Related papers: Entropy and long-range correlations in DNA sequenc…
We study the N-step binary stationary ergodic Markov chain and analyze its differential entropy. Supposing that the correlations are weak we express the conditional probability function of the chain through the pair correlation function and…
The goal of this paper is to develop an estimate for the entropy of random long-range correlated symbolic sequences with elements belonging to a finite alphabet. As a plausible model, we use the high-order additive stationary ergodic Markov…
We describe general approach to classification of character sequences (texts, DNA) using relative entropy estimated by off-the-shelf compression and Markov Chains and find them precise enough. We also notice that the method for estimating…
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…
Entropy estimation is a fundamental problem in information theory that has applications in various fields, including physics, biology, and computer science. Estimating the entropy of discrete sequences can be challenging due to limited data…
Understanding the structural complexity and predictability of complex networks is a central challenge in network science. Although recent studies have revealed a relationship between compression-based entropy and link prediction…
In this paper we consider the convergence of the conditional entropy to the entropy rate for Markov chains. Convergence of certain statistics of long range dependent processes, such as the sample mean, is slow. It has been shown in Carpio…
Shannon entropy is widely used to measure the complexity of DNA sequences but suffers from saturation effects that limit its discriminative power for long uniform segments. We introduce a novel metric, the entropy rank ratio R, which…
A theory of systems with long-range correlations based on the consideration of binary N-step Markov chains is developed. In our model, the conditional probability that the i-th symbol in the chain equals zero (or unity) is a linear function…
Proteins are essential components of living systems, capable of performing a huge variety of tasks at the molecular level, such as recognition, signalling, copy, transport, ... The protein sequences realizing a given function may largely…
The entropy loss due to the formation of one or multiple loops in circular and linear DNA chains is calculated from a scaling approach in the limit of long chain segments. The analytical results allow to obtain a fast estimate for the…
We consider a strictly substochastic matrix or an stochastic matrix with absorbing states. By using quasi-stationary distributions one shows there is a canonical associated stationary Markov chain. Based upon $2-$stringing representation of…
We study plane trees as a model for RNA secondary structure, assigning energy to each tree based on the Nearest Neighbor Thermodynamic Model, and defining a corresponding Gibbs distribution on the trees. Through a bijection between plane…
Given a sequence composed of a limit number of characters, we try to "read" it as a "text". This involves to segment the sequence into "words". The difficulty is to distinguish good segmentation from enormous number of random ones.Aiming at…
RNA motifs typically consist of short, modular patterns that include base pairs formed within and between modules. Estimating the abundance of these patterns is of fundamental importance for assessing the statistical significance of matches…
Markov chains are a natural and well understood tool for describing one-dimensional patterns in time or space. We show how to infer $k$-th order Markov chains, for arbitrary $k$, from finite data by applying Bayesian methods to both…
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 main goal of this paper is to develop an estimate for the entropy of random stationary ergodic symbolic sequences with elements belonging to a finite alphabet. We present here the detailed analytical study of the entropy for the…
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…
We prove that under mild positivity assumptions the entropy rate of a hidden Markov chain varies analytically as a function of the underlying Markov chain parameters. A general principle to determine the domain of analyticity is stated. An…