Two-sample Bayesian Nonparametric Hypothesis Testing

In this article we describe Bayesian nonparametric procedures for two-sample hypothesis testing. Namely, given two sets of samples $\mathbf{y}^{\scriptscriptstyle(1)}\;$\stackrel{\scriptscriptstyle{iid}}{\s im}$\;F^{\scriptscriptstyle(1)}$ and $\mathbf{y}^{\scriptscriptstyle(2 )}\;$\stackrel{\scriptscriptstyle{iid}}{\sim}$\;F^{\scriptscriptstyle( 2)}$, with $F^{\scriptscriptstyle(1)},F^{\scriptscriptstyle(2)}$ unknown, we wish to evaluate the evidence for the null hypothesis $H_0:F^{\scriptscriptstyle(1)}\equiv F^{\scriptscriptstyle(2)}$ versus the alternative $H_1:F^{\scriptscriptstyle(1)}\neq F^{\scriptscriptstyle(2)}$. Our method is based upon a nonparametric P\'{o}lya tree prior centered either subjectively or using an empirical procedure. We show that the P\'{o}lya tree prior leads to an analytic expression for the marginal likelihood under the two hypotheses and hence an explicit measure of the probability of the null $\mathrm{Pr}(H_0|\{\mathbf {y}^{\scriptscriptstyle(1)},\mathbf{y}^{\scriptscriptstyle(2)}\}\mathbf{)}$.Comment: Published at http://dx.doi.org/10.1214/14-BA914 in the Bayesian Analysis (http://projecteuclid.org/euclid.ba) by the International Society of Bayesian Analysis (http://bayesian.org/

Paleoproterozoic sterol biosynthesis and the rise of oxygen

Natural products preserved in the geological record can function as ‘molecular fossils’, providing insight into organisms and physiologies that existed in the deep past. One important group of molecular fossils is the steroidal hydrocarbons (steranes), which are the diagenetic remains of sterol lipids. Complex sterols with modified side chains are unique to eukaryotes, although simpler sterols can also be synthesized by a few bacteria. Sterol biosynthesis is an oxygen-intensive process; thus, the presence of complex steranes in ancient rocks not only signals the presence of eukaryotes, but also aerobic metabolic processes. In 1999, steranes were reported in 2.7 billion year (Gyr)-old rocks from the Pilbara Craton in Australia, suggesting a long delay between photosynthetic oxygen production and its accumulation in the atmosphere (also known as the Great Oxidation Event) 2.45–2.32 Gyr ago. However, the recent reappraisal and rejection of these steranes as contaminants pushes the oldest reported steranes forward to around 1.64 Gyr ago (ref. 6). Here we use a molecular clock approach to improve constraints on the evolution of sterol biosynthesis. We infer that stem eukaryotes shared functionally modern sterol biosynthesis genes with bacteria via horizontal gene transfer. Comparing multiple molecular clock analyses, we find that the maximum marginal probability for the divergence time of bacterial and eukaryal sterol biosynthesis genes is around 2.31 Gyr ago, concurrent with the most recent geochemical evidence for the Great Oxidation Event. Our results therefore indicate that simple sterol biosynthesis existed well before the diversification of living eukaryotes, substantially predating the oldest detected sterane biomarkers (approximately 1.64 Gyr ago), and furthermore, that the evolutionary history of sterol biosynthesis is tied to the first widespread availability of molecular oxygen in the ocean–atmosphere system

Squeezing in the audio gravitational wave detection band

We demonstrate the generation of broad-band continuous-wave optical squeezing down to 200Hz using a below threshold optical parametric oscillator (OPO). The squeezed state phase was controlled using a noise locking technique. We show that low frequency noise sources, such as seed noise, pump noise and detuning fluctuations, present in optical parametric amplifiers have negligible effect on squeezing produced by a below threshold OPO. This low frequency squeezing is ideal for improving the sensitivity of audio frequency measuring devices such as gravitational wave detectors.Comment: 5 pages, 6 figure

The impact of histopathology and NAB2-STAT6 fusion subtype in classification and grading of meningeal solitary fibrous tumor/hemangiopericytoma.

