidong Fang and Huiling Li proved that there are only finitely many non-trivial linear spaces that admit a line-transitive, point-imprimitive group action, for a given value of gcd(k,r), where k is the line size and r is the number of lines on a point. The aim of this paper is to make that result effective. W... | \section{Introduction}
A {\em finite linear space} ${\cal S}=({\cal P},{\cal L})$ consists of a finite set
${\cal P}$ of points and a non-empty set ${\cal L}$ of distinguished subsets of
${\cal P}$ called lines such that any two points lie in exactly one line and
each line contains at least two points. A linear space ... | {
"timestamp": "2007-01-31T07:26:17",
"yymm": "0701",
"arxiv_id": "math/0701629",
"language": "en",
"url": "https://arxiv.org/abs/math/0701629",
"abstract": "In 1991, Weidong Fang and Huiling Li proved that there are only finitely many non-trivial linear spaces that admit a line-transitive, point-imprimitiv... |
https://arxiv.org/abs/2209.10028 | Lines in quasi-metric spaces with four points | A set of n non-collinear points in the Euclidean plane defines at least n different lines. Chen and Chvátal in 2008 conjectured that the same results is true in metric spaces for an adequate definition of line. More recently, this conjecture was studied in the context of quasi-metric spaces. In this work we prove that ... | \section{Introduction}
The Chen and Chvátal's conjecture, introduced in 2008 (see \cite{CC}), affirms that every finite metric space $M$ with $n\geq 2$ points has the so called \emph{de Bruijn and Erdös} (DBE) property:
\begin{equation}
M \text{ has a \emph{line} containing all the points or at least $n$ different \... | {
"timestamp": "2022-09-22T02:05:06",
"yymm": "2209",
"arxiv_id": "2209.10028",
"language": "en",
"url": "https://arxiv.org/abs/2209.10028",
"abstract": "A set of n non-collinear points in the Euclidean plane defines at least n different lines. Chen and Chvátal in 2008 conjectured that the same results is t... |
https://arxiv.org/abs/2006.11402 | Subspace controllability of multi-partite spin networks | In a network of spin 1/2 particles, controlled through an external electro-magnetic field, the gyromagnetic ratio of each spin is a parameter that characterizes the interaction of the spin with the external control field. Multipartite networks are such that the spins are divided into subsets according to their gyromagn... | \section{Introduction and statement of main result}
The dynamics of quantum mechanical systems, subject to a control electromagnetic field, can often be described by the Schr\"odinger equation in the form
\be{Scro1}
\dot \psi=A \psi+\sum_{j=1}^mB_j u_j \psi,
\end{equation}
where $u_j$, $j=1,...,m$, are the control ... | {
"timestamp": "2020-06-23T02:04:11",
"yymm": "2006",
"arxiv_id": "2006.11402",
"language": "en",
"url": "https://arxiv.org/abs/2006.11402",
"abstract": "In a network of spin 1/2 particles, controlled through an external electro-magnetic field, the gyromagnetic ratio of each spin is a parameter that charact... |
https://arxiv.org/abs/2005.13081 | Decomposition of Topological Azumaya Algebras | Let $\mathcal{A}$ be a topological Azumaya algebra of degree $mn$ over a CW complex $X$. We give conditions for the positive integers $m$ and $n$, and the space $X$ so that $\mathcal{A}$ can be decomposed as the tensor product of topological Azumaya algebras of degrees $m$ and $n$. Then we prove that if $m<n$ and the d... | \section{Introduction}
The classical theory of central simple algebras over a field was generalized by Azumaya \cite{Azu1951} and Auslander-Goldman \cite{AG1960} by introducing the concept of Azumaya algebra over a local commutative ring and over an arbitrary commutative ring, respectively. This concept was generalize... | {
