This paper investigates the power of Probabilistic Büchi Automata (PBA) when the threshold probability of acceptance is non-extremal, i.e., is a value strictly between 0 and 1. Many practical randomized algorithms are designed to work under non-extremal threshold probabilities and thus it is important to study power of PBAs for such cases. The paper presents a number of surprising expressivenes...

In this paper, we determine the dimensions of the residue codes of extremal Type II Z4-codes for lengths 32 and 40. We demonstrate that every binary doubly even self-dual code of length 32 can be realized as the residue code of some extremal Type II Z4-code. It is also shown that there is a unique extremal Type II Z4-code of length 32 whose residue code has the smallest dimension 6 up to equiva...

Let X be a symmetric, isotropic random vector in R m and let 1 . , n independent copies of We show that under mild assumptions on ‖ 2 (a suitable thin-shell bound) the tail-decay marginals 〈 u 〉 matrix A whose columns are i / exhibits Gaussian-like behaviour following sense: for an arbitrary subset T ⊂ distortion sup t ∈ ⁡ | − is almost same as if were Gaussian matrix. simple outcome our result...

Unlike the extremal Reissner-Nordström black hole in ordinary spacetime, the one in anti-de Sitter spacetime is a minimum of action and has zero entropy if quantization is carried out after extremaliza-tion. However, if extremalization is carried out after quantization, then the entropy is a quarter of the area as in the usual case. While the entropy of ordinary (non-extremal) black holes has b...

In this paper, we construct new families of graphs whose automorphism groups are transitive on 3-paths. These graphs are constructed from certain Lie algebras related to generalized Kac-Moody algebras of rank two. We will show that one particular subfamily gives new lower bounds on the number of edges in extremal graphs with no cycles of length fourteen.

A k-uniform hypergraph is s-almost intersecting if every edge is disjoint from exactly s other edges. Gerbner, Lemons, Palmer, Patkós and Szécsi conjectured that for every k, and s > s0(k), every k-uniform s-almost intersecting hypergraph has at most (s + 1) ( 2k−2 k−1 ) edges. We prove a strengthened version of this conjecture and determine the extremal graphs. We also give some related result...

The intersection shadow theorem of Katona is an important tool in extremal set theory. The original proof is purely combinatorial. The aim of the present paper is to show how it is using linear independence latently.

Let G ⊂C be a bounded simply connected domain with boundary Γ and let E ⊂G be a regular compact set with connected complement. In this paper we investigate asymptotics of the extremal constants: χn = inf p∈Pkn sup q∈Pn−kn ||pq ||E ||pq ||Γ , n = 1,2, . . . , where ‖ ·‖K is the supremum norm on a compact set K ,Pm is the set of all algebraic polynomials of degree at most m, and kn/n→ θ ∈ [0,1] a...

We study s-extremal codes over F4 or over F2. A Type I self-dual code over F4 or over F2 of length n and minimum distance d is s-extremal if the minimum weight of its shadow is largest possible. The purpose of this paper is to give some results which are missing in a series of papers by Bachoc and Gaborit [2], by Gaborit [6], and by Bautista, et. al. [1]. In particular, we give an explicit form...