Related papers: Entropy and long-range correlations in DNA sequenc…
In this four-part prospectus, we first give a brief introduction to the motivation for studying entanglement entropy and some recent development. Then follows a summary of our recent work about entanglement entropy in states with…
We observe a length-$n$ sample generated by an unknown,stationary ergodic Markov process (\emph{model}) over a finite alphabet $\mathcal{A}$. Given any string $\bf{w}$ of symbols from $\mathcal{A}$ we want estimates of the conditional…
Parts of DNA sequences known as exons and introns play very different role in coding and storage of genetic information. Here we show that their conducting properties are also very different. Taking into account long-range correlations…
We propose utilizing entropy as a diagnostic tool to distinguish between constant and dynamical dark energy models. Entropy, a measure of the system's disorder or information content, captures the complexity and evolution of the universe.…
Using random walk sampling methods for feature learning on networks, we develop a method for generating low-dimensional node embeddings for directed graphs and identifying transition states of stochastic chemical reacting systems. We…
Markov chains are a class of probabilistic models that have achieved widespread application in the quantitative sciences. This is in part due to their versatility, but is compounded by the ease with which they can be probed analytically.…
We describe a simple method of umbrella trajectory sampling for Markov chains. The method allows the estimation of large-deviation rate functions, for path-extensive dynamic observables, for an arbitrary number of models within a certain…
The determination of a patient's DNA sequence can, in principle, reveal an increased risk to fall ill with particular diseases [1,2] and help to design "personalized medicine" [3]. Moreover, statistical studies and comparison of genomes [4]…
We use charge sensing to detect entropy changes in a double quantum dot defined by electrostatic gating of a GaAs/AlGaAs heterostructure. This system can be tuned to be two separate systems, like two independent, artificial atoms, or a…
Decoding sequences that stem from multiple transmissions of a codeword over an insertion, deletion, and substitution channel is a critical component of efficient deoxyribonucleic acid (DNA) data storage systems. In this paper, we consider a…
The dynamics of loops at the DNA denaturation transition is studied. A scaling argument is used to evaluate the asymptotic behavior of the autocorrelation function of the state of complementary bases (either open or closed). The long-time…
The short supercoiled circular DNA molecules are shown to be glassy systems and canonical Metropolis Monte Carlo simulations of the systems tend to get stuck in local metastable energy basins. A novel Monte Carlo algorithm is developed to…
Average block entanglement in the 1D XX-model with uncorrelated random couplings is known to grow as the logarithm of the block size, in similarity to conformal systems. In this work we study random spin chains whose couplings present long…
Many proteins interact with and deform double-stranded DNA in cells. Single-molecule experiments have studied the elasticity of DNA with helix-deforming proteins, including proteins that bend DNA. These experiments increase the need for…
Several processes in the cell, such as gene regulation, start when key proteins recognise and bind to short DNA sequences. However, as these sequences can be hundreds of million times shorter than the genome, they are hard to find by simple…
Generalized entropies are studied as Lyapunov functions for the Master equation (Markov chains). Three basic properties of these Lyapunov functions are taken into consideration: universality (independence of the kinetic coefficients),…
We study a class of dynamical systems generated by random substitutions, which contains both intrinsically ergodic systems and instances with several measures of maximal entropy. In this class, we show that the measures of maximal entropy…
This work presents a novel means for understanding learning dynamics and scaling relations in neural networks. We show that certain measures on the spectrum of the empirical neural tangent kernel, specifically entropy and trace, yield…
Information theory has been taken as a prospective tool for quantifying the complexity of complex networks. In this paper, we first study the information entropy or uncertainty of a path using the information theory. Then we apply the path…
We present a framework based on conditional entropy and the Dirichlet distribution for classifying chromosomes based on the degree to which they use synonymous codons uniformly or preferentially, that is, whether or not codons that code for…