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Gene duplication is a fundamental evolutionary mechanism that contributes to biological complexity and diversity (Fortna et al., 2004). Traditionally, research has focused on the duplication of gene sequences (Zhang, 1914). However,…
A number of signal processing and statistical methods can be used in analyzing either pieces of text or DNA sequences. These techniques can be used in a number of ways, such as determining authorship of documents, finding genes in DNA, and…
We describe a framework for systematic enumeration of families combinatorial structures which possess a certain regularity. More precisely, we describe how to obtain the differential equations satisfied by their generating series. These…
The statistical properties of local alignment algorithms with gaps are analyzed theoretically for uncorrelated and correlated DNA sequences. In the vicinity of the log-linear phase transition, the statistics of alignment with gaps is shown…
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 $1/f$…
Black box deep learning models trained on genomic sequences excel at predicting the outcomes of different gene regulatory mechanisms. Therefore, interpreting these models may provide novel insights into the underlying biology, supporting…
We consider uniform random permutations drawn from a family enumerated through generating trees. We develop a new general technique to establish a central limit theorem for the number of consecutive occurrences of a fixed pattern in such…
The detection of local genomic signals using high-throughput DNA sequencing data can be cast as a problem of scanning a Poisson random field for local changes in the rate of the process. We propose a likelihood-based framework for for such…
Systems with time delay play an important role in modeling of many physical and biological processes. In this paper we describe generic properties of systems with time delay, which are related to the appearance and stability of periodic…
It is shown that metric representation of DNA sequences is one-to-one. By using the metric representation method, suppression of nucleotide strings in the DNA sequences is determined. For a DNA sequence, an optimal string length to display…
Large-scale statistical analysis of data sets associated with genome sequences plays an important role in modern biology. A key component of such statistical analyses is the computation of $p$-values and confidence bounds for statistics…
DNA is subject to large deformations in a wide range of biological processes. Two key examples illustrate how such deformations influence the readout of the genetic information: the sequestering of eukaryotic genes by nucleosomes, and DNA…
Continuous symmetries are fundamental to many scientific and learning problems, yet they are often unknown a priori. Existing symmetry discovery approaches typically search directly in the space of transformation generators or rely on…
Gene regulation is a complex process involving the role of several genomic elements which work in concert to drive spatio-temporal expression. The experimental characterization of gene regulatory elements is a very complex and…
Data compression plays an important role to deal with high volumes of DNA sequences in the field of Bioinformatics. Again data compression techniques directly affect the alignment of DNA sequences. So the time needed to decompress a…
Discrete scale invariance (DSI) has recently been documented in time-to-failure rupture, earthquake processes and financial crashes, in the fractal geometry of growth processes and in random systems. The main signature of DSI is the…
A classic and fundamental result about the decomposition of random sequences into a mixture of simpler ones is de Finetti's Theorem. In its original form it applies to infinite 0-1 valued exchangeable sequences. Later it was extended and…
Our world is ambiguous and this is reflected in the data we use to train our algorithms. This is particularly true when we try to model natural processes where collected data is affected by noisy measurements and differences in measurement…
The nucleotide sequence representation of DNA can be inadequate for resolving protein-DNA binding sites and regulatory substrates, such as those involved in gene expression and horizontal gene transfer. Considering that sequence-like…
Motivation: Most existing methods for DNA sequence analysis rely on accurate sequences or genotypes. However, in applications of the next-generation sequencing (NGS), accurate genotypes may not be easily obtained (e.g. multi-sample…