Radical divergence

Element and Radical: the Divergence of Synonyms

The nouns “element” and “radical” are prominent words in the chemist’s vocabulary. That their meanings nowadays are radically different is a fact that is elementary to all, yet, given their prominence, it is striking that a millennium ago they were virtually synonyms. By the late eighteenth century, Lavoisier and his colleagues had assigned them different denotations. Given the fundamental stat...

Dating divergence of Polystigma and other Sordariomycetes

Studies on the evolutionary history of ascomycetes in terms of time scale will help to understand historical patterns that shape their biodiversity. Until now most of dating studies of ascomycetes have focused on major events in fungal evolution but not on divergence events within smaller groups of fungi e.g. within Sordariomycetes. We used molecular dating to estimate the time of separation of...

Penalized Bregman Divergence Estimation via Coordinate Descent

Variable selection via penalized estimation is appealing for dimension reduction. For penalized linear regression, Efron, et al. (2004) introduced the LARS algorithm. Recently, the coordinate descent (CD) algorithm was developed by Friedman, et al. (2007) for penalized linear regression and penalized logistic regression and was shown to gain computational superiority. This paper explores...

Asymptotic Distribution of Divergence Measure with Applications

Rényi Divergence and Kullback-Leibler Divergence

Rényi divergence is related to Rényi entropy much like Kullback-Leibler divergence is related to Shannon’s entropy, and comes up in many settings. It was introduced by Rényi as a measure of information that satisfies almost the same axioms as Kullback-Leibler divergence, and depends on a parameter that is called its order. In particular, the Rényi divergence of order 1 equals the Kullback-Leibl...