scholarly journals An Edge-Signed Generalization of Chordal Graphs, Free Multiplicities on Braid Arrangements, and Their Characterizations

2009 ◽  
Vol DMTCS Proceedings vol. AK,... (Proceedings) ◽  
Author(s):  
Takuro Abe ◽  
Koji Nuida ◽  
Yasuhide Numata
Keyword(s):  
Special Kind ◽  
Chordal Graph ◽  
Hyperplane Arrangements ◽  
Chordal Graphs ◽  
Nous Proposons ◽  
Signed Graphs ◽  
International Audience ◽  
Perfect Elimination Ordering

International audience In this article, we propose a generalization of the notion of chordal graphs to signed graphs, which is based on the existence of a perfect elimination ordering for a chordal graph. We give a special kind of filtrations of the generalized chordal graphs, and show a characterization of those graphs. Moreover, we also describe a relation between signed graphs and a certain class of multiarrangements of hyperplanes, and show a characterization of free multiarrangements in that class in terms of the generalized chordal graphs, which generalizes a well-known result by Stanley on free hyperplane arrangements. Finally, we give a remark on a relation of our results with a recent conjecture by Athanasiadis on freeness characterization for another class of hyperplane arrangements. Dans cet article, nous proposons une généralisation de la notion des graphes triangulés à graphes signés, qui est basée sur l'existence d'un ordre d'élimination simplicial à un graphe triangulé. Nous donnons un genre spécial de filtrations des graphes triangulés généralisés, et montrons une caractérisation de ces graphes. De plus, nous décrivons aussi une relation entre graphes signés et une certaine classe de multicompositions d'hyperplans, et montrons une caractérisation de multicompositions libres dans cette classe en termes des graphes triangulés généralisés, qui généralise un résultat célèbre de Stanley sur compositions libres d'hyperplans. Finalement, nous donnons une remarque sur une relation de nos résultats avec une conjecture récente d'Athanasiadis sur une caractérisation du freeness d'une autre classe de compositions d'hyperplans.

scholarly journals Chamber Structure For Double Hurwitz Numbers

2010 ◽  
Vol DMTCS Proceedings vol. AN,... (Proceedings) ◽  
Author(s):  
Renzo Cavalieri ◽  
Paul JOHNSON ◽  
Hannah Markwig
Keyword(s):  
Main Tool ◽  
Hyperplane Arrangements ◽  
Lattice Points ◽  
Piecewise Polynomial ◽  
Nous Proposons ◽  
Hurwitz Numbers ◽  
Wall Crossing ◽  
Piecewise Polynomial Functions ◽  
International Audience ◽  
Branch Divisor

International audience Double Hurwitz numbers count covers of the sphere by genus $g$ curves with assigned ramification profiles over $0$ and $\infty$, and simple ramification over a fixed branch divisor. Goulden, Jackson and Vakil (2005) have shown double Hurwitz numbers are piecewise polynomial in the orders of ramification, and Shadrin, Shapiro and Vainshtein (2008) have determined the chamber structure and wall crossing formulas for $g=0$. We provide new proofs of these results, and extend them in several directions. Most importantly we prove wall crossing formulas for all genera. The main tool is the authors' previous work expressing double Hurwitz number as a sum over labelled graphs. We identify the labels of the graphs with lattice points in the chambers of certain hyperplane arrangements, which give rise to piecewise polynomial functions. Our understanding of the wall crossing for these functions builds on the work of Varchenko (1987). This approach to wall crossing appears novel, and may be of broader interest. This extended abstract is based on a new preprint by the authors. Les nombres de Hurwitz doubles dénombrent les revêtements de la sphère par une surface de genre $g$ avec ramifications prescrites en $0$ et $\infty$, et dont les autres valeurs critiques sont non dégénérées et fixées. Goulden, Jackson et Vakil (2005) ont prouvé que les nombres de Hurwitz doubles sont polynomiaux par morceaux en l'ordre des ramifications prescrites, et Shadrin, Shapiro et Vainshtein (2008) ont déterminé la structure des chambres et ont établis des formules pour traverser les murs en genre $0$. Nous proposons des nouvelles preuves de ces résultats, et les généralisons dans plusieurs directions. En particulier, nous prouvons des formules pour traverser les murs en tout genre. L'outil principal est le précédent travail des auteurs exprimant les nombres de Hurwitz doubles comme somme de graphes étiquetés. Nous identifions les étiquetages avec les points entiers à l'intérieur d'une chambre d'un arrangement d'hyperplans, qui sont connu pour donner une fonction polynomiale par morceaux. Notre étude des formules pour traverser les murs de ces fonctions se base sur un travail antérieur de Varchenko (1987). Cette approche paraît nouvelle, et peut être d'un large intérêt. Ce résumé élargi se base sur un papier nouveau des auteurs.

