We show the equivalence of three properties for an infinitely divisible distribution: subexponentiality density, density its Lévy measure and tail between under monotonic-type assumptions on density. The key assumption is that asymptotic to a non-increasing function or almost decreasing. Our conditions are natural cover rather wide class distributions. Several significant analyzing densities ha...

Necessary and sufficent conditions are obtained for ¿(/-factorization of operators on /,. In particular it is shown that uniform invertibility of the compressions of the operator is not sufficient to insure an LU-factorization of the operator, thus answering a question of de Boor, Jia, and Pinkus. The question of when a bounded linear operator on lp, 1 < p <, oo, has an Li/-factorization has be...

The c = 1 string in the Liouville field theory approach is shown to possess a nontrivial tree-level S-matrix which satisfies factorization property implied by unitary, if all the extra massive physical states are included. Research supported in part by the Robert A. Welch Foundation and NSF Grant PHY 9009850 Adress after September 1, 1991: Department of Physics and Astronomy, University of Roch...

Power corrections to differential cross sections near a kinematic threshold are analysed by Dressed Gluon Exponentiation. Exploiting the factorization property of soft and collinear radiation, the dominant radiative corrections in the threshold region are resummed, yielding a renormalization-scale-invariant expression for the Sudakov exponent. The interplay between Sudakov logs and renormalons ...

We propose a fast structured selected inversion method for extracting the diagonal blocks of the inverse of a sparse symmetric matrix A, using the multifrontal method and rank structures. When A arises from the discretization of some PDEs and has a low-rank property (the intermediate dense matrices in the factorization have small off-diagonal numerical ranks), structured approximations of the d...

A one-factorization of a regular graph G is uniform if the union of any two one-factors is isomorphic to the same two-factor H, which is a disjoint union of even cycles. There are only several infinite classes of known uniform one-factorizations of complete graphs. An opposite property may be dealt with; one can ask about the existence of one-factorization such that the union of any two one-fac...

Binary label information is widely used semantic information in discriminative dictionary learning and non-negative matrix factorization. A Discriminative Dictionary Learning (DDL) algorithm uses the label of some data samples to enhance the discriminative property of sparse signals. A discriminative Non-negative Matrix Factorization (NMF) utilizes label information in learning discriminative b...

A k-factor of a graph G is a k-regular spanning subgraph of G. A k-factorization is a partition of E(G) into k-factors. Let K(n, p) be the complete multipartite graph with p parts, each of size n. If V1, ..., Vp are the p parts of V (K(n, p)), then a holey k-factor of deficiency Vi of K(n, p) is a k-factor of K(n, p)− Vi for some i satisfying 1 ≤ i ≤ p. Hence a holey k-factorization is a set of...

THE HILBERT SPACE OF PROBABILITY MASS FUNCTIONS AND APPLICATIONS ON PROBABILISTIC INFERENCE Bayramog̃lu, Muhammet Fatih Ph.D., Department of Electrical and Electronics Engineering Supervisor : Assoc. Prof. Dr. Ali Özgür Yılmaz September 2011, 123 pages The Hilbert space of probability mass functions (pmf) is introduced in this thesis. A factorization method for multivariate pmfs is proposed by u...

The non-negative matrix factorization provides a valuable tool for the analysis of positive data by representing it as an additive linear superposition of a small number of non-negative basis elements. This property allows the base elements to be interpreted in the same domain as the input data. The problem though lies in the ambiguity of equally valid solutions from which only one is obtained....