Related papers: Entropy and long-range correlations in DNA sequenc…
We investigate the localization property of an electron in the disordered two-chain system (ladder model) with long-range correlation as a simple model for electronic property in DNA sequence. The chains are constructed by repetition of the…
We propose a novel, tractable latent state inference scheme for Markov jump processes, for which exact inference is often intractable. Our approach is based on an entropic matching framework that can be embedded into the well-known…
We study electronic transport in long DNA chains using the tight-binding approach for a ladder-like model of DNA. We find insulating behavior with localizaton lengths xi ~ 25 in units of average base-pair seperation. Furthermore, we observe…
Entropy estimation, due in part to its connection with mutual information, has seen considerable use in the study of time series data including causality detection and information flow. In many cases, the entropy is estimated using…
In this paper, we review the literature on statistical long-range correlation in DNA sequences. We examine the current evidence for these correlations, and conclude that a mixture of many length scales (including some relatively long ones)…
A theory of systems with long-range correlations based on the consideration of binary N-step Markov chains is developed. In the model, the conditional probability that the i-th symbol in the chain equals zero (or unity) is a linear function…
Recent advances in the understanding of the melting behavior of double-stranded DNA with statistical mechanics methods lead to improved estimates of the weight factors for the dissociation events of the chains, in particular for interior…
This paper considers the speed of convergence (mixing) of a finite Markov kernel $P$ with respect to the Kullback-Leibler divergence (entropy). Given a Markov kernel one defines either a discrete-time Markov chain (with the $n$-step…
Specific protein-protein interactions are crucial in the cell, both to ensure the formation and stability of multi-protein complexes, and to enable signal transduction in various pathways. Functional interactions between proteins result in…
The focus of this article is on entropy and Markov processes. We study the properties of functionals which are invariant with respect to monotonic transformations and analyze two invariant "additivity" properties: (i) existence of a…
We investigate the memory properties of discrete sequences built upon a finite number of states. We find that the block entropy can reliably determine the memory for systems modeled as Markov chains of arbitrary finite order. Further, we…
A new approach to non-extensive thermodynamical systems with non-additive energy and entropy is proposed. The main idea of the paper is based on the statistical matching of the thermodynamical systems with the additive multi-step Markov…
The past few decades have seen great leaps in technologies to analyze cells and tissues. Omics methods in particular now allow us unprecedented access to their the molecular composition where the base-level resolution of transcripts and…
We consider a Markov chain $(x_n)$ whose kernel is indexed by a scaling parameter $\gamma>0$, refered to as the step size. The aim is to analyze the behavior of the Markov chain in the doubly asymptotic regime where $n\to\infty$ then…
We investigate the longest common substring problem for encoded sequences and its asymptotic behaviour. The main result is a strong law of large numbers for a re-scaled version of this quantity, which presents an explicit relation with the…
Under certain conditions, the dynamics of coarse-grained models of solvated proteins can be described using a Markov state model, which tracks the evolution of populations of configurations. The transition rates among states that appear in…
Investigations of molecular bonds between single molecules and molecular complexes by the dynamic force spectroscopy are subject to large fluctuations at nanoscale and possible other aspecific binding, which mask the experimental output.…
A new object of the probability theory, the two-sided chain of symbols (introduced in Ref. arXiv:physics/0306170) is used to study isotropy properties of binary multi-step Markov chains with the long-range correlations. Established…
Motivation: Entropy measurements on hierarchical structures have been used in methods for information retrieval and natural language modeling. Here we explore its application to semantic similarity. By finding shared ontology terms,…
This study investigates entropy's potential for analyzing scientific research patterns across disciplines. Originating from thermodynamics, entropy now measures uncertainty and diversity in information systems. We examine Shannon Entropy,…