Related papers: RNA secondary structures having a compatible seque…
RNA sequencing (RNA-seq) enables characterization and quantification of individual transcriptomes as well as detection of patterns of allelic expression and alternative splicing. Current RNA-seq protocols depend on high-throughput…
The statistical mechanics of heteropolymer structure formation is studied in the context of RNA secondary structures. A designed RNA sequence biased energetically towards a particular native structure (a hairpin) is used to study the…
The nucleon properties and structure should be modified by short-range correlations (SRC) among nucleons. By analyzing SRC ratio data, we extract the mass of nucleon in the SRC pair and the expected number of pn-SRC pairs in deuterium,…
Properties of several sorts of lattices of convex subsets of R^n are examined. The lattice of convex sets containing the origin turns out, for n>1, to satisfy a set of identities strictly between those of the lattice of all convex subsets…
It is the first step for understanding how RNA structure folds from base sequences that to know how its secondary structure is formed. Traditional energy-based algorithms are short of precision, particularly for non-nested sequences, while…
One of the most challenging and long-standing problems in computational biology is the prediction of three-dimensional protein structure from amino acid sequence. A promising approach to infer spatial proximity between residues is the study…
Non-coding RNAs are ubiquitous, but the discovery of new RNA gene sequences far outpaces research on their structure and functional interactions. We mine the evolutionary sequence record to derive precise information about function and…
Multiple sequence alignment (MSA) has been one of the most important problems in bioinformatics for more decades and it is still heavily examined by many mathematicians and biologists. However, mostly because of the practical motivation of…
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…
Low-rank modeling has many important applications in computer vision and machine learning. While the matrix rank is often approximated by the convex nuclear norm, the use of nonconvex low-rank regularizers has demonstrated better empirical…
The problem of reconstructing a sequence of independent and identically distributed symbols from a set of equal size, consecutive, fragments, as well as a dependent reference sequence, is considered. First, in the regime in which the…
Elementary cellular automata deterministically map a binary sequence to another using simple local rules. Visualizing the structure of this mapping is difficult because the number of nodes (i.e. possible binary sequences) grows…
Understanding the base pairing of an RNA sequence provides insight into its molecular structure.By mining suboptimal sampling data, RNAprofiling 1.0 identifies the dominant helices in low-energy secondary structures as features, organizes…
While artificial intelligence has made remarkable strides in revealing the relationship between biological macromolecules' primary sequence and tertiary structure, designing RNA sequences based on specified tertiary structures remains…
The task of RNA design given a target structure aims to find a sequence that can fold into that structure. It is a computationally hard problem where some version(s) have been proven to be NP-hard. As a result, heuristic methods such as…
We describe Structured Random Binding (SRB), a minimal model of protein-protein interactions rooted in the statistical physics of disordered systems. In this model, nonspecific binding is a generic consequence of the interaction between…
The topological filtration of interacting RNA complexes is studied and the role is analyzed of certain diagrams called irreducible shadows, which form suitable building blocks for more general structures. We prove that for two interacting…
This work presents a mathematical model that establishes an interesting connection between nucleotide frequencies in human single-stranded DNA and the famous Fibonacci's numbers. The model relies on two assumptions. First, Chargaff's second…
Genetic regulatory networks (GRNs) have been widely studied, yet there is a lack of understanding with regards to the final size and properties of these networks, mainly due to no network currently being complete. In this study, we analyzed…
We consider the Combinatorial RNA Design problem, a minimal instance of RNA design where one must produce an RNA sequence that adopts a given secondary structure as its minimal free-energy structure. We consider two free-energy models where…