Generative models are commonly used in statistical pattern recognition to describe the probability distributions of patterns in a vector space. In recent years, sustained by the wide range of mathematical tools available in vector space, many algorithms for constructing generative models have been developed. Compared with the advanced development of the generative model for vectors, the develop...

Ricci curvature was proposed by Ollivier in a general framework of metric measure spaces, and it has been studied extensively in the context of graphs in recent years. In this paper we obtain the exact formulas for Ollivier’s Ricci-curvature for bipartite graphs and for the graphs with girth at least 5. These are the first formulas for Ricci-curvature that hold for a wide class of graphs, and e...

A number of cardiovascular and pulmonary complications have been reported to occur occasionally after insertion of a total hip prothesis. Of the proposed causes of these reactions, the possibility of fat embolism has received considerable support. The increase in intramedullary pressure, produced by the mechanical compression of the femoral canal during the insertion of the stem, seems to be th...

let $mathcal m$ be a factor von neumann algebra. it is shown that every nonlinear $*$-lie higher derivation$d={phi_{n}}_{ninmathbb{n}}$ on $mathcal m$ is additive. in particular, if $mathcal m$ is infinite type $i$factor, a concrete characterization of $d$ is given.

This thesis is concerned with a so-called speedup technique for Dijkstra’s algorithm: Contraction hierarchies. We present a model of contraction hierachies sufficiently sophisticated to capture real-world applications but yet concise enough to lend itself to theoretical investigations. This model reveals an interrelation between contraction hierarchies and filled graphs that directly relates th...

In this paper we give a method to associate a graph with an arbitrary density matrix referred to a standard orthonormal basis in the Hilbert space of a finite dimensional quantum system. We study the related issues like classification of pure and mixed states, Von-Neumann entropy, separability of multipartite quantum states and quantum operations in terms of the graphs associated with quantum s...

background von hippel-lindau (vhl) disease is a hereditary, autosomal dominant syndrome which is manifested by a range of different benign and malignant tumors. this disease can present with different clinical presentations such as; retinal angioma (ra), hemangioblastoma (hb) of the central nervous system (cns), pheochromocytoma (pheo), and epididymal cystadenoma. tumors are usually accompanied...