scholarly journals On economical set representations of graphs

2009 ◽  
Vol Vol. 11 no. 2 (Graph and Algorithms) ◽  
Author(s):  
Jing Kong ◽  
Yaokun Wu
Keyword(s):  
Chordal Graphs ◽  
Minimum Size ◽  
Extremal Graphs ◽  
Intersection Numbers ◽  
International Audience ◽  
Perfect Elimination Ordering ◽  
Set Representations

Graphs and Algorithms International audience In this paper we discuss the bounds of and relations among various kinds of intersection numbers of graphs. Especially, we address extremal graphs with respect to the established bounds. The uniqueness of the minimum-size intersection representations for some graphs is also studied. In the course of this work, we introduce a superclass of chordal graphs, defined in terms of a generalization of simplicial vertex and perfect elimination ordering.

scholarly journals Analysis of Texture Applied to Renal Echography

2005 ◽  
Vol Volume 3, Special Issue... ◽  
Author(s):  
M. Tahiri Alaoui ◽  
S.M. Farssi ◽  
K. Touzani ◽  
P. Bunel
Keyword(s):  
Statistical Analysis ◽  
Ultrasound Image ◽  
Ultrasound Images ◽  
Nous Proposons ◽  
Human Organs ◽  
Cortical Zone ◽  
International Audience ◽  
Renal Echography

International audience Renal echography remains the least expensive means for the exploration of the kidney. The system that we propose is a contribution for the diagnostic automatic of the kidney on ultrasound image. The analysis of texture is a technique which proved reliable in the field of the characterization of the human organs on ultrasound images. Indeed, our contribution aims at the characterization of the images of echographic textures of the kidney. This characterization is, in a first level, structural to evaluate the presence (form and position) of the various components of the kidney (clusters, medullary cortical zone). The statistical analysis of texture constitutes our second approach by carrying out virtual punctures on the kidney in order to be able to evaluate its state by quantifying the texture of the various areas characteristic of the kidney . L'échographie rénale reste le moyen le moins coûteux pour l'exploration du rein. Le système que nous proposons est une contribution à l'amélioration du diagnostic automatique du rein par l'analyse de texture, une technique qui a fait ses preuves dans le domaine de la caractérisation des organes humains sur des images ultrasoniques. Dans un premier temps, la caractérisation structurelle des images de texture échographique du rein permettra de visualiser (forme et position) les différentes composantes du rein (glomérules, médullaire, zone corticale). Elle sera complétée par l'analyse statistique de texture qui consistera à réaliser des ponctions virtuelles sur le rein pour en évaluer l'état général en quantifiant la texture des différentes régions caractéristiques

scholarly journals p-box: a new graph model

2015 ◽  
Vol Vol. 17 no. 1 (Graph Theory) ◽  
Author(s):  
Mauricio Soto ◽  
Christopher Thraves-Caro
Keyword(s):  
Graph Theory ◽  
Graph Model ◽  
Directed Path ◽  
Outerplanar Graphs ◽  
New Model ◽  
Model Based ◽  
Representative Element ◽  
International Audience ◽  
Graph Families

Graph Theory International audience In this document, we study the scope of the following graph model: each vertex is assigned to a box in ℝd and to a representative element that belongs to that box. Two vertices are connected by an edge if and only if its respective boxes contain the opposite representative element. We focus our study on the case where boxes (and therefore representative elements) associated to vertices are spread in ℝ. We give both, a combinatorial and an intersection characterization of the model. Based on these characterizations, we determine graph families that contain the model (e. g., boxicity 2 graphs) and others that the new model contains (e. g., rooted directed path). We also study the particular case where each representative element is the center of its respective box. In this particular case, we provide constructive representations for interval, block and outerplanar graphs. Finally, we show that the general and the particular model are not equivalent by constructing a graph family that separates the two cases.

scholarly journals Classes of graphs with restricted interval models

1999 ◽  
Vol Vol. 3 no. 4 ◽  
Author(s):  
Andrzej Proskurowski ◽  
Jan Arne Telle
Keyword(s):  
Maximum Clique ◽  
Interval Graphs ◽  
Induced Subgraph ◽  
Graph Theoretic ◽  
Graph Classes ◽  
International Audience ◽  
Forbidden Induced Subgraph ◽  
Nested Hierarchy ◽  
Graph Families

International audience We introduce q-proper interval graphs as interval graphs with interval models in which no interval is properly contained in more than q other intervals, and also provide a forbidden induced subgraph characterization of this class of graphs. We initiate a graph-theoretic study of subgraphs of q-proper interval graphs with maximum clique size k+1 and give an equivalent characterization of these graphs by restricted path-decomposition. By allowing the parameter q to vary from 0 to k, we obtain a nested hierarchy of graph families, from graphs of bandwidth at most k to graphs of pathwidth at most k. Allowing both parameters to vary, we have an infinite lattice of graph classes ordered by containment.

