Bounds on Nonsymmetric Divergence Measure in terms of Other Symmetric and Nonsymmetric Divergence Measures

PubMed Central

Jain, K. C.; Chhabra, Praphull

2014-01-01

Vajda (1972) studied a generalized divergence measure of Csiszar's class, so called “Chi-m divergence measure.” Variational distance and Chi-square divergence are the special cases of this generalized divergence measure at m = 1 and m = 2, respectively. In this work, nonparametric nonsymmetric measure of divergence, a particular part of Vajda generalized divergence at m = 4, is taken and characterized. Its bounds are studied in terms of some well-known symmetric and nonsymmetric divergence measures of Csiszar's class by using well-known information inequalities. Comparison of this divergence with others is done. Numerical illustrations (verification) regarding bounds of this divergence are presented as well. PMID:27437464

Ecosystems response and restitution time across the K/Pg boundary transition at high-latitudes, Southern Hemisphere, New Zealand - a palynological approach

NASA Astrophysics Data System (ADS)

Willumsen, Pi; Vajda, Vivi

2010-05-01

Several major groups of biota/fauna disappeared globally across the Cretaceous-Paleogene boundary (K/Pg boundary) and several other important groups suffered considerable, but not complete, species-level extinction. For marine phytoplankton - a major driver of ocean productivity - darkness and suppression of photosynthesis, in the aftermath of the asteroid impact, was likely a major killing mechanism. Thus, in the marine realm there is a separation in extinction rate between strongly affected groups with calcareous shells and groups that had organic cysts or siliceous tests. Detailed regional records of the long-term post-K/Pg boundary therefore still need to be undertaken to enhance the understanding of how each of the major microfossil groups recovered to elucidate recovery in different ecosystem types following this unique event. Throughout the New Zealand region, widespread deposition of siliceous sediments occurred during the Late Cretaceous to early Paleocene indicating the existence of a south Pacific upwelling regime (Hollis 1993, 1995; Strong et al. 1995). Silica concentration in the oceans increased after the K/Pg event and remained high for 1-2 millions years during the early Paleogene, reflecting high bio-siliceous productivity in the aftermath of the K/Pg boundary event (Hollis et al. 1995, 2003). The geological archives of New Zealand includes outcrops from several basins which provide a unique possibility for examining ecosystem response and restitution time from latest Cretaceous to early Paleogene in a suite of depositional environments spanning from terrestrial to bathyal (Willumsen 2000, Vajda et al. 2001, Vajda and Raine 2003). High-resolution palynological comparative studies of organic-walled microfossils such as dinoflagellate assemblages (dinocysts), spores and pollen are currently carried out on New Zealand sediments. The recovery period in the marine realm is much extended compared with the much shorter recovery time reflected by the

Optimizing Marine Corps Pilot Conversion to the Joint Strike Fighter

DTIC Science & Technology

2010-06-01

Office of Civilian Manpower Management. Included are a summary of modeling efforts and the mathematics behind them, models for aggregate manpower...Vajda for the Admiralty of the Royal Navy. They also mention work by one of the first actuaries , John Rowe, who as early as 1779, conducted studies...idea of using mathematical and statistical techniques to obtain better information on the manpower requirements has its roots in personnel research