Related papers: New symmetry in nucleotide sequences
We propose a new interpretation of measures of information and disorder by connecting these concepts to group theory in a new way. Entropy and group theory are connected here by their common relation to sets of permutations. A combinatorial…
The evident contrast between the time symmetry of fundamental microscopic laws and the time asymmetry of macroscopic processes is a challenging physical problem. The observation of unitary evolution of a general physical system by an…
We review with a tutorial scope the information theory foundations of quantum statistical physics. Only a small proportion of the variables that characterize a system at the microscopic scale can be controlled, for both practical and…
Genomes may be analyzed from an information viewpoint as very long strings, containing functional elements of variable length, which have been assembled by evolution. In this work an innovative information theory based algorithm is…
Rate-distortion theory provides bounds for compressing data produced by an information source to a specified encoding rate that is strictly less than the source's entropy. This necessarily entails some loss, or distortion, between the…
A composition of a nonnegative integer (n) is a sequence of positive integers whose sum is (n). A composition is palindromic if it is unchanged when its terms are read in reverse order. We provide a generating function for the number of…
It is shown that different ways of interacting strings formed in high energy nucleus-nucleus collisions cause a different strength of the chaoticity parameter lambda of Bose-Einstein correlations. In particular, in the case of percolation…
Symmetry is an important factor in solving many constraint satisfaction problems. One common type of symmetry is when we have symmetric values. In a recent series of papers, we have studied methods to break value symmetries. Our results…
Word embeddings are ubiquitous in NLP and information retrieval, but it is unclear what they represent when the word is polysemous. Here it is shown that multiple word senses reside in linear superposition within the word embedding and…
In this work we explore the dissimilarity between symmetric word pairs, by comparing the inter-word distance distribution of a word to that of its reversed complement. We propose a new measure of dissimilarity between such distributions.…
Identifying palindromes in sequences has been an interesting line of research in combinatorics on words and also in computational biology, after the discovery of the relation of palindromes in the DNA sequence with the HIV virus. Efficient…
We explore the notion of degree of asymmetry for integer sequences and related combinatorial objects. The degree of asymmetry is a new combinatorial statistic that measures how far an object is from being symmetric. We define this notion…
We consider words as a network of interacting letters, and approximate the probability distribution of states taken on by this network. Despite the intuition that the rules of English spelling are highly combinatorial (and arbitrary), we…
An increase in the novelty of news predicts negative stock market returns and negative macroeconomic outcomes over the next year. We quantify news novelty - changes in the distribution of news text - through an entropy measure, calculated…
We present information value, a measure which quantifies the predictability of an utterance relative to a set of plausible alternatives. We introduce a method to obtain interpretable estimates of information value using neural text…
The information entropies in coordinate and momentum spaces and their sum ($S_r$, $S_k$, $S$) are evaluated for many nuclei using "experimental" densities or/and momentum distributions. The results are compared with the harmonic oscillator…
When we vary the moduli of a compactification it may become entropically favourable at some point for a state of branes and strings to rearrange itself into a new configuration. We observe that for the elementary string with two large…
In Shannon's seminal paper, entropy of printed English, treated as a stationary stochastic process, was estimated to be roughly 1 bit per character. However, considered as a means of communication, language differs considerably from its…
Statistical mechanics relies on the complete though probabilistic description of a system in terms of all the microscopic variables. Its object is to derive therefrom static and dynamic properties involving some reduced set of variables.…
Permutation entropy quantifies the diversity of possible orderings of the values a random or deterministic system can take, as Shannon entropy quantifies the diversity of values. We show that the metric and permutation entropy…