The generalized binomial distribution in Tsallis statistics (power-law system) is explicitly formulated from the precise q-Stirling’s formula. The α-divergence (or q-divergence) is uniquely derived from the generalized binomial distribution in the sense that when α → −1 (i.e., q → 1) it recovers KL divergence obtained from the standard binomial distribution. Based on these combinatorial conside...

In this paper, the concept of the classical f -divergence for a pair of measures is extended to the mixed f -divergence for multiple pairs of measures. The mixed f -divergence provides a way to measure the difference between multiple pairs of (probability) measures. Properties for the mixed f -divergence are established, such as permutation invariance and symmetry in distributions. An Alexandro...

Abstract Recently, Taneja [7] studied two one parameter generalizations of J-divergence, Jensen-Shannon divergence and Arithmetic-Geometric divergence. These two generalizations in particular contain measures like: Hellinger discrimination, symmetric chi-square divergence, and triangular discrimination. These measures are well known in the literature of Statistics and Information theory. In thi...

In this paper, the concept of the classical f -divergence (for a pair of measures) is extended to the mixed f divergence (for multiple pairs of measures). The mixed f -divergence provides a way to measure the difference between multiple pairs of (probability) measures. Properties for the mixed f -divergence are established, such as permutation invariance and symmetry in distributions. An Alexan...

Recent large-scale studies of evolutionary changes in gene expression among mammalian species have led to the proposal that gene expression divergence may be neutral with respect to organismic fitness. Here, we employ a comparative analysis of mammalian gene sequence divergence and gene expression divergence to test the hypothesis that the evolution of gene expression is predominantly neutral. ...

Gene expression divergence is one of the mechanisms thought to be involved in the emergence of incipient species. Next-generation sequencing has become an extremely valuable tool for the study of this process by allowing whole transcriptome sequencing, or RNA-Seq. We have conducted a 454 GS-FLX pyrosequencing experiment to refine our understanding of adaptive divergence between dwarf and normal...

Let X be a divergence-free vector field defined on a closed, connected Riemannian manifold. In this paper, we show the equivalence between the following conditions: • X is a divergence-free vector field satisfying the shadowing property. • X is a divergence-free vector field satisfying the Lipschitz shadowing property. • X is an expansive divergence-free vector field. • X has no singularities a...

Results involving the approximation of the difference between two integral means are utilised to obtain bounds on the Integral Mean Divergence and the f−divergence due to Csiszár. The current work does not restrict the functions involved to be convex. If convexity is imposed then the Integral Mean Divergence is the Hermite-Hadamard divergence introduced by Shioya and Da-te.

Gene flow plays a fundamental role in plant evolutionary history, yet its role in population divergence--and ultimately speciation--remains poorly understood. We investigated gene flow and the modalities of divergence in the domesticated Zea mays ssp. mays and three wild Zea taxa using sequence polymorphism data from 26 nuclear loci. We described diversity across loci and assessed evidence for ...

Entropy-based divergence measures have shown promising results in many areas of engineering and image processing. In this paper, we define a new generalized divergence measure, namely, the Jensen–Rényi divergence. Some properties such as convexity and its upper bound are derived. Based on the Jensen–Rényi divergence, we propose a new approach to the problem of image registration. Some appealing...