One possibility of defining a quantum Rényi $\alpha $ -divergence two states is to optimize the classical their post-measurement probability distributions over all possible measurements (measured divergence), and maybe regularize thes...

Sequence mismatch analysis (MMA) and Bayesian skyline plots (BSP) are commonly used to reconstruct historical demography. A survey of 173 research articles (2009-2014), which included estimates of historical population sizes from mtDNA or cpDNA, shows a widespread genetic signature of demographic or spatial population expansion in species of all major taxonomic groups. Associating these expansi...

Fundamental to understanding how biodiversity arises and adapts is whether evolution is predictable in the face of stochastic genetic and demographic factors. Here we show rapid parallel evolution across two closely related but geographically isolated radiations of Nicaraguan crater lake cichlid fishes. We find significant morphological, ecological and genetic differentiation between ecomorphs ...

Five species of migratory thrushes (Turdidae) occupy a transcontinental distribution across northern North America. They have largely overlapping breeding ranges, relatively similar ecological niches, and mutualistic relationships with northern woodland communities as insectivores and seed-dispersing frugivores. As an assemblage of ecologically similar species, and given other vertebrate studie...

We discuss Bregman divergences and the very close relationship between a class of these divergences and the regular family of exponential distributions before applying them to various topology preserving dimension reducing algorithms. We apply these methods to identification of structure in magnetic resonance images of the brain and show that different divergences reveal different structure in ...

We describe the underlying probabilistic interpretation of alpha and beta divergences. We first show that beta divergences are inherently tied to Tweedie distributions, a particular type of exponential family, known as exponential dispersion models. Starting from the variance function of a Tweedie model, we outline how to get alpha and beta divergences as special cases of Csiszár’s f and Bregma...

The copepod Eurytemora affinis has a broad geographic range within the Northern Hemisphere, inhabiting coastal regions of North America, Asia, and Europe. A phylogenetic approach was used to determine levels of genetic differentiation among populations of this species, and interpopulation crosses were performed to determine reproductive compatibility. DNA sequences from two mitochondrial genes,...

We isolate logarithmic divergences from bosonic string amplitudes on a disc. These divergences are compared with “tadpole” divergences in the effective field theory with a covariant cosmological term implied by the counting of string coupling constants. We find an inconsistency between the two. This is a serious problem which could undermine the ability to remove divergences from the bosonic st...