"timestamp": "2020-05-28T02:06:39",
"yymm": "2005",
"arxiv_id": "2005.13081",
"language": "en",
"url": "https://arxiv.org/abs/2005.13081",
"abstract": "Let $\\mathcal{A}$ be a topological Azumaya algebra of degree $mn$ over a CW complex $X$. We give conditions for the positive integers $m$ and $n$, and th... |
https://arxiv.org/abs/1709.00404 | Unbiased Hamiltonian Monte Carlo with couplings | We propose a methodology to parallelize Hamiltonian Monte Carlo estimators. Our approach constructs a pair of Hamiltonian Monte Carlo chains that are coupled in such a way that they meet exactly after some random number of iterations. These chains can then be combined so that resulting estimators are unbiased. This all... | \section{Introduction \label{sec:Context-and-goal}}
\subsection{Parallel computation with Hamiltonian Monte Carlo \label{subsec:Parallelizing-Hamiltonian-Monte}}
Hamiltonian Monte Carlo is a Markov chain Monte Carlo method to approximate
integrals with respect to a target probability distribution $\pi$ on
$\mathbb{R}^... | {
"timestamp": "2018-08-28T02:21:51",
"yymm": "1709",
"arxiv_id": "1709.00404",
"language": "en",
"url": "https://arxiv.org/abs/1709.00404",
"abstract": "We propose a methodology to parallelize Hamiltonian Monte Carlo estimators. Our approach constructs a pair of Hamiltonian Monte Carlo chains that are coup... |
https://arxiv.org/abs/2301.07872 | Automorphisms of weighted projective hypersurfaces | We prove several results concerning automorphism groups of quasismooth complex weighted projective hypersurfaces; these generalize and strengthen existing results for hypersurfaces in ordinary projective space. First, we establish a Grothendieck-Lefschetz type theorem for these hypersurfaces. We next provide a characte... | \section{Introduction}
Hypersurfaces in projective space are among the most well-studied varieties. In particular, a great deal is known about their automorphism groups, due to landmark theorems of Grothendieck-Lefschetz \cite{SGA2}, Matsumura-Monsky \cite{MM}, and others. In this paper, we generalize and strengthen... | {
"timestamp": "2023-01-20T02:05:52",
"yymm": "2301",
"arxiv_id": "2301.07872",
"language": "en",
"url": "https://arxiv.org/abs/2301.07872",
"abstract": "We prove several results concerning automorphism groups of quasismooth complex weighted projective hypersurfaces; these generalize and strengthen existing... |
https://arxiv.org/abs/2211.11819 | Descent modulus and applications | The norm of the gradient $\nabla$f (x) measures the maximum descent of a real-valued smooth function f at x. For (nonsmooth) convex functions, this is expressed by the distance dist(0, $\partial$f (x)) of the subdifferential to the origin, while for general real-valued functions defined on metric spaces by the notion o... | \section{Introduction\label{sec01:Intro}}
In \cite{BCD2018} the following surprising result was obtained: two
$\mathcal{C}^{2}$-smooth convex bounded from below functions defined on a
Hilbert space $\mathcal{H}$ are equal up to an additive constant, provided
they have the same modulus of derivative at every point. In... | {
"timestamp": "2022-11-23T02:01:24",
"yymm": "2211",
"arxiv_id": "2211.11819",
"language": "en",
"url": "https://arxiv.org/abs/2211.11819",
"abstract": "The norm of the gradient $\\nabla$f (x) measures the maximum descent of a real-valued smooth function f at x. For (nonsmooth) convex functions, this is ex... |
