Related papers: Expectation of the Site Frequency Spectrum
Rate variation among the sites of a molecular sequence is commonly found in applications of phylogenetic inference. Several approaches exist to account for this feature but they do not usually enable the investigator to pinpoint the sites…
We consider a single genetic locus with two alleles $A_1$ and $A_2$ in a large haploid population. The locus is subject to selection and two-way, or recurrent, mutation. Assuming the allele frequencies follow a Wright-Fisher diffusion and…
Statistical properties of the site frequency spectrum associated with Lambda-coalescents are our objects of study. In particular, we derive recursions for the expected value, variance, and covariance of the spectrum, extending earlier…
Biologists have long sought a way to explain how statistical properties of genetic sequences emerged and are maintained through evolution. On the one hand, non-random structures at different scales indicate a complex genome organisation. On…
We discuss spectral properties of a charged quantum particle confined to a chain graph consisting of an infinite array of rings under influence of a magnetic field assuming a $\delta$-coupling at the points where the rings touch. We start…
The study of correlation structure in the primary sequences of DNA is reviewed. The issues reviewed include: symmetries among 16 base-base correlation functions, accurate estimation of correlation measures, the relationship between $1/f$…
Periodic patterns play the important regulatory and structural roles in genomic DNA sequences. Commonly, the underlying periodicities should be understood in a broad statistical sense, since the corresponding periodic patterns have been…
Background: Several sources of noise obfuscate the identification of single nucleotide variation (SNV) in next generation sequencing data. For instance, errors may be introduced during library construction and sequencing steps. In addition,…
The estimation of parameters in the frequency spectrum of a seasonally persistent stationary stochastic process is addressed. For seasonal persistence associated with a pole in the spectrum located away from frequency zero, a new…
The number of substitutions (of nucleotides, amino acids, ...) that take place during the evolution of a sequence is a stochastic variable of fundamental importance in the field of molecular evolution. Although the mean number of…
Much of the on-going statistical analysis of DNA sequences is focused on the estimation of characteristics of coding and non-coding regions that would possibly allow discrimination of these regions. In the current approach, we concentrate…
The problem of detecting a binding site -- a substring of DNA where transcription factors attach -- on a long DNA sequence requires the recognition of a small pattern in a large background. For short binding sites, the matching probability…
We derive explicit formulas for the two first moments of he site frequency spectrum $(SFS_{n,b})_{1\leq b\leq n-1}$ of the Bolthausen-Sznitman coalescent along with some precise and efficient approximations, even for small sample sizes $n$.…
The temporal evolution of microwave pulses transmitted through random dielectric samples is obtained from the Fourier transform of field spectra. Large fluctuations are found in the local or single channel delay time, which is the first…
When considering binary strings, it's natural to wonder how many distinct subsequences might exist in a given string. Given that there is an existing algorithm which provides a straightforward way to compute the number of distinct…
Genome sequencing technology has improved significantly in few last years and resulted in abundance genetic data. Artificial intelligence has been employed to analyze genetic data in response to its sheer size and variability. Gene…
Normal approximations for descents and inversions of permutations of the set $\{1,2,...,n\}$ are well known. A number of sequences that occur in practice, such as the human genome and other genomes, contain many repeated elements. Motivated…
A mutator is an allele that increases the mutation rate throughout the genome by disrupting some aspect of DNA replication or repair. Mutators that increase the mutation rate by the order of 100 fold have been observed to spontaneously…
Fluctuation scaling is observed phenomenon from complex networks through finance to ecology. It means that the variance and the mean of a specific quantity are related as $\ev{\sigma^2|n}\propto \ev{n|A}^{2\alpha}$ with $1/2\geq \alpha \geq…
The nucleotide composition of human genes with a special emphasis on transcription-related strand asymmetries is analyzed. Such asymmetries may be associated with different mutational rates in two principal factors. The first one is…