Related papers: Markov Chain-based Sampling for Exploring RNA Seco…
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…
The prevalent method for RNA secondary structure prediction for a single sequence is free energy minimization based on the nearest neighbor thermodynamic model (NNTM). One of the least well-developed parts of the model is the energy…
We give a Large Deviation Principle (LDP) with explicit rate function for the distribution of vertex degrees in plane trees, a combinatorial model of RNA secondary structures. We calculate the typical degree distributions based on nearest…
We analyze the structure of DNA molecules of different organisms by using the additive Markov chain approach. Transforming nucleotide sequences into binary strings, we perform statistical analysis of the corresponding "texts". We develop…
We define a class of properties on random plane trees, which we call subtree additive properties, inspired by the combinatorics of certain biologically-interesting properties in a plane tree model of RNA secondary structure. The class of…
This paper introduces a concept of approximate spectral gap to analyze the mixing time of Markov Chain Monte Carlo (MCMC) algorithms for which the usual spectral gap is degenerate or almost degenerate. We use the idea to analyze a class of…
We propose a new toy model of a heteropolymer chain capable of forming planar secondary structures typical for RNA molecules. In this model the sequential intervals between neighboring monomers along a chain are considered as quenched…
The standard coalescent is widely used in evolutionary biology and population genetics to model the ancestral history of a sample of molecular sequences as a rooted and ranked binary tree. In this paper, we present a representation of the…
RNA molecules are known to form complex secondary structures including pseudoknots. A systematic framework for the enumeration, classification and prediction of secondary structures is critical to determine the biological significance of…
Pairwise ordered tree alignment are combinatorial objects that appear in RNA secondary structure comparison. However, the usual representation of tree alignments as supertrees is ambiguous, i.e. two distinct supertrees may induce identical…
RNA molecules form a sequence-specific self-pairing pattern at low temperatures. We analyze this problem using a random pairing energy model as well as a random sequence model that includes a base stacking energy in favor of helix…
We propose a method for the classification of objects that are structured as random trees. Our aim is to model a distribution over the node label assignments in settings where the tree data structure is associated with node attributes…
We consider the problem of uniformly generating a spanning tree, of a connected undirected graph. This process is useful to compute statistics, namely for phylogenetic trees. We describe a Markov chain for producing these trees. For cycle…
RNA motifs typically consist of short, modular patterns that include base pairs formed within and between modules. Estimating the abundance of these patterns is of fundamental importance for assessing the statistical significance of matches…
Combinatorial analysis of a certain abstract of RNA structures has been studied to investigate their statistics. Our approach regards the backbone of secondary structures as an alternate sequence of paired and unpaired sets of nucleotides,…
This work considers the problem of learning the structure of multivariate linear tree models, which include a variety of directed tree graphical models with continuous, discrete, and mixed latent variables such as linear-Gaussian models,…
Questions in computational molecular biology generate various discrete optimization problems, such as DNA sequence alignment and RNA secondary structure prediction. However, the optimal solutions are fundamentally dependent on the…
RNA function crucially depends on its structure. Thermodynamic models currently used for secondary structure prediction rely on computing the partition function of folding ensembles, and can thus estimate minimum free-energy structures and…
Markov chains are a convenient means of generating realizations of networks, since they require little more than a procedure for rewiring edges. If a rewiring procedure exists for generating new graphs with specified statistical properties,…
The particle Gibbs sampler is a Markov chain Monte Carlo (MCMC) algorithm to sample from the full posterior distribution of a state-space model. It does so by executing Gibbs sampling steps on an extended target distribution defined on the…