Related papers: Enumeration of RNA complexes via random matrix the…
Natural protein sequences contain a record of their history. A common constraint in a given protein family is the ability to fold to specific structures, and it has been shown possible to infer the main native ensemble by analyzing…
We briefly review the random matrix theory for large N by N matrices viewed as free random variables in a context of stochastic diffusion. We establish a surprising link between the spectral properties of matrix-valued multiplicative…
Using each node's degree as a proxy for its importance, the topological hierarchy of a complex network is introduced and quantified. We propose a simple dynamical process used to construct networks which are either maximally or minimally…
The entropy of a hierarchical network topology in an ensemble of sparse random networks with "hidden variables" associated to its nodes, is the log-likelihood that a given network topology is present in the chosen ensemble.We obtain a…
To a pair (X,f), X compact ANR and f a continuous angle valued map defined on X, a fixed field and a nonnegative integer one assigns a finite configuration of complex numbers with multiplicities located in the punctured complex plane and a…
An injective word over a finite alphabet $V$ is a sequence $w=v_1v_2\cdots v_t$ of distinct elements of $V$. The set $\mathrm{inj}(V)$ of injective words on $V$ is partially ordered by inclusion. A complex of injective words is the order…
The statistical mechanics of spin models, such as the Ising or Potts models, on generic random graphs can be formulated economically by considering the N --> 1 limit of Hermitian matrix models. In this paper we consider the N --> 1 limit in…
Models for RNA secondary structures (the topology of folded RNA) without pseudo knots are disordered systems with a complex state-space below a critical temperature. Hence, a complex dynamical (glassy) behavior can be expected, when…
Complex networks describe a wide range of systems in nature and society, much quoted examples including the cell, a network of chemicals linked by chemical reactions, or the Internet, a network of routers and computers connected by physical…
Single-cell RNA-seq data are challenging because of the sparseness of the read counts, the tiny expression of many relevant genes, and the variability in the efficiency of RNA extraction for different cells. We consider a simple…
In this paper we introduce the concept of a quota complex and study how the topology of these quota complexes changes as the quota is changed. This problem is a simple "linear" version of the general question in Morse Theory of how the…
We consider the reflected entropy and the associated entanglement spectrum for free fermions reduced to two intervals in 1+1 dimensions. Working directly in the continuum theory the reflected entropy can be extracted from the spectrum of a…
We introduce the Insertion Chain Complex, a higher-dimensional extension of insertion graphs, as a new framework for analyzing finite sets of words. We study its topological and combinatorial properties, in particular its homology groups,…
In this work we show that there is a direct relationship between a graph's topology and the free energy of a spin system on the graph. We develop a method of separating topological and enthalpic contributions to the free energy, and find…
We study the dynamics of synthetic molecules whose architectures are generated by space transformations from a point group acting on seed resonators. We show that the dynamical matrix of any such molecule can be reproduced as the left…
Generative neural networks can produce data samples according to the statistical properties of their training distribution. This feature can be used to test modern computational neuroscience hypotheses suggesting that spontaneous brain…
Recurrence properties of systems and associated sets of integers that suffice for recurrence are classical objects in topological dynamics. We describe relations between recurrence in different sorts of systems, study ways to formulate…
Temporal gene expression data (Wen, et. al.) was analyzed using the recently introduced inverse modeling technique of Embedded Complex Logistic Maps (ECLM). Preliminary results indicate scale-free structure in the gene regulatory network…
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…
A new method is given for computing generators of the homology groups with integer coefficients for any finite $T_0$-space. An important role in this method is played by irreducible cycles which are defined here and give rise to continuous…