Related papers: Multifractal characterisation of complete genomes
Discrete multiplicative turbulent cascades are described using a formalism involving infinitely divisible random measures. This permits to consider the continuous limit of a cascade developed on a continuum of scales, and to provide the…
We derive an exact expression for the probability density function of the cascade size (total progeny) in a continuous state branching process when the generations are Gamma distributed. The distribution has application in the modelling of…
We introduce a new family of models for growing networks. In these networks new edges are attached preferentially to vertices with higher number of connections, and new vertices are created by already existing ones, inheriting part of their…
We prove that certain quotients of entire functions are characteristic functions. Under some conditions, the probability measure corresponding to a characteristic function of that type has a density which can be expressed as a generalized…
In a recent article a generalization of the binomial distribution associated with a sequence of positive numbers was examined. The analysis of the nonnegativeness of the formal expressions was a key-point to allow to give them a statistical…
We determine the Renyi entropies K_q of symbol sequences generated by human chromosomes. These exhibit nontrivial behaviour as a function of the scanning parameter q. In the thermodynamic formalism, there are phase transition-like phenomena…
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 derive out naturally some important distributions such as high order normal distributions and high order exponent distributions and the Gamma distribution from a geometrical way. Further, we obtain the exact mean-values of integral form…
We formulate the statistics of the discrete multicomponent fragmentation event using a methodology borrowed from statistical mechanics. We generate the ensemble of all feasible distributions that can be formed when a single integer…
Horizontal gene transfer inference approaches are usually based on gene sequences: parametric methods search for patterns that deviate from a particular genomic signature, while phylogenetic methods use sequences to reconstruct the gene and…
We introduce a simple model for DNA evolution. Using the method of Peng et al.$^1$, we investigate the fractal properties of the system. For small chains and chains of intermediate size we find a fractal exponent that indicates the…
Using a probabilistic approach, we derive some interesting combinatorial identities involving gamma and beta functions. These results generalize certain well-known combinatorial identities involving binomial coefficients and special…
We connect shift-invariant characteristic kernels to infinitely divisible distributions on $\mathbb{R}^{d}$. Characteristic kernels play an important role in machine learning applications with their kernel means to distinguish any two…
For a sample of absolutely bounded i.i.d. random variables with a continuous density the cumulative distribution function of the sample variance is represented by a univariate integral over a Fourier series. If the density is a polynomial…
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…
We derive the exact probability density function of the product of $N$ independent variance-gamma random variables with zero location parameter. We then apply this formula to derive formulas for the cumulative distribution function and…
The codons, sixtyfour in number, are distributed over the coding parts of DNA sequences. The distribution function is the plot of frequency-versus-rank of the codons. These distributions are characterised by parameters that are almost…
The normal distribution is well-known for several results that it is the only to fulfil. The aim of the present paper is to show that many of these characterizations actually follow from the fact that the derivative of the log-density of…
In this research, we consider a mixture of genome fragments of a certain bacteria set. The problem of mixture separation is studied under the assumption that all the genomes present in the mixture are completely sequenced or are close to…
Let $X$ and $Y$ be independent variance-gamma random variables with zero location parameter; then the exact probability density function of the ratio $X/Y$ is derived. Some basic distributional properties are also derived, including…