Related papers: Inverted and mirror repeats in model nucleotide se…
It is a well-known fact that genetic sequences may contain sections with repeated units, called repeats, that differ in length over a population, with a length distribution of geometric type. A simple class of recombination models with…
We investigate 738 complete genomes of viruses to detect the presence of short inverted repeats. The number of inverted repeats found is compared with the prediction obtained for a Bernoullian and for a Markovian control model. We find as a…
In several previous works, I presented the mirror symmetry in the set of protein amino acids, expressed through the number of atoms. Here, however, the same thing is shown but over the number of nucleons and molecules mass. Compared to the…
Some natural proteins display recurrent structural patterns. Despite being highly similar at the tertiary structure level, repetitions within a single repeat protein can be extremely variable at the sequence level. We propose a mathematical…
We investigate the number of inverted repeats observed in 37 complete genomes of bacteria. The number of inverted repeats observed is much higher than expected using Markovian models of DNA sequences in most of the eubacteria. By using the…
For fixed $m > 1$, we study the product of $m$ independent $N \times N$ elliptic random matrices as $N$ tends to infinity. Our main result shows that the empirical spectral distribution of the product converges, with probability $1$, to the…
By a classical principle of probability theory, sufficiently thin subsequences of general sequences of random variables behave like i.i.d.\ sequences. This observation not only explains the remarkable properties of lacunary trigonometric…
We consider the asymptotic behavior of posterior distributions and Bayes estimators based on observations which are required to be neither independent nor identically distributed. We give general results on the rate of convergence of the…
Let $ \prod_{i=1}^d (X-\alpha_i Y) \in{\mathbb C}[X,Y]$ be a binary form and let $\epsilon_1,\dots,\epsilon_d$ be nonzero complex numbers. We consider the family of binary forms $ \prod_{i=1}^d (X-\alpha_i \epsilon_i^aY)$, $a\in {\mathbb…
A reflexive generalized inverse and the Moore-Penrose inverse are often confused in statistical literature but in fact they have completely different behaviour in case the population covariance matrix is not a multiple of identity. In this…
Recent studies have revealed that for the majority of species the length distributions of duplicated sequences in natural DNA follow a power-law tail. We study duplication-mutation models for processes in natural DNA sequences and the…
We analyze the absolute spectral gap of Markov chains on graphs obtained from a cycle of $n$ vertices and perturbed only at approximately $n^{1/\rho}$ random locations with an appropriate, possibly sparse, interconnection structure.…
The analysis of intermittent data is improved. The standard method of recovering the history of a particle cascade is proved in general not to reproduce the structure of the true cascade. The recovering corrections to the standard method…
The problem of reconstructing a sequence of independent and identically distributed symbols from a set of equal size, consecutive, fragments, as well as a dependent reference sequence, is considered. First, in the regime in which the…
After the recent advancement of sequencing strategies, mirror repeats have been found to be present in the gene sequence of many organisms and species. This presence of mirror repeats in most of the sequences indicates towards some…
Multiplicative random cascade model naturally reproduces the intermittency or multifractality, which is frequently shown among hierarchical complex systems such as turbulence and financial markets. As described herein, we investigate the…
We study the backward scatterings of plane waves by reciprocal scatterers and reveal that $n$-fold ($n\geq3$) rotation symmetry is sufficient to secure invariant backscattering for arbitrarily-polarized incident plane waves. It is further…
Probabilistic modeling is cyclical: we specify a model, infer its posterior, and evaluate its performance. Evaluation drives the cycle, as we revise our model based on how it performs. This requires a metric. Traditionally, predictive…
In the course of evolution, proteins undergo important changes in their amino acid sequences, while their three-dimensional folded structure and their biological function remain remarkably conserved. Thanks to modern sequencing techniques,…
Nonlinear complexity is an important measure for assessing the randomness of sequences. In this paper we investigate how circular shifts affect the nonlinear complexities of finite-length binary sequences and then reveal a more explicit…