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RNA secondary structures of increasing complexity are probed combining single molecule stretching experiments and stochastic unfolding/refolding simulations. We find that force-induced unfolding pathways cannot usually be interpretated by…
The prevalence of neutral mutations implies that biological systems typically have many more genotypes than phenotypes. But can the way that genotypes are distributed over phenotypes determine evolutionary outcomes? Answering such questions…
Pattern analysis of tandem repeats in gene is an indispensable computational approach to the understanding of the gene expression and pathogenesis of diseases. This research applied a computational motif model and database techniques to…
Let $\beta>1$ be a real number and $M: \mathbb{R}\to {\rm GL(\CC^d)}$ be a uniformly almost periodic matrix-valued function. We study the asymptotic behavior of the product $$ P_n(x) =M(\beta^{n-1}x)... M(\beta x) M(x). $$ Under some…
Quenched disorder in graphene is characterized by 5 constants and experiences the logarithmic renormalization even from the spatial scales smaller than the Fermi wavelength. We derive and solve renormalization group equations (RGEs)…
We consider two different genus expansions of the free energy functions of Hermitian one-matrix models, one using fat graphs, one using ordinary graphs (thin graphs). Some structural results are first proved for the thin version of genus…
We examine the behavior of the coefficients of powers of polynomials over a finite field of prime order. Extending the work of Allouche-Berthe, 1997, we study a(n), the number of occurring strings of length n among coefficients of any power…
The mechanical behavior of composite materials is significantly influenced by their structure and constituent materials. One emerging class of composite materials is irregular network reinforced composites (NRC's), whose reinforcing phase…
The presence of low dimensional chaos in the protein secondary structures, using the binary coded $\alpha$-helices and $\beta$-sheet motifs, has been investigated. In order to analyse symbolic DNA/RNA sequences the assignment, based on the…
We study asymptotics of the partition function $Z_N$ of a Laguerre-type random matrix model when the matrix order $N$ tends to infinity. By using the Deift-Zhou steepest descent method for Riemann-Hilbert problems, we obtain an asymptotic…
We modify and extend the recently developed statistical mechanical model for predicting the thermodynamic properties of chain molecules having noncovalent double-stranded conformations, as in RNA or ssDNA, and $\beta-$sheets in protein, by…
Delays in protein synthesis cause a confounding effect when constructing Gene Regulatory Networks (GRNs) from RNA-sequencing time-series data. Accurate GRNs can be very insightful when modelling development, disease pathways, and drug…
A key property of neural networks is their capacity of adapting to data during training. Yet, our current mathematical understanding of feature learning and its relationship to generalization remain limited. In this work, we provide a…
We obtain bivariate asymptotics for the number of (unicellular) combinatorial maps (a model of discrete surfaces) as both the size and the genus grow. This work is related to two research topics that have been very active recently:…
We investigate the effects excluded volume on the stretching of a single DNA in solution. We find that for small force F, the extension h is not linear in F but proportion to F^{\chi}, with \chi=(1-\nu)/\nu, where \nu is the well-known…
Coherent propagation of two interacting particles in $1d$ weak random potential is considered. An accurate estimate of the matrix element of interaction in the basis of localized states leads to mapping onto the relevant matrix model. This…
Modeling gene regulatory networks (GRNs) is an important topic in systems biology. Although there has been much work focusing on various specific systems, the generic behavior of GRNs with continuous variables is still elusive. In…
In this article we establish the asymptotic behavior of generating functions related to the exponential sum over finite fields of elementary symmetric functions and their perturbations. This asymptotic behavior allows us to calculate the…
We show that the folding rates (k_F) of RNA are determined by N, the number of nucleotides. By assuming that the distribution of free energy barriers separating the folded and the unfolded states is Gaussian, which follows from central…
We derive the single molecule equation of state (force-extension relation) for DNA molecules bearing sliding loops and deflection defects. Analytical results are obtained in the large force limit by employing an analogy with instantons in…