https://arxiv.org/abs/2302.12355 | Fundamental Bounds on Online Strategic Classification | We study the problem of online binary classification where strategic agents can manipulate their observable features in predefined ways, modeled by a manipulation graph, in order to receive a positive classification. We show this setting differs in fundamental ways from non-strategic online classification. For instance... | \section{Supplementary Materials}
\subsection{Proof of~\Cref{thm:biased-weighted-maj-vote-mistake-bound}}
\medskip
\noindent\textbf{\Cref{thm:biased-weighted-maj-vote-mistake-bound}} (Restated)\textbf{.}\emph{
\Cref{alg:biased-weighted-maj-vote} makes at most $e(\Delta+2)(\ln|\mathcal{H}|+\mathsf{OPT})$ mistakes ... | {
"timestamp": "2023-02-27T02:03:03",
"yymm": "2302",
"arxiv_id": "2302.12355",
"language": "en",
"url": "https://arxiv.org/abs/2302.12355",
"abstract": "We study the problem of online binary classification where strategic agents can manipulate their observable features in predefined ways, modeled by a mani... |
https://arxiv.org/abs/1907.00268 | The valley version of the Extended Delta Conjecture | The Shuffle Theorem of Carlsson and Mellit gives a combinatorial expression for the bigraded Frobenius characteristic of the ring of diagonal harmonics, and the Delta Conjecture of Haglund, Remmel and the second author provides two generalizations of the Shuffle Theorem to the delta operator expression $\Delta'_{e_k} e... | \section{Introduction}
Let $X=\{x_1,x_2,\ldots,x_n\}$ and $Y=\{y_1,y_2,\ldots,y_n\}$ be two sets of $n$ commuting variables. The {\em ring of diagonal harmonics} consists of
those polynomials in $\mathbb{Q}[X,Y]$ which satisfy
the following system of differential equations
$$
\partial_{x_1}^a\partial_{y_1}^b\,f(X,Y)+... | {
"timestamp": "2019-07-10T02:19:09",
"yymm": "1907",
"arxiv_id": "1907.00268",
"language": "en",
"url": "https://arxiv.org/abs/1907.00268",
"abstract": "The Shuffle Theorem of Carlsson and Mellit gives a combinatorial expression for the bigraded Frobenius characteristic of the ring of diagonal harmonics, a... |
https://arxiv.org/abs/2006.01434 | Resummed Wentzel-Kramers-Brillouin Series: Quantization and Physical Interpretation | The Wentzel-Kramers-Brillouin (WKB) perturbative series, a widely used technique for solving linear waves, is typically divergent and at best, asymptotic, thus impeding predictions beyond the first few leading-order effects. Here, we report a closed-form formula that exactly resums the perturbative WKB series to all-or... | \section{Introduction}
Linear waves are ubiquitous in the world of physics with applications ranging from quantum mechanics \cite{berry1972} to electromagnetism, fluid dynamics, and astrophysics \cite{iyer1987}. The properties of these waves are encoded in their dispersion relations, which reveal the nature of the me... | {
"timestamp": "2022-02-23T02:26:41",
"yymm": "2006",
"arxiv_id": "2006.01434",
"language": "en",
"url": "https://arxiv.org/abs/2006.01434",
"abstract": "The Wentzel-Kramers-Brillouin (WKB) perturbative series, a widely used technique for solving linear waves, is typically divergent and at best, asymptotic,... |
https://arxiv.org/abs/2210.11914 | Generalized Turan number for the edge blow-up graph | Let $H$ be a graph and $p$ be an integer. The edge blow-up $H^p$ of $H$ is the graph obtained from replacing each edge in $H$ by a copy of $K_p$ where the new vertices of the cliques are all distinct. Let $C_k$ and $P_k$ denote the cycle and path of length $k$, respectively. In this paper, we find sharp upper bounds fo... | \section{Introduction}
\textbf{Notation. }In this paper, we use $C_k$, $P_k$, $M_k$ and $S_k$ to denote the cycle, path, matching and star with $k$ edges, respectively.
Let $K_t$ be the complete graph on $t$ vertices and $K_{s,t}$ be the complete bipartite graph with parts of size $s$ and $t$.
