Related papers: Ising model description of long range correlations…
We consider self-avoiding walk, percolation and the Ising model with long and finite range. By means of the lace expansion we prove mean-field behavior for these models if $d>2(\alpha\wedge2)$ for self-avoiding walk and the Ising model, and…
We propose a computational method to measure and visualize interrelationships among any number of DNA sequences allowing, for example, the examination of hundreds or thousands of complete mitochondrial genomes. An "image distance" is…
Using basic properties of p-adic numbers, we consider a simple new approach to describe main aspects of DNA sequence and genetic code. Central role in our investigation plays an ultrametric p-adic information space which basic elements are…
A time series model of CDS sequences in complete genome is proposed. A map of DNA sequence to integer sequence is given. The correlation dimensions and Hurst exponents of CDS sequences in complete genome of bacteria are calculated. Using…
A three dimensional mesoscopic model is applied to study the properties of short DNA chains in a confining environment. The cylindrical channel is represented by a hard-wall repulsive potential incorporated in the system Hamiltonian. The…
For short DNA molecules in crowded environments, we evaluate macroscopic parameters such as the average end-to-end distance and the twist conformation by tuning the strength of the site specific confinement driven by the crowders. The…
We provide, on an extensive dataset and using several different distances, confirmation of the hypothesis that CGR patterns are preserved along a genomic DNA sequence, and are different for DNA sequences originating from genomes of…
Although mechanical properties of DNA are well characterized at the kilo base-pair range, a number of recent experiments have suggested that DNA is more flexible at shorter length scales, which correspond to the regime that is crucial for…
An inhomogeneous helicoidal nearest-neighbor model with continuous degrees of freedom is shown to predict the same DNA melting properties as traditional long-range Ising models, for free DNA molecules in solution, as well as superhelically…
The log-det distance between two aligned DNA sequences was introduced as a tool for statistically consistent inference of a gene tree under simple non-mixture models of sequence evolution. Here we prove that the log-det distance, coupled…
Whether long-range interactions allow for a form of causality in non-relativistic quantum models remains an open question with far-reaching implications for the propagation of information and thermalization processes. Here, we study the…
We provide a general framework for analyzing degree correlations between nodes separated by more than one step (i.e., beyond nearest neighbors) in complex networks. One probability and four conditional probabilities are introduced to fully…
We study a minimal model for genome evolution whose elementary processes are single site mutation, duplication and deletion of sequence regions and insertion of random segments. These processes are found to generate long-range correlations…
We introduce a coarse-grained model of DNA with bases modeled as rigid-body ellipsoids to capture their anisotropic stereochemistry. Interaction potentials are all physicochemical and generated from all-atom simulation/parameterization with…
Despite the significance of the high flexibility exhibited by short DNAs, there remains an incomplete understanding of their anomalous persistence length. In this study, we propose a novel approach wherein each fundamental characteristic of…
The structure of DNA in the nucleosome core particle is studied using an elastic model that incorporates anisotropy in the bending energetics and twist-bend coupling. Using the experimentally determined structure of nucleosomal DNA [T.J.…
A discrete nonlinear Schrodinger (NLS) model with long-range dispersive interactions describing the dynamical structure of DNA is proposed. Dispersive interactions of two types: the power dependence $r^{-s}$ and the exponential dependence…
This paper contains three types of results: 1. the construction of ground state solutions for a long-range Ising model whose interfaces stay at a bounded distance from any given hyperplane, 2. the construction of nonlocal minimal surfaces…
The flexibility of short DNA chains is investigated via computation of the average correlation function between dimers which defines the persistence length. Path integration techniques have been applied to confine the phase space available…
Gene annotation has traditionally required direct comparison of DNA sequences between an unknown gene and a database of known ones using string comparison methods. However, these methods do not provide useful information when a gene does…