Related papers: Enumeration of RNA complexes via random matrix the…
In this work we obtain the planar free energy for the Hermitian one-matrix model with various choices of the potential. We accomplish this by applying an approach that bypasses the usual diagonalization of the matrices and the introduction…
We present a diagrammatic technique for calculating the free energy of the Hermitian one-matrix model to all orders of 1/N expansion in the case where the limiting eigenvalue distribution spans arbitrary (but fixed) number of disjoint…
The topological interaction arising in interlinked polymeric rings such as DNA catenanes is considered. More specifically, the free energy for a pair of linked random walk rings is derived where the distance $R$ between two segments each of…
In biology, predicting RNA secondary structures plays a vital role in determining its physical and chemical properties. Although we have powerful energy models to predict them as well as parametric analysis to understand the models…
The study of gene regulation and expression is often discussed in quantitative terms. In particular, the expression of genes is regularly characterized with respect to how much, how fast, when and where. Whether discussing the level of gene…
This contribution focuses on the fascinating RNA molecule, its sequence-dependent folding driven by base-pairing interactions, the interplay between these interactions and natural evolution, and its multiple regulatory roles. The four of us…
Motivation: RNA design aims to find RNA sequences that fold into a given target secondary structure, a problem also known as RNA inverse folding. However, not all target structures are designable. Recent advances in RNA designability have…
We extend the relation between random matrices and free probability theory from the level of expectations to the level of all correlation functions (which are classical cumulants of traces of products of the matrices). We introduce the…
We review a collection of models of random simplicial complexes together with some of the most exciting phenomena related to them. We do not attempt to cover all existing models, but try to focus on those for which many important results…
Random Hermitian matrices are used to model complex systems without time-reversal invariance. Adding an external source to the model can have the effect of shifting some of the matrix eigenvalues, which corresponds to shifting some of the…
Single-cell RNA sequencing (scRNA-seq) is a relatively new technology that has stimulated enormous interest in statistics, data science, and computational biology due to the high dimensionality, complexity, and large scale associated with…
Using force as a probe to map the folding landscapes of RNA molecules has become a reality thanks to major advances in single molecule pulling experiments. Although the unfolding pathways under tension are complicated to predict studies in…
We introduce a new class of large structured random matrices characterized by four fundamental properties which we discuss. We prove that this class is stable under matrix-valued and pointwise non-linear operations. We then formulate an…
One of the most important applications of topological recursion concerns spectral curves for which the functions $(x,y)$ defining the spectral curve are allowed to have logarithmic singularities. This occurs for instance for Seiberg-Witten…
We construct ensembles of random integrable matrices with any prescribed number of nontrivial integrals and formulate integrable matrix theory (IMT) -- a counterpart of random matrix theory (RMT) for quantum integrable models. A type-M…
We consider the additive superimposition of an extensive number of independent Euclidean Random Matrices in the high-density regime. The resolvent is computed with techniques from free probability theory, as well as with the replica method…
We focus on functional renormalization for ensembles of several (say $n\geq 1$) random matrices, whose potentials include multi-traces, to wit, the probability measure contains factors of the form $ \exp[-\mathrm{Tr}(V_1)\times\ldots\times…
We consider Gaussian fields of real symmetric, complex Hermitian or quaternionic Hermitian matrices over an electrical network, and describe how the isomorphisms between these fields and random walks give rise to topological expansions…
We extend recent methods for parametric sequence alignment to the parameter space for scoring RNA folds. This involves the construction of an RNA polytope. A vertex of this polytope corresponds to RNA secondary structures with common…
We consider higher-rank versions of the standard numerical range for matrices. A central motivation for this investigation comes from quantum error correction. We develop the basic structure theory for the higher-rank numerical ranges, and…