We state a sparse approximate version of the blow-up lemma, showing that regular partitions in sufficiently pseudorandom graphs behave almost like complete partite graphs for embedding graphs with maximum degree ∆. We show that (p, γ)-jumbled graphs, with γ = o(pmax(2∆,∆+3/2)n), are “sufficiently pseudorandom”. The approach extends to random graphs Gn,p with p ( log n n )1/∆.

The properties of hard photon radiation in W pair production at LEP 2 are studied, with emphasis on the energy loss relevant to the W mass measurement. We use a combination of the exact 1-photon matrix element and leading logarithmic structure functions. Defining unobservable, observable and initial state photons in the phase space, it is shown that neither the one-photon matrix element nor the...

We propose a coding scheme based on the use of systematic linear codes with low-density generator matrix (LDGM codes) for channel coding and joint source-channel coding of multi-terminal correlated binary sources. In both cases, the structures of the LDGM encoder and decoder are shown, and a concatenated scheme aimed at reducing the error floor is proposed. Several decoding possibilities are in...

We present several general results that show how algebraic dynamical systems with a slow degree growth and also rational automorphisms can be used to construct stronger pseudorandom number generators. We then give several concrete constructions that illustrate the applicability of these general results.

It is still an open challenge in coding theory how to design a systematic linear (n, k)− code C over GF(2) with maximal minimum distance d. In this study, based on matroid theory (MT), a limited class of good systematic binary linear codes (n, k, d ) is constructed, where n = 2 1 + · · · + 2 δ and d = 2 − 2 + · · · + 2 δ− 1 for k≥ 4, 1≤ δ < k. These codes are well known as special cases of code...

The celebrated Feng-Rao bound estimates the minimum distance of codes defined by means of their parity check matrices. From the Feng-Rao bound it is clear how to improve a large family of codes by leaving out certain rows in their parity check matrices. In this paper we derive a simple lower bound on the minimum distance of codes defined by means of their generator matrices. From our bound it i...

We present a generalisation of Twisted Reed– Solomon codes containing a new large class of MDS codes. We prove that the code class contains a large subfamily that is closed under duality. Furthermore, we study the Schur squares of the new codes and show that their dimension is often large. Using these structural properties, we single out a subfamily of the new codes which could be considered fo...

The generator matrix of a continuous-time stochastic automata network (SAN) is a sum of tensor products of smaller matrices, which may have entries that are functions of the global state space. This paper specifies easy to check conditions for a class of ordinarily lumpable partitionings of the generator of a continuous-time SAN in which aggregation is performed automaton by automaton. When the...

We provide a class of quantum evolution beyond Markovian semigroup. This is governed by hybrid Davies like generator such that dissipation controlled suitable memory kernel and decoherence standard GKLS generator. These two processes commute both them with the unitary systems Hamiltonian. The corresponding gives rise to semi-Markov diagonal elements density matrix. However, needs not be complet...

We discuss some of the experimental motivation for the need for semigroup decay laws, and the quantum Lax-Phillips theory of scattering and unstable systems. In this framework, the decay of an unstable system is described by a semigroup. The spectrum of the generator of the semigroup corresponds to the singularities of the Lax-Phillips S-matrix. In the case of discrete (complex) spectrum of the...