The Hamilton-Jacobi approach has proved to be a powerful and elegant method for extracting the skeleton of a shape. The approach is based on the fact that the inward evolving boundary flux is conservative everywhere except at skeletal points. Nonetheless this method appears to overlook the fact that the linear density of the evolving boundary front is not constant where the front is curved. In ...

Batsell and Polking (1985) developed one of the important choice models that address the problem of independence from irrelevant alternatives. In this note, we propose an estimation method that directly estimates Batsell and Polking’s model. Compared to the indirect estimation method suggested by Batsell and Polking, the direct method is simpler, making the BP model more accessible to potential...

This paper reports on results on the entropy of the Spanish language. They are based on an analysis of natural language for n-word symbols (n = 1 to 18), trigrams, digrams, and characters. The results obtained in this work are based on the analysis of twelve different literary works in Spanish, as well as a 279917 word news file provided by the Spanish press agency EFE. Entropy values are calcu...

Abstract. In this note, we construct families of functionals of the type of F-functional and W-functional of Perelman. We prove that these new functionals are nondecreasing under the Ricci flow. As applications, we give a proof of the theorem that compact steady Ricci breathers must be Ricci-flat. Using these new functionals, we also give a new proof of Perelman’s no non-trivial expanding breat...

A direct method for constructing large sets of t-designs is based on the concept of assembling orbits of a permutation group G on ksubsets of a v-set into block sets of t-designs so that these designs form a large set. If G is t-homogeneous, then any orbit is a t-design and therefore we obtain a large set by partitioning the set of orbits into parts consisting of the same number of k-subsets. I...

Expressions for the multi-dimensional densities of Brownian bridge local time are derived by two diierent methods: A direct method based on Kac's formula for Brownian functionals and an indirect one based on a limit theorem for strata of random mappings.

Consider two sequences of bounded random variables, a value and a timing process, that satisfy the large deviation principle (LDP) with rate function J (·, ·) and whose cumulative process satisfies the LDP with rate function I (·). Under mixing conditions, an LDP for estimates of I constructed by transforming an estimate of J is proved. For the case of a cumulative renewal process it is demonst...

Consider two sequences of bounded random variables, a value and a timing process, that satisfy the large deviation principle (LDP) with rate-function J(· , ·) and whose cumulative process satisfies the LDP with rate-function I(·). Under mixing conditions, an LDP for estimates of I constructed by transforming an estimate of J is proved. For the case of cumulative renewal processes it is demonstr...

3-D tracking of free-moving objects has to deal with brightness variations pronounced by the shape of the tracked surface. Pixel-based tracking techniques, though versatile, are particularly affected by such variations. Here, we evaluate two illumination-adaptive methods for a novel efficient pixel-based 3-D tracking approach. Brightness adaption by means of an illumination basis is compared to...