Related papers: Expectation of the Site Frequency Spectrum
This article is dedicated to the following class of problems. Start with an $N\times N$ Hermitian matrix randomly picked from a matrix ensemble - the reference matrix. Applying a rank-$t$ perturbation to it, with $t$ taking the values $1\le…
A spin chain, describing a nucleotides sequence, is identified by the labels of a vector state of an irreducible representation of U_q->0(sl2). A master equation for the distribution function is written, where the intensity of the one-spin…
We study the population genetics of two neutral alleles under reversible mutation in the \Lambda-processes, a population model that features a skewed offspring distribution. We describe the shape of the equilibrium allele frequency…
We consider a general branching population where the lifetimes of individuals are i.i.d.\ with arbitrary distribution and where each individual gives birth to new individuals at Poisson times independently from each other. In addition, we…
The spectrum of a supernova is a summation of numerous overlapping atomic line signatures. Consequently, empirical measurements are limited in application when compound features are assumed to be due to one or two spectral lines. Here I…
Spectral variability of radio sources encodes information about the conditions of intervening media, source structure, and emission processes. With new low-frequency radio interferometers observing over wide fractional bandwidths, studies…
Gene duplications are one of major primary driving forces for evolutionary novelty. We took population genetics models of genes duplicate to study how evolutionary forces acting during the fixation of mutant allele at duplicate loci. We…
Linear functions of the site frequency spectrum (SFS) play a major role for understanding and investigating genetic diversity. Estimators of the mutation rate (e.g. based on the total number of segregating sites or average of the pairwise…
A DNA palindrome is a segment of double-stranded DNA sequence with inver- sion symmetry which may form secondary structures conferring significant biolog- ical functions ranging from RNA transcription to DNA replication. To test if the…
It is generally difficult to predict the positions of mutations in genomic DNA at the nucleotide level. Retroviral DNA insertion is one mode of mutation, resulting in host infections that are difficult to treat. This mutation process…
This work is devoted to investigating the evolution of concentration in a genetic regulation system, when the synthesis reaction rate is under additive and multiplicative asymmetric stable L\'evy fluctuations. By focusing on the impact of…
We explore the large-scale behavior of nucleotide compositional strand asymmetries along human chromosomes. As we observe for 7 of 9 origins of replication experimentally identified so far, the (TA+GC) skew displays rather sharp upward…
In this article, we review existing probabilistic models for modeling abundance of fixed-length strings (k-mers) in DNA sequencing data. These models capture dependence of the abundance on various phenomena, such as the size and repeat…
Various approaches to alignment-free sequence comparison are based on the length of exact or inexact word matches between two input sequences. Haubold {\em et al.} (2009) showed how the average number of substitutions between two DNA…
We provide an analytical argument for understanding the likely nature of parameter shifts between those coming from an analysis of a dataset and from a subset of that dataset, assuming differences are down to noise and any intrinsic…
Two major sources of stochasticity in the dynamics of neutral alleles result from resampling of finite populations (genetic drift) and the random genetic background of nearby selected alleles on which the neutral alleles are found (linked…
The stationary sampling distribution of a neutral decoupled Moran or Wright-Fisher diffusion with neutral mutations is known to first order for a general rate matrix with small but otherwise unconstrained mutation rates. Using this…
We consider the quantum site percolation model on graphs with an amenable group action. It consists of a random family of Hamiltonians. Basic spectral properties of these operators are derived: non-randomness of the spectrum and its…
We consider a popular online change-point problem of detecting a transient change in distributions of i.i.d. random variables. For this change-point problem, several change-point procedures are formulated and some advanced results for a…
Statistical consistency in phylogenetics has traditionally referred to the accuracy of estimating phylogenetic parameters for a fixed number of species as we increase the number of characters. However, as sequences are often of fixed length…