Uemura [1] discovered the mapping formula for Type 1 Vague events and presented an alternative problem as example of its application. Since it is well known that leads to sequential Bayesian inference, flow subsequent research was make multidimensional, introduce concept time, derive a Markov (decision) process. Furthermore, we formulated stochastic differential equations them [2]. This paper r...

Solutions to optimization problems of convex type are typically characterized by saddle point conditions in which the primal vector is paired with a dual ‘multiplier’ vector. This paper investigates the behavior of such a primal-dual pair with respect to perturbations in parameters on which the problem depends. A necessary and sufficient condition in terms of certain matrices is developed for t...

Inconsistencies between a phylogenetic tree calculated from a set of related genes and known species phylogeny may be due to duplications events in the gene family under study. Tree Mapping attempts to pinpoint gene duplications in order to explain such discrepancies. The e ort in this explanation is measured using a tree mapping measure. Very little algorithmic work has so far been invested in...

We present a model for predicting the eye-movements of observers who is viewing dynamic sequences of images. As an indicator for the degree of saliency we evaluate an invariant of the spatio-temporal structure tensor that indicates an intrinsic dimension of at least two. The saliency is used to derive a list of candidate locations. Out of this list, the currently attended location is selected a...

A simple procedure to map two probability measures in R is the so-called Knothe-Rosenblatt rearrangement, which consists in rearranging monotonically the marginal distributions of the last coordinate, and then the conditional distributions, iteratively. We show that this mapping is the limit of solutions to a class of Monge-Kantorovich mass transportation problems with quadratic costs, with the...

We present a new, simple, and elegant algorithm for computing the optimal mapping for the Monge-Kantorovich problem with quadratic cost. The method arises from a reformulation of the dual problem into an unconstrained minimization of a convex, continuous functional, for which the derivative can be explicitly found. The Monge-Kantorovich problem has applications in many fields; examples from ima...

In other words, when (u; u(0N); 11 1;u(01)) belongs to U , asymptotically periodic inputs produce asymptotically periodic outputs with the same period. The proof of this theorem makes use of a contraction-mapping fixed-point argument. The techniques used in our omitted proofs are also useful in connection with related problems that are " more nonlinear. " In particular, related results are give...

Let G be a series-parallel graph with integer edge weights. A p-coloring of G is a mapping of vertices of G into Zp (ring of integers modulo p) so that the distance between colors of adjacent vertices u and v is at least the weight of the edge uv. We describe a quadratic time p-coloring algorithm where p is either twice the maximum edge weight or the largest possible sum of three weights of edg...