Related papers: Dynamic Entropies, Long--Range Correlations and Fl…
We derive an exact representation of the exchange-correlation energy within density functional theory (DFT) which spawns a class of approximations leading to correct long-range asymptotic behavior. In what amounts to be the simplest…
We study a minimal model for genome evolution whose elementary processes are single site mutation, duplication and deletion of sequence regions and insertion of random segments. These processes are found to generate long-range correlations…
For certain groups, parabolic subgroups appear as stabilizers of flags of sets or vector spaces. Quotients by these parabolic subgroups represent orbits of flags, and their cardinalities asymptotically reveal entropies (as rates of…
We derive upper and lower bounds on the overall compression ratio of the 1978 Lempel-Ziv (LZ78) algorithm, applied independently to $k$-blocks of a finite individual sequence. Both bounds are given in terms of normalized empirical entropies…
This paper addresses the question of the fluctuations of the empirical entropy of a chain of infinite order. We assume that the chain takes values on a finite alphabet and loses memory exponentially fast. We consider two possible…
In this letter we present a very general method to extract information from a generic string of characters, e.g. a text, a DNA sequence or a time series. Based on data-compression techniques, its key point is the computation of a suitable…
Understanding the complexity of human language requires an appropriate analysis of the statistical distribution of words in texts. We consider the information retrieval problem of detecting and ranking the relevant words of a text by means…
Low correlation (finite length) sequences are used in communications and remote sensing. One seeks codebooks of sequences in which each sequence has low aperiodic autocorrelation at all nonzero shifts, and each pair of distinct sequences…
This paper considers three kinds of length sequences of the complete genome. Detrended fluctuation analysis, spectral analysis, and the mean distance spanned within time $L$ are used to discuss the correlation property of these sequences.…
A numerical method is proposed to remove the quenched randomness from a data sequence of numbers. A polymer chain of beads is introduced with both a hard core interaction and an appropriate energy associated with the data sequence. The…
As is the case of many signals produced by complex systems, language presents a statistical structure that is balanced between order and disorder. Here we review and extend recent results from quantitative characterisations of the degree of…
We consider the problem of identifying tandem scattered subsequences within a string. Our algorithm identifies a longest subsequence which occurs twice without overlap in a string. This algorithm is based on the Hunt-Szymanski algorithm,…
In this article, we prove Shannon-MacMillan-Breiman Theorem for Wireless Sensor Networks modelled as coloured geometric random graphs. For large $n,$ we show that a Wireless Sensor Network consisting of $n$ sensors in $[0,1]^d$ connected by…
We numerically study the structure of the interactions occurring in three-dimensional systems of hard spheres at jamming, focusing on the large-scale behavior. Given the fundamental role they play in the configuration of jammed packings, we…
Experimental data are presented on particle correlations and fluctuations in various high-energy multiparticle collisions, with special emphasis on evidence for scaling-law evolution in small phase-space domains. The notions of…
Using Brownian dynamics simulations, we study the migration of long charged chains in an electrophoretic microchannel device consisting of an array of microscopic entropic traps with alternating deep regions and narrow constrictions. Such a…
The correlation part of the pair density is separated into two components, one of them being predominant at short electronic ranges and the other at long ranges. The analysis of the intracular part of these components permits to classify…
The complexity of the primary structure of human DNA is explored using methods from nonequilibrium statistical mechanics, dynamical systems theory and information theory. The use of chi-square tests shows that DNA cannot be described as a…
The problem addressed concerns the determination of the average number of successive attempts of guessing a word of a certain length consisting of letters with given probabilities of occurrence. Both first- and second-order approximations…
This paper proposes a method to disentangle and quantify interactions among words that are encoded inside a DNN for natural language processing. We construct a tree to encode salient interactions extracted by the DNN. Six metrics are…