We consider tensor product random fields Yd, d∈N, whose covariance functions are Gaussian kernels with a given sequence of length scale parameters. investigate the growth average case approximation complexity nYd(ε) Yd for arbitrary fixed ε∈(0,1) and d→∞. Namely, we find criteria boundedness depending on d nYd(ε)→∞ when d→∞ any ε∈(0,1). In latter obtain necessary sufficient conditions following...

We prove a joint local limit law for the distribution of the r largest components of decomposable logarithmic combinatorial structures, including assemblies, multisets and selections. Our method is entirely probabilistic, and requires only weak conditions that may readily be verified in practice. Combinatorics, Probability and Computing (1999) 8, 193–208. Printed in the United Kingdom c © 1999 ...

We formulate a novel approach to infer conditional independence models or Markov structure of a multivariate distribution. Specifically, our objective is to place informative prior distributions over decomposable graphs and sample efficiently from the induced posterior distribution. The key idea we develop in this paper is a parametrization of decomposable hypergraphs using the geometry of poin...

Entanglement in symmetric quantum states and the theory of copositive matrices are intimately related concepts. For simplest states, i.e., diagonal (DS) it has been shown that there exists a correspondence between exceptional (non-exceptional) non-decomposable (decomposable) Witnesses (EWs). Here we show EWs symmetric, but not DS, can also be constructed from extended matrices, providing new ex...

We consider the problem of learning Bayesian networks optimally, when subject to background knowledge in the form of ancestral constraints. Our approach is based on a recently proposed framework for optimal structure learning based on non-decomposable scores, which is general enough to accommodate ancestral constraints. The proposed framework exploits oracles for learning structures using decom...

In symmetric tensor decomposition one expresses a given symmetric tensor T a sum of tensor powers of a number of vectors: T = v⊗d 1 + · · · + v ⊗d k . Orthogonal decomposition is a special type of symmetric tensor decomposition in which in addition the vectors v1, ..., vk are required to be pairwise orthogonal. We study the properties of orthogonally decomposable tensors. In particular, we give...

We consider the dihamiltonian decomposition problem for 3regular graphs. A graphG is dihamiltonian decomposable if in the digraph obtained fromG by replacing each edge of G as two directed edges, the set of edges are partitioned into 3 edge-disjoint directed hamiltonian cycles. We suggest some conditions for dihamiltonian decomposition of 3-regular graphs: for a 3-regular graph G, it is dihamil...

A planar set P is said to be cover-decomposable if there is a constant k = k(P ) such that every k-fold covering of the plane with translates of P can be decomposed into two coverings. It is known that open convex polygons are cover-decomposable. Here we show that closed, centrally symmetric convex polygons are also cover-decomposable. We also show that an infinite-fold covering of the plane wi...

This paper aimed to demonstrate the capabilities of decomposable semi-regenerative processes for investigation k-out-of-n system. Proposed in 1955 by W. Smith, regeneration idea has come a long way terms development and found widespread applications. First, we briefly recall history main results theory regenerative, semi-regenerative, processes. Then, methods are used study renewable system wit...