Meningeal solitary fibrous tumor (SFT)/hemangiopericytoma (HPC) is a rare tumor with propensity for recurrence and metastasis. Although multiple classification schemes have been proposed, optimal risk stratification remains unclear, and the prognostic impact of fusion status is uncertain. We compared the 2016 WHO CNS tumor grading scheme (CNS-G), a three-tier system based on histopathologic phenotype and mitotic count, to the 2013 WHO soft-tissue counterpart (ST-G), a two-tier system based on mitotic count alone, in a cohort of 133 patients [59 female, 74 male; mean age 54 years (range 20-87)] with meningeal SFT/HPC. Tumors were pathologically confirmed through review of the first tumor resection (n = 97), local recurrence (n = 35), or distant metastasis (n = 1). A STAT6 immunostain showed nuclear expression in 132 cases. NAB2-STAT6 fusion was detected in 99 of 111 successfully tested tumors (89%) including the single STAT6 immunonegative tumor. Tumors were classified by CNS-G as grade 1 (n = 43), 2 (n = 41), or 3 (n = 49), and by ST-G as SFT (n = 84) or malignant SFT (n = 49). Necrosis was present in 16 cases (12%). On follow-up, 42 patients had at least one subsequent recurrence or metastasis (7 metastasis only, 33 recurrence only, 2 patients had both). Twenty-nine patients died. On univariate analysis, necrosis (p = 0.002), CNS-G (p = 0.01), and ST-G (p = 0.004) were associated with recurrence-free (RFS) but not overall survival (OS). NAB2-STAT6 fusion type was not significantly associated with RFS or OS, but was associated with phenotype. A modified ST-G incorporating necrosis showed higher correlation with RFS (p = 0.0006) and remained significant (p = 0.02) when considering only the primary tumors. From our data, mitotic rate and necrosis appear to stratify this family of tumors most accurately and could be incorporated in a future grading scheme

