url stringlengths 31 38 | title stringlengths 7 229 | abstract stringlengths 44 2.87k | text stringlengths 319 2.51M | meta dict |
|---|---|---|---|---|
https://arxiv.org/abs/1710.01845 | Exponential convergence rate of ruin probabilities for level-dependent Lévy-driven risk processes | We explicitly find the rate of exponential long-term convergence for the ruin probability in a level-dependent Lévy-driven risk model, as time goes to infinity. Siegmund duality allows to reduce the pro blem to long-term convergence of a reflected jump-diffusion to its stationary distribution, which is handled via Lyap... | \section{Introduction}
A non-life insurance company holds at time $t=0$ an initial capital $u = X(0)\geq0$, collects premiums at a rate $p(x)>0$ depending on the current level of the capital $X(t)=x$, and pays from time to time a compensation (when a claim is filed). The aggregated size of claims up to time $t>0$ is m... | {
"timestamp": "2018-07-02T02:04:59",
"yymm": "1710",
"arxiv_id": "1710.01845",
"language": "en",
"url": "https://arxiv.org/abs/1710.01845",
"abstract": "We explicitly find the rate of exponential long-term convergence for the ruin probability in a level-dependent Lévy-driven risk model, as time goes to inf... |
https://arxiv.org/abs/0802.2329 | Hilbert functions of multigraded algebras, mixed multiplicities of ideals and their applications | This paper is a survey on major results on Hilbert functions of multigraded algebras and mixed multiplicities of ideals, including their applications to the computation of Milnor numbers of complex analytic hypersurfaces with isolated singularity, multiplicities of blowup algebras and mixed volumes of polytopes. | \section{Introduction}
Let $R=\bigoplus_{t=0}^\infty R_t$ be a
Noetherian graded algebra over a field $k$. Then $R_t$ is a finite dimensional
$k$-vector space. In his historic paper, \cite{hi1} Hilbert considered
the generating function
$$H(R,z):=\sum_{t=0}^\infty H_R(t)z^t$$
of the sequence $H_R(t):=\dim_kR_t.$... | {
"timestamp": "2008-02-17T04:07:34",
"yymm": "0802",
"arxiv_id": "0802.2329",
"language": "en",
"url": "https://arxiv.org/abs/0802.2329",
"abstract": "This paper is a survey on major results on Hilbert functions of multigraded algebras and mixed multiplicities of ideals, including their applications to the... |
https://arxiv.org/abs/1508.03699 | On the structure of braid groups on complexes | We consider the braid groups $\mathbf{B}_n(X)$ on finite simplicial complexes $X$, which are generalizations of those on both manifolds and graphs that have been studied already by many authors. We figure out the relationships between geometric decompositions for $X$ and their effects on braid groups, and provide an al... | \section{Introduction}
The braid group $\mathbf{B}_n(D^2)$ on a 2-disk $D^2$ was firstly introduced by E.~Artin in 1920's, and Fox and Neuwirth generalized it to braid groups $\mathbf{B}_n(X)$ on arbitrary topological spaces $X$ via {\em configuration spaces}, which are defined as follows. For a compact, connected top... | {
"timestamp": "2015-08-18T02:02:07",
"yymm": "1508",
"arxiv_id": "1508.03699",
"language": "en",
"url": "https://arxiv.org/abs/1508.03699",
"abstract": "We consider the braid groups $\\mathbf{B}_n(X)$ on finite simplicial complexes $X$, which are generalizations of those on both manifolds and graphs that h... |
https://arxiv.org/abs/1503.06789 | The Liouville theorem as a problem of common eigenfunctions | It is shown that, by appropriately defining the eigenfunctions of a function defined on the extended phase space, the Liouville theorem on solutions of the Hamilton--Jacobi equation can be formulated as the problem of finding common eigenfunctions of $n$ constants of motion in involution, where $n$ is the number of deg... | \section{Introduction}
In the framework of the Hamiltonian formulation of classical mechanics, the Liouville theorem asserts that, for a mechanical system with $n$ degrees of freedom, if we have $n$ constants of motion in involution, $F_{1}, F_{2}, \ldots, F_{n}$ (that is, $\{ F_{i}, F_{j} \} = 0$ for $i, j = 1, 2, \l... | {
"timestamp": "2015-03-25T01:00:21",
"yymm": "1503",
"arxiv_id": "1503.06789",
"language": "en",
"url": "https://arxiv.org/abs/1503.06789",
"abstract": "It is shown that, by appropriately defining the eigenfunctions of a function defined on the extended phase space, the Liouville theorem on solutions of th... |
https://arxiv.org/abs/2007.02524 | The moduli space of stable rank 2 parabolic bundles over an elliptic curve with 3 marked points | We explicitly describe the moduli space $M^s(X,3)$ of stable rank 2 parabolic bundles over an elliptic curve $X$ with trivial determinant bundle and 3 marked points. Specifically, we exhibit $M^s(X,3)$ as a blow-up of an embedded elliptic curve in $(\mathbb{CP}^1)^3$. The moduli space $M^s(X,3)$ can also be interpreted... | \section{Introduction}
Given a curve $C$, one can define a moduli space $M^s(C,n)$ of stable
rank 2 parabolic bundles over $C$ with trivial determinant bundle and
$n$ marked points.
The space $M^s(C,n)$ has the structure of a smooth complex
manifold of dimension $3(g-1) + n$, where $g$ is the genus of the curve $C$.
I... | {
"timestamp": "2020-07-07T02:22:48",
"yymm": "2007",
"arxiv_id": "2007.02524",
"language": "en",
"url": "https://arxiv.org/abs/2007.02524",
"abstract": "We explicitly describe the moduli space $M^s(X,3)$ of stable rank 2 parabolic bundles over an elliptic curve $X$ with trivial determinant bundle and 3 mar... |
https://arxiv.org/abs/1711.11285 | A characterization of Zoll Riemannian metrics on the 2-sphere | The simple length spectrum of a Riemannian manifold is the set of lengths of its simple closed geodesics. We prove a theorem claimed by Lusternik: in any Riemannian 2-sphere whose simple length spectrum consists of only one element L, any geodesic is simple closed with length L. | \section{Introduction}
A remarkable class of closed Riemannian manifolds is given by those all of whose geodesics are closed. A detailed account of the state of the art of the research on this subject up to the late 1970s is contained in the celebrated monograph of Besse \cite{Besse:1978pr}, while for more recent resu... | {
"timestamp": "2018-08-28T02:03:49",
"yymm": "1711",
"arxiv_id": "1711.11285",
"language": "en",
"url": "https://arxiv.org/abs/1711.11285",
"abstract": "The simple length spectrum of a Riemannian manifold is the set of lengths of its simple closed geodesics. We prove a theorem claimed by Lusternik: in any ... |
https://arxiv.org/abs/1610.03523 | Noncommutative potential theory | We propose to view hermitian metrics on trivial holomorphic vector bundles $E\to\Omega$ as noncommutative analogs of functions defined on the base $\Omega$, and curvature as the notion corresponding to the Laplace operator or $\partial\overline\partial$. We discuss noncommutative generalizations of basic results of ord... | \section{Introduction}
Traditional potential theory is the study of the Laplace operator, harmonic and subharmonic functions, and related notions.
The Laplacian, while an analytic object, has geometric content as well:\ the curvature of a holomorphic line bundle over a Riemann surface is expressed through it.
By nonco... | {
"timestamp": "2016-10-13T02:00:45",
"yymm": "1610",
"arxiv_id": "1610.03523",
"language": "en",
"url": "https://arxiv.org/abs/1610.03523",
"abstract": "We propose to view hermitian metrics on trivial holomorphic vector bundles $E\\to\\Omega$ as noncommutative analogs of functions defined on the base $\\Om... |
https://arxiv.org/abs/1507.02173 | On Integer Additive Set-Filtered Graphs | Let $\mathbb{N}_0$ denote the set of all non-negative integers and $\mathcal{P}(\mathbb{N}_0)$ be its power set. An integer additive set-labeling (IASL) of a graph $G$ is an injective function $f:V(G)\to \mathcal{P}(\mathbb{N}_0)$ such that the induced function $f^+:E(G) \to \mathcal{P}(\mathbb{N}_0)$ is defined by $f^... | \section{Introduction}
For all terms and definitions, not defined specifically in this paper, we refer to \cite{BM} and \cite{FH} and \cite{DBW}. Unless mentioned otherwise, all graphs considered here are simple, finite and have no isolated vertices.
The {\em sumset} of two non-empty sets $A$ and $B$, denoted b... | {
"timestamp": "2015-07-09T02:10:17",
"yymm": "1507",
"arxiv_id": "1507.02173",
"language": "en",
"url": "https://arxiv.org/abs/1507.02173",
"abstract": "Let $\\mathbb{N}_0$ denote the set of all non-negative integers and $\\mathcal{P}(\\mathbb{N}_0)$ be its power set. An integer additive set-labeling (IASL... |
https://arxiv.org/abs/1710.07634 | Fractional Newton-Raphson Method | The Newton-Raphson (N-R) method is useful to find the roots of a polynomial of degree n. However, this method is limited since it diverges for the case in which polynomials only have complex roots if a real initial condition is taken. In the present work, we explain an iterative method that is created using the fractio... | \section{Newton-Raphson Method}
For the one-dimensional case the N-R method is one of the most used methods to find the roots $x_*$ of a function $f:\nset{R} \to \nset{R} $, with $f\in C^2(\nset{R})$, $i.e.$, $\set{x_*\in \nset{R} \ : \ f(x_*)=0}$, this due to its easy implementation and its rapid convergence. The N-R... | {
"timestamp": "2019-05-07T02:14:51",
"yymm": "1710",
"arxiv_id": "1710.07634",
"language": "en",
"url": "https://arxiv.org/abs/1710.07634",
"abstract": "The Newton-Raphson (N-R) method is useful to find the roots of a polynomial of degree n. However, this method is limited since it diverges for the case in... |
https://arxiv.org/abs/1408.2277 | Some properties of a Rudin-Shapiro-like sequence | We introduce the sequence $(i_n)_{n \geq 0}$ defined by $i_n = (-1)^{inv_2(n)}$, where $inv_2(n)$ denotes the number of inversions (i.e., occurrences of 10 as a scattered subsequence) in the binary representation of n. We show that this sequence has many similarities to the classical Rudin-Shapiro sequence. In particul... | \section{Introduction}
Loosely speaking, a \emph{digital sequence} is a sequence whose $n$-th
term is defined based on some property of the digits of $n$ when
written in some chosen base. The prototypical digital sequence is the
\emph{sum-of-digits function} $s_k(n)$, which is equal to the sum of
the digits of the bas... | {
"timestamp": "2014-08-12T02:10:08",
"yymm": "1408",
"arxiv_id": "1408.2277",
"language": "en",
"url": "https://arxiv.org/abs/1408.2277",
"abstract": "We introduce the sequence $(i_n)_{n \\geq 0}$ defined by $i_n = (-1)^{inv_2(n)}$, where $inv_2(n)$ denotes the number of inversions (i.e., occurrences of 10... |
https://arxiv.org/abs/1409.3475 | Piecewise straightening and Lipschitz simplicial volume | We study the Lipschitz simplicial volume, which is a metric version of the simplicial volume. We introduce the piecewise straightening procedure for singular chains, which allows us to generalize the proportionality principle and the product inequality to the case of complete Riemannian manifolds of finite volume with ... | \section{Introduction}
The simplicial volume is a homotopy invariant of manifolds defined for a closed manifold $M$ as
$$
\|M\| :=inf\{|c|_1\::\: \text{$c$ is a fundamental cycle with $\mathbb{R}$ coefficients}\},
$$
where $|\cdot|_1$ is an $\ell^1$-norm on $C_*(M,\mathbb{R})$ (which we will denote for simplicity as $C... | {
"timestamp": "2015-02-17T02:18:16",
"yymm": "1409",
"arxiv_id": "1409.3475",
"language": "en",
"url": "https://arxiv.org/abs/1409.3475",
"abstract": "We study the Lipschitz simplicial volume, which is a metric version of the simplicial volume. We introduce the piecewise straightening procedure for singula... |
https://arxiv.org/abs/1301.4630 | The vanishing ideal of a finite set of points with multiplicity structures | Given a finite set of arbitrarily distributed points in affine space with arbitrary multiplicity structures, we present an algorithm to compute the reduced Groebner basis of the vanishing ideal under the lexicographic ordering. Our method discloses the essential geometric connection between the relative position of the... | \section{Introduction}
To describe the problem, first we give the definitions below.
