Using the replica-symmetric mean-field theory approach the thermodynamic and retrieval properties of extremely diluted symmetric Q-Ising neural networks are studied. In particular, capacity-gain parameter and capacity-temperature phase diagrams are derived for Q = 3, 4 and Q = ∞. The zero-temperature results are compared with those obtained from a study of the dynamics of the model. Furthermore...

We revive the study of the symmetric three-term recurrence equations. Our main result shows that these equations have a natural symplectic structure, that is, every symmetric three-term recurrence equation is a special discrete symplectic system. The assumptions on the coefficients in this paper are weaker and more natural than those in the current literature. In addition, our result implies th...

Quasi-symmetric 3-designs with block intersection numbers x, y (0 ≤ x ≤ y < k) are studied. It is proved that the parameter λ of a quasi-symmetric 3-(v, k, λ) design satisfies a quadratic whose coefficients are polynomial functions of k, x and y. We use this quadratic to prove that there exist finitely many quasi-symmetric 3-designs under either of the following two restrictions: 1. The block i...

The k-th symmetric product of a graph G with vertex set V with edge set E is a graph G{k} with vertices as k-sets of V , where two k-sets are connected by an edge if and only if their symmetric difference is an edge in E . Using the isoperimetric properties of the vertex-induced subgraphs of G and Sobolev inequalities on graphs, we obtain various edge-isoperimetric inequalities pertaining to th...

let be a set and let be the set of subsets of . the pair in which is a collection of elements of (blocks) is called a design if every element of appears in , times. is called a symmetric design if . in a symmetric design, each element of appears times in blocks of . a mapping between two designs and is an isomorphism if is a one-to-one correspondence and . every isomorphism of a design, , to it...

We use the double affine Hecke algebra of type GLN to construct an explicit consistent system of q-difference equations, which we call the bispectral quantum Knizhnik-Zamolodchikov (BqKZ) equations. BqKZ includes, besides Cherednik’s quantum affine KZ equations associated to principal series representations of the underlying affine Hecke algebra, a compatible system of q-difference equations ac...

Local Graph Structure (LGS) and its variation Symmetric Local Graph Structure (SLGS) have been proven to be effective for image recognition. However, they have shortcomings without considering the contribution of the difference between the target pixel and the surrounding pixels, and the difference between surrounding pixels to the feature value of the target pixel. To overcome the shortcomings...

261 Davis, J.A., New constructions of divisible designs, Discrete Mathematics 120 (1993) 261-268. A construction is given for a (p2"(p+l),p,p2"+ 1(p+l),p2"+ ,p"(p+l)) (pa prime) divisible difference set in the group H x z~.+, where His any abelian group of order p+ 1. This can be used to generate a symmetric semi-regular divisible design; this is a new set of parameters for .l. 1 ;<'0, and thos...

The present paper introduces new sign tests for testing for conditionally symmetric martingaledifference assumptions as well as for testing that conditional distributions of two (arbitrary) martingale-difference sequences are the same. Our analysis is based on the results that demonstrate that randomization over zero values of three-valued random variables in a conditionally symmetric martingal...