Related papers: Topological Entropy of DNA Sequences
We propose a new way of defining entropy of a system, which gives a general form which may be nonextensive as Tsallis entropy, but is linearly dependent on component entropies, like Renyi entropy, which is extensive. This entropy has a…
This paper defines and discusses the dimension notion of topological slow entropy of any subset for Z^d actions. Also, the notion of measure-theoretic slow entropy for Z^d actions is presented, which is modified from Brin and Katok [2].…
Tight bounds on the block entropy of patterns of sequences generated by independent and identically distributed (i.i.d.) sources are derived. A pattern of a sequence is a sequence of integer indices with each index representing the order of…
We apply a common measure of randomness, the entropy, in the context of iterated functions on a finite set with n elements. For a permutation, it turns out that this entropy is asymptotically (for a growing number of iterations) close to…
In this work we implement the so-called matching time estimators for estimating the entropy rate as well as the entropy production rate for symbolic sequences. These estimators are based on recurrence properties of the system, which have…
The probabilistic interpretation of the standard Regge-Gribov model with triple pomeron interactions is discussed. It is stated that introduction of probabilities within this model is not unique and depends on what is meant under the…
In the context of state estimation under communication constraints, several notions of dynamical entropy play a fundamental role, among them: topological entropy and restoration entropy. In this paper, we present a theorem which…
We attempt to provide a mesoscopic treatment of the origin of black hole entropy in (3+1)-dimensional spacetimes. We ascribe this entropy to the non-trivial topology of the space-like sections $\Sigma$ of the horizon. This is not forbidden…
Complexity metrics and machine learning (ML) models have been utilized to analyze the lengths of segmental genomic entities like: exons, introns, intergenic and repeat/unique DNA sequences, in each of the 22 human chromosomes. The purpose…
Topological entropy is not lower semi-continous: small perturbation of the dynamical system can lead to a collapse of entropy. In this note we show that for some special classes of dynamical systems (geodesic flows, Reeb flows, positive…
In this thesis, we provide an initial investigation into bounds for topological entropy of switched linear systems. Entropy measures, roughly, the information needed to describe the behavior of a system with finite precision on finite time…
Emergent patterns in complex systems are related to many intriguing phenomena in modern science and philosophy. Several conceptions such as weak, strong and robust emergence have been proposed to emphasize different epistemological and…
We study the change in topological entanglement entropy that occurs when a two-dimensional system in a topologically ordered phase undergoes a transition to another such phase due to the formation of a Bose condensate. We also consider the…
This paper provides tight bounds on the R\'enyi entropy of a function of a discrete random variable with a finite number of possible values, where the considered function is not one-to-one. To that end, a tight lower bound on the R\'enyi…
The genes of eukaryotes are characterized by protein coding fragments, the exons, interrupted by introns, i.e. stretches of DNA which do not carry any useful information for the protein synthesis. We have analyzed the melting behavior of…
The method of maximum entropy has been very successful but there are cases where it has either failed or led to paradoxes that have cast doubt on its general legitimacy. My more optimistic assessment is that such failures and paradoxes…
Measuring the complexity of tree structures can be beneficial in areas that use tree data structures for storage, communication, and processing purposes. This complexity can then be used to compress tree data structures to their…
In the present paper we prove a family of tight upper and lower bounds for the Shannon entropy and von Neumann entropy based on the p-norms. This allows us to have an entropy estimate, a criterion for the finiteness of it and a bound on the…
High-entropy alloys, which exist in the high-dimensional composition space, provide enormous unique opportunities for realizing unprecedented structural and functional properties. A fundamental challenge, however, lies in how to predict the…
Entropy and differential entropy are important quantities in information theory. A tractable extension to singular random variables-which are neither discrete nor continuous-has not been available so far. Here, we present such an extension…