{\bfseries Definition 1:} $D\subseteq \mathbb{N}_{0}^{n}$ is called
a lower set as long as $\forall d\in D$ if $d_{i}\neq 0$, $d-e_{i}$ lies in $D$ where $e_{i}=(0, \ldots, 0, 1, 0,
\ldots, 0)$ with the 1 situated at the $i$-th posit... | {
"timestamp": "2013-01-22T02:01:30",
"yymm": "1301",
"arxiv_id": "1301.4630",
"language": "en",
"url": "https://arxiv.org/abs/1301.4630",
"abstract": "Given a finite set of arbitrarily distributed points in affine space with arbitrary multiplicity structures, we present an algorithm to compute the reduced ... |
https://arxiv.org/abs/2110.09190 | Secure domination number of $k$-subdivision of graphs | Let $G=(V,E)$ be a simple graph. A dominating set of $G$ is a subset $D\subseteq V$ such that every vertex not in $D$ is adjacent to at least one vertex in $D$. The cardinality of a smallest dominating set of $G$, denoted by $\gamma(G)$, is the domination number of $G$. A dominating set $D$ is called a secure dominatin... | \section{Introduction}
Let $G = (V,E)$ be a simple graph with $n$ vertices. Throughout this paper we consider only simple graphs. A set $D\subseteq V(G)$ is a dominating set if every vertex in $V(G)- D$ is adjacent to at least one vertex in $D$.
The domination number $\gamma(G)$ is the minimum cardinality of a domi... | {
"timestamp": "2021-10-19T02:34:49",
"yymm": "2110",
"arxiv_id": "2110.09190",
"language": "en",
"url": "https://arxiv.org/abs/2110.09190",
"abstract": "Let $G=(V,E)$ be a simple graph. A dominating set of $G$ is a subset $D\\subseteq V$ such that every vertex not in $D$ is adjacent to at least one vertex ... |
https://arxiv.org/abs/1706.01367 | Symmetric cohomology of groups | We investigate the relationship between the symmetric, exterior and classical cohomologies of groups. The first two theories were introduced respectively by Staic and Zarelua. We show in particular, that there is a map from exterior cohomology to symmetric cohomology which is a split monomorphism in general and an isom... | \section{Introduction}
Let $G$ be a group and $M$ be a $G$-module. In order to better understand 3-algebras arising in lattice field theory \cite{triangle}, Staic defined a variant of group cohomology, which he denoted by $HS^*(G,M)$ and called \emph{symmetric cohomology of groups} \cite{staic}. Some aspects of this t... | {
"timestamp": "2017-06-15T02:07:21",
"yymm": "1706",
"arxiv_id": "1706.01367",
"language": "en",
"url": "https://arxiv.org/abs/1706.01367",
"abstract": "We investigate the relationship between the symmetric, exterior and classical cohomologies of groups. The first two theories were introduced respectively ... |
https://arxiv.org/abs/1710.10065 | Further results on the $(b, c)$-inverse, the outer inverse $A^{(2)}_{T, S}$ and the Moore-Penrose inverse in the Banach context | In this article properties of the $(b, c)$-inverse, the inverse along an element, the outer inverse with prescribed range and null space $A^{(2)}_{T, S}$ and the Moore-Penrose inverse will be studied in the contexts of Banach spaces operators, Banach algebras and $C^*$-algebras. The main properties to be considered are... | \section{Introduction}
Recently two outer inverses have been introduced: the $(b, c)$-inverse and the inverse along an element, see \cite{D} and \cite{mary}, respectively.
These two inverses are related; in fact, the latter is a particular case of the former. It is worth noticing one of the main properties of these... | {
"timestamp": "2017-10-30T01:06:33",
"yymm": "1710",
"arxiv_id": "1710.10065",
"language": "en",
"url": "https://arxiv.org/abs/1710.10065",
"abstract": "In this article properties of the $(b, c)$-inverse, the inverse along an element, the outer inverse with prescribed range and null space $A^{(2)}_{T, S}$ ... |
https://arxiv.org/abs/2208.10223 | Boundary representations of mapping class groups | Let $S = S_g$ be a closed orientable surface of genus $g \geq 2$ and $Mod(S)$ be the mapping class group of $S$. In this paper, we show that the boundary representation of $Mod(S)$ is ergodic using statistical hyperbolicity, which generalizes the classical result of Masur on ergodicity of the action of $Mod(S)$ on the ... | \section{Introduction}
\noindent Let $S = S_{g}$ be a closed, connected, orientable surface of genus $g$. Recall that the mapping class group $\M(S)$ of $S$ is defined to be the group of isotopy classes of orientation-preserving homeomorphisms of $S$. Throughout this paper, the genus $g$ is assumed to be at least $2$. ... | {
"timestamp": "2022-08-23T02:26:01",
"yymm": "2208",
"arxiv_id": "2208.10223",
"language": "en",
"url": "https://arxiv.org/abs/2208.10223",
"abstract": "Let $S = S_g$ be a closed orientable surface of genus $g \\geq 2$ and $Mod(S)$ be the mapping class group of $S$. In this paper, we show that the boundary... |
https://arxiv.org/abs/1207.4556 | Refined Quicksort asymptotics | The complexity of the Quicksort algorithm is usually measured by the number of key comparisons used during its execution. When operating on a list of $n$ data, permuted uniformly at random, the appropriately normalized complexity $Y_n$ is known to converge almost surely to a non-degenerate random limit $Y$. This assume... | \section{Introduction and result}
Quicksort, invented by Hoare \cite{Ho62}, is one of the most
widely used algorithms for sorting. Given a list $\Gamma=(u_1,\ldots,u_n)\in\Rset^n$, Quicksort starts picking a key (i.e., an element), say the first one $u_1$, as ``pivot'' element. The other keys in $\Gamma$ are then p... | {
"timestamp": "2013-01-25T02:01:38",
"yymm": "1207",
"arxiv_id": "1207.4556",
"language": "en",
"url": "https://arxiv.org/abs/1207.4556",
"abstract": "The complexity of the Quicksort algorithm is usually measured by the number of key comparisons used during its execution. When operating on a list of $n$ da... |
https://arxiv.org/abs/1411.0537 | Toric graph associahedra and compactifications of $M_{0,n}$ | To any graph $G$ one can associate a toric variety $X(\mathcal{P}G)$, obtained as a blowup of projective space along coordinate subspaces corresponding to connected subgraphs of $G$. The polytope of this toric variety is the graph associahedron of $G$, a class of polytopes that includes the permutohedron, associahedron... | \section{Introduction}
In this note, we study the relationship between two families of blowups of projective space. The first is given by Hassett's spaces of weighted pointed stable rational curves~\cite{Has03}. The second is a family of toric varieties built as blowups of projective space, from polytopes known as \te... | {
"timestamp": "2015-08-14T02:10:53",
"yymm": "1411",
"arxiv_id": "1411.0537",
"language": "en",
"url": "https://arxiv.org/abs/1411.0537",
"abstract": "To any graph $G$ one can associate a toric variety $X(\\mathcal{P}G)$, obtained as a blowup of projective space along coordinate subspaces corresponding to ... |
https://arxiv.org/abs/math/0603106 | Lattice Grids and Prisms are Antimagic | An \emph{antimagic labeling} of a finite undirected simple graph with $m$ edges and $n$ vertices is a bijection from the set of edges to the integers $1,...,m$ such that all $n$ vertex sums are pairwise distinct, where a vertex sum is the sum of labels of all edges incident with the same vertex. A graph is called \emph... | \section{Introduction}
All graphs in this paper are finite, undirected and simple. In 1990,
Hartsfield and Ringel \cite{HaRi} introduced the concept of
\emph{antimagic} graph. An \emph{antimagic labeling} of a graph with $m$ edges and
$n$ vertices is a bijection from the set of edges to the integers
$1,\ldots,m$ such t... | {
"timestamp": "2006-03-04T02:26:26",
"yymm": "0603",
"arxiv_id": "math/0603106",
"language": "en",
"url": "https://arxiv.org/abs/math/0603106",
"abstract": "An \\emph{antimagic labeling} of a finite undirected simple graph with $m$ edges and $n$ vertices is a bijection from the set of edges to the integers... |
https://arxiv.org/abs/2202.09983 | Chaos for foliated spaces and pseudogroups | We generalize "sensitivity to initial conditions" to foliated spaces and pseudogroups, offering a definition of Devaney chaos in this setting. In contrast to the case of group actions, where sensitivity follows from the other two conditions of Devaney chaos, we show that this is true only for compact foliated spaces, e... | \section{Introduction}
There are several definitions of chaos for dynamical systems (Li-Yorke chaos, positive entropy, ...), but in this article we will consider only Devaney's, first introduced in~\cite{Devaney}.
\begin{definition}[Devaney chaos] \label{d:dev}
A continuous map $f\colon X\to X$ on a metric space $(... | {
"timestamp": "2022-02-23T02:13:41",
"yymm": "2202",
"arxiv_id": "2202.09983",
"language": "en",
"url": "https://arxiv.org/abs/2202.09983",
"abstract": "We generalize \"sensitivity to initial conditions\" to foliated spaces and pseudogroups, offering a definition of Devaney chaos in this setting. In contra... |
https://arxiv.org/abs/math/0701113 | Hardy-type Inequalities Via Auxiliary Sequences | We prove some Hardy-type inequalities via an approach that involves constructing auxiliary sequences. | \section{Introduction}
\label{sec 1} \setcounter{equation}{0}
Suppose throughout that $p\neq 0, \frac{1}{p}+\frac{1}{q}=1$.
Let $l^p$ be the Banach space of all complex sequences ${\bf a}=(a_n)_{n \geq 1}$ with norm
\begin{equation*}
||{\bf a}||: =(\sum_{n=1}^{\infty}|a_n|^p)^{1/p} < \infty.
\end{equation*}
... | {
"timestamp": "2007-05-25T05:29:35",
"yymm": "0701",
"arxiv_id": "math/0701113",
"language": "en",
"url": "https://arxiv.org/abs/math/0701113",
"abstract": "We prove some Hardy-type inequalities via an approach that involves constructing auxiliary sequences.",
"subjects": "Classical Analysis and ODEs (ma... |
https://arxiv.org/abs/1907.06233 | Pointwise adaptive kernel density estimation under local approximate differential privacy | We consider non-parametric density estimation in the framework of local approximate differential privacy. In contrast to centralized privacy scenarios with a trusted curator, in the local setup anonymization must be guaranteed already on the individual data owners' side and therefore must precede any data mining tasks.... | \section{Introduction}
In the modern information era data are routinely collected in all areas of private and public life.
Although the availability of massive data sets is essential to answer important scientific and societal questions, the individual data owners (who may be individuals, households, research institut... | {
"timestamp": "2019-07-16T02:16:37",
"yymm": "1907",
"arxiv_id": "1907.06233",
"language": "en",
"url": "https://arxiv.org/abs/1907.06233",
"abstract": "We consider non-parametric density estimation in the framework of local approximate differential privacy. In contrast to centralized privacy scenarios wit... |
https://arxiv.org/abs/2205.14314 | On a singular limit of the Kobayashi--Warren--Carter energy | By introducing a new topology, a representation formula of the Gamma limit of the Kobayashi-Warren-Carter energy is given in a multi-dimensional domain. A key step is to study the Gamma limit of a single-well Modica-Mortola functional. The convergence introduced here is called the sliced graph convergence, which is fin... | \section{Introduction} \label{S1}
We consider the Kobayashi--Warren--Carter energy, which is a sum of a weighted total variation and a single-well Modica--Mortola energy.
Their explicit forms are
\begin{align}
E^\varepsilon_\mathrm{KWC}(u,v) &:= \int_\Omega \alpha(v)|Du|
+ E^\varepsilon_\mathrm{sMM}(v), \label{eq:... | {
"timestamp": "2022-05-31T02:05:22",
"yymm": "2205",
"arxiv_id": "2205.14314",
"language": "en",
"url": "https://arxiv.org/abs/2205.14314",
"abstract": "By introducing a new topology, a representation formula of the Gamma limit of the Kobayashi-Warren-Carter energy is given in a multi-dimensional domain. A... |
https://arxiv.org/abs/1805.02210 | Formal factorization of higher order irregular linear differential operators | We study the problem of decomposition (non-commutative factorization) of linear ordinary differential operators near an irregular singular point. The solution (given in terms of the Newton diagram and the respective characteristic numbers) is known for quite some time, though the proofs are rather involved.We suggest a... | \section{Introduction}
The local theory of linear ordinary differential equations exists in two closely related but different flavors. First, one can consider systems of first order linear equations near a singular point. Such systems form an infinite-dimensional space on which several groups of gauge transformation... | {
"timestamp": "2018-05-08T02:11:45",
"yymm": "1805",
"arxiv_id": "1805.02210",
"language": "en",
"url": "https://arxiv.org/abs/1805.02210",
"abstract": "We study the problem of decomposition (non-commutative factorization) of linear ordinary differential operators near an irregular singular point. The solu... |
https://arxiv.org/abs/2206.11651 | Attractor separation and signed cycles in asynchronous Boolean networks | The structure of the graph defined by the interactions in a Boolean network can determine properties of the asymptotic dynamics. For instance, considering the asynchronous dynamics, the absence of positive cycles guarantees the existence of a unique attractor, and the absence of negative cycles ensures that all attract... |
\section{Introduction}
A \EM{Boolean network} (BN) is a finite dynamical system usually defined by a function
\[
f:\{0,1\}^n\to\{0,1\}^n,\qquad x=(x_1,\dots,x_n)\mapsto f(x)=(f_1(x),\dots,f_n(x)).
