We consider the space of w-mixtures that are the set of finite statistical mixtures sharing the same prescribed component distributions. The geometry induced by the Kullback-Leibler (KL) divergence on this family of w-mixtures is a dually flat space in information geometry called the mixture family manifold. It follows that the KL divergence between two w-mixtures is equivalent to a Bregman Div...

In image and signal processing, the beta-divergence is well known as a similarity measure between two positive objects. However, it is unclear whether or not the distance-like structure of beta-divergence is preserved, if we extend the domain of the beta-divergence to the negative region. In this article, we study the domain of the beta-divergence and its connection to the Bregman-divergence as...

It has been shown that gene body DNA methylation is associated with gene expression. However, whether and how deviation of gene body DNA methylation between duplicate genes can influence their divergence remains largely unexplored. Here, we aim to elucidate the potential role of gene body DNA methylation in the fate of duplicate genes. We identified paralogous gene pairs from Arabidopsis and ri...

Mahalanobis’ D-square (D2) statistics was applied to assess diversity in the 9 genotypes collectedof semi-arid region of India (7 genotypes from Gujarat and Rajasthan for normal toxic and two fromOrissa csmcri’s plantation of non toxic nature. These genotypes were grouped into five. Cluster I andIII had two genotypes, cluster II had three genotypes and cluster VI and V contributed as solitaryge...

a cartan manifold is a smooth manifold m whose slit cotangent bundle 0t *m is endowed with a regularhamiltonian k which is positively homogeneous of degree 2 in momenta. the hamiltonian k defines a (pseudo)-riemannian metric ij g in the vertical bundle over 0 t *m and using it, a sasaki type metric on 0 t *m is constructed. a natural almost complex structure is also defined by k on 0 t *m in su...

Multi-synchronous collaboration allows people to work concurrently on copies of a shared document which generates divergence. Divergence awareness allows to localize where divergence is located and estimate how much divergence exists among the copies. Existing divergence awareness metrics are highly coupled to their original applications and can not be used outside their original scope. In this...

In this article we study the field of Hilbertian metrics and positive definit (pd) kernels on probability measures, they have a real interest in kernel methods. Firstly we will make a study based on the Alpha-Beta-divergence to have a Hilbercan metric by proposing an improvement of this divergence by constructing it so that its is symmetrical the Alpha-Beta-Symmetric-divergence (ABS-divergence)...