We present characterizations of connected graphs G of order n ≥ 2 for which h + (G) = n. It is shown that for every two integers n and m with 1 ≤ n − 1 ≤ m ≤ n 2 , there exists a connected graph G of order n and size m such that for each integer k with 2 ≤ k ≤ n, there exists an orientation of G with hull number k. 1. Introduction. The (directed) distance d(u, v) from a vertex u to a vertex v i...

Many applications give rise to dynamical systems in the form of a vector field with a phase space of moderate dimension. Examples are the Lorenz equations, mechanical and other oscillators, and models of spiking neurons. The key to understanding the global dynamics of such a system are the stable and unstable manifolds of the saddle points, of the saddle periodic orbits and, more generally, of ...

we obtain the expression of ricci tensor for a $gcr$-lightlikesubmanifold of indefinite complex space form and discuss itsproperties on a totally geodesic $gcr$-lightlike submanifold of anindefinite complex space form. moreover, we have proved that everyproper totally umbilical $gcr$-lightlike submanifold of anindefinite kaehler manifold is a totally geodesic $gcr$-lightlikesubmanifold.

We propose a novel method for the problem of 3D surface mesh segmentation. This mesh segmentation method is based on differential geometry and geodesic distance information. In our algorithm, vertices of the same group of surface types are allowed to join a segment. The geodesic distance is estimated using shortest path between connected vertices, which can be computed from well known algorithm...

Multi-class image segmentation is a complex problem that poses several challenges: developing better classifiers, designing more discriminative features, finding efficient optimization techniques and modeling the relations between image pixels in different image regions. In this paper we focus on the last one. A common way to address the problem of structured prediction is to model it as a Cond...

The non-rigid registration of surfaces is a complex and difficult task for which there are many important applications, such as comparing shape between deformable objects and comparing associated function. This paper presents a new approach for brain surface matching by determining the correspondence of 3D point sets between pairs of surfaces. The algorithm is based on shape using a combination...

We consider the problem of semi-supervised regression when the predictor variables are drawn from an unknown manifold. A simple approach to this problem is to first use both the labeled and unlabeled data to estimate the manifold geodesic distance between pairs of points, and then apply a k nearest neighbor regressor based on these distance estimates. We prove that given sufficiently many unlab...

3D shape context is a method to define matching points between similar shapes. It can be used as a pre-processing step in a non-rigid registration. The main limitation of the method is point mismatching, which includes long geodesic distance mismatch causing wrong topological structure, and neighbors crossing mismatch between two adjacent points. In this paper, we propose a topological structur...

This paper presents a method for finding cutting paths on a 3D triangular mesh surface to reduce the stretch in the flattened surface. The cutting paths link the surface boundary and the nodes where the Gaussian curvature is high, and their total length is minimized. First, a linear algorithm for computing an approximate boundary geodesic distance map is introduced; the map encapsulates the und...

We investigate the integrability of the discrete non-linear equation governing the dependence on geodesic distance of planar graphs with inner vertices of even valences. This equation follows from a bijection between graphs and blossom trees and is expressed in terms of generating functions for random walks. We construct explicitly an infinite set of conserved quantities for this equation, also...