\]
BNs have many applications. In particular, since the seminal papers of McCulloch and Pitts \cite{MP43}, Hopfield \c... | {
"timestamp": "2022-06-24T02:15:27",
"yymm": "2206",
"arxiv_id": "2206.11651",
"language": "en",
"url": "https://arxiv.org/abs/2206.11651",
"abstract": "The structure of the graph defined by the interactions in a Boolean network can determine properties of the asymptotic dynamics. For instance, considering... |
https://arxiv.org/abs/1701.06377 | Counting Arithmetical Structures on Paths and Cycles | Let $G$ be a finite, simple, connected graph. An arithmetical structure on $G$ is a pair of positive integer vectors $\mathbf{d},\mathbf{r}$ such that $(\mathrm{diag}(\mathbf{d})-A)\mathbf{r}=0$, where $A$ is the adjacency matrix of $G$. We investigate the combinatorics of arithmetical structures on path and cycle grap... | \section{Introduction}\label{sec:intro}
This paper is about the combinatorics of arithmetical structures on path and cycle graphs. We begin by recalling some basic facts about graphs, Laplacians, and critical groups.
Let $G$ be a finite, connected graph with $n\geq 2$ vertices, let $A$ be its adjacency matrix, and l... | {
"timestamp": "2018-07-25T02:03:20",
"yymm": "1701",
"arxiv_id": "1701.06377",
"language": "en",
"url": "https://arxiv.org/abs/1701.06377",
"abstract": "Let $G$ be a finite, simple, connected graph. An arithmetical structure on $G$ is a pair of positive integer vectors $\\mathbf{d},\\mathbf{r}$ such that $... |
https://arxiv.org/abs/2106.00380 | The influence of the symmetry of identical particles on flight times | In this work, our purpose is to show how the symmetry of identical particles can influence the time evolution of free particles in the nonrelativistic and relativistic domains. For this goal, we consider a system of either two distinguishable or indistinguishable (bosons and fermions) particles. Two classes of initial ... | \section{Introduction}
It is well understood that the symmetry of indistinguishable particles has a
profound influence on their dynamics. A feature which is well documented is
the ``bunching" of bosons \cite{brown1956,jeltes2007} and ``anti-bunching" of
fermions \cite{henny1999,oliver1999,kiesel2002,ianuzzi2006,rom200... | {
"timestamp": "2021-06-02T02:19:26",
"yymm": "2106",
"arxiv_id": "2106.00380",
"language": "en",
"url": "https://arxiv.org/abs/2106.00380",
"abstract": "In this work, our purpose is to show how the symmetry of identical particles can influence the time evolution of free particles in the nonrelativistic and... |
https://arxiv.org/abs/0707.1357 | Calculations of canonical averages from the grand canonical ensemble | Grand canonical and canonical ensembles become equivalent in the thermodynamic limit, but when the system size is finite the results obtained in the two ensembles deviate from each other. In many important cases, the canonical ensemble provides an appropriate physical description but it is often much easier to perform ... | \section{Introduction}
Whenever we need to work with a system of many quantum particles
it is much easier to perform the calculation in the grand canonical ensemble
than the corresponding calculations in the canonical ensemble.
For example, the calculations of the grand canonical partition function for ideal gas of
fer... | {
"timestamp": "2008-02-04T00:34:38",
"yymm": "0707",
"arxiv_id": "0707.1357",
"language": "en",
"url": "https://arxiv.org/abs/0707.1357",
"abstract": "Grand canonical and canonical ensembles become equivalent in the thermodynamic limit, but when the system size is finite the results obtained in the two ens... |
https://arxiv.org/abs/1008.1458 | The index quasi-periodicity and multiplicity of closed geodesics | In this paper, we prove the existence of at least two distinct closed geodesics on every compact simply connected irreversible or reversible Finsler (including Riemannian) manifold of dimension not less than 2. | \section{Introduction and main results
The closed geodesic problem is a traditional and active topic in dynamical
systems and differential geometry for more than one hundred years.
Studies of closed geodesics can be traced back to J. Jacobi, J. Hadamard,
H. Poincar\'e, G. D. Birkhoff, M. Morse, L. Lyusternik and Schn... | {
"timestamp": "2010-08-24T02:01:38",
"yymm": "1008",
"arxiv_id": "1008.1458",
"language": "en",
"url": "https://arxiv.org/abs/1008.1458",
"abstract": "In this paper, we prove the existence of at least two distinct closed geodesics on every compact simply connected irreversible or reversible Finsler (includ... |
https://arxiv.org/abs/1411.2023 | Schrödinger spectrum generated by the Cornell potential | The eigenvalues $E_{n\ell}^d(a,c)$ of the $d$-dimensional Schrödinger equation with the Cornell potential $V(r)=-a/r+c\,r$, $a,c>0$ are analyzed by means of the envelope method and the asymptotic iteration method (AIM). Scaling arguments show that it is sufficient to know $E(1,\lambda)$, and the envelope method provide... | \section{Introduction}\label{intro}
\noindent The Schr\"dinger equation with the Cornell potential is an important non-relativistic model for the study of quark-antiquark systems \cite{alford,chung, claudio,eichten,eichten1978,eichten1980, evans,chen,hamz}. For example, it is used in describing the masses and decay wi... | {
"timestamp": "2014-11-10T02:12:58",
"yymm": "1411",
"arxiv_id": "1411.2023",
"language": "en",
"url": "https://arxiv.org/abs/1411.2023",
"abstract": "The eigenvalues $E_{n\\ell}^d(a,c)$ of the $d$-dimensional Schrödinger equation with the Cornell potential $V(r)=-a/r+c\\,r$, $a,c>0$ are analyzed by means ... |
https://arxiv.org/abs/math/0501305 | On Aumann's Theorem that the sphere does not admit a mean | We prove that the circle S_1 does not have a 2-mean, i.e., S_1 times S_1 cannot have a retraction r onto its diagonal with r(x,y) = r(y,x), whenever x,y in S_1. Our proof is combinatorial and topological rather than analytical. | \section{Introduction}
{\sc Aumann} and {\sc Caratheodory} \cite{AuCa34}, \cite{Au35} and
\cite{Au43} were among the pioneers who first considered the question
about the structure of spaces for which the topological product $X^n$ has
a symmetric retraction onto its diagonal, \ie \ {\em a $n$-mean}. They
studied such o... | {
"timestamp": "2005-01-19T23:07:29",
"yymm": "0501",
"arxiv_id": "math/0501305",
"language": "en",
"url": "https://arxiv.org/abs/math/0501305",
"abstract": "We prove that the circle S_1 does not have a 2-mean, i.e., S_1 times S_1 cannot have a retraction r onto its diagonal with r(x,y) = r(y,x), whenever x... |
https://arxiv.org/abs/1609.08121 | Improving the Randomization Step in Feasibility Pump | Feasibility pump (FP) is a successful primal heuristic for mixed-integer linear programs (MILP). The algorithm consists of three main components: rounding fractional solution to a mixed-integer one, projection of infeasible solutions to the LP relaxation, and a randomization step used when the algorithm stalls. While m... | \section{Introduction}
Primal heuristics are used within mixed-integer linear programming (MILP) solvers for finding good integer feasible solutions quickly~\cite{lodiF:2011}. \emph{Feasibility pump} (FP) is a very successful primal heuristic for mixed-binary LPs that was introduced in~\cite{FischettiGL05}. At its cor... | {
"timestamp": "2016-09-27T02:12:49",
"yymm": "1609",
"arxiv_id": "1609.08121",
"language": "en",
"url": "https://arxiv.org/abs/1609.08121",
"abstract": "Feasibility pump (FP) is a successful primal heuristic for mixed-integer linear programs (MILP). The algorithm consists of three main components: rounding... |
https://arxiv.org/abs/1304.5010 | Small-Bias Sets for Nonabelian Groups: Derandomizing the Alon-Roichman Theorem | In analogy with epsilon-biased sets over Z_2^n, we construct explicit epsilon-biased sets over nonabelian finite groups G. That is, we find sets S subset G such that | Exp_{x in S} rho(x)| <= epsilon for any nontrivial irreducible representation rho. Equivalently, such sets make G's Cayley graph an expander with eigenv... | \section{Introduction}
Small-bias sets are useful combinatorial objects for derandomization,
and are particularly well-studied over the Boolean hypercube $\{0,1\}^n$. Specifically, if we identify the hypercube with the group ${\mathbb{Z}}_2^n$, then a \emph{character} $\chi$ is a homomorphism from ${\mathbb{Z}}_2^n$ ... | {
"timestamp": "2013-05-01T02:03:15",
"yymm": "1304",
"arxiv_id": "1304.5010",
"language": "en",
"url": "https://arxiv.org/abs/1304.5010",
"abstract": "In analogy with epsilon-biased sets over Z_2^n, we construct explicit epsilon-biased sets over nonabelian finite groups G. That is, we find sets S subset G ... |
https://arxiv.org/abs/1903.05548 | Schubert polynomials as projections of Minkowski sums of Gelfand-Tsetlin polytopes | Gelfand-Tsetlin polytopes are classical objects in algebraic combinatorics arising in the representation theory of $\mathfrak{gl}_n(\mathbb{C})$. The integer point transform of the Gelfand-Tsetlin polytope $\mathrm{GT}(\lambda)$ projects to the Schur function $s_{\lambda}$. Schur functions form a distinguished basis of... | \section{Introduction}
\label{sec:intro}
Schubert polynomials, introduced by Lascoux and Sch\"utzenberger in 1982 \cite{LS}, are extensively studied in algebraic combinatorics \cite{BJS, FK1993, laddermoves, nilcoxeter, thomas, prismtableaux, lenart, manivel, multidegree, KM, sottile}. They represent cohomology cl... | {
"timestamp": "2019-03-28T01:00:46",
"yymm": "1903",
"arxiv_id": "1903.05548",
"language": "en",
"url": "https://arxiv.org/abs/1903.05548",
"abstract": "Gelfand-Tsetlin polytopes are classical objects in algebraic combinatorics arising in the representation theory of $\\mathfrak{gl}_n(\\mathbb{C})$. The in... |
https://arxiv.org/abs/1705.10293 | Solutions of the Schroedinger equation for piecewise harmonic potentials: remarks on the asymptotic behavior of the wave functions | We discuss the solutions of the Schroedinger equation for piecewise potentials, given by the harmonic oscillator potential for $\vert x\vert >a$ and an arbitrary function for $\vert x\vert <a$, using elementary methods. The study of this problem sheds light on usual errors when discussing the asymptotic behavior of the... | \section{Introduction}\label{sec:intro}
The Schroedinger equation for the linear harmonic oscillator reads
\begin{equation}
\frac{d^2\psi}{dz^2}+({\mathcal E}-\frac{z^2}{4})\psi=0\, ,
\label{Schroed}
\end{equation}
where $z=\sqrt{2 m \omega/\hbar}\, x$, $\mathcal{E}=E/(\hbar\omega)$, $x$ is the coordinate of the oscil... | {
"timestamp": "2017-05-30T02:12:25",
"yymm": "1705",
"arxiv_id": "1705.10293",
"language": "en",
"url": "https://arxiv.org/abs/1705.10293",
"abstract": "We discuss the solutions of the Schroedinger equation for piecewise potentials, given by the harmonic oscillator potential for $\\vert x\\vert >a$ and an ... |
https://arxiv.org/abs/1803.06376 | A Generalised Method for Empirical Game Theoretic Analysis | This paper provides theoretical bounds for empirical game theoretical analysis of complex multi-agent interactions. We provide insights in the empirical meta game showing that a Nash equilibrium of the meta-game is an approximate Nash equilibrium of the true underlying game. We investigate and show how many data sample... | \section{Conclusion}\label{sec:conclusions}
In this paper we have generalised the heuristic payoff table method introduced by Walsh et al. \cite{Walsh02} to two-population asymmetric games. We call such games \textit{meta-games} as they consider complex strategies instead of atomic actions as found in normal-form games... | {
"timestamp": "2018-03-20T01:01:11",
"yymm": "1803",
"arxiv_id": "1803.06376",
"language": "en",
"url": "https://arxiv.org/abs/1803.06376",
"abstract": "This paper provides theoretical bounds for empirical game theoretical analysis of complex multi-agent interactions. We provide insights in the empirical m... |
https://arxiv.org/abs/1705.02298 | Consistent Sensor, Relay, and Link Selection in Wireless Sensor Networks | In wireless sensor networks, where energy is scarce, it is inefficient to have all nodes active because they consume a non-negligible amount of battery. In this paper we consider the problem of jointly selecting sensors, relays and links in a wireless sensor network where the active sensors need to communicate their me... | \section{Convex relaxation}
\label{Convexrelaxation}
We relax the nonconvex program~\eqref{Problem.nonconvex} by substituting the $\ell_0$-pseudo norm, with the $\ell_1$ norm, and by substituting the nonconvex constraint~\eqref{eq.Tminw} with the convex surrogate
