Related papers: A model capturing novel strand symmetries in bacte…
The effect of heterogeneous sequence composition on the denaturation of double stranded DNA is investigated. The resulting pair-binding energy variation is found to have a negligible effect on the critical properties of the smooth second…
Next Generation Sequencing (NGS) technologies generate large amounts of short read data for many different organisms. The fact that NGS reads are generally short makes it challenging to assemble the reads and reconstruct the original genome…
We propose a new distance metric for DNA sequences, which can be defined on any evolutionary Markov model with infinitesimal generator matrix Q. That is the new metric can be defined under existing models such as Jukes-Cantor model,…
The problem of genealogy of permutations has been solved partially by Stefan (odd order) and Acosta-Hum\'anez & Bernhardt (power of two). It is well known that Sharkovskii's theorem shows the relationship between the cardinal of the set of…
The nature of the quantitative distribution of the 64 DNA codons in the human genome has been an issue of debate for over a decade. Some groups have proposed that the quantitative distribution of the DNA codons ordered as a rank-frequency…
Network reconstruction consists in determining the unobserved pairwise couplings between $N$ nodes given only observational data on the resulting behavior that is conditioned on those couplings -- typically a time-series or independent…
The band gap, a key concept in solid-state physics, is traditionally explained by the Bragg diffraction of electron waves in the periodic potential of a crystal. Although widely accepted, this framework raises fundamental issues in…
Parts of DNA sequences known as exons and introns play very different role in coding and storage of genetic information. Here we show that their conducting properties are also very different. Taking into account long-range correlations…
Motivated by a model presented by S. Gudder, we study a quantum generalization of Markov chains and discuss the relation between these maps and open quantum random walks, a class of quantum channels described by S. Attal et al. We consider…
We propose a simple tractable pair hidden Markov model for pairwise sequence alignment that accounts for the presence of short tandem repeats. Using the framework of gain functions, we design several optimization criteria for decoding this…
We investigate knotting probabilities of long double-stranded DNA strands in a coarse-grained Kratky-Porod model for DNA with Monte Carlo simulations. Various ionic conditions are implemented by adjusting the effective diameter of monomers.…
The classic algorithms of Needleman--Wunsch and Smith--Waterman find a maximum a posteriori probability alignment for a pair hidden Markov model (PHMM). In order to process large genomes that have undergone complex genome rearrangements,…
The denaturation of the double helix is a template for fundamental biological functions such as replication and transcription involving the formation of local fluctuational openings. The denaturation transition is studied for heterogeneous…
This work approaches human chromosome mapping by developing algorithms for ordering markers associated with radiation hybrid data. Motivated by recent work of Boehnke et al. [1], we formulate the ordering problem by developing stochastic…
A tandem cell is proposed for DNA sequencing in which an exonuclease enzyme cleaves bases (mononucleotides) from a strand of DNA for identification inside a nanopore. It has two nanopores and three compartments with the structure [cis1,…
Most DNA sequencing technologies are based on the shotgun paradigm: many short reads are obtained from random unknown locations in the DNA sequence. A fundamental question, studied in arXiv:1203.6233, is what read length and coverage depth…
We consider random permutations derived by sampling from stick-breaking partitions of the unit interval. The cycle structure of such a permutation can be associated with the path of a decreasing Markov chain on $n$ integers. Under certain…
The sequence-dependent elasticity of double-helical DNA on a nm length scale can be captured by the rigid base-pair model, whose strains are the relative position and orientation of adjacent base-pairs. Corresponding elastic potentials have…
The translocation of a short DNA fragment through a nanopore is addressed when the perforated membrane contains an embedded electrode. Accurate numerical solutions of the coupled Poisson, Nernst-Planck, and Stokes equations for a realistic,…
We study the problem of learning sparse structure changes between two Markov networks $P$ and $Q$. Rather than fitting two Markov networks separately to two sets of data and figuring out their differences, a recent work proposed to learn…