The tidal marshes of North America are home to a diverse collection of morphologically differentiated reptiles, birds, and mammals. We reviewed the existing molecular studies on endemic tidal-marsh vertebrates, including turtles, snakes, sparrows, rails, shrews, and rodents. We found both deep and shallow divergences from their nearest upland relatives in all geographic regions. In the Northeas...

The concept of classical f -divergences gives a unified framework to construct and study measures of dissimilarity of probability distributions; special cases include the relative entropy and the Rényi divergences. Various quantum versions of this concept, and more narrowly, the concept of Rényi divergences, have been introduced in the literature with applications in quantum information theory;...

In this paper, we review and extend a family of log-det divergences for symmetric positive definite (SPD) matrices and discuss their fundamental properties. We show how to generate from parameterized Alpha-Beta (AB) and Gamma log-det divergences many well known divergences, for example, the Stein’s loss, S-divergence, called also Jensen-Bregman LogDet (JBLD) divergence, the Logdet Zero (Bhattac...

The concept of classical f -divergences gives a unified framework to construct and study measures of dissimilarity of probability distributions; special cases include the relative entropy and the Rényi divergences. Various quantum versions of this concept, and more narrowly, the concept of Rényi divergences, have been introduced in the literature with applications in quantum information theory;...

Projection theorems of divergences enable us to find reverse projection of a divergence on a specific statistical model as a forward projection of the divergence on a different but rather “simpler” statistical model, which, in turn, results in solving a system of linear equations. Reverse projection of divergences are closely related to various estimation methods such as the maximum likelihood ...

The phylogeny of butterflies, Parnassius stubbendorfii and P. glacialis, collected at various localities in the Japan archipelago and the eastern part of the Asian continent was analyzed using mitochondrial DNA sequences coding for NADH dehydrogenase subunit 5 (805 bp). The molecular phylogenetic trees revealed that P. glacialis and P. stubbendorfii diverged from a common ancestor, and then the...