\begin{equation}\label{eq.Tminw_cvx}
T_{ip} \leq \min\{... | {
"timestamp": "2017-05-08T02:08:38",
"yymm": "1705",
"arxiv_id": "1705.02298",
"language": "en",
"url": "https://arxiv.org/abs/1705.02298",
"abstract": "In wireless sensor networks, where energy is scarce, it is inefficient to have all nodes active because they consume a non-negligible amount of battery. I... |
https://arxiv.org/abs/1808.07260 | On an improvement of LASSO by scaling | A sparse modeling is a major topic in machine learning and statistics. LASSO (Least Absolute Shrinkage and Selection Operator) is a popular sparse modeling method while it has been known to yield unexpected large bias especially at a sparse representation. There have been several studies for improving this problem such... | \section{}
\section{Introduction}
A sparse modeling is a major topic in machine learning and
statistics. Especially, LASSO (Least Absolute Shrinkage and Selection
Operator) is a popular method that has been extensively
studied\cite{LARS,KF2000,FL2001,LASSO,HZ2006,NM2007,ZHT2007}. LASSO is
an $\ell_1$ penalized least ... | {
"timestamp": "2018-08-23T02:06:19",
"yymm": "1808",
"arxiv_id": "1808.07260",
"language": "en",
"url": "https://arxiv.org/abs/1808.07260",
"abstract": "A sparse modeling is a major topic in machine learning and statistics. LASSO (Least Absolute Shrinkage and Selection Operator) is a popular sparse modelin... |
https://arxiv.org/abs/math/0703381 | Polynomial ideals and directed graphs | In this paper it is shown that it is possible to associate several polynomial ideals to a directed graph $D$ in order to find properties of it. In fact by using algebraic tools it is possible to give appropriate procedures for automatic reasoning on cycles and directed cycles of graphs. | \section{Introduction}
The aim of this paper is to study some problems in graph theory
with commutative algebra tools. Connections between simplicial
complexes and polynomial
rings were first studied in ( \cite{Sta96}). There were also studies on the
connections between ideals and undirected graphs, as in Simis, V... | {
"timestamp": "2007-03-13T16:48:23",
"yymm": "0703",
"arxiv_id": "math/0703381",
"language": "en",
"url": "https://arxiv.org/abs/math/0703381",
"abstract": "In this paper it is shown that it is possible to associate several polynomial ideals to a directed graph $D$ in order to find properties of it. In fac... |
https://arxiv.org/abs/1911.08801 | Ray Effect Mitigation for the Discrete Ordinates Method Using Artificial Scattering | Solving the radiative transfer equation with the discrete ordinates (S$_N$) method leads to a non-physical imprint of the chosen quadrature set on the solution. To mitigate these so-called ray effects, we propose a modification of the S$_N$ method, which we call artificial scattering S$_N$ (as-S$_N$). The method adds a... |
\section{Results}
In the following, we evaluate the proposed method within the scope of two numerical test cases: (i) the line-source problem is used as it is inherently prone to ray-effects when using the S$_N$ method, and (ii) the lattice test case models---in a very simplified way---neutrons in a fission reactor w... | {
"timestamp": "2019-11-22T02:09:19",
"yymm": "1911",
"arxiv_id": "1911.08801",
"language": "en",
"url": "https://arxiv.org/abs/1911.08801",
"abstract": "Solving the radiative transfer equation with the discrete ordinates (S$_N$) method leads to a non-physical imprint of the chosen quadrature set on the sol... |
https://arxiv.org/abs/quant-ph/0410127 | A systematic study on the exact solution of the position dependent mass Schroedinger equation | An algebraic method of constructing potentials for which the Schroedinger equation with position dependent mass can be solved exactly is presented. A general form of the generators of su(1,1) algebra has been employed with a unified approach to the problem. Our systematic approach reproduces a number of earlier results... | \section{Introduction}
The study of position dependent mass (PDM) Schr\"{o}dinger equation has
recently attracted some interest\cite{roy, milan} arising from the study of
electronic properties of semiconductors, liquid crystals, quantum dots, the
recent progress of crystal-growth techniques for production of non-unifo... | {
"timestamp": "2004-10-17T12:12:18",
"yymm": "0410",
"arxiv_id": "quant-ph/0410127",
"language": "en",
"url": "https://arxiv.org/abs/quant-ph/0410127",
"abstract": "An algebraic method of constructing potentials for which the Schroedinger equation with position dependent mass can be solved exactly is prese... |
https://arxiv.org/abs/hep-lat/9609047 | Monte Carlo Study of Cluster-Diameter Distribution: A New Observable to Estimate Correlation Lengths | We report numerical simulations of two-dimensional $q$-state Potts models with emphasis on a new quantity for the computation of spatial correlation lengths. This quantity is the cluster-diameter distribution function $G_{diam}(x)$, which measures the distribution of the diameter of stochastically defined cluster. Theo... | \section{Introduction}
The physics of phase transitions is essentially governed by the behavior of
the spatial correlation length $\xi$. While in some problems, e.g. at a
continuous phase transition where $\xi$ diverges, it is often sufficient to
know the qualitative behavior, there are also many applications which re... | {
"timestamp": "1996-09-28T21:12:16",
"yymm": "9609",
"arxiv_id": "hep-lat/9609047",
"language": "en",
"url": "https://arxiv.org/abs/hep-lat/9609047",
"abstract": "We report numerical simulations of two-dimensional $q$-state Potts models with emphasis on a new quantity for the computation of spatial correla... |
https://arxiv.org/abs/2202.04096 | Berry phase in the rigid rotor: the emergent physics of odd antiferromagnets | The rigid rotor is a classic problem in quantum mechanics, describing the dynamics of a rigid body with its centre of mass held fixed. The configuration space of this problem is $SO(3)$, the space of all rotations in three dimensions. This is a topological space with two types of closed loops: trivial loops that can be... | \section{Introduction}
The rotation of a rigid body is a fundamental problem in classical and quantum mechanics. It is one of the early problems where quantum spectra could be worked out and compared against experiments. It laid the foundation for the field of microwave rotational spectroscopy
\cite{Bunker2006,Xu2011},... | {
"timestamp": "2022-05-05T02:06:12",
"yymm": "2202",
"arxiv_id": "2202.04096",
"language": "en",
"url": "https://arxiv.org/abs/2202.04096",
"abstract": "The rigid rotor is a classic problem in quantum mechanics, describing the dynamics of a rigid body with its centre of mass held fixed. The configuration s... |
https://arxiv.org/abs/1903.07995 | Bose-Einstein condensation in spherically symmetric traps | We present a pedagogical introduction to Bose-Einstein condensation in traps with spherical symmetry, namely the spherical box and the thick shell, sometimes called bubble trap. In order to obtain the critical temperature for Bose-Einstein condensation, we describe how to calculate the cumulative state number and densi... | \section{Introduction}
A Bose-Einstein condensate (BEC) corresponds to the macroscopic occupation
of the lowest energy quantum state by the particles of a system
\cite{bose24}. Bose-Einstein condensation occurs when the system is cooled below a critical
temperature $T_c$ and the mean interparticle distance
$\bar{l}=\r... | {
"timestamp": "2019-03-20T01:21:31",
"yymm": "1903",
"arxiv_id": "1903.07995",
"language": "en",
"url": "https://arxiv.org/abs/1903.07995",
"abstract": "We present a pedagogical introduction to Bose-Einstein condensation in traps with spherical symmetry, namely the spherical box and the thick shell, someti... |
https://arxiv.org/abs/2205.08609 | Bagged Polynomial Regression and Neural Networks | Series and polynomial regression are able to approximate the same function classes as neural networks. However, these methods are rarely used in practice, although they offer more interpretability than neural networks. In this paper, we show that a potential reason for this is the slow convergence rate of polynomial re... | \section{Introduction}
Deep learning models have become ubiquitous in the machine learning literature. A cornerstone of the success of deep neural networks is that they can over-fit the training data while maintaining excellent generalization error. This feat is possible by training very large (over-parametrized) mod... | {
"timestamp": "2022-05-19T02:01:54",
"yymm": "2205",
"arxiv_id": "2205.08609",
"language": "en",
"url": "https://arxiv.org/abs/2205.08609",
"abstract": "Series and polynomial regression are able to approximate the same function classes as neural networks. However, these methods are rarely used in practice,... |
https://arxiv.org/abs/1503.04499 | Cumulative Conditional Expectation Index | In this paper we study the cumulative conditional expectation function (CCEF) in the copula context. It is shown how to compute CCEF in terms of the cumulative copula function, this natural representation allows to deduce some useful properties, for instance with applications to convex combination of copulas. We introd... | \section{Introduction}
In this paper we explore $\mathbb{E}[V\vert U \leq u]$ as a function of $u \in (0,1),$ we denote this quantity as {\it{cumulative conditional expectation function}}. One of the motivations of working with this quantity is its use for making decisions in real problems.
Our target is to give the... | {
"timestamp": "2015-03-17T01:11:57",
"yymm": "1503",
"arxiv_id": "1503.04499",
"language": "en",
"url": "https://arxiv.org/abs/1503.04499",
"abstract": "In this paper we study the cumulative conditional expectation function (CCEF) in the copula context. It is shown how to compute CCEF in terms of the cumul... |
https://arxiv.org/abs/1408.5271 | An algorithmic framework for obtaining lower bounds for random Ramsey problems | In this paper we introduce a general framework for proving lower bounds for various Ramsey type problems within random settings. The main idea is to view the problem from an algorithmic perspective: we aim at providing an algorithm that finds the desired colouring with high probability. Our framework allows to reduce t... | \section{Applications}\label{sec:applications}
\subsection{Anti-Ramsey property -- proper coloring} \label{sec:ar_proper}
The key ingredient for the proof of Theorem \ref{thm:ar_proper} is the following lemma whose proof we defer to the next section.
\begin{lemma} \label{lemma:ar_proper_cases}
Let $F$ be a graph is... | {
"timestamp": "2014-08-25T02:08:54",
"yymm": "1408",
"arxiv_id": "1408.5271",
"language": "en",
"url": "https://arxiv.org/abs/1408.5271",
"abstract": "In this paper we introduce a general framework for proving lower bounds for various Ramsey type problems within random settings. The main idea is to view th... |
https://arxiv.org/abs/1001.0489 | Absence of torsion for NK_1(R) over associative rings | When R is a commutative ring with identity, and if k is a natural number with kR = R, then C. Weibel proved that SK_1(R[X]) has no k-torsion. We reprove his result for any associative ring R with identity in which kR = R. | \section{Introduction}
~~~~Let $R$ be an associative ring with identity element $1$.
Let ${\rm K_1}(R)$ denote the Whitehead group. In case $R$ is commutative, let ${\rm SK_1}(R)$ be the kernel of
the determinant map from ${\rm K_1}(R)$ to the group of units of $R$.
Let ${\rm W}(R)$ be the ring of big Witt vectors.... | {
"timestamp": "2010-01-04T12:48:47",
"yymm": "1001",
"arxiv_id": "1001.0489",
"language": "en",
"url": "https://arxiv.org/abs/1001.0489",
"abstract": "When R is a commutative ring with identity, and if k is a natural number with kR = R, then C. Weibel proved that SK_1(R[X]) has no k-torsion. We reprove his... |
https://arxiv.org/abs/math/0610165 | Multiplication maps and vanishing theorems for toric varieties | We use multiplication maps to give a characteristic-free approach to vanishing theorems on toric varieties. Our approach is very elementary but is enough powerful to prove vanishing theorems. | \section{Introduction}\label{sec1}
The main purpose of this paper is to understand
various vanishing theorems on toric varieties
through multiplication maps.
We give an elementary and unified approach to vanishing theorems on
toric varieties.
The following theorem is the main theorem of this paper.