The vertex and edge... | {
"timestamp": "2022-10-24T02:12:31",
"yymm": "2210",
"arxiv_id": "2210.11914",
"language": "en",
"url": "https://arxiv.org/abs/2210.11914",
"abstract": "Let $H$ be a graph and $p$ be an integer. The edge blow-up $H^p$ of $H$ is the graph obtained from replacing each edge in $H$ by a copy of $K_p$ where the... |
https://arxiv.org/abs/2009.00130 | On the Zarankiewicz problem for graphs with bounded VC-dimension | The problem of Zarankiewicz asks for the maximum number of edges in a bipartite graph on $n$ vertices which does not contain the complete bipartite graph $K_{k,k}$ as a subgraph. A classical theorem due to Kővári, Sós, and Turán says that this number of edges is $O\left(n^{2 - 1/k}\right)$. An important variant of this... | \section{Introduction}
The problem of Zarankiewicz is a central problem in extremal graph theory. It asks for the maximum number of edges $\operatorname{ex}(n,K_{k,k})$ in a bipartite graph on $n$ vertices, where each side of the bipartition contains $n/2$ vertices and which does not contain the complete bipartite gra... | {
"timestamp": "2020-09-02T02:05:05",
"yymm": "2009",
"arxiv_id": "2009.00130",
"language": "en",
"url": "https://arxiv.org/abs/2009.00130",
"abstract": "The problem of Zarankiewicz asks for the maximum number of edges in a bipartite graph on $n$ vertices which does not contain the complete bipartite graph ... |
https://arxiv.org/abs/1308.5966 | Growth rate degeneracies in kinematic dynamos | We consider the classical problem of kinematic dynamo action in simple steady flows. Due to the adjointness of the induction operator, we show that the growth rate of the dynamo will be exactly the same for two types of magnetic boundary conditions: the magnetic field can be normal (infinite magnetic permeability, also... | \section{Introduction}
The growth of magnetic fields due to dynamo action, both in astrophysical bodies and in laboratory experiments, is expected to depend not only on the details of the flow field, but also on the conditions on the magnetic field applied at the boundaries.
In the laboratory there are two physically... | {
"timestamp": "2013-09-25T02:08:36",
"yymm": "1308",
"arxiv_id": "1308.5966",
"language": "en",
"url": "https://arxiv.org/abs/1308.5966",
"abstract": "We consider the classical problem of kinematic dynamo action in simple steady flows. Due to the adjointness of the induction operator, we show that the grow... |
https://arxiv.org/abs/1708.02223 | Negligibility of parabolic elements in relatively hyperbolic groups | We study density of parabolic elements in a finitely generated relatively hyperbolic group $G$ with respect to a word metric. We prove this density to be zero (apart from degenerate cases) and the limit defining the density to converge exponentially fast; this has recently been proven independently by W. Yang. As a cor... | \section{Introduction}
\label{s:intro}
A group $G$ is hyperbolic to a collection of subgroups $\{ H_\omega \}_{\omega \in \Omega}$ if, loosely speaking, it is hyperbolic except for the part that is inside the set $\mathcal{P}$ consisting of elements in the subgroups $H_\omega$ and their conjugates. It is therefore nat... | {
"timestamp": "2017-08-10T02:08:46",
"yymm": "1708",
"arxiv_id": "1708.02223",
"language": "en",
"url": "https://arxiv.org/abs/1708.02223",
"abstract": "We study density of parabolic elements in a finitely generated relatively hyperbolic group $G$ with respect to a word metric. We prove this density to be ... |
https://arxiv.org/abs/2207.07070 | Boundary Effects on Ideal Fluid Forces and Kelvin's Minimum Energy Theorem | The electrostatic force on a charge above a neutral conductor is generally attractive. Surprisingly, that force becomes repulsive in certain geometries (Levin & Johnson 2011), a result that follows from an energy theorem in electrostatics. Based on the analogous minimum energy theorem of Kelvin (1849), valid in the the... | \section{Introduction}
It is generally stated that the electrostatic force on a charge above a conductor is attractive \citep[pp. 99]{Griffiths}.
