This paper introduces a new importance sampling technique to increase the efficiency of rare event simulation. By using a multidimensional rotational invariant auxiliary density, this method can be applied to estimate risk measures for credit risk portfolios where the method of importance sampling via mean shifting is not suitable. The loss distribution of the portfolio is obtained by simulatin...

We investigate a nonlinear inverted pendulum impacting between two rigid walls under external periodic excitation. Based on KAM theory, we prove that there are three regions (corresponding to different energies) occupied by quasi-periodic solutions in phase space when the excitation is small. Moreover, rotational motion maintained perturbation gets larger. The existence of subharmonic obtained ...

P. J. Basser, S. Pajevic NICHD / NIH, Bethesda, MD, United States, CIT / NIH, Bethesda, MD, United States SYNOPSIS: We propose that a necessary condition for an optimally designed DT-MRI experiment is that a new normal distribution for the estimated diffusion tensor, p(D) ∝ exp(1/2 D:A:D), be characterized by an isotropic 4-order precision tensor, A. This requirement ensures that statistical pr...

Despite the fact that image texture features extracted from high-resolution remotely sensed images over urban areas have demonstrated their ability to distinguish different classes, they are still far from being ideal. Multiresolution grayscale and rotation invariant texture classification with Local Binary Patterns (LBPs) have proven to be a very powerful texture feature. In this paper we perf...

The Brunn-Minkowski theory in convex geometry concerns, among other things, the volumes, mixed and surface area measures of bodies. We study generalizations these concepts to Borel with density Rn– particular, weighted versions volumes (the so-called measures) when dealing up three distinct then formulate analyze classical measures, obtain a new integral formula for measure As an application, w...

The Kolmogorov-Sinai entropy is a far reaching dynamical generalization of Shannon entropy of information systems. This entropy works perfectly for probability measure preserving (p.m.p.) transformations. However, it is not useful when there is no finite invariant measure. There are certain successful extensions of the notion of entropy to infinite measure spaces, or transformations with ...