Some importa... | {
"timestamp": "2006-11-30T04:35:33",
"yymm": "0610",
"arxiv_id": "math/0610165",
"language": "en",
"url": "https://arxiv.org/abs/math/0610165",
"abstract": "We use multiplication maps to give a characteristic-free approach to vanishing theorems on toric varieties. Our approach is very elementary but is eno... |
https://arxiv.org/abs/2202.11842 | U-statistics of growing order and sub-Gaussian mean estimators with sharp constants | This paper addresses the following question: given a sample of i.i.d. random variables with finite variance, can one construct an estimator of the unknown mean that performs nearly as well as if the data were normally distributed? One of the most popular examples achieving this goal is the median of means estimator. Ho... | \section{Introduction.}
\label{sec:intro}
Let $X_1,\ldots,X_N$ be i.i.d. random variables with distribution $P$ having mean $\mu$ and finite variance $\sigma^2$. At the core of this paper is the following question: given $1\leq t \leq t_{\max}(N)$, construct an estimator $\widetilde \mu_N = \widetilde \mu_N(X_1,\ldots... | {
"timestamp": "2022-06-22T02:45:34",
"yymm": "2202",
"arxiv_id": "2202.11842",
"language": "en",
"url": "https://arxiv.org/abs/2202.11842",
"abstract": "This paper addresses the following question: given a sample of i.i.d. random variables with finite variance, can one construct an estimator of the unknown... |
https://arxiv.org/abs/2010.10072 | Starlike Functions associated with a Petal Shaped Domain | This paper deals with some radius results and inclusion relations that are established for functions in a newly defined subclass of starlike functions associated with a petal shaped domain. | \section{Introduction}
Let the open unit disk $\{z\in\mathbb{C}:|z|<1\}$ be represented by $\mathbb{D}$ and denote the class of all analytic functions in $\mathbb{D}$ by $\mathcal{H}$. Consider $\mathcal{A}_n$ as the class of analytic functions $f$ in $\mathbb{D}$ represented by
\begin{equation}\label{A_n}
f(z)=z+a_... | {
"timestamp": "2020-10-21T02:13:48",
"yymm": "2010",
"arxiv_id": "2010.10072",
"language": "en",
"url": "https://arxiv.org/abs/2010.10072",
"abstract": "This paper deals with some radius results and inclusion relations that are established for functions in a newly defined subclass of starlike functions ass... |
https://arxiv.org/abs/1303.1052 | Random walk attachment graphs | We consider the random walk attachment graph introduced by Saramäki and Kaski and proposed as a mechanism to explain how behaviour similar to preferential attachment may appear requiring only local knowledge. We show that if the length of the random walk is fixed then the resulting graphs can have properties significan... | \section{Introduction}
There is currently great interest in the preferential attachment
model of network growth, usually called the Barab\'{a}si-Albert
\cite{ba,scalefreedefs} model, though it dates back at least to Yule \cite{yule}, and was
discussed also by Simon \cite{simon}. In the simplest version of this an... | {
"timestamp": "2013-07-24T02:04:15",
"yymm": "1303",
"arxiv_id": "1303.1052",
"language": "en",
"url": "https://arxiv.org/abs/1303.1052",
"abstract": "We consider the random walk attachment graph introduced by Saramäki and Kaski and proposed as a mechanism to explain how behaviour similar to preferential a... |
https://arxiv.org/abs/1501.07774 | Near Optimal Subdivision Algorithms for Real Root Isolation | We describe a subroutine that improves the running time of any subdivision algorithm for real root isolation. The subroutine first detects clusters of roots using a result of Ostrowski, and then uses Newton iteration to converge to them. Near a cluster, we switch to subdivision, and proceed recursively. The subroutine ... | \section{Introduction}
Given a polynomial $f \in \RR[x]$ of degree $n$, the problem is to isolate the
real roots of $f$ in an input interval $I_0$, i.e.,
compute disjoint intervals which contain exactly one real root of
$f$, and together contain all roots of $f$ in $I_0\cap \RR$.
Subdivision based algorithms
have be... | {
"timestamp": "2015-02-02T02:10:57",
"yymm": "1501",
"arxiv_id": "1501.07774",
"language": "en",
"url": "https://arxiv.org/abs/1501.07774",
"abstract": "We describe a subroutine that improves the running time of any subdivision algorithm for real root isolation. The subroutine first detects clusters of roo... |
https://arxiv.org/abs/1806.01163 | VADU 2018 Open Problem Session | We state the problems discussed in the open problem session at Variational Analysis Down Under (VADU2018) conference held in honour of Prof. Asen Dontchev's 70th birthday on 19--21 February 2018 at Federation University Australia,this https URL. | \section{Existence of local calm selections}
This problem was proposed by Asen Dontchev. All background material, including notation, history, etc. can be found in \cite{book}. We are grateful to Asen for providing this description.
\proclaim Theorem (Bartle-Graves (1952)). Let $X$ and $Y$ be
Banach spaces and let $f... | {
"timestamp": "2018-06-05T02:19:08",
"yymm": "1806",
"arxiv_id": "1806.01163",
"language": "en",
"url": "https://arxiv.org/abs/1806.01163",
"abstract": "We state the problems discussed in the open problem session at Variational Analysis Down Under (VADU2018) conference held in honour of Prof. Asen Dontchev... |
https://arxiv.org/abs/1107.5971 | Injective hulls of certain discrete metric spaces and groups | Injective metric spaces, or absolute 1-Lipschitz retracts, share a number of properties with CAT(0) spaces. In the 1960es, J. R. Isbell showed that every metric space X has an injective hull E(X). Here it is proved that if X is the vertex set of a connected locally finite graph with a uniform stability property of inte... | \section{Introduction}
A metric space $Y$ is called {\em injective} if for every metric space~$B$
and every $1$-Lipschitz map $f \colon A \to Y$ defined on a set $A \subset B$
there exists a $1$-Lipschitz extension $\overline f \colon B \to Y$ of $f$.
The terminology is in accordance with the notion of an injective... | {
"timestamp": "2012-06-29T02:07:52",
"yymm": "1107",
"arxiv_id": "1107.5971",
"language": "en",
"url": "https://arxiv.org/abs/1107.5971",
"abstract": "Injective metric spaces, or absolute 1-Lipschitz retracts, share a number of properties with CAT(0) spaces. In the 1960es, J. R. Isbell showed that every me... |
https://arxiv.org/abs/1912.00060 | Uniformly vertex-transitive graphs | We introduce uniformly vertex-transitive graphs as vertex-transitive graphs satisfying a stronger condition on their automorphism groups, motivated by a problem which arises from a Sinkhorn-type algorithm. We use the derangement graph $D(\Gamma)$ of a given graph $\Gamma$ to show that the uniform vertex-transitivity of... | \section{Introduction and main results}\label{sec:int}
The motivation for our article arose from \cite{NSW19}, where a Sinkhorn-type algorithm was presented for determining whether or not a given finite graph has quantum symmetries. This algorithm can only be applied to graphs which are vertex-transitive in a stronger... | {
"timestamp": "2019-12-03T02:01:33",
"yymm": "1912",
"arxiv_id": "1912.00060",
"language": "en",
"url": "https://arxiv.org/abs/1912.00060",
"abstract": "We introduce uniformly vertex-transitive graphs as vertex-transitive graphs satisfying a stronger condition on their automorphism groups, motivated by a p... |
https://arxiv.org/abs/1507.04484 | Correspondences and singular varieties | What is generally known as the "Bloch--Srinivas method" consists of decomposing the diagonal of a smooth projective variety, and then considering the action of correspondences in cohomology. In this note, we observe that this same method can also be extended to singular and quasi--projective varieties. We give two appl... | \section{Introduction}
\label{intro}
Let $X$ be a smooth complex projective variety. The cycle class maps
\[ cl^i\colon A^iX_{\mathbb{Q}}\to H^{2i}(X,\mathbb{Q})\]
from Chow groups to singular cohomology have given rise to some of the most profound and fascinating conjectures in algebraic geometry: the Hodge conje... | {
"timestamp": "2015-07-17T02:05:44",
"yymm": "1507",
"arxiv_id": "1507.04484",
"language": "en",
"url": "https://arxiv.org/abs/1507.04484",
"abstract": "What is generally known as the \"Bloch--Srinivas method\" consists of decomposing the diagonal of a smooth projective variety, and then considering the ac... |
https://arxiv.org/abs/1509.02533 | Absorbing random-walk centrality: Theory and algorithms | We study a new notion of graph centrality based on absorbing random walks. Given a graph $G=(V,E)$ and a set of query nodes $Q\subseteq V$, we aim to identify the $k$ most central nodes in $G$ with respect to $Q$. Specifically, we consider central nodes to be absorbing for random walks that start at the query nodes $Q$... | \section{Introduction}
A fundamental problem in graph mining is to
identify the most central nodes in a graph.
Numerous centrality measures have been proposed,
including
degree centrality,
closeness centrality~\cite{closenesscentrality},
betweenness centrality~\cite{betweennesscentrality},
random-walk centrality~\... | {
"timestamp": "2015-09-10T02:00:32",
"yymm": "1509",
"arxiv_id": "1509.02533",
"language": "en",
"url": "https://arxiv.org/abs/1509.02533",
"abstract": "We study a new notion of graph centrality based on absorbing random walks. Given a graph $G=(V,E)$ and a set of query nodes $Q\\subseteq V$, we aim to ide... |
https://arxiv.org/abs/1604.01794 | Optimal initial condition of passive tracers for their maximal mixing in finite time | The efficiency of a fluid mixing device is often limited by fundamental laws and/or design constraints, such that a perfectly homogeneous mixture cannot be obtained in finite time. Here, we address the natural corollary question: Given the best available mixer, what is the optimal initial tracer pattern that leads to t... | \section{Introduction}
Given a fluid velocity field $\mathbf u(\mathbf x,t)$, a passive tracer satisfies the linear advection equation
\begin{equation}
\partial_{t}\rho +\mathbf u\cdot \pmb\nabla \rho=0,\quad \rho(\mathbf x,t_0)=f(\mathbf x)
\label{eq:adveq}
\end{equation}
where the scalar field $\rho(\mathbf x,t)$ den... | {
"timestamp": "2016-11-22T02:00:47",
"yymm": "1604",
"arxiv_id": "1604.01794",
"language": "en",
"url": "https://arxiv.org/abs/1604.01794",
"abstract": "The efficiency of a fluid mixing device is often limited by fundamental laws and/or design constraints, such that a perfectly homogeneous mixture cannot b... |
https://arxiv.org/abs/1201.1948 | Rigorous Enclosures of a Slow Manifold | Slow-fast dynamical systems have two time scales and an explicit parameter representing the ratio of these time scales. Locally invariant slow manifolds along which motion occurs on the slow time scale are a prominent feature of slow-fast systems. This paper introduces a rigorous numerical method to compute enclosures ... | \section{Introduction}\label{S_Intro}
Invariant manifolds and their intersections are important features that organize qualitative properties of dynamical systems. Three types of manifolds have been prominent in the subject: (1) compact invariant tori ~\cite{Dl01}, (2) stable and unstable manifolds of equilibria and p... | {
"timestamp": "2012-09-20T02:02:18",
"yymm": "1201",
"arxiv_id": "1201.1948",
"language": "en",
"url": "https://arxiv.org/abs/1201.1948",
"abstract": "Slow-fast dynamical systems have two time scales and an explicit parameter representing the ratio of these time scales. Locally invariant slow manifolds alo... |
https://arxiv.org/abs/1905.06998 | Majorization bounds for Ritz values of self-adjoint matrices | A priori, a posteriori, and mixed type upper bounds for the absolute change in Ritz values of self-adjoint matrices in terms of submajorization relations are obtained. Some of our results prove recent conjectures by Knyazev, Argentati, and Zhu, which extend several known results for one dimensional subspaces to arbitra... | \section{Introduction}
The study of sensitivity of Ritz values of Rayleigh quotients of self-adjoint matrices (i.e. the changes in the
eigenvalues of compressions of a self-adjoint matrix) is a well established and active research field in applied mathematics
\cite{AKPRitz,BosDr,AKFEM,AKMaj,AKProxy,LiLi,Mathias,Ovt,T... | {
"timestamp": "2020-07-10T02:00:57",
"yymm": "1905",
"arxiv_id": "1905.06998",
"language": "en",
"url": "https://arxiv.org/abs/1905.06998",
"abstract": "A priori, a posteriori, and mixed type upper bounds for the absolute change in Ritz values of self-adjoint matrices in terms of submajorization relations ... |
https://arxiv.org/abs/2202.00568 | Stochastic 2D Signal Generative Model with Wavelet Packets Basis Regarded as a Random Variable and Bayes Optimal Processing | This study deals with two-dimensional (2D) signal processing using the wavelet packet transform. When the basis is unknown the candidate of basis increases in exponential order with respect to the signal size. Previous studies do not consider the basis as a random vaiables. Therefore, the cost function needs to be used... | \section{Introduction}
This study deals with two-dimensional (2D) signal processing using the wavelet packet transform. Specifically, We perform 2D signal processing based on statistical decision theory (see e.g. \cite{berger}) with Bayes risk function as the evaluation criterion.
