Related papers: New symmetry in nucleotide sequences
In our paper selected linguistic features of genomes to study the statistics of the gene codes are considered. We present the information theory from which it follows that if the system is described by distributions of hyperbolic type it…
Knowledge discovery from data is an inherently iterative process. That is, what we know about the data greatly determines our expectations, and therefore, what results we would find interesting and/or surprising. Given new knowledge about…
An uncertainty relation for the R\'enyi entropies of conjugate quantum observables is used to obtain a strong Heisenberg limit of the form ${\rm RMSE} \geq f(\alpha)/(\langle N\rangle+\frac12)$, bounding the root mean square error of any…
We present a new recursive generation algorithm for prefix normal words. These are binary strings with the property that no substring has more 1s than the prefix of the same length. The new algorithm uses two operations on binary strings,…
A unifying theory is put forward that entropy is equal to action. The crowning derivation is based on information theoretic methods and uses our hypothesis that "particles move via the discrete Bernoulli Process." While this hypothesis…
This work presents a new approach for classification of genomic sequences from measurements of complex networks and information theory. For this, it is considered the nucleotides, dinucleotides and trinucleotides of a genomic sequence. For…
Active feedback between geometry and physics is woven throughout the study of Nature at its fundamental level, and is of key importance in string theory. Methods of complex algebraic geometry in particular have brought about an unrivaled…
Entropy and other fundamental quantities of information theory are customarily expressed and manipulated as functions of probabilities. Here we study the entropy H and subentropy Q as functions of the elementary symmetric polynomials in the…
We review the recent progress in the investigation of powerfree words, with particular emphasis on binary cubefree and ternary squarefree words. Besides various bounds on the entropy, we provide bounds on letter frequencies and consider…
We consider the expected length of the longest common subsequence between two random words of lengths $n$ and $(1-\varepsilon)kn$ over $k$-symbol alphabet. It is well-known that this quantity is asymptotic to $\gamma_{k,\varepsilon} n$ for…
A problem of reconstructing words from their subwords involves determining the minimum amount of information needed, such as multisets of scattered subwords of a specific length or the frequency of scattered subwords from a given set, in…
The black hole information paradox and the black hole entropy are currently extensively researched. The consensus about the solution of the information paradox is not yet reached, and it is not yet clear what can we learn about quantum…
Beyond the local constraints imposed by grammar, words concatenated in long sequences carrying a complex message show statistical regularities that may reflect their linguistic role in the message. In this paper, we perform a systematic…
The syntactic structure of a sentence can be represented as a graph, where vertices are words and edges indicate syntactic dependencies between them. In this setting, the distance between two linked words is defined as the difference…
We construct a family of ergodic measures on random substitution subshifts (RS-subshifts) associated to a primitive random substitution. In particular, the word frequencies of every finite legal word exist for almost every element of the…
Wave packet fractional revivals is a relevant feature in the long time scale evolution of a wide range of physical systems, including atoms, molecules and nonlinear systems. We show that the sum of information entropies in both position and…
We investigate symbolic sequences and in particular information carriers as e.g. books and DNA-strings. First the higher order Shannon entropies are calculated, a characteristic root law is detected. Then the algorithmic entropy is…
Information entropy is applied to the state of knowledge of reaction amplitudes in pseudoscalar meson photoproduction, and a scheme is developed that quantifies the information content of a measured set of polarization observables. It is…
We study a new type of effective interactions in terms of the $CPT$-even dimension-six Chern-Simons-like term, which could originate from superstring theory, to generate the cosmological birefringence. We use the neutrino number asymmetry…
The interactions between three or more random variables are often nontrivial, poorly understood, and yet, are paramount for future advances in fields such as network information theory, neuroscience, genetics and many others. In this work,…