Search results for "Polygon"

Filtering with dissipativity for T-S fuzzy systems with time-varying delay: Reciprocally convex approach

2013

This paper is focused on the problem of reliable filter design with strictly dissipativity for a class of discrete-time T-S fuzzy time-delay systems. Our attention is paid on the design of reliable filter to ensure a strictly dissipative performance for the filtering error system. By employing the reciprocally convex approach, a sufficient condition of dissipativity analysis is obtained for T-S fuzzy delayed systems with sensor failures. A desired reliable filter is designed by solving a convex optimization problem.

Locally convex quasi *-algebras with sufficiently many *-representations

2012

AbstractThe main aim of this paper is the investigation of conditions under which a locally convex quasi ⁎-algebra (A[τ],A0) attains sufficiently many (τ,tw)-continuous ⁎-representations in L†(D,H), to separate its points. Having achieved this, a usual notion of bounded elements on A[τ] rises. On the other hand, a natural order exists on (A[τ],A0) related to the topology τ, that also leads to a kind of bounded elements, which we call “order bounded”. What is important is that under certain conditions the latter notion of boundedness coincides with the usual one. Several nice properties of order bounded elements are extracted that enrich the structure of locally convex quasi ⁎-algebras.

Reduced reference 3D mesh quality assessment based on statistical models

2015

International audience; During their geometry processing and transmission 3D meshes are subject to various visual processing operations like compression, watermarking, remeshing, noise addition and so forth. In this context it is indispensable to evaluate the quality of the distorted mesh, we talk here about the mesh visual quality (MVQ) assessment. Several works have tried to evaluate the MVQ using simple geometric measures, However this metrics do not correlate well with the subjective score since they fail to reflect the perceived quality. In this paper we propose a new objective metric to evaluate the visual quality between a mesh with a perfect quality called reference mesh and its dis…

No-Reference 3D Mesh Quality Assessment Based on Dihedral Angles Model and Support Vector Regression

2016

International audience; 3D meshes are subject to various visual distortions during their transmission and geometrical processing. Several works have tried to evaluate the visual quality using either full reference or reduced reference approaches. However, these approaches require the presence of the reference mesh which is not available in such practical situations. In this paper, the main contribution lies in the design of a computational method to automatically predict the perceived mesh quality without reference and without knowing beforehand the distortion type. Following the no-reference (NR) quality assessment principle, the proposed method focuses only on the distorted mesh. Specific…

On the exhaustive generation of k-convex polyominoes

2017

The degree of convexity of a convex polyomino P is the smallest integer k such that any two cells of P can be joined by a monotone path inside P with at most k changes of direction. In this paper we present a simple algorithm for computing the degree of convexity of a convex polyomino and we show how it can be used to design an algorithm that generates, given an integer k, all k-convex polyominoes of area n in constant amortized time, using space O(n). Furthermore, by applying few changes, we are able to generate all convex polyominoes whose degree of convexity is exactly k.

Approximation Algorithms for Multicoloring Planar Graphs and Powers of Square and Triangular Meshes

2006

A multicoloring of a weighted graph G is an assignment of sets of colors to the vertices of G so that two adjacent vertices receive two disjoint sets of colors. A multicoloring problem on G is to find a multicoloring of G. In particular, we are interested in a minimum multicoloring that uses the least total number of colors. The main focus of this work is to obtain upper bounds on the weighted chromatic number of some classes of graphs in terms of the weighted clique number. We first propose an 11/6-approximation algorithm for multicoloring any weighted planar graph. We then study the multicoloring problem on powers of square and triangular meshes. Among other results, we show that the infi…

A combinatorial view on string attractors

2021

Abstract The notion of string attractor has recently been introduced in [Prezza, 2017] and studied in [Kempa and Prezza, 2018] to provide a unifying framework for known dictionary-based compressors. A string attractor for a word w = w 1 w 2 ⋯ w n is a subset Γ of the positions { 1 , … , n } , such that all distinct factors of w have an occurrence crossing at least one of the elements of Γ. In this paper we explore the notion of string attractor by focusing on its combinatorial properties. In particular, we show how the size of the smallest string attractor of a word varies when combinatorial operations are applied and we deduce that such a measure is not monotone. Moreover, we introduce a c…

2021

This paper proposes a new method for blind mesh visual quality assessment (MVQA) based on a graph convolutional network. For that, we address the node classification problem to predict the perceived visual quality. First, two matrices representing the 3D mesh are considered: a graph adjacency matrix and a feature matrix. Both matrices are used as input to a shallow graph convolutional network. The network consists of two convolutional layers followed by a max-pooling layer to provide the final feature representation. With this structure, the Softmax classifier predicts the quality score category without the reference mesh’s availability. Experiments are conducted on four publicly available …

F-signature of pairs: Continuity, p-fractals and minimal log discrepancies

2011

This paper contains a number of observations on the {$F$-signature} of triples $(R,\Delta,\ba^t)$ introduced in our previous joint work. We first show that the $F$-signature $s(R,\Delta,\ba^t)$ is continuous as a function of $t$, and for principal ideals $\ba$ even convex. We then further deduce, for fixed $t$, that the $F$-signature is lower semi-continuous as a function on $\Spec R$ when $R$ is regular and $\ba$ is principal. We also point out the close relationship of the signature function in this setting to the works of Monsky and Teixeira on Hilbert-Kunz multiplicity and $p$-fractals. Finally, we conclude by showing that the minimal log discrepancy of an arbitrary triple $(R,\Delta,\b…

A fixed point theorem for G-monotone multivalued mapping with application to nonlinear integral equations

2017

We extend notion and theorem of [21] to the case of a multivalued mapping defined on a metric space endowed with a finite number of graphs. We also construct an example to show the generality of our result over existing results. Finally, we give an application to nonlinear integral equations