Wavelet packet transform has been ap... | {
"timestamp": "2022-05-03T02:30:07",
"yymm": "2202",
"arxiv_id": "2202.00568",
"language": "en",
"url": "https://arxiv.org/abs/2202.00568",
"abstract": "This study deals with two-dimensional (2D) signal processing using the wavelet packet transform. When the basis is unknown the candidate of basis increase... |
https://arxiv.org/abs/1501.03643 | On robust width property for Lasso and Dantzig selector | Recently, Cahill and Mixon completely characterized the sensing operators in many compressed sensing instances with a robust width property. The proposed property allows uniformly stable and robust reconstruction of certain solutions from an underdetermined linear system via convex optimization. However, their theory d... | \section{Introduction}
One of the main assignments of compressed sensing is to understand when it is possible to recover structured solutions to underdetermined systems of linear equations \cite{candes2014math}. During the past decade, there have developed many reconstruction guarantees; well-known concepts include res... | {
"timestamp": "2016-04-05T02:09:35",
"yymm": "1501",
"arxiv_id": "1501.03643",
"language": "en",
"url": "https://arxiv.org/abs/1501.03643",
"abstract": "Recently, Cahill and Mixon completely characterized the sensing operators in many compressed sensing instances with a robust width property. The proposed ... |
https://arxiv.org/abs/math/0703134 | On the spectral norm of a random Toeplitz matrix | Suppose that $T_n$ is a Toeplitz matrix whose entries come from a sequence of independent but not necessarily identically distributed random variables with mean zero. Under some additional tail conditions, we show that the spectral norm of $T_n$ is of the order $\sqrt{n \log n}$. The same result holds for random Hankel... | \section{Introduction and results}\label{S:intro}
Let $X_0,X_1,X_2,\dotsc$ be a family of independent random
variables. For $n\ge 2$, $T_n$ denotes the $n\times n$ random
symmetric Toeplitz matrix $T_n = \big[ X_{|j-k|}\big]_{1\le j, k\le
n}$,
\[
T_n = \begin{bmatrix}
X_0 & X_1 & X_2 & \cdots & X_{n-2} & X_{n-1} \\
X_... | {
"timestamp": "2007-03-12T18:55:38",
"yymm": "0703",
"arxiv_id": "math/0703134",
"language": "en",
"url": "https://arxiv.org/abs/math/0703134",
"abstract": "Suppose that $T_n$ is a Toeplitz matrix whose entries come from a sequence of independent but not necessarily identically distributed random variables... |
https://arxiv.org/abs/0805.4120 | Mixed Volume Techniques for Embeddings of Laman Graphs | Determining the number of embeddings of Laman graph frameworks is an open problem which corresponds to understanding the solutions of the resulting systems of equations. In this paper we investigate the bounds which can be obtained from the viewpoint of Bernstein's Theorem. The focus of the paper is to provide the meth... | \section{Introduction}
Let $G=(V,E)$ be a graph on $n$ vertices with $2n-3$ edges. If each
subset of $k$ vertices spans at most $2k-3$ edges, we say that $G$ has the
{\it Laman property} and call it a {\it Laman graph} (see \cite{Laman}).
A {\it framework} is a tuple $(G,L)$ where $G=(V,E)$ is a graph and $L=\{l_{i,j}... | {
"timestamp": "2009-03-13T14:48:56",
"yymm": "0805",
"arxiv_id": "0805.4120",
"language": "en",
"url": "https://arxiv.org/abs/0805.4120",
"abstract": "Determining the number of embeddings of Laman graph frameworks is an open problem which corresponds to understanding the solutions of the resulting systems ... |
https://arxiv.org/abs/2212.06429 | Extensions and automorphisms of Rota-Baxter groups | The notion of Rota-Baxter groups was recently introduced by Guo, Lang and Sheng [{\em Adv. Math.} 387 (2021), 107834, 34 pp.] in the geometric study of Rota-Baxter Lie algebras. They are closely related to skew braces as observed by Bardakov and Gubarev. In this paper, we study extensions of Rota-Baxter groups by const... | \section{Introduction}
The Rota-Baxter operators, first introduced in 1960 by G. Baxter \cite{GB60} in the fluctuation theory of probability. Such operators can be viewed as a generalization of the integral operator on the algebra of continuous functions. In the past two decades, these operators gained great importanc... | {
"timestamp": "2022-12-14T02:09:20",
"yymm": "2212",
"arxiv_id": "2212.06429",
"language": "en",
"url": "https://arxiv.org/abs/2212.06429",
"abstract": "The notion of Rota-Baxter groups was recently introduced by Guo, Lang and Sheng [{\\em Adv. Math.} 387 (2021), 107834, 34 pp.] in the geometric study of R... |
https://arxiv.org/abs/2203.14534 | A Combinatorial Proof of a generalization of a Theorem of Frobenius | In this article, we shall generalize a theorem due to Frobenius in group theory, which asserts that if $p$ is a prime and $p^{r}$ divides the order of a finite group, then the number of subgroups of order $p^{r}$ is $\equiv$ 1(mod $p$). Interestingly, our proof is purely combinatorial and does not use much group theory... | \section*{1.Introduction}
Although Sylow's theorems are taught in almost all undergraduate
courses in abstract algebra, a generalization due to Frobenius does not seem to be as
well known as it ought to be. Frobenius' generalization states that
if $p$ is a prime and $p^{r}$ divides the order $N$ of a finite group
$G$,... | {
"timestamp": "2022-03-29T02:43:59",
"yymm": "2203",
"arxiv_id": "2203.14534",
"language": "en",
"url": "https://arxiv.org/abs/2203.14534",
"abstract": "In this article, we shall generalize a theorem due to Frobenius in group theory, which asserts that if $p$ is a prime and $p^{r}$ divides the order of a f... |
https://arxiv.org/abs/2002.10139 | Some results on pure ideals and trace ideals of projective modules | Let $R$ be a commutative ring with the unit element. It is shown that an ideal $I$ in $R$ is pure if and only if Ann$(f)+I=R$ for all $f\in I$. If $J$ is the trace of a projective $R$-module $M$, we prove that $J$ is generated by the ``coordinates" of $M$ and $JM = M$. These lead to a few new results and alternative pr... | \section{Introduction and Preliminaries}
The concept of the trace ideals of modules has been the subject of research by some mathematicians around late 50's until late 70's and has again been active in recent years (see, e.g. \cite{Beckwith}, \cite{Dao et al.}, \cite{Herbera}, \cite{Herzog}, \cite{Jondrup}, \cite{li... | {
"timestamp": "2021-07-14T02:19:37",
"yymm": "2002",
"arxiv_id": "2002.10139",
"language": "en",
"url": "https://arxiv.org/abs/2002.10139",
"abstract": "Let $R$ be a commutative ring with the unit element. It is shown that an ideal $I$ in $R$ is pure if and only if Ann$(f)+I=R$ for all $f\\in I$. If $J$ is... |
https://arxiv.org/abs/1606.03773 | Remez-type inequalities for the hyperbolic cross polynomials | In this paper we study the Remez-type inequalities for trigonometric polynomials with harmonics from hyperbolic crosses. The interrelation between the Remez and Nikolskii inequalities for individual functions and its applications are discussed. | \section{Introduction}
In many questions in analysis one deals with a problem of finding the best possible way to estimate the global norm $\|f\|_{X(\Omega)}$ in terms of local norms $\|f\|_{X(\Omega\setminus B )}$.
In some cases, this problem can be reduced to the problem for certain approximation methods, in particu... | {
"timestamp": "2016-06-14T02:13:23",
"yymm": "1606",
"arxiv_id": "1606.03773",
"language": "en",
"url": "https://arxiv.org/abs/1606.03773",
"abstract": "In this paper we study the Remez-type inequalities for trigonometric polynomials with harmonics from hyperbolic crosses. The interrelation between the Rem... |
https://arxiv.org/abs/1102.4302 | Non-Archimedean Unitary Operators | We describe a subclass of the class of normal operators on Banach spaces over non-Archimedean fields (A. N. Kochubei, J. Math. Phys. 51 (2010), article 023526) consisting of operators whose properties resemble those of unitary operators. In particular, an analog of Stone's theorem about one-parameter groups of unitary ... | \section{INTRODUCTION}
{\bf 1.1}. In a previous paper \cite{K1}, we found a class of
non-Archimedean normal operators, bounded linear operators on Banach
spaces over non-Archimedean fields possessing orthogonal, in the
non-Archimedean sense, spectral decompositions. It is a natural problem
now to find out what o... | {
"timestamp": "2011-02-22T02:04:12",
"yymm": "1102",
"arxiv_id": "1102.4302",
"language": "en",
"url": "https://arxiv.org/abs/1102.4302",
"abstract": "We describe a subclass of the class of normal operators on Banach spaces over non-Archimedean fields (A. N. Kochubei, J. Math. Phys. 51 (2010), article 0235... |
https://arxiv.org/abs/2106.09103 | Approximately invertible elements in non-unital normed algebras | We introduce a concept of approximately invertible elements in non-unital normed algebras which is, on one side, a natural generalization of invertibility when having approximate identities at hand, and, on the other side, it is a direct extension of topological invertibility to non-unital algebras. Basic observations ... | \section{Introduction}
Invertibility is one of the central concepts in the study of unital Banach (or, more generally, topological) algebras. However, this concept is closely related to the existence of an identity in the algebra. Every non-unital Banach algebra $\mathcal{A}$ may be embedded into a unital algebra $\... | {
"timestamp": "2021-06-18T02:02:47",
"yymm": "2106",
"arxiv_id": "2106.09103",
"language": "en",
"url": "https://arxiv.org/abs/2106.09103",
"abstract": "We introduce a concept of approximately invertible elements in non-unital normed algebras which is, on one side, a natural generalization of invertibility... |
https://arxiv.org/abs/2302.11475 | Degrees and Network Design: New Problems and Approximations | While much of network design focuses mostly on cost (number or weight of edges), node degrees have also played an important role. They have traditionally either appeared as an objective, to minimize the maximum degree (e.g., the Minimum Degree Spanning Tree problem), or as constraints which might be violated to give bi... | \section{Introduction}
The overarching theme of network design problems is to find ``inexpensive'' subgraphs that satisfy some type of connectivity constraints. The notion of ``inexpensive'' is often either the number of edges (unweighted cost) or the sum of edge costs (weighted cost). However, it has long been recog... | {
"timestamp": "2023-02-23T02:17:26",
"yymm": "2302",
"arxiv_id": "2302.11475",
"language": "en",
"url": "https://arxiv.org/abs/2302.11475",
"abstract": "While much of network design focuses mostly on cost (number or weight of edges), node degrees have also played an important role. They have traditionally ... |
https://arxiv.org/abs/1907.09507 | Robust and optimal sparse regression for nonlinear PDE models | This paper investigates how models of spatiotemporal dynamics in the form of nonlinear partial differential equations can be identified directly from noisy data using a combination of sparse regression and weak formulation. Using the 4th-order Kuramoto-Sivashinsky equation for illustration, we show how this approach ca... | \section{Introduction}
Partial differential equations (PDEs) provide a natural description for the temporal evolution of spatially extended systems in various fields of science and engineering.
Historically and practically important examples include wave equations arising in many areas of physics, the Schr\"{o}dinger... | {
"timestamp": "2019-07-24T02:01:15",
"yymm": "1907",
"arxiv_id": "1907.09507",
"language": "en",
"url": "https://arxiv.org/abs/1907.09507",
"abstract": "This paper investigates how models of spatiotemporal dynamics in the form of nonlinear partial differential equations can be identified directly from nois... |
https://arxiv.org/abs/2203.12725 | Robust Coordinate Ascent Variational Inference with Markov chain Monte Carlo simulations | Variational Inference (VI) is a method that approximates a difficult-to-compute posterior density using better behaved distributional families. VI is an alternative to the already well-studied Markov chain Monte Carlo (MCMC) method of approximating densities. With each algorithm, there are of course benefits and drawba... | \section{Introduction}
In Bayesian statistics, computing a posterior distribution is of primary interest; however, finding a closed form expression for the posterior proves to be a difficult task \citep{blei2017}. The main hurdle comes with computing the normalizing constant, since integration (especially in more than ... | {
"timestamp": "2022-03-25T01:06:04",
"yymm": "2203",
"arxiv_id": "2203.12725",
"language": "en",
"url": "https://arxiv.org/abs/2203.12725",
"abstract": "Variational Inference (VI) is a method that approximates a difficult-to-compute posterior density using better behaved distributional families. VI is an a... |
https://arxiv.org/abs/1907.00892 | Sampling And Reconstruction Of Diffusive Fields On Graphs | In this paper, the focus is on the reconstruction of a diffusive field and the localization of the underlying driving sources on arbitrary graphs by observing a significantly smaller subset of vertices of the graph uniformly in time. Specifically, we focus on the heat diffusion equation driven by an initial field and a... | \section{Introduction}
Graph signal processing extends tools from classical signal processing to deal with data defined on networks and other irregular domains~\cite{ortega2018graph,shuman2013Emerging,sandryhaila2014big}.
We often come across such datasets in many diverse applications such as environmental sensing, tr... | {
"timestamp": "2019-07-02T02:34:26",
"yymm": "1907",
"arxiv_id": "1907.00892",
"language": "en",
"url": "https://arxiv.org/abs/1907.00892",
"abstract": "In this paper, the focus is on the reconstruction of a diffusive field and the localization of the underlying driving sources on arbitrary graphs by obser... |
https://arxiv.org/abs/1408.3887 | Completion of continuity spaces with uniformly vanishing asymmetry | The classical Cauchy completion of a metric space (by means of Cauchy sequences) as well as the completion of a uniform space (by means of Cauchy filters) are well-known to rely on the symmetry of the metric space or uniform space in question. For qausi-metric spaces and quasi-uniform spaces various non-equivalent comp... | \section{Introduction}
The theories of the completion of metric spaces and the completion
of uniform spaces are well-known and understood. There is little to
no doubt as to what completion should mean in these cases and there
are several (equivalent of course) constructions of the completions.
