Universal lossless coding in the presence of finitely many abrupt changes in the statistics of the source, at unknown points, is investigated. The minimum description length (MDL) principle is derived for this setting. In particular, it is shown that for any uniquely decipherable code, for almost every combination of statistical parameter vectors governing each segment, and for almost every vec...

In recent years codes that are not Uniquely Decipherable (UD) have been studied partitioning them in classes that localize the ambiguities of the code. A natural question is how we can extend the notion of maximality to codes that are not UD. In this paper we give an answer to this question. To do this we introduce a partial order in the set of submonoids of a monoid showing the existence, in t...

Using the most recent updated physics, calibrated solar models have been computed with the new thermonuclear reaction rates of NACRE, the recently available European compilation. Comparisons with models computed with the reaction rates of Caughlan & Fowler (1988) and of Adelberger et al. (1998) are made for global structure, expected neutrinos fluxes, chemical composition and sound speed profil...

Traditional Adomian decomposition method (ADM) usually fails to solve singular initial value problems of Emden-Fowler type. To overcome this shortcoming, a new and effective modification of ADM that only requires calculation of the first Adomian polynomial is formally proposed in the present paper. Three singular initial value problems of Emden-Fowler type with , 1 α  , 2 and , 2  and have be...

A ring R is uniquely (nil) clean in case for any $a in R$ there exists a uniquely idempotent $ein R$ such that $a-e$ is invertible (nilpotent). Let $C =(A V W B)$ be the Morita Context ring. We determine conditions under which the rings $A,B$ are uniquely (nil) clean. Moreover we show that the center of a uniquely (nil) clean ring is uniquely (nil) clean.

In this paper, we introduce the notion of k-comma codes a proper generalization of the notion of comma-free codes. For a given positive integer k, a k-comma code is a set L over an alphabet Σ with the property that LΣL ∩ ΣLΣ = ∅. Informally, in a k-comma code, no codeword can be a subword of the catenation of two other codewords separated by a “comma” of length k. A k-comma code is indeed a cod...

By looking at quantum data compression in the second quantisation, we present a new model for the efficient generation and use of variable length codes. In this picture lossless data compression can be seen as the minimum energy required to faithfully represent or transmit classical information contained within a quantum state. In order to represent information we create quanta in some predefin...