Advancing Shannon entropy for measuring diversity in systems

From economic inequality and species diversity to power laws and the analysis of multiple trends and trajectories, diversity within systems is a major issue for science. Part of the challenge is measuring it. Shannon entropy H has been used to re-think diversity within probability distributions, based on the notion of information. However, there are two major limitations to Shannon's approach. First, it cannot be used to compare diversity distributions that have different levels of scale. Second, it cannot be used to compare parts of diversity distributions to the whole. To address these limitations, we introduce a re-normalization of probability distributions based on the notion of case-based entropy Cc as a function of the cumulative probability c. Given a probability density p(x), Cc measures the diversity of the distribution up to a cumulative probability of c, by computing the length or support of an equivalent uniform distribution that has the same Shannon information as the conditional distribution of ^pc(x) up to cumulative probability c. We illustrate the utility of our approach by re-normalizing and comparing three well-known energy distributions in physics, namely, the Maxwell-Boltzmann, Bose-Einstein and Fermi-Dirac distributions for energy of sub-atomic particles. The comparison shows that Cc is a vast improvement over H as it provides a scale-free comparison of these diversity distributions and also allows for a comparison between parts of these diversity distributions

The Sexual Behavior Sequelae of Childhood Sexual Abuse in College Women

The present investigation examined the association between childhood sexual abuse (CSA) and a variety of sexual behaviors in adulthood while controlling for the confounding effects of family environment and adolescent/adult sexual assault. Three hundred ninety female undergraduates completed measures of CSA, adolescent/adult sexual assault, family environment (physical abuse, emotional abuse, neglect, quality of the parent-child bond), sexual satisfaction and functioning, propensity to engage in casual sex, attraction to sexual aggression, sexual fantasy, and sexual preference. The results indicated that CSA, after controlling for confounding variables, was associated with increased sexual activity, a propensity for casual sex, and sexual fantasies staining elements of force. The relationships, however, tended to be small. Finally, CSA was associated with a preference for sexual images containing themes of domination. The results of the present study suggest that CSA is uniquely associated with adult sexuality after controlling for the potentially confounding effects of family environment and adolescent/adult sexual assault

No Transitional Justice Without Transition: Darfur - A Case Study

Article published in the Michigan State International Law Review

Guide to Bahamian Ichnology: Pleistocene, Holocene, and Modern Environments: A Field Trip Guide

This guide was prepared for the Fourth International Ichnofabric Workshop (IIW- 4) to be hosted by the Bahamian Field Station and held on San Salvador Island on March 15-22, 1997. About 35 scientists representing 15 countries are registered to attend the workshop. The focus of discussion in the infonnal scientific sessions will be the uses of ichnofabric analysis in sedimentary geology. An ichnofabric is the texture or internal structure created within a sedimentary substrate from the bioturbating activity of organisms. Ichnofabric analysis is a new and emerging area of ichnology (the study of trace fossils), and its methods are proving useful in enhancing sedimentary facies recognition and interpretations, event correlation, paleoenvironmental and paleoecological reconstructions, reservoir prediction, and more. Ichnologists are field oriented, and San Salvador Island, with its diverse and largely pristine modem tropical, carbonate environments and well exposed Pleistocene and Holocene rock record, provides provides a fantastic natural laboratory for the study of all aspects of carbonate geology. San Salvador also is a geologically and ichnologically well known island, so proven field localities are readily available. This doesn\u27t mean that new ichnologic discoveries and interpretations won\u27t be forthcoming - they certainly will be, and probably some will occur during the time of the IIW-4 workshop. My colleague Brian White and I have been working in the Bahamas for just over 15 years. We know a great deal about Bahamian geology, but with every field excursion we find something new, and I often think that we have just scratched the surface! The centerpiece of this guide is the descriptions of six Ichno-localities on San Salvador Island that provide outstanding examples of modem traces or trace fossils and illustrate a veriety of ichnologic principles. In addition, in composite form, the stops provide a good overview of the Pleistocene, Holocene, and modem geology and environments of San Salvador. All of the stops are readily accessible from the main roads on the island. The initial chapter provides a brief introduction to the geology of the Bahamas and San Salvador for first-time visitors. The three chapters at the end of the guide are thematic and designed to expand the ichnologic perspectives to include borer organisms, plant trace fossils, and ichnologic sites in the Bahamas beyond San Salvador. I hope this guide will be useful to a broad spectrum of visitors to the Bahamian Field Station for several years to come, as well as to ichnologists unable to attend this workshop but with an interest in carbonates. See other Smith authored Field Trip Guides of Gerace Research Centre

A Sea-Level Lowstand (Devil\u27s Point Event) Recorded in Bahamian Reefs: Comparison with Other Last Interglacial Climate Proxies

Reprinted from: Benjamin J. Greenstein and Cindy K. Carney (eds.) Proceedings of the 10th Symposium on the Geology of the Bahamas and Other Carbonate Regions: San Salvador, Gerace Research Cente

Bahamian Sangamonian Coral Reefs and Sea-Level Change

Reprinted from James L. Carew (ed.) May 30–June 3, 1996, Proceedings of the 8th Symposium on the Geology of the Bahamas and Other Carbonate Regions: Bahamian Field Station, San Salvador, Bahamas

A Simulated Annealing Algorithm for the Optimization of Multistage Depressed Collector Efficiency

The microwave traveling wave tube amplifier (TWTA) is widely used as a high-power transmitting source for space and airborne communications. One critical factor in designing a TWTA is the overall efficiency. However, overall efficiency is highly dependent upon collector efficiency; so collector design is critical to the performance of a TWTA. Therefore, NASA Glenn Research Center has developed an optimization algorithm based on Simulated Annealing to quickly design highly efficient multi-stage depressed collectors (MDC)

Disproportionality as a Framework to Target Pollution Reduction from Urban Landscapes

New federal water quality regulations regarding impaired waters and urban stormwater alongside a growing need to reverse eutrophication of urban lakes are creating demand to decrease nutrient export from urban landscapes, particularly lawns. We propose that Nowak’s disproportionality framework could be used to target specific households likely to generate disproportionate levels of nutrient export. The biophysical dimension would be based on landscape vulnerability (slope; soil type; proximity to lakes); the social dimension would target “inappropriate” lawn management behaviors leading to high nutrient export on these vulnerable landscapes. Understanding of lawn nutrient cycling (biophysical dimension) and homeowner beliefs and attitudes (social dimension) would be used to develop targeted, specific messages for homeowners with inappropriate management practices. A lawn management program developed with this disproportionality framework would probably be very effective, highly economical and fair, targeting only homeowners who are creating a disproportionate impact