Estimation of Distribution Overlap of Urn Models

A classical problem in statistics is estimating the expected coverage of a sample, which has had applications in gene expression, microbial ecology, optimization, and even numismatics. Here we consider a related extension of this problem to random samples of two discrete distributions. Specifically, we estimate what we call the dissimilarity probability of a sample, i.e., the probability of a draw from one distribution not being observed in k draws from another distribution. We show our estimator of dissimilarity to be a U-statistic and a uniformly minimum variance unbiased estimator of dissimilarity over the largest appropriate range of k. Furthermore, despite the non-Markovian nature of our estimator when applied sequentially over k, we show it converges uniformly in probability to the dissimilarity parameter, and we present criteria when it is approximately normally distributed and admits a consistent jackknife estimator of its variance. As proof of concept, we analyze V35 16S rRNA data to discern between various microbial environments. Other potential applications concern any situation where dissimilarity of two discrete distributions may be of interest. For instance, in SELEX experiments, each urn could represent a random RNA pool and each draw a possible solution to a particular binding site problem over that pool. The dissimilarity of these pools is then related to the probability of finding binding site solutions in one pool that are absent in the other.Comment: 27 pages, 4 figure

Stratiform clouds and their interaction with atmospheric motions

During the 1987 to 1988 academic year, three projects were finished and plans were made to redirect and focus work in a proposal now being reviewed. The completed work involves study of waves on an equatorial beta-plane in shear flow, investigation of the influence of orography on the index cycle, and analysis of a model of cloud street development in a thermally-forced, sheared environment. The proposed work involves study of boundary layer circulations supporting stratocumulus decks and investigation of how the radiative effects of these clouds modulate larger-scale flows such as those associated with the index oscillation

Material Morphology and energy barriers to electrical ageing

A distribution of the parameters representing activation energy of the ageing process within the Dissado-Montanari-Mazzanti (DMM) lifetime model has been shown to model experimental lifetime distributions of PET films well. The results imply small differences in the local environments of the moieties involved in the ageing process. Very small changes in the minimum activation energy values have a pronounced effect on the resultant lifetimes of polymer specimens. Changes in the distributions of activation energies with field and temperature can be explained by assuming the ageing process to be one whereby polymer segments on lamella surfaces crystallise to create free volume within the polymer

Improved diamond coring bits developed for dry and chip-flush drilling

Two rotary diamond bit designs, one operating with a chip-flushing fluid, the second including auger section to remove drilled chips, enhance usefulness of tool for exploratory and industrial core-drilling of hard, abrasive mineral deposits and structural masonry

Rear-View Mirror: Statutory and Constitutional Issues Raised Amidst Governor Roy Cooper\u27s COVID-19 Shutdown Orders

The COVID-19 pandemic rattled the world. Upon its arrival in the United States, the virus resulted in governors across the country using broad emergency powers to deal with the pandemic. North Carolina Governor Roy Cooper’s executive orders, beginning in March of 2020, pushed statutory and constitutional boundaries. This Comment assesses the limits of Governor Cooper’s emergency authority under the North Carolina Emergency Management Act and the North Carolina Constitution. Additionally, this Comment evaluates whether the North Carolina Emergency Management Act should be amended and whether Governor Cooper’s orders violated individuals’ rights under both the North Carolina Constitution and the Federal Constitution