scholarly journals Contribution to image restoration using a neural network model

2002 ◽  
Vol Volume 1, 2002 ◽  
Author(s):  
Karim Achour ◽  
Nadia Zenati ◽  
Oualid Djekoune
Keyword(s):  
Neural Network ◽  
Image Restoration ◽  
Network Model ◽  
Neural Network Model ◽  
Hopfield Neural Network ◽  
Optimization Method ◽  
Nous Proposons ◽  
International Audience ◽  
High Level

International audience The reduction of the blur and the noise is an important task in image processing. Indeed, these two types of degradation are some undesirable components during some high level treatments. In this paper, we propose an optimization method based on neural network model for the regularized image restoration. We used in this application a modified Hopfield neural network. We propose two algorithms using the modified Hopfield neural network with two updating modes : the algorithm with a sequential updates and the algorithm with the n-simultaneous updates. The quality of the obtained result attests the efficiency of the proposed method when applied on several images degraded with blur and noise. La réduction du bruit et du flou est une tâche très importante en traitement d'images. En effet, ces deux types de dégradations sont des composantes indésirables lors des traitements de haut niveau. Dans cet article, nous proposons une méthode d'optimisation basée sur les réseaux de neurones pour résoudre le problème de restauration d'images floues-bruitées. Le réseau de neurones utilisé est le réseau de « Hopfield ». Nous proposons deux algorithmes utilisant deux modes de mise à jour: Un algorithme avec un mode de mise à jour séquentiel et un algorithme avec un mode de mise à jour n-simultanée. L'efficacité de la méthode mise en œuvre a été testée sur divers types d'images dégradées.

A Geometric Characterization of Nonnegative Bands

2004 ◽  
Vol 47 (2) ◽  
pp. 257-263
Author(s):  
Alka Marwaha
Keyword(s):  
Invariant Subspace ◽  
Geometric Structure ◽  
Finite Rank ◽  
Special Kind ◽  
Maximal Rank ◽  
Geometric Characterization ◽  
Idempotent Operators ◽  
Rank One ◽  
Standard Subspace

AbstractA band is a semigroup of idempotent operators. A nonnegative band S in having at least one element of finite rank and with rank (S) > 1 for all S in S is known to have a special kind of common invariant subspace which is termed a standard subspace (defined below).Such bands are called decomposable. Decomposability has helped to understand the structure of nonnegative bands with constant finite rank. In this paper, a geometric characterization of maximal, rank-one, indecomposable nonnegative bands is obtained which facilitates the understanding of their geometric structure.

scholarly journals Some New Classes of Open Distance-Pattern Uniform Graphs

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Bibin K. Jose
Keyword(s):  
Nonempty Subset ◽  
Chordal Graphs ◽  
Outerplanar Graph ◽  
Outerplanar Graphs ◽  
Induced Subgraphs ◽  
Minimum Cardinality ◽  
Maximal Outerplanar Graphs ◽  
Split Graphs ◽  
Strongly Chordal Graphs

Given an arbitrary nonempty subset M of vertices in a graph G=(V,E), each vertex u in G is associated with the set fMo(u)={d(u,v):v∈M,u≠v} and called its open M-distance-pattern. The graph G is called open distance-pattern uniform (odpu-) graph if there exists a subset M of V(G) such that fMo(u)=fMo(v) for all u,v∈V(G), and M is called an open distance-pattern uniform (odpu-) set of G. The minimum cardinality of an odpu-set in G, if it exists, is called the odpu-number of G and is denoted by od(G). Given some property P, we establish characterization of odpu-graph with property P. In this paper, we characterize odpu-chordal graphs, and thereby characterize interval graphs, split graphs, strongly chordal graphs, maximal outerplanar graphs, and ptolemaic graphs that are odpu-graphs. We also characterize odpu-self-complementary graphs, odpu-distance-hereditary graphs, and odpu-cographs. We prove that the odpu-number of cographs is even and establish that any graph G can be embedded into a self-complementary odpu-graph H, such that G and G¯ are induced subgraphs of H. We also prove that the odpu-number of a maximal outerplanar graph is either 2 or 5.

Clique Partitions of Chordal Graphs

1993 ◽  
Vol 2 (4) ◽  
pp. 409-415 ◽  
Author(s):  
Paul Erdős ◽  
Edward T. Ordman ◽  
Yechezkel Zalcstein
Keyword(s):  
Chordal Graph ◽  
Chordal Graphs ◽  
Split Graph ◽  
Threshold Graph

To partition the edges of a chordal graph on n vertices into cliques may require as many as n2/6 cliques; there is an example requiring this many, which is also a threshold graph and a split graph. It is unknown whether this many cliques will always suffice. We are able to show that (1 − c)n2/4 cliques will suffice for some c > 0.

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