In this paper we study the sequences generated by a neuronal equation of the form xn " 1[!ki"1 aixn#i # Θ], where k is the size of the memory. We show that in the case where all the parameters (ai)1%i%k are strictly positive reals and k is a multiple of 6 (i.e., k " 6m), there exists a subset B " &w1, w2, . . . , wΑ( of &1, 2, . . . , m # 1( and for which there exists a neuronal equation of mem...

We present explicit constructions of centrally symmetric 2-neighborly d-dimensional polytopes with about 3 ≈ (1.73) vertices and of centrally symmetric k-neighborly d-polytopes with about 2 2 2 k vertices. Using this result, we construct for a fixed k ≥ 2 and arbitrarily large d and N , a centrally symmetric d-polytope with N vertices that has at least ( 1− k · (γk) ) ( N k ) faces of dimension...

Let 〈X ,Y〉 be a pair of Banach spaces in separating duality [18, Chapter IV]. A convex set M ⊂ X is called cone if λx ∈M for any x ∈M, λ ≥ 0. A cone M is called pointed if M∩ (−M)= {0}. Suppose that X is endowed with a locally convex topology τ, which is always assumed to be compatible with the duality 〈X ,Y〉, and K ⊂ X is a τ-closed pointed cone. An element ξ ∈ Y is called strictly positive if...

We study the robustness of quantum computers under the influence of errors modelled by strictly contractive channels. A channel T is defined to be strictly contractive if, for any pair of density operators ρ, σ in its domain, ‖Tρ− Tσ‖1 ≤ k ‖ρ− σ‖1 for some 0 ≤ k < 1 (here ‖·‖1 denotes the trace norm). In other words, strictly contractive channels render the states of the computer less distingui...

We consider a strictly regular random (k, s)-SAT problem and propose a GSRR model for generating its instances. By applying the first moment method and the asymptotic approximation of the γth coefficient for generating function f(z), where λ and γ are growing at a fixed rate, we obtain a new upper bound 2 log 2−(k+1) log 2/2+ εk for this problem, which is below the best current known upper boun...

A perfect matching in a hypergraph is set of edges that partition the vertices. We study complexity deciding existence orderable and separable hypergraphs. show class hypergraphs strictly contained Accordingly, we for each fixed k, k-hypergraphs polynomial time doable, but $$k\ge 3$$ , it NP-complete

Let H be any complex inner product space with inner product < ·, · >. We say that f : | C → | C is Hermitian positive definite on H if the matrix ( f(< z,z >) )n r,s=1 (∗) is Hermitian positive definite for all choice of z, . . . ,z in H, all n. It is strictly Hermitian positive definite if the matrix (∗) is also non-singular for any choice of distinct z, . . . ,z in H. In this article we prove...