Quick Calculation for Sample Size while Controlling False Discovery Rate with Application to Microarray Analysis

Sample size estimation is important in microarray or proteomic experiments since biologists can typically afford only a few repetitions. In the multiple testing problems involving these experiments, it is more powerful and more reasonable to control false discovery rate (FDR) or positive FDR (pFDR) instead of type I error, e.g., family-wise error rate (FWER) (Storey and Tibshirani, 2003). However, the traditional approach of estimating sample size is no longer applicable to controlling FDR, which has left most practitioners to rely on haphazard guessing. We propose a procedure to calculate sample size while controlling false discovery rate. Two major definitions of the false discovery rate (FDR in Benjamini and Hochberg, 1995, and pFDR in Storey, 2002) vary slightly. Our procedure applies to both definitions. The proposed method is straightforward to apply and requires minimal computation, as illustrated with two sample t-tests and F-tests. We have also demonstrated by simulation that, with the calculated sample size, the desired level of power is achievable by the q-value procedure (Storey, Taylor and Siegmund, 2004) when gene expressions are either independent or dependent

Rational foundation of GR in terms of statistical mechanic in the AdS/CFT framework

In this article, we work out the microscopic statistical foundation of the supergravity description of the simplest 1/2 BPS sector in the AdS(5)/CFT(4). Then, all the corresponding supergravity observables are related to thermodynamical observables, and General Relativity is understood as a mean-field theory. In particular, and as an example, the Superstar is studied and its thermodynamical properties clarified.Comment: 13 pages, 6 eps figures, latex, some improvements introduced, reference added, typos correcte

An efficient compressive sensing based PS-DInSAR method for surface deformation estimation

Permanent scatterers differential interferometric synthetic aperture radar (PS-DInSAR) is a technique for detecting surface micro-deformation, with an accuracy at the centimeter to millimeter level. However, its performance is limited by the number of SAR images available (normally more than 20 are needed). Compressive Sensing (CS) has been proven to be an effective signal recovery method with only a very limited number of measurements. Applying CS to PS-DInSAR, a novel CS-PS-DInSAR method is proposed to estimate the deformation with fewer SAR images. By analyzing the PS-DInSAR process in detail, first the sparsity representation of deformation velocity difference is obtained; then, the mathematical model of CS-PS-DInSAR is derived and the restricted isometry property (RIP) of the measurement matrix is discussed to validate the proposed CS-PS-DInSAR in theory. The implementation of CS-PS-DInSAR is achieved by employing basis pursuit algorithms to estimate the deformation velocity. With the proposed method, DInSAR deformation estimation can be achieved by a much smaller number of SAR images, as demonstrated by simulation result

AdS pp-waves

We obtain the pp-waves of D=5 and D=4 gauged supergravities supported by $U(1)^3$ and $U(1)^4$ gauge field strengths respectively. We show that generically these solutions preserve 1/4 of the supersymmetry, but supernumerary supersymmetry can arise for appropriately constrained harmonic functions associated with the pp-waves. In particular it implies that the solutions are independent of the light-cone coordinate $x^+$. We also obtain the pp-waves in the Freedman-Schwarz model.Comment: Latex, 19 pages, minor changes, to appear in JHE

An image reconstruction algorithm based on the semiparametric model for electrical capacitance tomography

AbstractElectrical capacitance tomography (ECT) is considered as a promising tomography technology, and exactly reconstructing the original objects is highly desirable in real applications. In this paper, a generalized image reconstruction model that simultaneously considers the inaccurate property in the measured capacitance data and the linearization approximation error is presented. A generalized objective function, which has been developed using a combinational M-estimation and an extended stabilizing item, is proposed. The objective function unifies six estimation methods into a concise formula, where different estimation methods can be easily obtained by selecting different parameters. The homotopy method that integrates the beneficial advantages of the alternant iteration scheme is employed to solve the proposed objective function. Numerical simulations are implemented to evaluate the numerical performances and effectiveness of the proposed algorithm, and the numerical results reveal that the proposed algorithm is efficient and overcomes the numerical instability in the process of ECT image reconstruction. For the reconstructed objects in this paper, a dramatic improvement in accuracy and spatial resolution can be achieved, which indicates that the proposed algorithm is a promising candidate for solving ECT inverse problems

