Mesh decomposition is critical for analyzing, understanding, editing and reusing of mesh models. Although there are many methods for mesh decomposition, most utilize only triangular meshes. In this paper, we present an automated method for decomposing a volumetric mesh into semantic components. Our method consists of three parts. First, the outer surface mesh of the volumetric mesh is decompose...

We describe the generic change of the partial multiplicities at a given eigenvalue λ0 of a regular matrix pencil A0 + λA1 under perturbations with low normal rank. More precisely, if the pencil A0 + λA1 has exactly g nonzero partial multiplicities at λ0, then for most perturbations B0 + λB1 with normal rank r < g the perturbed pencil A0 + B0 + λ(A1 + B1) has exactly g − r nonzero partial multip...

A weighting of the edges of a graph is called irregular if the weighted degrees of the vertices are all different. In this note we show that such a weighting is possible from the weight set {1, 2, . . . , 6dnδ e} for all graphs not containing a component with exactly 2 vertices or two isolated vertices.

Given a connected irregular graph G of order n, write μ for the largest eigenvalue of its adjacency matrix, ∆ for its maximum degree, andD for its diameter. We prove that ∆− μ > 1 (D + 2)n and this bound is tight up to a constant factor. This improves previous results of Stevanović and Zhang, and extends a result of Alon and Sudakov.

1 CONTENTS 2 Figure 1: A partitioned 2D irregular mesh of an airfoil. The shading of a mesh element indicates the processor to which i t is mapped. 0.1 Introduction Algorithms that nd good partitionings of unstructured and irregular graphs are critical for the eecient execution of scientiic simulations on high performance parallel computers. In these simulations, computation is performed iterat...

The emergence of Graph Convolutional Network (GCN) has greatly boosted the progress graph learning. However, two disturbing factors, noise and redundancy in data, lack interpretation for prediction results, impede further development GCN. One solution is to recognize a predictive yet compressed subgraph get rid obtain interpretable part graph. This setting similar information bottleneck (IB) pr...

We give a decomposition formula for the Bartholdi zeta function of a graph G which is partitioned into some irregular coverings. As a corollary, we obtain a decomposition formula for the Bartholdi zeta function of G which is partitioned into some regular coverings. © 2005 Elsevier B.V. All rights reserved.

Homology groups and their generators of a 2D image are computed using a hierarchical structure i.e. irregular graph pyramid. In this paper we show that the generators of the first homology groups of a 2D image, computed with this pyramid based method always fit on the borders of the regions.

Homology groups and their generators of a 2D image are computed using a hierarchical structure i.e. irregular graph pyramid. In this paper we show that the generators of the first homology groups of a 2D image, computed with this pyramid based method always fit on the boundaries of the regions.

This is the first part of project toward proving BCOV's Feymann graph sum formula all genera Gromov-Witten invariants quintic Calabi-Yau threefolds. In this paper, we introduce notion N-Mixed-Spin-P fields, construct their moduli spaces, virtual cycles, localization formulas, and a vanishing result associated with irregular graphs.