The role of heterotrophic microflagellates in plankton communities

Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution June 1984The distribution and feeding behavior of bacterivorous micro flagellates (2-20 μm protozoa) and their ingestion by copepods were examined in an attempt to assess the importance of these protozoa as a trophic link between planktonic bacteria and zooplankton. The abundance of microflagellates relative to other picoplankton (0.2-2.0 μm) and nanoplankton (2-20 μm) populations in water samples in the North Atlantic and in Lake Ontario and on macroaggregates in the North Atlantic was determined using direct microscopical and culture estimation techniques. Seasonal, vertical and geographical changes in the density of microflagellates were generally not greater than one order of magnitude. Microscopical counts of heterotrophic nanoplankton (presumably microflagellates) typically ranged from a few hundred to a few thousand m1-1 for a variety of planktonic environments. They constituted approximately 1/3 to 1/2 of the nanoplankton in the euphotic zone and dominated the nanoplankton in the aphotic zone. Most Probable Number (MPN) estimation of the density of bacterivorous protozoa indicated that microflagellates were, on average, an order of magnitude more abundant than bacterivorous ciliates and amoebae. MPN and direct microscopical counts of microflagellates differed by as much as 104. This discrepancy was smaller in eutrophic environments (e.g. Continental Shelf and Lake Ontario) and on macroscopic detrital aggregates. All microbial populations enumerated were highly concentrated on macroscopic detrital aggregates relative to their abundance in the water surrounding the aggregates. Enrichment factors (the ratio of abundance of a population on a macroaggregate to its abundance in the surrounding water) increased along a eutrophic-to-oligotrophic gradient because of the combined effects of an increased abundance of microorganisms on macroaggregates in oligotrophic environments and a decreased abundance in the surrounding water in these same environments. Average enrichment factors for direct microscopical counts of heterotrophic nanoplankton (range = 17-114) were not as large as enrichment factors observed for MPN estimates of the number of bacterivorous microflagellates (range = 273-18400). Microflagellates numerically dominated the bacterivorous protozoa cultured from macroaggregates by one to two orders of magnitude, but ciliates and amoebae were also highly enriched on macroaggregates. Microenvironments are therefore a potentially important aspect for the ecology of planktonic microorganisms. Observations on the microbial colonization of mucus sloughed by ctenophores and discarded appendicularian houses suggest that these materials may be important sources of macroaggregates. Batch and continuous culture experiments were conducted with clonal cultures of microflagellates to test their ability to grow on various types and densities of bacteria. The doubling time of Monas sp. 1 ranged from 43 hr (when fed the cyanobacterium Synechococcus Strain WH 8101) to 6.9 hr (when fed the heterotrophic bacterium Serratia marinorubra). Cell yields (i.e. the conversion of bacterial biomass into protozoan biomass) of Monas sp. 1 fed two species of heterotrophic bacteria were greater than yields for the microflagellate fed two species chroococcoid cyanobacteria (range = 7-68%). Cell yields of two other species of microflagellates (Monas sp. 2 and Cryptobia maris) were 48% and 61%, respectively, on the bacterium Pseudomonas halodurans. Microflagellates grew in continuous culture at concentrations of bacteria which were lower than bacterial densities required for the growth of ciliates as shown by other investigations. Therefore, microflagellates appear to be well-adapted for grazing bacterioplankton. Microflagellates were also investigated for their ability to graze bacteria attached to particles. Bodo nanorensis and Rhynchomonas nasuta both showed a marked ability to graze attached bacteria and a limited ability to graze unattached cells. These results suggest that microflagellates may also be important consumers of bacteria attached to particles in the plankton and may explain the highly elevated densities of microflagellates on macroaggregates. Grazing experiments performed with the copepod Acartia tonsa indicated that heterotrophic microflagellates were ingested by the copepods at rates comparable to the ingestion of phytoplankton of similar size. The presence of heterotrophic microflagellates did not depress filtration rates of the copepods, and one species (Cryptobia maris) appeared to be selectively grazed. Survival of A. tonsa on a diet of heterotrophic microflagellates was similar to survival on a diet of phytoplankton and was significantly longer than survival of starved Controls or copepods fed only bacteria. Due to their ability to grow at in-situ densities of planktonic bacteria, their relatively high cell yields, and their acceptability as food for zooplankton, it is concluded that bacterivorous microflagellates may constitute an important trophic link between bacteria and zooplankton. This link may provide a mechanism whereby organic material and energy from the detrital food chain can be returned to the classical phytoplankton-copepod-fish food chain.This research was supported by National Science Foundation grants OCE80-2444l and OCE82-l4928 and Ocean Industry Program grant 4473 awarded to Dr. Laurence P. Madin, NSF Doctoral Dissertation grant OCE8l-l299l, the Woods Hole Oceanographic Institution Education Program and the Wood Hole Oceanographic Institution Biology Department

Ultraviolet asymptotics of scalar and pseudoscalar correlators in hot Yang-Mills theory

Inspired by recent lattice measurements, we determine the short-distance (a > omega >> pi T) asymptotics of scalar (trace anomaly) and pseudoscalar (topological charge density) correlators at 2-loop order in hot Yang-Mills theory. The results are expressed in the form of an Operator Product Expansion. We confirm and refine the determination of a number of Wilson coefficients; however some discrepancies with recent literature are detected as well, and employing the correct values might help, on the qualitative level, to understand some of the features observed in the lattice measurements. On the other hand, the Wilson coefficients show slow convergence and it appears uncertain whether this approach can lead to quantitative comparisons with lattice data. Nevertheless, as we outline, our general results might serve as theoretical starting points for a number of perhaps phenomenologically more successful lines of investigation.Comment: 27 pages. v2: minor improvements, published versio

Evaluating the potential for the environmentally sustainable control of foot and mouth disease in Sub-Saharan Africa