However, \citet[]{levin2011} showed that the force may be repulsive in certain geometries. Repulsion occurs when the electric field energy depends non-monotonically on the ch... | {
"timestamp": "2022-07-15T02:20:35",
"yymm": "2207",
"arxiv_id": "2207.07070",
"language": "en",
"url": "https://arxiv.org/abs/2207.07070",
"abstract": "The electrostatic force on a charge above a neutral conductor is generally attractive. Surprisingly, that force becomes repulsive in certain geometries (L... |
https://arxiv.org/abs/1904.10215 | Multicast Communications in Tree Networks with Heterogeneous Capacity Constraints | A widely studied problem in communication networks is that of finding the maximum number of communication requests that can be scheduled concurrently, subject to node and/or link capacity constraints. In this paper, we consider the problem of finding the largest number of multicast communication requests that can be se... |
\section{Simulation Results}
\begin{figure*}[ht]
\centering
\includegraphics[width=0.8\textwidth]{Figures/Random.jpg}
\caption{Approximation ratio of the greedy algorithm on random $\vpt$ graphs. The histogram is for 30.000 instances on random trees of 50 to 150 nodes, and number of paths from twice to four times ... | {
"timestamp": "2020-05-25T02:11:51",
"yymm": "1904",
"arxiv_id": "1904.10215",
"language": "en",
"url": "https://arxiv.org/abs/1904.10215",
"abstract": "A widely studied problem in communication networks is that of finding the maximum number of communication requests that can be scheduled concurrently, sub... |
https://arxiv.org/abs/2203.08721 | Axiomatization via translation: Hiz's warning for predicate logic | The problems of logical translation of axiomatizations and the choice of primitive operators have surfaced several times over the years. An early issue was raised by H. Hi{\. z} in the 1950s on the incompleteness of translated calculi. Further pertinent work, some of it touched on here, was done in the 1970s by W. Fran... | \section{Introduction} \label{Intro}
A translation \textbf{t} from a language $\mathcal{L}$, thought of as the set of its formulas, to the language $\mathcal{L}'$ is a function from $\mathcal{L}$ to $\mathcal{L}'$ (on which one may impose further demands of compositionality etc., as desired). We say that \textbf{t} \... | {
"timestamp": "2022-03-17T01:37:59",
"yymm": "2203",
"arxiv_id": "2203.08721",
"language": "en",
"url": "https://arxiv.org/abs/2203.08721",
"abstract": "The problems of logical translation of axiomatizations and the choice of primitive operators have surfaced several times over the years. An early issue wa... |
https://arxiv.org/abs/1703.04180 | MEDL and MEDLA: Methods for Assessment of Scaling by Medians of Log-Squared Nondecimated Wavelet Coefficients | High-frequency measurements and images acquired from various sources in the real world often possess a degree of self-similarity and inherent regular scaling. When data look like a noise, the scaling exponent may be the only informative feature that summarizes such data. Methods for the assessment of self-similarity by... | \section{Introduction}
At first glance, data that scale look like noisy observations, and often
the large scale features
(basic descriptive statistics, trends, smoothed functional estimates, etc.)
carry no useful information.
For example, the pupil diameter in humans fluctuates at a high frequency
(hundreds of Hz), a... | {
"timestamp": "2017-03-14T01:09:26",
"yymm": "1703",
"arxiv_id": "1703.04180",
"language": "en",
"url": "https://arxiv.org/abs/1703.04180",
"abstract": "High-frequency measurements and images acquired from various sources in the real world often possess a degree of self-similarity and inherent regular scal... |
https://arxiv.org/abs/math/0512077 | The neighborhood complex of a random graph | For a graph G, the neighborhood complex N[G] is the simplicial complex having all subsets of vertices with a common neighbor as its faces. It is a well known result of Lovasz that if N[G] is k-connected, then the chromatic number of G is at least k + 3.We prove that the connectivity of the neighborhood complex of a ran... | \section{Introduction}
In 1978, L\'{a}szl\'{o} Lov\'{a}sz proved Kneser's conjecture
\cite{Lovasz}, that if the $n$-subsets of a $(2n+k)$-set are
partitioned into $k+1$ families, at least one family contains a
disjoint pair. He restated the problem graph theoretically and
then proved a more general theorem about graph... | {
"timestamp": "2006-02-01T11:04:37",
"yymm": "0512",
"arxiv_id": "math/0512077",
"language": "en",
"url": "https://arxiv.org/abs/math/0512077",
"abstract": "For a graph G, the neighborhood complex N[G] is the simplicial complex having all subsets of vertices with a common neighbor as its faces. It is a wel... |
https://arxiv.org/abs/1304.4648 | Construction of Self-dual Codes over $F_p+vF_p$ | In this paper, we determine all self-dual codes over $F_p+vF_p$ ($v^2=v$) in terms of self-dual codes over the finite field $F_p$ and give an explicit construction for self-dual codes over $F_p+vF_p$, where $p$ is a prime. | \section{Introduction}
Codes over finite rings were initiated in the early 1970s \cite{Blake1972, Blake1975}.
They have received much attention since the seminal work \cite{HK},
which showed that certain good nonlinear
binary codes could be found as images of linear codes over $\mathbb{Z}_4$ under the Gray map.