The situation is differe... | {
"timestamp": "2014-08-19T02:13:44",
"yymm": "1408",
"arxiv_id": "1408.3887",
"language": "en",
"url": "https://arxiv.org/abs/1408.3887",
"abstract": "The classical Cauchy completion of a metric space (by means of Cauchy sequences) as well as the completion of a uniform space (by means of Cauchy filters) a... |
https://arxiv.org/abs/1110.5672 | Kazhdan--Lusztig cells and the Frobenius--Schur indicator | Let $W$ be a finite Coxeter group. It is well-known that the number of involutions in $W$ is equal to the sum of the degrees of the irreducible characters of $W$. Following a suggestion of Lusztig, we show that this equality is compatible with the decomposition of $W$ into Kazhdan--Lusztig cells. The proof uses a gener... | \section{Introduction} \label{sec0}
Let $G$ be a finite group and assume that all complex irreducible
characters of $G$ can be realised over the real numbers. Then, by
a well-known result due to Frobenius and Schur, the number of
involutions in $G$ (that is, elements $g \in G$ such that $g^2=1$) is
equal to the sum... | {
"timestamp": "2011-12-20T02:01:16",
"yymm": "1110",
"arxiv_id": "1110.5672",
"language": "en",
"url": "https://arxiv.org/abs/1110.5672",
"abstract": "Let $W$ be a finite Coxeter group. It is well-known that the number of involutions in $W$ is equal to the sum of the degrees of the irreducible characters o... |
https://arxiv.org/abs/1707.02078 | Computational Krylov-based methods for large-scale differential Sylvester matrix problems | In the present paper, we propose Krylov-based methods for solving large-scale differential Sylvester matrix equations having a low rank constant term. We present two new approaches for solving such differential matrix equations. The first approach is based on the integral expression of the exact solution and a Krylov m... | \section{Introduction}
In the present paper, we consider the differential Sylvester
matrix equation (DSE in short) of the form
\begin{equation}\label{sylv1}
\left\{
\begin{array}{l}
\dot X(t)=A(t)\,X(t)+X(t)\,B(t)+E(t)F(t)^T;\; (DSE) \\
\;X(t_0)=X_0,\; \; t \in [t_0, \, T_f],
\end{array}
\right.
\end{equation}
\n... | {
"timestamp": "2017-07-10T02:04:35",
"yymm": "1707",
"arxiv_id": "1707.02078",
"language": "en",
"url": "https://arxiv.org/abs/1707.02078",
"abstract": "In the present paper, we propose Krylov-based methods for solving large-scale differential Sylvester matrix equations having a low rank constant term. We ... |
https://arxiv.org/abs/math/9802108 | Partial norms and the convergence of general products of matrices | Motivated by the theory of inhomogeneous Markov chains, we determine a sufficient condition for the convergence to 0 of a general product formed from a sequence of real or complex matrices. When the matrices have a common invariant subspace $H$, we give a sufficient condition for the convergence to 0 on $H$ of a genera... | \section{Introduction}
\label{sec1}
\setcounter{equation}{0}
Recently there has been much interest in conditions for the
convergence
of infinite products of real or complex matrices. Several
investigations have concentrated
on products taken in one direction -- left or right,
see for example the recent papers by Beyn ... | {
"timestamp": "1998-02-23T04:42:44",
"yymm": "9802",
"arxiv_id": "math/9802108",
"language": "en",
"url": "https://arxiv.org/abs/math/9802108",
"abstract": "Motivated by the theory of inhomogeneous Markov chains, we determine a sufficient condition for the convergence to 0 of a general product formed from ... |
https://arxiv.org/abs/2205.13068 | Tight Lower Bounds on Worst-Case Guarantees for Zero-Shot Learning with Attributes | We develop a rigorous mathematical analysis of zero-shot learning with attributes. In this setting, the goal is to label novel classes with no training data, only detectors for attributes and a description of how those attributes are correlated with the target classes, called the class-attribute matrix. We develop the ... |
\section{Lower Bounds for Zero-Shot Learning with Attributes}\label{sec:adv}
In this section, we formally define our lower bound. Consider a PMF $p$ with support over $\{0,1\}^n \times [k]$. We say that $p$ satisfies the class-feature matrix $\bm{A}$ if (as in constraints \eqref{matrix-class-attribute-relation}) f... | {
"timestamp": "2022-05-27T02:04:37",
"yymm": "2205",
"arxiv_id": "2205.13068",
"language": "en",
"url": "https://arxiv.org/abs/2205.13068",
"abstract": "We develop a rigorous mathematical analysis of zero-shot learning with attributes. In this setting, the goal is to label novel classes with no training da... |
https://arxiv.org/abs/1502.06332 | A sharp subelliptic Sobolev embedding theorem with weights | The purpose of this short article is to prove some potential estimates that naturally arise in the study of subelliptic Sobolev inequalites for functions. This will allow us to prove a local subelliptic Sobolev inequality with the optimal amount of smoothing, as well as a variant of that which describes quantitatively ... | \section{Statement of results}
Subelliptic Sobolev-type estimates in general have received a lot of attention over the years. We list some results that share a similar theme as ours: Capogna-Danielli-Garofalo \cite{MR1312686}, Cohn-Lu-Wang \cite{MR2345338}, Franchi-Gallot-Wheeden \cite{MR1314734}, Franchi-Lu-Wheeden \... | {
"timestamp": "2015-07-14T02:14:38",
"yymm": "1502",
"arxiv_id": "1502.06332",
"language": "en",
"url": "https://arxiv.org/abs/1502.06332",
"abstract": "The purpose of this short article is to prove some potential estimates that naturally arise in the study of subelliptic Sobolev inequalites for functions.... |
https://arxiv.org/abs/0902.1290 | Boolean Inner product Spaces and Boolean Matrices | This article discusses the concept of Boolean spaces endowed with a Boolean valued inner product and their matrices. A natural inner product structure for the space of Boolean n-tuples is introduced. Stochastic boolean vectors and stochastic and unitary Boolean matrices are studied. A dimension theorem for orthonormal ... | \section{Introduction}
\qquad A Boolean space $\mathcal{L}_{n}\left( \mathcal{B}\right) $ is the
set of all $n$-tuples of elements of a fixed Boolean algebra $\mathcal{B}$.
The elements of $\mathcal{L}_{n}\left( \mathcal{B}\right) $ are called
Boolean vectors and they possess a natural linear space-like structure.
Mor... | {
"timestamp": "2009-02-08T05:54:24",
"yymm": "0902",
"arxiv_id": "0902.1290",
"language": "en",
"url": "https://arxiv.org/abs/0902.1290",
"abstract": "This article discusses the concept of Boolean spaces endowed with a Boolean valued inner product and their matrices. A natural inner product structure for t... |
https://arxiv.org/abs/1109.4454 | Parrondo's paradox via redistribution of wealth | Toral (2002) considered an ensemble of N\geq2 players. In game B a player is randomly selected to play Parrondo's original capital-dependent game. In game A' two players are randomly selected without replacement, and the first transfers one unit of capital to the second. Game A' is fair (with respect to total capital),... | \section{Introduction}
The original Parrondo (1996) games can be described in terms of probabilities $p:=1/2-\eps$ and
\begin{equation}\label{old-param}
p_0:={1\over10}-\eps,\qquad p_1=p_2:={3\over4}-\eps,
\end{equation}
where $\eps>0$ is a small bias parameter (less than 1/10, of course). In game $A$, the player tos... | {
"timestamp": "2011-09-22T02:00:55",
"yymm": "1109",
"arxiv_id": "1109.4454",
"language": "en",
"url": "https://arxiv.org/abs/1109.4454",
"abstract": "Toral (2002) considered an ensemble of N\\geq2 players. In game B a player is randomly selected to play Parrondo's original capital-dependent game. In game ... |
https://arxiv.org/abs/1705.08365 | A Short Proof for a Lower Bound on the Zero Forcing Number | We provide a short proof of a conjecture of Davila and Kenter concerning a lower bound on the zero forcing number $Z(G)$ of a graph $G$. More specifically, we show that $Z(G)\geq (g-2)(\delta-2)+2$ for every graph $G$ of girth $g$ at least $3$ and minimum degree $\delta$ at least $2$. | \section{Introduction}
We consider finite, simple, and undirected graphs and use standard terminology.
For an integer $n$, let $[n]$ denote the set of positive integers at most $n$.
For a graph $G$,
a set $Z$ of vertices of $G$ is a {\it zero forcing set} of $G$
if the elements of $V(G)\setminus Z$ have a lin... | {
"timestamp": "2017-05-24T02:10:10",
"yymm": "1705",
"arxiv_id": "1705.08365",
"language": "en",
"url": "https://arxiv.org/abs/1705.08365",
"abstract": "We provide a short proof of a conjecture of Davila and Kenter concerning a lower bound on the zero forcing number $Z(G)$ of a graph $G$. More specifically... |
https://arxiv.org/abs/2203.11416 | Statistics on Almost-Fibonacci Pattern-Avoiding Permutations | We prove that $|Av_n(231,312,1432)|$, $|Av_n(312,321,1342)|$ $|Av_n(231,312,4321,21543)|$, and $ |Av_n(321,231,4123,21534)|$, are all equal to $F_{n+1} - 1$ where $F_n$ is the $n$-th Fibonacci number using the convention $F_0 = F_1 = 1$ and $Av_n(S)$ is the set of all permutations of length $n$ that avoid all of the pa... | \section{Introduction}
We say two sequences $a_1a_2\ldots a_k$ and $b_1b_2\ldots b_k$ of positive integers are \emph{order isomorphic} whenever $a_i < a_j$ if and only if $b_i < b_j$ for all $1\leq i,j \leq k$. A sequence $\pi$ \emph{contains} a sequence (or pattern) $\sigma$ whenever $\pi$ has a subsequence that is or... | {
"timestamp": "2022-03-23T01:11:13",
"yymm": "2203",
"arxiv_id": "2203.11416",
"language": "en",
"url": "https://arxiv.org/abs/2203.11416",
"abstract": "We prove that $|Av_n(231,312,1432)|$, $|Av_n(312,321,1342)|$ $|Av_n(231,312,4321,21543)|$, and $ |Av_n(321,231,4123,21534)|$, are all equal to $F_{n+1} - ... |
https://arxiv.org/abs/2002.02359 | Nonconforming discretizations of convex minimization problems and precise relations to mixed methods | This article discusses nonconforming finite element methods for convex minimization problems and systematically derives dual mixed formulations. Duality relations lead to simple error estimates that avoid an explicit treatment of nonconformity errors. A reconstruction formula provides the discrete solution of the dual ... |
\section{Introduction}
Mixed finite element methods as introduced in~\cite{RavTho77,BoBrFo13}
provide an attractive framework to
approximate partial differential equations in divergence form
since they lead to accurate approximations of fluxes.
For the Poisson problem it is well understood
that a close connection ... | {
"timestamp": "2020-02-07T02:13:07",
"yymm": "2002",
"arxiv_id": "2002.02359",
"language": "en",
"url": "https://arxiv.org/abs/2002.02359",
"abstract": "This article discusses nonconforming finite element methods for convex minimization problems and systematically derives dual mixed formulations. Duality r... |
https://arxiv.org/abs/2203.01419 | Electrostatic partners and zeros of orthogonal and multiple orthogonal polynomials | For a given polynomial $P$ with simple zeros, and a given semiclassical weight $w$, we present a construction that yields a linear second-order differential equation (ODE), and in consequence, an electrostatic model for zeros of $P$. The coefficients of this ODE are written in terms of a dual polynomial that we call th... | \section{Introduction}
Hermite polynomials
\begin{equation} \label{hermiteH}
H_N(x)=N!\sum_{\ell=0}^{\left\lfloor N/2\right\rfloor}\frac{(-1)
{\ell}(2x)^{N-2\ell}}{\ell!\;(N-2\ell)!}=2^Nx^N+\dots
\end{equation}
are probably the simplest representatives of the family of \textit{classical} orthogonal polynomial... | {
"timestamp": "2022-03-04T02:04:24",
"yymm": "2203",
"arxiv_id": "2203.01419",
"language": "en",
"url": "https://arxiv.org/abs/2203.01419",
"abstract": "For a given polynomial $P$ with simple zeros, and a given semiclassical weight $w$, we present a construction that yields a linear second-order differenti... |
https://arxiv.org/abs/1201.3221 | Spanning trees and even integer eigenvalues of graphs | For a graph $G$, let $L(G)$ and $Q(G)$ be the Laplacian and signless Laplacian matrices of $G$, respectively, and $\tau(G)$ be the number of spanning trees of $G$. We prove that if $G$ has an odd number of vertices and $\tau(G)$ is not divisible by $4$, then (i) $L(G)$ has no even integer eigenvalue, (ii) $Q(G)$ has no... | \section{Introduction}
The graphs we consider are simple, that is, without loops or multiple edges.
Let $G$ be a graph.
The {\em order} of $G$ is the number of vertices of $G$.
We denote by $A(G)$ the adjacency matrix,
by $\li(G)$ the line graph and by $\tau(G)$ the number of spanning trees of $G$.
