— The stochastic discrimination (SD) theory considers learning as building models of uniform coverage over data distributions. Despite successful trials of the derived SD method in several application domains, a number of difficulties related to its practical implementation still exist. This paper reports analysis of simple examples as a first step towards presenting the practical implementatio...

In this paper, we present coreset constructions for the fuzzy Kmeans problem. First, we show that one can construct a weak coresets for fuzzy K-means. Second, we show that there are coresets for fuzzy K-means with respect to balanced fuzzy K-means solutions. Third, we use these coresets to develop a randomized approximation algorithm whose runtime is polynomial in the number of the given points...

In our previous paper on this topic, we introduced the notion of k-Hessian measure associated with a continuous k-convex function in a domain Ω in Euclidean n-space, k = 1, · · · , n, and proved a weak continuity result with respect to local uniform convergence. In this paper, we consider k-convex functions, not necessarily continuous, and prove the weak continuity of the associated k-Hessian m...

A calibration ¢ is a differential form on a Riemannian manifold with two additional properties. First, the form should be closed under exterior differentiation. Second, it should be less than or equal to the volume form on each oriented submanifold (of the same dimension as the degree of the form ¢). Each calibration ¢ determines a geometry of submanifolds, namely those oriented submanifolds fo...

linear–dendrite copolymers containing hyper branched poly(citric acid) and linear poly(ethylene glycol) blocks pca–peg–pca are promising nonmaterial to use  in nanomedicine. to investigate their potential application in biological systems (especially for drug carries) oniom2 calculations were applied to study the nature of particular interactions between drug and the polymeric nanoparticles.  b...

Based on a study of the 2-category of weak distributive laws, we describe a method of iterating Street’s weak wreath product construction. That is, for any 2-category K and for any non-negative integer n, we introduce 2-categories Wdl(K), of (n + 1)-tuples of monads in K pairwise related by weak distributive laws obeying the Yang-Baxter equation. The first instance Wdl(K) coincides with Mnd(K),...