Gene... | {
"timestamp": "2013-04-18T02:00:48",
"yymm": "1304",
"arxiv_id": "1304.4648",
"language": "en",
"url": "https://arxiv.org/abs/1304.4648",
"abstract": "In this paper, we determine all self-dual codes over $F_p+vF_p$ ($v^2=v$) in terms of self-dual codes over the finite field $F_p$ and give an explicit const... |
https://arxiv.org/abs/1403.7427 | Robust optimal solutions in interval linear programming with forall-exists quantifiers | We introduce a novel kind of robustness in linear programming. A solution x* is called robust optimal if for all realizations of objective functions coefficients and constraint matrix entries from given interval domains there are appropriate choices of the right-hand side entries from their interval domains such that x... | \section{Introduction}
Robustness in mathematical programming was intensively studied from diverse points of view \cite{BenBoy2006,BenNem2009,BenGor2004,BenNem2002, SoyMur2013}. Generally, robustness corresponds to stability of some key characteristics under limited input data change.
In case of uncertainties in the o... | {
"timestamp": "2014-03-31T02:08:37",
"yymm": "1403",
"arxiv_id": "1403.7427",
"language": "en",
"url": "https://arxiv.org/abs/1403.7427",
"abstract": "We introduce a novel kind of robustness in linear programming. A solution x* is called robust optimal if for all realizations of objective functions coeffic... |
https://arxiv.org/abs/1201.0660 | Stable complexity and simplicial volume of manifolds | Let the complexity of a closed manifold M be the minimal number of simplices in a triangulation of M. Such a quantity is clearly submultiplicative with respect to finite coverings, and by taking the infimum on all finite coverings of M normalized by the covering degree we can promote it to a multiplicative invariant, a... | \section*{Introduction}
Following Milnor and Thurston \cite{MiThu}, a numerical invariant $\alpha(M)$ associated to any closed $n$-manifold $M$ is a \emph{characteristic number} if for every degree-$d$ covering $M\stackrel{d}{\to} N$ we have $\alpha(M) = d\cdot \alpha(N)$. Two important characteristic numbers are the E... | {
"timestamp": "2012-08-22T02:02:43",
"yymm": "1201",
"arxiv_id": "1201.0660",
"language": "en",
"url": "https://arxiv.org/abs/1201.0660",
"abstract": "Let the complexity of a closed manifold M be the minimal number of simplices in a triangulation of M. Such a quantity is clearly submultiplicative with resp... |
https://arxiv.org/abs/2010.01655 | Completeness of Positive Linear Recurrence Sequences | A sequence of positive integers is complete if every positive integer is a sum of distinct terms. A positive linear recurrence sequence (PLRS) is a sequence defined by a homogeneous linear recurrence relation with nonnegative coefficients of the form $H_{n+1} = c_1 H_n + \cdots + c_L H_{n-L+1}$ and a particular set of ... | \section{Introduction}
The Fibonacci numbers are one of the most studied integer sequences. One of their many interesting properties is that they can be used to construct a unique decomposition for any positive integer. Zeckendorf proved that every positive integer can be written uniquely as a sum of non-consecutive... | {
"timestamp": "2021-09-01T02:06:36",
"yymm": "2010",
"arxiv_id": "2010.01655",
"language": "en",
"url": "https://arxiv.org/abs/2010.01655",
"abstract": "A sequence of positive integers is complete if every positive integer is a sum of distinct terms. A positive linear recurrence sequence (PLRS) is a sequen... |