Strategies to control transboundary diseases have in the past generated unintended negative consequences for both the environment and local human populations. Integrating perspectives from across disciplines, including livestock, veterinary and conservation sectors, is necessary for identifying disease control strategies that optimise environmental goods and services at the wildlife-livestock interface. Prompted by the recent development of a global strategy for the control and elimination of foot-and-mouth disease (FMD), this paper seeks insight into the consequences of, and rational options for potential FMD control measures in relation to environmental, conservation and human poverty considerations in Africa. We suggest a more environmentally nuanced process of FMD control that safe-guards the integrity of wild populations and the ecosystem dynamics on which human livelihoods depend while simultaneously improving socio-economic conditions of rural people. In particular, we outline five major issues that need to be considered: 1) improved understanding of the different FMD viral strains and how they circulate between domestic and wildlife populations; 2) an appreciation for the economic value of wildlife for many African countries whose presence might preclude the country from ever achieving an FMD-free status; 3) exploring ways in which livestock production can be improved without compromising wildlife such as implementing commodity-based trading schemes; 4) introducing a participatory approach involving local farmers and the national veterinary services in the control of FMD; and 5) finally the possibility that transfrontier conservation might offer new hope of integrating decision-making at the wildlife-livestock interface

Microcystin Prevalence throughout Lentic Waterbodies in Coastal Southern California.

Toxin producing cyanobacterial blooms have increased globally in recent decades in both frequency and intensity. Despite the recognition of this growing risk, the extent and magnitude of cyanobacterial blooms and cyanotoxin prevalence is poorly characterized in the heavily populated region of southern California. Recent assessments of lentic waterbodies (depressional wetlands, lakes, reservoirs and coastal lagoons) determined the prevalence of microcystins and, in some cases, additional cyanotoxins. Microcystins were present in all waterbody types surveyed although toxin concentrations were generally low across most habitats, as only a small number of sites exceeded California's recreational health thresholds for acute toxicity. Results from passive samplers (Solid Phase Adsorption Toxin Tracking (SPATT)) indicated microcystins were prevalent throughout lentic waterbodies and that traditional discrete samples underestimated the presence of microcystins. Multiple cyanotoxins were detected simultaneously in some systems, indicating multiple stressors, the risk of which is uncertain since health thresholds are based on exposures to single toxins. Anatoxin-a was detected for the first time from lakes in southern California. The persistence of detectable microcystins across years and seasons indicates a low-level, chronic risk through both direct and indirect exposure. The influence of toxic cyanobacterial blooms is a more complex stressor than presently recognized and should be included in water quality monitoring programs

Gravitational Waves from the Dynamical Bar Instability in a Rapidly Rotating Star

A rapidly rotating, axisymmetric star can be dynamically unstable to an m=2 "bar" mode that transforms the star from a disk shape to an elongated bar. The fate of such a bar-shaped star is uncertain. Some previous numerical studies indicate that the bar is short lived, lasting for only a few bar-rotation periods, while other studies suggest that the bar is relatively long lived. This paper contains the results of a numerical simulation of a rapidly rotating gamma=5/3 fluid star. The simulation shows that the bar shape is long lived: once the bar is established, the star retains this shape for more than 10 bar-rotation periods, through the end of the simulation. The results are consistent with the conjecture that a star will retain its bar shape indefinitely on a dynamical time scale, as long as its rotation rate exceeds the threshold for secular bar instability. The results are described in terms of a low density neutron star, but can be scaled to represent, for example, a burned-out stellar core that is prevented from complete collapse by centrifugal forces. Estimates for the gravitational-wave signal indicate that a dynamically unstable neutron star in our galaxy can be detected easily by the first generation of ground based gravitational-wave detectors. The signal for an unstable neutron star in the Virgo cluster might be seen by the planned advanced detectors. The Newtonian/quadrupole approximation is used throughout this work.Comment: Expanded version to be published in Phys. Rev. D: 13 pages, REVTeX, 13 figures, 9 TeX input file

String Theory and Quantum Chromodynamics

I review recent progress on the connection between string theory and quantum chromodynamics in the context of the gauge/gravity duality. Emphasis is placed on conciseness and conceptual aspects rather than on technical details. Topics covered include the large-Nc limit of gauge theories, the gravitational description of gauge theory thermodynamics and hydrodynamics, and confinement/deconfinement thermal phase transitions.Comment: 38 pages, 24 figures. Lectures given at the RTN Winter School on "Strings, Supergravity and Gauge Theories" at CERN on January 15-19, 200