Related papers: Markov Chain-based Sampling for Exploring RNA Seco…
We propose a novel way of modelling time-varying networks, by inducing two-way sparsity on local models of node connectivity. This two-way sparsity separately promotes sparsity across time and sparsity across variables (within time).…
Hidden tree Markov models allow learning distributions for tree structured data while being interpretable as nondeterministic automata. We provide a concise summary of the main approaches in literature, focusing in particular on the…
A plane curve is a knot diagram in which each crossing is replaced by a 4-valent vertex, and so are dual to a subset of planar quadrangulations. The aim of this paper is to introduce a new tool for sampling diagrams via sampling of plane…
Biomolecular graph analysis has recently gained much attention in the emerging field of geometric deep learning. Here we focus on organizing biomolecular graphs in ways that expose meaningful relations and variations between them. We…
We consider local Markov chain Monte-Carlo algorithms for sampling from the weighted distribution of independent sets with activity $\l$, where the weight of an independent set $I$ is $\l^{|I|}$. A recent result has established that Gibbs…
Many methods have been developed for finding the commonalities between different organisms to study their phylogeny. The structure of metabolic networks also reveal valuable insights into metabolic capacity of species as well as into the…
Conformational entropy for atomic-level, three dimensional biomolecules is known experimentally to play an important role in protein-ligand discrimination, yet reliable computation of entropy remains a difficult problem. Here we describe…
It is known that the Kimura 3ST model of sequence evolution on phylogenetic trees can be extended quite naturally to arbitrary split systems. However, this extension relies heavily on mathematical peculiarities of the K3ST model, and…
The task of sampling efficiently the Gibbs-Boltzmann distribution of disordered systems is important both for the theoretical understanding of these models and for the solution of practical optimization problems. Unfortunately, this task is…
A growing number of RNA sequences are now known to have distributions of multiple stable sequences. Recent algorithms use the list of nucleotides in a sequence and auxiliary experimental data to predict such distributions. Although the…
In this paper, we consider a tree inference problem motivated by the critical problem in single-cell genomics of reconstructing dynamic cellular processes from sequencing data. In particular, given a population of cells sampled from such a…
We study the statistical mechanics of RNA secondary structures designed to have an attraction between two different types of structures as a model system for heteropolymer aggregation. The competition between the branching entropy of the…
We use a non-Markovian coupling and small modifications of techniques from the theory of finite Markov chains to analyze some Markov chains on continuous state spaces. The first is a Gibbs sampler on narrow contingency tables, the second a…
A method was developed for Bayesian inference of species phylogeny using the multi-species coalescent model. To improve the mixing properties of the Markov chain Monte Carlo (MCMC) algorithm that traverses the space of species trees, we…
We examine reaction networks (CRNs) through their associated continuous-time Markov processes. Studying the dynamics of such networks is in general hard, both analytically and by simulation. In particular, stationary distributions of…
In [Aldous,Pitman,1998] a tree-valued Markov chain is derived by pruning off more and more subtrees along the edges of a Galton-Watson tree. More recently, in [Abraham,Delmas,2012], a continuous analogue of the tree-valued pruning dynamics…
RNA design shows growing applications in synthetic biology and therapeutics, driven by the crucial role of RNA in various biological processes. A fundamental challenge is to find functional RNA sequences that satisfy given structural…
We consider a Spatial Markov Chain model for the spread of viruses. The model is based on the principle to represent a graph connecting nodes, which represent humans. The vertices between the nodes represent relations between humans. In…
Graphs are commonly used to model various complex systems, including social networks, power grids, transportation networks, and biological systems. In many applications, the connectivity of these networks can be expressed through the Mean…
In order to investigate the relationship between Shannon information measure of random variables, scholars such as Yeung utilized information diagrams to explore the structured representation of information measures, establishing…