The purp... | {
"timestamp": "2013-09-24T02:03:42",
"yymm": "1201",
"arxiv_id": "1201.3221",
"language": "en",
"url": "https://arxiv.org/abs/1201.3221",
"abstract": "For a graph $G$, let $L(G)$ and $Q(G)$ be the Laplacian and signless Laplacian matrices of $G$, respectively, and $\\tau(G)$ be the number of spanning trees... |
https://arxiv.org/abs/2208.03450 | An Optimal "It Ain't Over Till It's Over" Theorem | We study the probability of Boolean functions with small max influence to become constant under random restrictions. Let $f$ be a Boolean function such that the variance of $f$ is $\Omega(1)$ and all its individual influences are bounded by $\tau$. We show that when restricting all but a $\rho=\tilde{\Omega}((\log(1/\t... | \section{Introduction}
For any Boolean function $f:\{-1,1\}^{n}\to\{0,1\}$, the individual
\emph{influence} of the $i$th coordinate is the probability of flipping
the value of $f$ by flipping $x_{i}$ on a random input $x$. Let $x \oplus (-1)^{e_i}$
denote the string obtained by flipping the $i$th coordinate of $x$, th... | {
"timestamp": "2022-08-09T02:04:55",
"yymm": "2208",
"arxiv_id": "2208.03450",
"language": "en",
"url": "https://arxiv.org/abs/2208.03450",
"abstract": "We study the probability of Boolean functions with small max influence to become constant under random restrictions. Let $f$ be a Boolean function such th... |
https://arxiv.org/abs/math/0507163 | Permutohedra, associahedra, and beyond | The volume and the number of lattice points of the permutohedron P_n are given by certain multivariate polynomials that have remarkable combinatorial properties. We give several different formulas for these polynomials. We also study a more general class of polytopes that includes the permutohedron, the associahedron, ... | \section{Introduction}
The {\it permutohedron\/} $P_n(x_1,\dots,x_{n})$ is the convex hull of the $n!$
points obtained from $(x_1,\dots,x_{n})$ by permutations of the coordinates.
Permutohedra appear in representation theory as {\it weight polytopes} of
irreducible representations of $GL_n$ and in geometry as {\it mom... | {
"timestamp": "2005-07-07T23:11:28",
"yymm": "0507",
"arxiv_id": "math/0507163",
"language": "en",
"url": "https://arxiv.org/abs/math/0507163",
"abstract": "The volume and the number of lattice points of the permutohedron P_n are given by certain multivariate polynomials that have remarkable combinatorial ... |
https://arxiv.org/abs/1804.08483 | Erdős' Multiplication Table Problem for Function Fields and Symmetric Groups | Erdős first showed that the number of positive integers up to $x$ which can be written as a product of two number less than $\sqrt{x}$ has zero density. Ford then found the correct order of growth of the set of all these integers. We will use the tools developed by Ford to answer the analogous question in the function ... | \section{Introduction}\label{Intro}
Let $A(x)$ be the set of positive integers up to $x$ that can be written as a product of two numbers less than $\sqrt{x}$. Using estimates on the number of integers with a given number of prime divisors Erd\H{o}s \cite{E} was able to show that
$$|A(x)| \ll \frac{x}{(\log x)^{\d... | {
"timestamp": "2018-04-24T02:18:15",
"yymm": "1804",
"arxiv_id": "1804.08483",
"language": "en",
"url": "https://arxiv.org/abs/1804.08483",
"abstract": "Erdős first showed that the number of positive integers up to $x$ which can be written as a product of two number less than $\\sqrt{x}$ has zero density. ... |
https://arxiv.org/abs/2211.02319 | Evaluating a distance function | Computing the distance function to some surface or line is a problem that occurs very frequently. There are several ways of computing a relevant approximation of this function, using for example technique originating from the approximation of Hamilton Jacobi problems, or the fast sweeping method. Here we make a link wi... |
\section{Introduction}
In many cases, one has to evaluate the distance function to a surface $\Gamma_D$ \remi{which is part of the boundary of an open set $\Omega\in \mathbb R^d$}. An example in fluid mechanics is that of turbulence modelling: in some models, one of the parameters in the evaluation of the turbulent v... | {
"timestamp": "2022-12-02T02:10:09",
"yymm": "2211",
"arxiv_id": "2211.02319",
"language": "en",
"url": "https://arxiv.org/abs/2211.02319",
"abstract": "Computing the distance function to some surface or line is a problem that occurs very frequently. There are several ways of computing a relevant approxima... |
https://arxiv.org/abs/2008.11150 | Hidden Positivity and a New Approach to Numerical Computation of Hausdorff Dimension: Higher Order Methods | In [14], the authors developed a new approach to the computation of the Hausdorff dimension of the invariant set of an iterated function system or IFS. In this paper, we extend this approach to incorporate high order approximation methods. We again rely on the fact that we can associate to the IFS a parametrized family... | \section{Introduction}
\label{sec:intro}
In this paper, we continue previous work in finding rigorous estimates
for the Hausdorff dimension of invariant sets for iterated function
systems or IFS's. To describe the framework of the problem we are
considering, we let $S \subset \mathbb{R}$ be a nonempty compact set, and... | {
"timestamp": "2021-03-02T02:14:07",
"yymm": "2008",
"arxiv_id": "2008.11150",
"language": "en",
"url": "https://arxiv.org/abs/2008.11150",
"abstract": "In [14], the authors developed a new approach to the computation of the Hausdorff dimension of the invariant set of an iterated function system or IFS. In... |
https://arxiv.org/abs/1411.4906 | On Eigenvalues of Random Complexes | We consider higher-dimensional generalizations of the normalized Laplacian and the adjacency matrix of graphs and study their eigenvalues for the Linial-Meshulam model $X^k(n,p)$ of random $k$-dimensional simplicial complexes on $n$ vertices. We show that for $p=\Omega(\log n/n)$, the eigenvalues of these matrices are ... | \section{Introduction}
\label{sec:introduction}
Eigenvalues of graphs are a classical and well-studied subject, which goes back to a fundamental paper of Kirchhoff \cite{Kirchhoff:1847di}, in which he used the combinatorial graph Laplacian to analyze electrical networks and formulated his celebrated \emph{Matrix-Tree T... | {
"timestamp": "2015-08-26T02:10:29",
"yymm": "1411",
"arxiv_id": "1411.4906",
"language": "en",
"url": "https://arxiv.org/abs/1411.4906",
"abstract": "We consider higher-dimensional generalizations of the normalized Laplacian and the adjacency matrix of graphs and study their eigenvalues for the Linial-Mes... |
https://arxiv.org/abs/2207.09358 | Disoriented homology and double branched covers | This paper provides a convenient and practical method to compute the homology and intersection pairing of a branched double cover of the 4-ball.To projections of links in the 3-ball, and to projections of surfaces in the 4-ball into the boundary sphere, we associate a sequence of homology groups, called the disoriented... | \section{Introduction}
Branched covering spaces have proved to be an extremely efficient way of encoding embedding information about submanifolds \cite{ak,greene,lisca,OSz}. The basic information about a covering space is its homology; this is often the starting point for extracting other invariants, such as various g... | {
"timestamp": "2022-07-20T02:20:51",
"yymm": "2207",
"arxiv_id": "2207.09358",
"language": "en",
"url": "https://arxiv.org/abs/2207.09358",
"abstract": "This paper provides a convenient and practical method to compute the homology and intersection pairing of a branched double cover of the 4-ball.To project... |
https://arxiv.org/abs/1006.3030 | Satisfiability Thresholds for k-CNF Formula with Bounded Variable Intersections | We determine the thresholds for the number of variables, number of clauses, number of clause intersection pairs and the maximum clause degree of a k-CNF formula that guarantees satisfiability under the assumption that every two clauses share at most $\alpha$ variables. More formally, we call these formulas $\alpha$-int... | \section{Introduction}
Satisfiability of CNF is one of the most studied and versatile problems in computer science with its own journal (JSAT), competitions and an yearly conference, International Conference on Theory and Applications of Satisfiability Testing (SAT). In this paper we investigate a simple class of cr... | {
"timestamp": "2010-06-16T02:01:42",
"yymm": "1006",
"arxiv_id": "1006.3030",
"language": "en",
"url": "https://arxiv.org/abs/1006.3030",
"abstract": "We determine the thresholds for the number of variables, number of clauses, number of clause intersection pairs and the maximum clause degree of a k-CNF for... |
https://arxiv.org/abs/2212.12962 | Move-reduced graphs on a torus | We determine which bipartite graphs embedded in a torus are move-reduced. In addition, we classify equivalence classes of such move-reduced graphs under square/spider moves. This extends the class of minimal graphs on a torus studied by Goncharov-Kenyon, and gives a toric analog of Postnikov's results on a disk. | \section*{Introduction}\label{sec:intro}
Let ${\mathbb{T}}={\mathbb{R}}^2/{\mathbb{Z}}^2$ be a torus, and let $\Gamma$ be a bipartite graph embedded in ${\mathbb{T}}$. We say that two such graphs $\Gamma,\Gamma'$ are \emph{move-equivalent} if they are related by the moves \Msq--\Mres shown in \cref{fig:intro:moves}. W... | {
"timestamp": "2022-12-27T02:12:53",
"yymm": "2212",
"arxiv_id": "2212.12962",
"language": "en",
"url": "https://arxiv.org/abs/2212.12962",
"abstract": "We determine which bipartite graphs embedded in a torus are move-reduced. In addition, we classify equivalence classes of such move-reduced graphs under s... |
https://arxiv.org/abs/2103.07913 | Factorizations of regular graphs of infinite degree | Let $\mathcal{H}=\{H_i: i<\alpha \}$ be an indexed family of graphs for some ordinal number $\alpha$. $\mathcal{H}$-decomposition of a graph $G$ is a family $\mathcal{G}=\{G_i: i<\alpha \}$ of edge-disjoint subgraphs of $G$ such that $G_i$ is isomorphic to $H_i$ for every $i<\alpha$ and $\bigcup\{E(G_i):i<\alpha\}=E(G)... | \section{Introduction}
The study of matchings and related notions is arguably one of the most popular topics in graph theory.
This includes matchability, factorization, packing and decomposition problems. The most basic necessary condition for the existence of a decomposition of a given graph into perfect matchings ... | {
"timestamp": "2021-03-16T01:18:04",
"yymm": "2103",
"arxiv_id": "2103.07913",
"language": "en",
"url": "https://arxiv.org/abs/2103.07913",
"abstract": "Let $\\mathcal{H}=\\{H_i: i<\\alpha \\}$ be an indexed family of graphs for some ordinal number $\\alpha$. $\\mathcal{H}$-decomposition of a graph $G$ is ... |
https://arxiv.org/abs/1706.08167 | Phase retrieval using alternating minimization in a batch setting | This paper considers the problem of phase retrieval, where the goal is to recover a signal $z\in C^n$ from the observations $y_i=|a_i^* z|$, $i=1,2,\cdots,m$. While many algorithms have been proposed, the alternating minimization algorithm has been one of the most commonly used methods, and it is very simple to impleme... | \section{Introduction}
This article concerns the phase retrieval problem as follows: let $\boldsymbol{z}\in\mathbb{C}^n$ be an unknown vector; given $m$ known sensing vectors $\{\boldsymbol{a}_i\}_{i=1}^m\in\mathbb{C}^n$ and the observations
\[
y_i=|\boldsymbol{a}_i^*\boldsymbol{z}|, i=1,2,\cdots,m,
\]
then can we reco... | {
"timestamp": "2018-09-17T02:02:32",
"yymm": "1706",
"arxiv_id": "1706.08167",
"language": "en",
"url": "https://arxiv.org/abs/1706.08167",
"abstract": "This paper considers the problem of phase retrieval, where the goal is to recover a signal $z\\in C^n$ from the observations $y_i=|a_i^* z|$, $i=1,2,\\cdo... |
https://arxiv.org/abs/2102.09289 | Note on induced paths in sparse random graphs | We show that for $d\ge d_0(\epsilon)$, with high probability, the random graph $G(n,d/n)$ contains an induced path of length $(3/2-\epsilon)\frac{n}{d}\log d$. This improves a result obtained independently by Luczak and Suen in the early 90s, and answers a question of Fernandez de la Vega. Along the way, we generalize ... | \section{Introduction}
Let $G(n,p)$ denote the binomial random graph on $n$ vertices, where each edge is included independently with probability~$p$. In this note, we are concerned with \emph{induced} subgraphs of $G(n,p)$, specifically trees and paths.
The study of induced trees in $G(n,p)$ was initiated by Erd\H{o}... | {
"timestamp": "2021-02-19T02:16:37",
"yymm": "2102",
"arxiv_id": "2102.09289",
"language": "en",
"url": "https://arxiv.org/abs/2102.09289",
"abstract": "We show that for $d\\ge d_0(\\epsilon)$, with high probability, the random graph $G(n,d/n)$ contains an induced path of length $(3/2-\\epsilon)\\frac{n}{d... |
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