https://arxiv.org/abs/2112.12559 | Multigrid solvers for isogeometric discretizations of the second biharmonic problem | We develop a multigrid solver for the second biharmonic problem in the context of Isogeometric Analysis (IgA), where we also allow a zero-order term. In a previous paper, the authors have developed an analysis for the first biharmonic problem based on Hackbusch's framework. This analysis can only be extended to the sec... | \section{Introduction}
We consider multigrid methods for biharmonic problems discretized by Isogeometric Analysis (IgA). In particular, we consider the following model problem:
Given a bounded domain $\Omega\subset \mathbb R^d$, $d\in\{2,3\}$, with Lipschitz boundary $\partial\Omega$,
a parameter $\beta \geq 0$ and suf... | {
"timestamp": "2021-12-24T02:17:10",
"yymm": "2112",
"arxiv_id": "2112.12559",
"language": "en",
"url": "https://arxiv.org/abs/2112.12559",
"abstract": "We develop a multigrid solver for the second biharmonic problem in the context of Isogeometric Analysis (IgA), where we also allow a zero-order term. In a... |
https://arxiv.org/abs/2207.10873 | The rational Chow rings of moduli spaces of hyperelliptic curves with marked points | We determine the rational Chow ring of the moduli space $\mathcal{H}_{g,n}$ of $n$-pointed smooth hyperelliptic curves of genus $g$ when $n \leq 2g+6$. We also show that the Chow ring of the partial compactification $\mathcal{I}_{g,n}$, parametrizing $n$-pointed irreducible nodal hyperelliptic curves, is generated by t... | \section{Introduction}
The intersection theory of the moduli space of genus $g$ curves $\mathcal{M}_g$ is of central interest in algebraic geometry. The Chow ring with rational coefficients $A^*(\mathcal{M}_g)$ is completely understood for $g\leq 9$ \cite{FaberI, FaberII, Izadi, PenevVakil, 789}. On the other hand, muc... | {
"timestamp": "2022-07-25T02:07:17",
"yymm": "2207",
"arxiv_id": "2207.10873",
"language": "en",
"url": "https://arxiv.org/abs/2207.10873",
"abstract": "We determine the rational Chow ring of the moduli space $\\mathcal{H}_{g,n}$ of $n$-pointed smooth hyperelliptic curves of genus $g$ when $n \\leq 2g+6$. ... |
https://arxiv.org/abs/1709.03462 | The horofunction boundary of finite-dimensional $\ell_p$ spaces | We give a complete description of the horofunction boundary of finite-dimensional $\ell_p$ spaces for $1\leq p\leq \infty$. We also study the variation norm on $\mathbb{R}^{\mathcal{N}}$, $\mathcal{N}=\{1,...,N\}$, and the corresponding horofunction boundary. As a consequence, we describe the horofunctions for Hilbert'... | \section{Introduction}
There has recently been growing interest in the horofunction boundary of
metric spaces. It is a powerful tool in the study of self-mappings of convex
cones \cite{Gaubert_Vigeral2012,Karlsson2014} and random walks on groups
\cite{Karlsson_Ledrappier2011}. The horofunction boundary has been stud... | {
"timestamp": "2018-12-31T02:19:15",
"yymm": "1709",
"arxiv_id": "1709.03462",
"language": "en",
"url": "https://arxiv.org/abs/1709.03462",
"abstract": "We give a complete description of the horofunction boundary of finite-dimensional $\\ell_p$ spaces for $1\\leq p\\leq \\infty$. We also study the variatio... |
https://arxiv.org/abs/1706.03386 | Extensions of partial cyclic orders, Euler numbers and multidimensional boustrophedons | We enumerate total cyclic orders on $\left\{1,\ldots,n\right\}$ where we prescribe the relative cyclic order of consecutive triples $(i,{i+1},{i+2})$, these integers being taken modulo $n$. In some cases, the problem reduces to the enumeration of descent classes of permutations, which is done via the boustrophedon cons... | \section{Introduction}
\label{sec:introduction}
In this paper we enumerate some extensions of partial cyclic orders to total cyclic orders. In certain cases, this question is related to that of linear extensions of some posets.
