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Latent periodic elements in genomes play important roles in genomic functions. Many complex periodic elements in genomes are difficult to be detected by commonly used digital signal processing (DSP). We present a novel method to compute the…
Repetitive elements are important in genomic structures, functions and regulations, yet effective methods in precisely identifying repetitive elements in DNA sequences are not fully accessible, and the relationship between repetitive…
Sequencing by synthesis is used in many next-generation DNA sequencing technologies. Some of the technologies, especially those exploring the principle of single-molecule sequencing, allow incomplete nucleotide incorporation in each cycle.…
We propose that the distribution of DNA words in genomic sequences can be primarily characterized by a double Pareto-lognormal distribution, which explains lognormal and power-law features found across all known genomes. Such a distribution…
The so called long range correlation properties of DNA sequences are studied using the variance analyses of the density distribution of a single or a group of nucleotides in a model independent way. This new method which was suggested…
Apparent inconsistencies between different formulations of nucleon sum rules at finite density are resolved through a proper accounting of asymmetries in the spectral functions between positive- and negative-energy states.
A mathematical algorithm to describe DNA or RNA sequences of $N$ nucleotides by a string of $2N$ integers numbers is presented in the framework of the so called crystal basis model of the genetic code. The description allows to define a not…
In this paper, we review the literature on statistical long-range correlation in DNA sequences. We examine the current evidence for these correlations, and conclude that a mixture of many length scales (including some relatively long ones)…
Regular sequences are natural generalisations of fixed points of constant-length substitutions on finite alphabets, that is, of automatic sequences. Using the harmonic analysis of measures associated with substitutions as motivation, we…
DNA segments and sequences have been studied thoroughly during the past decades. One of the main problems in computational biology is the identification of exon-intron structures inside genes using mathematical techniques. Previous studies…
Recent advances in high-throughput genomics technologies have resulted in the sequencing of large numbers of (near) complete genomes. These genome sequences are being mined for important functional elements, such as genes. They are also…
Herein it is shown that in order to study the statistical properties of DNA sequences in bacterial chromosomes it suffices to consider only one half of the chromosome because they are similar to its corresponding complementary sequence in…
The spectral density of random matrices is studied through a quaternionic generalisation of the Green's function, which precisely describes the mean spectral density of a given matrix under a particular type of random perturbation. Exact…
Motivated by empirical observations of algebraic duplicated sequence length distributions in a broad range of natural genomes, we analytically formulate and solve a class of simple discrete duplication/substitution models that generate…
We consider a quasi one-dimensional chain of N chaotic scattering elements with periodic boundary conditions. The classical dynamics of this system is dominated by diffusion. The quantum theory, on the other hand, depends crucially on…
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…
Genomic signal processing has been used successfully in bioinformatics to analyze biomolecular sequences and gain varied insights into DNA structure, gene organization, protein binding, sequence evolution, etc. But challenges remain in…
The spectral symbols are useful tools to analyse the eigenvalue distribution when dealing with high dimensional linear systems. Given a matrix sequence with an asymptotic symbol, the last one depends only on the spectra of the individual…
This paper presents a probabilistic approach for DNA sequence analysis. A DNA sequence consists of an arrangement of the four nucleotides A, C, T and G and different representation schemes are presented according to a probability measure…
Filtered diode array spectrometers are routinely employed to infer the temporal evolution of spectral power from x-ray sources, but uniquely extracting spectral content from a finite set of broad, spectrally overlapping channel spectral…