Fermions from Half-BPS Supergravity

We discuss collective coordinate quantization of the half-BPS geometries of Lin, Lunin and Maldacena (hep-th/0409174). The LLM geometries are parameterized by a single function $u$ on a plane. We treat this function as a collective coordinate. We arrive at the collective coordinate action as well as path integral measure by considering D3 branes in an arbitrary LLM geometry. The resulting functional integral is shown, using known methods (hep-th/9309028), to be the classical limit of a functional integral for free fermions in a harmonic oscillator. The function $u$ gets identified with the classical limit of the Wigner phase space distribution of the fermion theory which satisfies u * u = u. The calculation shows how configuration space of supergravity becomes a phase space (hence noncommutative) in the half-BPS sector. Our method sheds new light on counting supersymmetric configurations in supergravity.Comment: 28 pages, 2 figures, epsf;(v3) eq. (3.3) clarified and notationally simplified; version to appear in JHE

Minisuperspace Quantization of "Bubbling AdS" and Free Fermion Droplets

We quantize the space of 1/2 BPS configurations of Type IIB SUGRA found by Lin, Lunin and Maldacena (hep-th/0409174), directly in supergravity. We use the Crnkovic-Witten-Zuckerman covariant quantization method to write down the expression for the symplectic structure on this entire space of solutions. We find the symplectic form explicitly around AdS_5 x S^5 and obtain a U(1) Kac-Moody algebra, in precise agreement with the quantization of a system of N free fermions in a harmonic oscillator potential, as expected from AdS/CFT. As a cross check, we also perform the quantization around AdS_5 x S^5 by another method, using the known spectrum of physical perturbations around this background and find precise agreement with our previous calculation.Comment: 22 Pages + 2 Appendices, JHEP3; v3: explanation of factor 2 mismatch added, references reordered, published versio

Complex Matrix Model and Fermion Phase Space for Bubbling AdS Geometries

We study a relation between droplet configurations in the bubbling AdS geometries and a complex matrix model that describes the dynamics of a class of chiral primary operators in dual N=4 super Yang Mills (SYM). We show rigorously that a singlet holomorphic sector of the complex matrix model is equivalent to a holomorphic part of two-dimensional free fermions, and establish an exact correspondence between the singlet holomorphic sector of the complex matrix model and one-dimensional free fermions. Based on this correspondence, we find a relation of the singlet holomorphic operators of the complex matrix model to the Wigner phase space distribution. By using this relation and the AdS/CFT duality, we give a further evidence that the droplets in the bubbling AdS geometries are identified with those in the phase space of the one-dimensional fermions. We also show that the above correspondence actually maps the operators of N=4 SYM corresponding to the (dual) giant gravitons to the droplet configurations proposed in the literature.Comment: 27 pages, 6 figures, some clarification, typos corrected, published versio

Integrated disease management of leaf spots and crown rust of oat

Non-Peer ReviewedCrown rust and leaf spots can reduce the yield and quality of oats. The objective of this research was to determine the effect of conventional fungicides, Actigard® and oat cultivars that vary in resistance to crown rust on leaf spot and crown rust severity, and oat yield and quality. Two experiments were established at each location in Saskatchewan: Saskatoon and Melfort. Experiment one consisted of three oat varieties: AC Morgan (crown rust susceptible), CDC Dancer (intermediate) and CDC Morrison (resistant) and three fungicide treatments: check (unsprayed), propiconazole and pyraclostrobin. Experiment two consisted of the application of Actigard® at two rates: 8.75 g ai/ha and 26.25 g ai/ha; three crop growth stages: seedling, boot and heading; on two varieties: CDC Dancer and CDC Morrison, with an unsprayed check for each variety. At Saskatoon, crown rust was observed while leaf spot severity was low. At Melfort, no crown rust was observed but leaf spot severity was low to moderate. Fungicide reduced the severity of crown rust and increased yield and quality of oat at Saskatoon for the susceptible variety (AC Morgan) and somewhat for the moderately susceptible variety (CDC Dancer). The crown rust resistant variety (CDC Morrison) did not benefit from fungicide. Leaf spots were reduced by fungicide application at Melfort, but little increase in yield or quality was detected. There was little difference between AC Morgan and CDC Morrison for leaf spot symptoms, but CDC Dancer appeared to suffer slightly more than the other varieties. There was no impact of fungicide on beta-glucan content at either location, although there were differences among varieties, but only at Saskatoon. Actigard® was not observed to have any positive or negative effects on disease severity (crown rust or leaf spots) or any of the factors measured, including nutritional characteristics, at either location, although there were differences among varieties for many of the factors measured

Generating Neutrino Mass in the 331 Model

A mechanism for generating small tree-level Majorana mass for neutrinos is implemented in the 331 Model. No additional fermions or scalars need to be added, and no mass scale greater than a few TeV is invoked.Comment: LaTex, 7 pages, no figures. Revised version to appear in Phys. Rev.