A (linear) order on a set $X$ is a reflexive, antisymmetric and transitive binary relation... | {
"timestamp": "2018-11-28T02:13:34",
"yymm": "1706",
"arxiv_id": "1706.03386",
"language": "en",
"url": "https://arxiv.org/abs/1706.03386",
"abstract": "We enumerate total cyclic orders on $\\left\\{1,\\ldots,n\\right\\}$ where we prescribe the relative cyclic order of consecutive triples $(i,{i+1},{i+2})$... |
https://arxiv.org/abs/0907.4652 | The stability of the Kronecker products of Schur functions | In the late 1930's Murnaghan discovered the existence of a stabilization phenomenon for the Kronecker product of Schur functions. For n sufficiently large, the values of the Kronecker coefficients appearing in the product of two Schur functions of degree n do not depend on the first part of the indexing partitions, but... | \section*{Introduction}
The understanding of the \emph{Kronecker coefficients of the symmetric group} (the multiplicities appearing when the tensor product of two irreducible representations of the symmetric group is decomposed into irreducibles; equivalently, the structural constants for the Kronecker product of symm... | {
"timestamp": "2009-08-06T23:45:09",
"yymm": "0907",
"arxiv_id": "0907.4652",
"language": "en",
"url": "https://arxiv.org/abs/0907.4652",
"abstract": "In the late 1930's Murnaghan discovered the existence of a stabilization phenomenon for the Kronecker product of Schur functions. For n sufficiently large, ... |
https://arxiv.org/abs/1902.03313 | Quasi-optimal and pressure robust discretizations of the Stokes equations by new augmented Lagrangian formulations | We approximate the solution of the stationary Stokes equations with various conforming and nonconforming inf-sup stable pairs of finite element spaces on simplicial meshes. Based on each pair, we design a discretization that is quasi-optimal and pressure robust, in the sense that the velocity $H^1$-error is proportiona... | \section{Introduction}
\label{S:introduction}
We consider the discretization of the stationary Stokes equations
\begin{equation}
\label{Stokes-strong}
-\mu \Lapl u + \Grad p = f
\quad \text{and} \quad
\Div u = 0
\quad \text{in } \Omega,
\qquad
u = 0
\quad \text{on } \partial \Omega
\end{equation}
with viscosity $\m... | {
"timestamp": "2019-02-12T02:03:17",
"yymm": "1902",
"arxiv_id": "1902.03313",
"language": "en",
"url": "https://arxiv.org/abs/1902.03313",
"abstract": "We approximate the solution of the stationary Stokes equations with various conforming and nonconforming inf-sup stable pairs of finite element spaces on ... |
https://arxiv.org/abs/math/9512204 | On isometric reflexions in Banach spaces | We obtain the following characterization of Hilbert spaces. Let $E$ be a Banach space whose unit sphere $S$ has a hyperplane of symmetry. Then $E$ is a Hilbert space iff any of the following two conditions is fulfilled: a) the isometry group ${\rm Iso}\, E$ of $E$ has a dense orbit in S; b) the identity component $G_0$... | \section*{INTRODUCTION}
Let $E$ be a real Banach space, $S=S(E)$ the unit sphere in $E$, ${\rm Iso}\,
E$ the isometry group of $E$ endowed with the strong operator topology, and
$G_0 = G_0(E)$ the identity component of ${\rm Iso}\, E$. {\it A reflexion} in
$E$ is an operator of the form $s_{e, e^*} = 1_E - 2e^* \otime... | {
"timestamp": "1998-03-31T20:24:39",
"yymm": "9512",
"arxiv_id": "math/9512204",
"language": "en",
"url": "https://arxiv.org/abs/math/9512204",
"abstract": "We obtain the following characterization of Hilbert spaces. Let $E$ be a Banach space whose unit sphere $S$ has a hyperplane of symmetry. Then $E$ is ... |
https://arxiv.org/abs/1804.03177 | Independence algebras, basis algebras and the distributivity condition | Stable basis algebras were introduced by Fountain and Gould and developed in a series of articles. They form a class of universal algebras, extending that of independence algebras. If a stable basis algebra $\mathbb{B}$ of finite rank satisfies the distributivity condition (a condition satisfied by all the previously k... | \section{Introduction and Preliminaries}\label{sec:intro}
The second author introduced the study of the endomorphism monoids of universal algebras called {\em $v^*$-algebras}, which she named {\em independence algebras}.
These algebras appear first in an article of
Narkiewicz \cite{nar} and were inspired by Marczew... | {
"timestamp": "2019-08-28T02:09:12",
"yymm": "1804",
"arxiv_id": "1804.03177",
"language": "en",
"url": "https://arxiv.org/abs/1804.03177",
"abstract": "Stable basis algebras were introduced by Fountain and Gould and developed in a series of articles. They form a class of universal algebras, extending that... |
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