Asymptotic Bayes-optimality under sparsity of some multiple testing procedures

Within a Bayesian decision theoretic framework we investigate some asymptotic optimality properties of a large class of multiple testing rules. A parametric setup is considered, in which observations come from a normal scale mixture model and the total loss is assumed to be the sum of losses for individual tests. Our model can be used for testing point null hypotheses, as well as to distinguish large signals from a multitude of very small effects. A rule is defined to be asymptotically Bayes optimal under sparsity (ABOS), if within our chosen asymptotic framework the ratio of its Bayes risk and that of the Bayes oracle (a rule which minimizes the Bayes risk) converges to one. Our main interest is in the asymptotic scheme where the proportion p of "true" alternatives converges to zero. We fully characterize the class of fixed threshold multiple testing rules which are ABOS, and hence derive conditions for the asymptotic optimality of rules controlling the Bayesian False Discovery Rate (BFDR). We finally provide conditions under which the popular Benjamini-Hochberg (BH) and Bonferroni procedures are ABOS and show that for a wide class of sparsity levels, the threshold of the former can be approximated by a nonrandom threshold.Comment: Published in at http://dx.doi.org/10.1214/10-AOS869 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Looping and reconfiguration dynamics of a flexible chain with internal friction

In recent past, experiments and simulations have suggested that apart from the solvent friction, friction arising from the protein itself plays an important role in protein folding by affecting the intra-chain loop formation dynamics. This friction is termed as internal friction in the literature. Using a flexible Gaussian chain with internal friction we analyze the intra- chain reconfiguration and loop formation times for all three topology classes namely end-to- end, end-to-interior and interior-to-interior. In a nutshell, bypassing expensive simulations we show how simple models like that of Rouse and Zimm can support the single molecule experiment and computer simulation results on intra-chain diffusion coefficients, looping time and even can predict the effects of tail length on the looping time

Henoch schonlein purpura in pregnancy: a lesser known phenomenon

Henoch Schonlein Purpura is a rare disease and its occurrence during pregnancy is exceptional. Very little information is found in the literature regarding this topic and only handful of case reports are available to throw light upon the same. Presented here is a case of a 30 year old primigravida with pre-existent disease with successful fetomaternal outcome subsequently

Thermo-optical characterization of novel MXene/Carbon-dot hybrid nanofluid for heat transfer applications

Nanofluid has emerged as a promising heat transfer fluid (HTF) due to their significant thermophysical, and optical characteristics enhancement over base fluids. Hybrid nanofluids with multiple nanomaterials have the advantage of synergistic properties in comparison to monocomponent nanofluids. The present study proposes an energy-efficient and cleaner synthesis method for developing carbon quantum dot (C-dot), MXene, and a hybrid MXene/C-dot hybrid nanofluids, for heat transfer application. In-situ microwave pyrolysis technique and two-step method were adopted for nanomaterial and nanofluid synthesis. The morphological, phase structural, chemical, and elemental compositional analysis of the nanomaterials was performed. The material characterization confirms the hybridization of C-dot on MXene nanosheets. The thermal conductivity and volumetric heat capacity of the nanofluids were measured using the transient plane source (TPS) method. Thermal conductivity was observed to increase with nanofluid concentration and temperature. Results indicate that MXene has the highest thermal conductivity enhancement (50 %) over water, followed by hybrid (42.2 %) and C-dot nanofluid (33.2 %). The volumetric heat capacity of nanofluids decreased with concentration and temperature. A semi-empirical correlation, as a function of nanofluid concentration and temperature, was coined for predicting thermal conductivity and volumetric heat capacity. Optical property characterization study shows that C-dot nanofluid exhibited considerable absorption along the UV range, while MXene nanofluid showed absorption in the visible and near-infrared (NIR) region. Hybrid nanofluids demonstrated complementary absorption properties of C-dot and MXene nanofluids

Perturbations on steady spherical accretion in Schwarzschild geometry

The stationary background flow in the spherically symmetric infall of a compressible fluid, coupled to the space-time defined by the static Schwarzschild metric, has been subjected to linearized perturbations. The perturbative procedure is based on the continuity condition and it shows that the coupling of the flow with the geometry of space-time brings about greater stability for the flow, to the extent that the amplitude of the perturbation, treated as a standing wave, decays in time, as opposed to the amplitude remaining constant in the Newtonian limit. In qualitative terms this situation simulates the effect of a dissipative mechanism in the classical Bondi accretion flow, defined in the Newtonian construct of space and time. As a result of this approach it becomes impossible to define an acoustic metric for a conserved spherically symmetric flow, described within the framework of Schwarzschild geometry. In keeping with this view, the perturbation, considered separately as a high-frequency travelling wave, also has its amplitude reduced.Comment: 8 pages, no figur

Secular instability in quasi-viscous disc accretion

A first-order correction in the $\alpha$-viscosity parameter of Shakura and Sunyaev has been introduced in the standard inviscid and thin accretion disc. A linearised time-dependent perturbative study of the stationary solutions of this "quasi-viscous" disc leads to the development of a secular instability on large spatial scales. This qualitative feature is equally manifest for two different types of perturbative treatment -- a standing wave on subsonic scales, as well as a radially propagating wave. Stability of the flow is restored when viscosity disappears.Comment: 15 pages, 2 figures, AASTeX. Added some new material and upgraded the reference lis

Evolution of transonicity in an accretion disc

For inviscid, rotational accretion flows driven by a general pseudo-Newtonian potential on to a Schwarzschild black hole, the only possible fixed points are saddle points and centre-type points. For the specific choice of the Newtonian potential, the flow has only two critical points, of which the outer one is a saddle point while the inner one is a centre-type point. A restrictive upper bound is imposed on the admissible range of values of the angular momentum of sub-Keplerian flows through a saddle point. These flows are very unstable to any deviation from a necessarily precise boundary condition. The difficulties against the physical realisability of a solution passing through the saddle point have been addressed through a temporal evolution of the flow, which gives a non-perturbative mechanism for selecting a transonic solution passing through the saddle point. An equation of motion for a real-time perturbation about the stationary flows reveals a very close correspondence with the metric of an acoustic black hole, which is also an indication of the primacy of transonicity.Comment: 18 page

Can Homeopathic Arsenic Remedy Combat Arsenic Poisoning in Humans Exposed to Groundwater Arsenic Contamination?: A Preliminary Report on First Human Trial

Groundwater arsenic (As) has affected millions of people globally distributed over 20 countries. In parts of West Bengal (India) and Bangladesh alone, over 100 million people are at risk, but supply of As-free water is grossly inadequate. Attempts to remove As by using orthodox medicines have mostly been unsuccessful. A potentized homeopathic remedy, Arsenicum Album-30, was administered to a group of As affected people and thereafter the As contents in their urine and blood were periodically determined. The activities of various toxicity marker enzymes and compounds in the blood, namely aspartate amino transferase, alanine amino transferase, acid phosphatase, alkaline phosphatase, lipid peroxidation and reduced glutathione, were also periodically monitored up to 3 months. The results are highly encouraging and suggest that the drug can alleviate As poisoning in humans