Search results for "combinatoric"

Convergence of Markovian Stochastic Approximation with discontinuous dynamics

2016

This paper is devoted to the convergence analysis of stochastic approximation algorithms of the form $\theta_{n+1} = \theta_n + \gamma_{n+1} H_{\theta_n}({X_{n+1}})$, where ${\left\{ {\theta}_n, n \in {\mathbb{N}} \right\}}$ is an ${\mathbb{R}}^d$-valued sequence, ${\left\{ {\gamma}_n, n \in {\mathbb{N}} \right\}}$ is a deterministic stepsize sequence, and ${\left\{ {X}_n, n \in {\mathbb{N}} \right\}}$ is a controlled Markov chain. We study the convergence under weak assumptions on smoothness-in-$\theta$ of the function $\theta \mapsto H_{\theta}({x})$. It is usually assumed that this function is continuous for any $x$; in this work, we relax this condition. Our results are illustrated by c…

Probabilistic interpretation of the Calderón problem

2017

In this paper, we use the theory of symmetric Dirichlet forms to give a probabilistic interpretation of Calderon's inverse conductivity problem in terms of reflecting diffusion processes and their corresponding boundary trace processes. This probabilistic interpretation comes in three equivalent formulations which open up novel perspectives on the classical question of unique determinability of conductivities from boundary data. We aim to make this work accessible to both readers with a background in stochastic process theory as well as researchers working on deterministic methods in inverse problems.

Multi-Dimensional Pattern Matching with Dimensional Wildcards: Data Structures and Optimal On-Line Search Algorithms

1997

We introduce a new multidimensional pattern matching problem that is a natural generalization of string matching, a well studied problem1. The motivation for its algorithmic study is mainly theoretical. LetA1:n1,?,1:nd be a text matrix withN=n1?ndentries andB1:m1,?,1:mr be a pattern matrix withM=m1?mrentries, whered?r?1 (the matrix entries are taken from an ordered alphabet ?). We study the problem of checking whether somer-dimensional submatrix ofAis equal toB(i.e., adecisionquery).Acan be preprocessed andBis given on-line. We define a new data structure for preprocessingAand propose CRCW-PRAM algorithms that build it inO(logN) time withN2/nmaxprocessors, wherenmax=max(n1,?,nd), such that …

On the number of singularities, zero curvature points and vertices of a simple convex space curve

1995

We prove a generalization of the 4 vertex theorem forC3 closed simple convex space curves including singular and zero curvature points.

Classification of cat ganglion retinal cells and implications for shape-function relationship

2002

This article presents a quantitative approach to ganglion cell classification by considering combinations of several geometrical features including fractal dimension, symmetry, diameter, eccentricity and convex hull. Special attention is given to moment and symmetry-based features. Several combinations of such features are fed to two clustering methods (Ward's hierarchical scheme and K-Means) and the respectively obtained classifications are compared. The results indicate the superiority of some features, also suggesting possible biological implications.

Strictly convex metric spaces with round balls and fixed points

2005

An upper bound for nonlinear eigenvalues on convex domains by means of the isoperimetric deficit

2010

We prove an upper bound for the first Dirichlet eigenvalue of the p-Laplacian operator on convex domains. The result implies a sharp inequality where, for any convex set, the Faber-Krahn deficit is dominated by the isoperimetric deficit.

R Code for Hausdorff and Simplex Dispersion Orderings in the 2D Case

2010

This paper proposes a software implementation using R of the Hausdorff and simplex dispersion orderings. A copy can be downloaded from http://www.uv.es/~ayala/software/fun-disp.R . The paper provides some examples using the functions exactHausdorff for the Hausdorff dispersion ordering and the function simplex for the simplex dispersion orderings. Some auxiliary functions are commented too.

The project scheduling polyhedron: Dimension, facets and lifting theorems

1993

Abstract The Project scheduling with resource constraints can be formulated as follows: given a graph G with node set N, a set H of directed arcs corresponding to precedence relations, and a set H′ of disjunctive arcs reflecting the resource incompatibilities, find among the subsets of H′ satisfying the resource constraints the set S that minimizes the longest path in graph (N, H ∪ S). We define the project scheduling polyhedron Qs as the convex hull of the feasible solutions. We investigate several classes of inequalities with respect to their facet-defining properties for the associated polyhedron. The dimension of Qs is calculated and several inequalities are shown to define facets. For …

Elementary Integration of Superelliptic Integrals

2021

Consider a superelliptic integral $I=\int P/(Q S^{1/k}) dx$ with $\mathbb{K}=\mathbb{Q}(\xi)$, $\xi$ a primitive $k$th root of unity, $P,Q,S\in\mathbb{K}[x]$ and $S$ has simple roots and degree coprime with $k$. Note $d$ the maximum of the degree of $P,Q,S$, $h$ the logarithmic height of the coefficients and $g$ the genus of $y^k-S(x)$. We present an algorithm which solves the elementary integration problem of $I$ generically in $O((kd)^{\omega+2g+1} h^{g+1})$ operations.