Related papers: RNA matrix models with external interactions and t…
We study the asymptotic expansion in $n$ for the partition function of $\beta$ matrix models with real analytic potentials in the multi-cut regime up to the $O(n^{-1})$ terms. As a result, we find the limit of the generating functional of…
The random flux model (defined here as a model of lattice fermions hopping under the influence of maximally random link disorder) is analysed field theoretically. It is shown that the long range physics of the model is described by the…
We obtain large N asymptotics for the Hermitian random matrix partition function \[Z_N(V)=\int_{\mathbb R^N}\prod_{i<j}(x_i-x_j)^2 \prod_{j=1}^N e^{-N V(x_j)}dx_j,\] in the case where the external potential $V$ is a polynomials such that…
This work examines field theories for RNA-like polymers with single strand and double strand polymers and a periodic base sequence. These field theories originate from lattice models, describe polymers in a good solvent, and in principle…
We obtain the topological expansion of the hermitian matrix model using its representation as a CFT on a hyperelliptic Riemann surface. To each branch point of the Riemann surface we associate an operator which represents a twist field…
We study the phase-ordering kinetics following a temperature quench of O(N) continuous symmetry models with and 4 on graphs. By means of extensive simulations, we show that the global pattern of scaling behaviours is analogous to the one…
We study the asymptotic behavior of permanents of $n \times n$ random matrices $A$ with positive entries. We assume that $A$ has either i.i.d. entries or is a symmetric matrix with the i.i.d. upper triangle. Under the assumption that…
We propose a new approach for modelling the process of RNA folding as a graph transformation guided by the global value of free energy. Since the folding process evolves towards a configuration in which the free energy is minimal, the…
The Laessig-Wiese (LW) field theory for the freezing transition of random RNA secondary structures is generalized to the situation of an external force. We find a second-order phase transition at a critical applied force f = f_c. For f <…
We introduce a simple model for DNA evolution. Using the method of Peng et al.$^1$, we investigate the fractal properties of the system. For small chains and chains of intermediate size we find a fractal exponent that indicates the…
Physiological changes which result in changes in bacterial gene expression are often accompanied by changes in the growth rate for fast adapting enteric bacteria. Since the availability of RNA polymerase (RNAP) in cells is dependent on the…
The asymptotic nature of perturbative expansions in quantum field theory can arise from the factorial growth in the number of Feynman diagrams with loop order, as with instantons, or from a series of individual diagrams whose values grow…
Intracellular fluctuations, mainly triggered by gene expression, are an inevitable phenomenon observed in living cells. It influences generation of phenotypic diversity in genetically identical cells. Such variation of cellular components…
Cellular processes do not follow deterministic rules; even in identical environments genetically identical cells can make random choices leading to different phenotypes. This randomness originates from fluctuations present in the…
A quantitative characterization of the relationship between molecular sequence and structure is essential to improve our understanding of how function emerges. This particular genotype-phenotype map has been often studied in the context of…
The structure of the QFT expansion is studied in the framework of a new "Invariant analytic" version of the perturbative QCD. Here, an invariant (running) coupling $a(Q^2/\Lambda^2)=\beta_1\alpha_s(Q^2)/4\pi$ is transformed into a…
The statistics of randomly branching double-folded ring polymers are relevant to the secondary structure of RNA, the large-scale branching of plectonemic DNA (and thus bacterial chromosomes), the conformations of single-ring polymers…
Our work is concerned with the generation and targeted design of RNA, a type of genetic macromolecule that can adopt complex structures which influence their cellular activities and functions. The design of large scale and complex…
For large dimensional non-Hermitian random matrices $X$ with real or complex independent, identically distributed, centered entries, we consider the fluctuations of $f(X)$ as a matrix where $f$ is an analytic function around the spectrum of…
In this paper, we analyze the asymptotic behavior of a system of interacting reinforced stochastic processes $({\bf Z}_n, {\bf N}_n)_n$ on a directed network of $N$ agents. The system is defined by the coupled dynamics ${\bf…