In this paper, we present a novel triangulation heuristic and a new genetic algorithm to solve the problem of optimal tree decomposition of Bayesian networks. The heuristic, named MinFillWeight, aims to select variables minimizing the multiplication of the weights on nodes of fill-in edges. The genetic algorithm, named IDHGA, employs a new order-reserving crossover operator and a mutation opera...

We consider unbounded fanin depth-2 circuits with arbitrary boolean functions as gates. The entropy of an operator f : {0, 1}n → {0, 1}m is defined as the logarithm of the maximum number of vectors distinguishable by at least one special subfunction of f . We prove that every depth-2 circuit for f requires at least entropy(f) wires. This generalizes and substantially simplifies the argument use...

The hyperbolic algebra A h , studied recently by Katavolos and Power [5], is the weak star closed operator algebra on L 2 (R) generated by H ∞ (R), as multiplication operators, and by the dilation operators V t , t ≥ 0, given by V t f (x) = e t/2 f (e t x). We show that A h is a reflexive operator algebra and that the four dimensional manifold Lat A h (with the natural topology) is the reflexiv...

The linearized collision operator of the Boltzmann equation can in a natural way be written as sum positive multiplication operator, frequency, and an integral operator. Compactness for monatomic single species is classical result, while corresponding results mixtures polyatomic where polyatomicity modeled by discrete internal energy variable, are more recently obtained. In this work compactnes...

Let k be the reporducing kernel for a Hilbert space H(k) of nanlytic functions on Bd, the open unit ball in C, d ≥ 1. k is called a complete NP kernel, if k0 ≡ 1 and if 1 − 1/kλ(z) is positive definite on Bd × Bd. Let D be a separable Hilbert space, and consider H(k) ⊗ D ∼= H(k,D), and think of it as a space of D-valued H(k)-functions. A theorem of McCullough and Trent, [10], partially extends ...

In this paper we first introduce a new multiplication on triangular Banach algebras. Then we study their Arens regularity as well as their topological centers . In this paper we first introduce a new multiplication on triangular Banach algebras. Then we study their Arens regularity as well as their topological centers . In this paper we first introduce a new multiplication on triangular Banach ...

In this paper we study the properties of multiplication invariant (MI) operators acting on subspaces vector-valued space L2(X;H). We characterize such in terms range functions by showing that there is an isomorphism between category MI spaces (with as morphisms) and measurable whose morphisms are operators. investigate how global operator reflected local pointwise its corresponding operator. al...

Abstract The aim of this paper is to provide necessary and sufficient conditions on the generator a multiplication operator acting in spaces functions bounded Young Riesz variation so that it is, among other things, invertible, continuous, finite rank, compact, Fredholm or has closed range. Furthermore, we characterize various spectra such operators give some estimates their measure non-compact...

Let [Formula: see text] be a compact metric space and let continuous. We study text]-algebra generated by all multiplication operators continuous functions on composition operator induced certain space. system of proper contractions text]. Suppose that are inverse branches is self-similar. consider the Hutchinson measure Then we show C[Formula: isomorphic to associated with under some conditions.

In this paper, we investigate the spectral and scattering theory for operators acting on topological crystals their perturbations. Special attention is paid to perturbations obtained by addition of an infinite number edges, and/or removal a finite them, but underlying measures multiplication operator are also considered. The description nature spectrum resulting existence completeness wave stan...