We investigate function classes h#Pi f which are deened as the closure of #P under the operation f and a set of known closure properties of #P, e.g. summa-tion over an exponential range. First, we examine operations f under which #P is closed (i.e., h#Pi f = #P) in every relativization. We obtain the following complete characterization of these operations: #P is closed under f in every rela-tiv...

in order to study the relationship between random boolean sets and some explanatory variables, this paper introduces a propagation model. this model can be applied when corresponding poisson process of the boolean model is related to explanatory variables and the random grains are not affected by these variables. an approximation for the likelihood is used to find pseudo-maximum likelihood esti...

LET f (z,w) ≡ f0(z)w + f1(z)w + · · · + fn(z) ∈ C[z,w]. Classically, the equation f (z,w) = 0 was said to define w as an (n-valued) algebraic function of z, provided that f0(z) was not identically 0 and that f (z,w) was squarefree and without factors of the form z− c. Then, indeed, the singular set B = {z: there are not n distinct solutions w to f (z,w) = 0} is finite; and as z varies in any si...

we first obtain some properties of a fundamentally nonexpansive self-mapping on a nonempty subset of a banach space and next show that if the banach space is having the opial condition, then the fixed points set of such a mapping with the convex range is nonempty. in particular, we establish that if the banach space is uniformly convex, and the range of such a mapping is bounded, closed and con...

Let VIP(F; C) denote the variational inequality problem associated with the mapping F and the closed convex set C. In this paper we introduce weak conditions on the mapping F that allow the development of a convergent cutting-plane framework for solving VIP(F; C). In the process we introduce, in a natural way, new and useful notions of generalized monotonicity for which rst order characterizati...

Abstract: In this paper, we introduce and study the extended Newton-type method for solving the variational inclusion 0∈ f (x)+g(x)+F(x), where f :Ω⊆X→Y is Fréchet differentiable in a neighborhood Ω of a point x̄ in X, g:Ω⊆X→Y is linear and differentiable at point x̄, and F is a set-valued mapping with closed graph acting in Banach spaces X and Y. Semilocal and local convergence of the extended N...

and Local Rule Learning in Attributed Networks Henry Soldano(B), Guillaume Santini, and Dominique Bouthinon 1 Université Paris 13, Sorbonne Paris Cité, L.I.P.N UMR-CNRS 7030 F-93430, Villetaneuse, France 2 Atelier de BioInformatique, ISYEB UMR 7205 CNRS MNHN UPMC EPHE, Museum d’Histoire Naturelle, F-75005, Paris, France Abstract. We address the problem of finding local patterns and related loca...

The purpose of this paper is to introduce the concept of pairwise F-closedness in bitopological spaces. This space contains both of pairwise strongcompactness and pairwise S-closedness and contained in pairwise quasi H-closedness. The characteristics and relationships concerning this new class of spaces with other corresponding types are established. Moreover, several of its basic and important...

We study the problem of listing all closed sets of a closure operator σ that is a partial function on the power set of some finite ground set E, i.e., σ : F → F with F ⊆ P(E). A very simple divide-and-conquer algorithm is analyzed that correctly solves this problem if and only if the domain of the closure operator is a strongly accessible set system. Strong accessibility is a strict relaxation ...

We analyze quasi-stationary distributions {μ}ε>0 of a family of Markov chains {X}ε>0 that are random perturbations of a bounded, continuous map F : M →M , where M is a closed subset of R. Consistent with many models in biology, these Markov chains have a closed absorbing set M0 ⊂ M such that F (M0) = M0 and F (M \ M0) = M \ M0. Under some large deviations assumptions on the random perturbations...