Related papers: RNA matrix models with external interactions and t…
We study theoretically the denaturation of single RNA molecules by mechanical stretching, focusing on signatures of the (un)folding pathway in molecular fluctuations. Our model describes the interactions between nucleotides by incorporating…
In this article, we quantitatively study, through stochastic models, the efects of several intracellular phenomena, such as cell volume growth, cell division, gene replication as well as fuctuations of available RNA polymerases and…
Genes with similar transcriptional activation kinetics can display very different temporal mRNA profiles due to differences in transcription time, degradation rate and RNA processing kinetics. Recent studies have shown that a…
This paper develops a deeper understanding of the structure and combinatorial significance of the partition function for Hermitian random matrices. The coefficients of the large N expansion of the logarithm of this partition function,also…
We study the asymptotic behavior of the spectra of matrices of the form $S_n = \frac{1}{n}XX^*$ where $X =\sum_{r=1}^K X_r$, where $X_r = A_r^\frac{1}{2}Z_rB_r^\frac{1}{2}$, $K \in \mathbb{N}$ and $A_r,B_r$ are sequences of positive…
A general result on the structure and dimension of the root subspaces of a matrix or a linear operator under finite rank perturbations is proved: The increase of dimension from the $n$-th power of the kernel of the perturbed operator to the…
We analyze the thermodynamic properties of a simplified model for folded RNA molecules recently studied by G. Vernizzi, H. Orland, A. Zee (in {\it Phys. Rev. Lett.} {\bf 94} (2005) 168103). The model consists of a chain of one-flavor base…
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…
The superscaling observed in inclusive electron scattering is described within the dilute Fermi gas model with interaction between the particles. The comparison with the relativistic Fermi gas (RFG) model without interaction shows an…
We study several-matrix models and show that when the potential is convex and a small perturbation of the Gaussian potential, the first order correction to the free energy can be expressed as a generating function for the enumeration of…
We investigate the interaction of a fluctuating alpha-effect with large-scale shear in a simple nonlinear 1-dimensional dynamo wave model. We firstly extend the calculations of Proctor (2007, MNRAS, 41, L39-L42) to include spatial variation…
I present here some results on the statistical behaviour of large random matrices in an ensemble where the probability distribution is not a function of the eigenvalues only. The perturbative expansion can be cast in a closed form and the…
Large RNA molecules often carry multiple functional domains whose spatial arrangement is an important determinant of their function. Pre-mRNA splicing, furthermore, relies on the spatial proximity of the splice junctions that can be…
Consider two-type linear-fractional branching processes in varying environments with asymptotically constant mean matrices. Let $\nu$ be the extinction time. Under certain conditions, we show that both $P(\nu=n)$ and $P(\nu>n)$ are…
A comparative simulation study of polymer brushes formed by grafting at a planar surface either flexible linear polymers (chain length $N_L$) or (non-catenated) ring polymers (chain length $N_R=2 N_L$) is presented. Two distinct off-lattice…
We calculate exponential growth constants describing the asymptotic behavior of several quantities enumerating classes of orientations of arrow variables on the bonds of several types of directed lattice strip graphs $G$ of finite width and…
Following Flory's ideality hypothesis the chemical potential of a test chain of length $n$ immersed into a dense solution of chemically identical polymers of length distribution P(N) is extensive in $n$. We argue that an additional…
We establish the asymptotic expansion in $\beta$ matrix models with a confining, off-critical potential, in the regime where the support of the equilibrium measure is a union of segments. We first address the case where the filling…
We provide a general formula for the eigenvalue density of large random $N\times N$ matrices of the form $A = M + LJR$, where $M$, $L$ and $R$ are arbitrary deterministic matrices and $J$ is a random matrix of zero-mean independent and…
For each $N\geq 1$, let $G_N$ be a simple random graph on the set of vertices $[N]=\{1,2, ..., N\}$, which is invariant by relabeling of the vertices. The asymptotic behavior as $N$ goes to infinity of correlation functions: $$ \mathfrak…