Related papers: A Gibbs approach to Chargaff's second parity rule
The paper is devoted to a reverse-mathematical study of some well-known consequences of Ramsey's theorem for pairs, focused on the chain-antichain principle $\mathsf{CAC}$, the ascending-descending sequence principle $\mathsf{ADS}$, and the…
Gibbs samplers are preeminent Markov chain Monte Carlo algorithms used in computational physics and statistical computing. Yet, their most fundamental properties, such as relations between convergence characteristics of their various…
A tandem duplication denotes the process of inserting a copy of a segment of DNA adjacent to its original position. More formally, a tandem duplication can be thought of as an operation that converts a string $S = AXB$ into a string $T =…
The reverse engineering problem with probabilities and sequential behavior is introducing here, using the expression of an algorithm. The solution is partially founded, because we solve the problem only if we have a Probabilistic Sequential…
Using numerical results from a density matrix renormalization group study as a guide, we develop a resonating valence bond (RVB) theory for coupled Heisenberg chains. We argue that simple topological effects mandate a short-range RVB…
The frequency distribution of DNA bases A, C, G, T exhibit fractal fluctuations ubiquitous to dynamical systems in nature. The power spectra of fractal fluctuations exhibit inverse power law form signifying long-range correlations between…
A statistical model of discrete finite length random processes with negative power law spectral densities is presented. The definition of terms is followed by a description of the spectral density trend. An algorithmic construction of…
Because the constant extension ensemble of single chain molecule is not always equivalent with constant force ensemble, a model of double-stranded conformations, as in RNA molecules and $\beta$-sheets in proteins, with fixed extension…
In a DNA sequence, we have the celebrated Watson-Crick complement $\overline{T}=A$, $\overline{A}=T$, $\overline{C}=G$, and $\overline{G}=C$. Given an integer $m\ge 2$, a secondary structure in a DNA sequence refers to the existence of two…
There are many Markov chains on infinite dimensional spaces whose one-step transition kernels are mutually singular when starting from different initial conditions. We give results which prove unique ergodicity under minimal assumptions on…
Experimental tests of QCD through its predictions for the strange-quark content of the proton have been drastically restricted by our lack of knowledge of the violation of charge symmetry (CSV). We find unexpectedly tiny CSV in the proton's…
In array-based DNA synthesis, multiple strands of DNA are synthesized in parallel to reduce the time cost from the sum of their lengths to the length their shortest common supersequences. To maximize the amount of information that can be…
Gamma-ray bursts (GRBs), among the most compelling astrophysical phenomena, are potential candidates for exploring the evolution of energy distribution among magnetic fields and particles through multiwavelength observations. The fraction…
We discuss the relationship between discrete-time processes (chains) and one-dimensional Gibbs measures. We consider finite-alphabet (finite-spin) systems, possibly with a grammar (exclusion rule). We establish conditions for a stochastic…
In this paper we consider a new normalization of matrices obtained by choosing distinct codewords at random from linear codes over finite fields and find that under some natural algebraic conditions of the codes their empirical spectral…
We study distributions of random vectors whose components are second order polynomials in Gaussian random variables. Assuming that the law of such a vector is not absolutely continuous with respect to Lebesgue measure, we derive some…
It is shown that a seemingly harmless reordering of the steps in a block Gibbs sampler can actually invalidate the algorithm. In particular, the Markov chain that is simulated by the "out-of-order" block Gibbs sampler does not have the…
A mechanism of double strand breaking (DSB) in DNA due to the action of two electrons is considered. These are the electrons produced in the vicinity of DNA molecules due to ionization of water molecules with a consecutive emission of two…
We study the power density spectrum (PDS) of artificial light curves of observed gamma-ray bursts (GRBs). We investigate statistical properties of GRB light curves by comparing the reported characteristics in the PDSs of the observed GRBs…
For a $k$-ary predicate $P$, a random instance of CSP$(P)$ with $n$ variables and $m$ constraints is unsatisfiable with high probability when $m \gg n$. The natural algorithmic task in this regime is \emph{refutation}: finding a proof that…