We show that the regularity of the gravitational metric tensor cannot be lifted from C to C by any C coordinate transformation in a neighborhood of a point of shock wave interaction in General Relativity, without forcing the determinant of the metric tensor to vanish at the point of interaction. This is in contrast to Israel’s Theorem [6] which states that such coordinate transformations always...

This paper presents a novel selective refinement scheme of progressive meshes. In previous schemes, topology information in the neighborhood of a collapsed edge is stored in the analysis phase. A vertex split or edge collapse transformation is possible in the synthesis phase only if the configuration of neighborhood vertices in the current mesh corresponds to the stored topology information. In...

The spatial genetic algorithm (SGA) is presented. Locality is realized by mapping GA population on a cellular automata. The role of neighborhood in genetic search is shown by comparing SGA with the parallel recornbinative simulated annealing (PRSA) approach proposed by Mahfoud and Goldberg in [1]. It appears, that not optimized SGA outdoes PRSA in loose and is only slightly worse in tight optim...

A permutation graph is an intersection graph of segments lying between two parallel lines. A Seidel complementation of a finite graph at a vertex v consists in complementing the edges between the neighborhood and the non-neighborhood of v. Two graphs are Seidel complement equivalent if one can be obtained from the other by a sequence of Seidel complementations. In this paper we introduce the ne...

Simulated annealing (SA) was inspired from annealing in metallurgy, a technique involving heating and controlled cooling of a material to increase the size of its crystals and reduce their defects, both are attributes of the material that depend on its thermodynamic free energy. In this Paper, firstly we will study SA in details on its initial feasible solution choosing, initial temperature sel...

Let H : <m×<n → <n be a locally Lipschitz function in a neighborhood of (ȳ, x̄) and H(ȳ, x̄) = 0 for ȳ ∈ <m and x̄ ∈ <n. The implicit function theorem in the sense of Clarke [1, 2] says that if πx∂H(ȳ, x̄) is of maximal rank, then there exist a neighborhood Y of ȳ and a Lipschitz function G(·) : Y → <n such that G(ȳ) = x̄ and for every y in Y , H(y,G(y)) = 0. In this paper, we shall further show tha...

Main methods, algorithms and applications of the Variable Neighborhood Search metaheuristic are surveyed, in view of a chapter of the Encyclopedia of Optimization.

In this paper we provide concrete combinatorial formal deformation algorithms, namely sequences of elementary collapses and expansions, which relate various previously extensively studied families of combinatorially defined polyhedral complexes. To start with, we give a sequence of elementary collapses leading from the barycentric subdivision of the neighborhood complex to the Lovász complex of...

In this paper, we study how an individual in a social network should decide whether or not to adopt a trend, based on how many people in his/her neighborhood in the social network adopted the trend. In particular we are interested in the question in what adoption policy leads to an optimal trend-adoption in the sense that an individual only adopts a trend if the majority of his/her social netwo...

Focus-group and photo-voice methodology were used to identify the salient factors of the neighborhood environment that encourage or discourage walking in older, urban African Americans. Twenty-one male (n = 2) and female (n = 19) African Americans age 60 years and older (M = 70 +/- 8.7, range = 61-85) were recruited from a large urban senior center. Photographs taken by the participants were us...