Moments of spectral functions: Monte Carlo evaluation and verification

The subject of the present study is the Monte Carlo path-integral evaluation of the moments of spectral functions. Such moments can be computed by formal differentiation of certain estimating functionals that are infinitely-differentiable against time whenever the potential function is arbitrarily smooth. Here, I demonstrate that the numerical differentiation of the estimating functionals can be more successfully implemented by means of pseudospectral methods (e.g., exact differentiation of a Chebyshev polynomial interpolant), which utilize information from the entire interval $(-\beta \hbar / 2, \beta \hbar/2)$. The algorithmic detail that leads to robust numerical approximations is the fact that the path integral action and not the actual estimating functional are interpolated. Although the resulting approximation to the estimating functional is non-linear, the derivatives can be computed from it in a fast and stable way by contour integration in the complex plane, with the help of the Cauchy integral formula (e.g., by Lyness' method). An interesting aspect of the present development is that Hamburger's conditions for a finite sequence of numbers to be a moment sequence provide the necessary and sufficient criteria for the computed data to be compatible with the existence of an inversion algorithm. Finally, the issue of appearance of the sign problem in the computation of moments, albeit in a milder form than for other quantities, is addressed.Comment: 13 pages, 2 figure

Atomic Cluster Au₁₀⁺ Is a Strong Broadband Midinfrared Chromophore

We report an intense broadband midinfrared absorption band in the Au10+ cluster in a region in which only molecular vibrations would normally be expected. Observed in the infrared multiple photon dissociation spectra of Au10Ar+, Au10(N2O)+, and Au10(OCS)+, the smooth feature stretches 700–3400  cm-1 (λ=14–2.9  μm). Calculations confirm unusually low-energy allowed electronic excitations consistent with the observed spectra. In Au10(OCS)+, IR absorption throughout the band drives OCS decomposition resulting in CO loss, providing an alternative method of bond activation or breaking

Properties of continuous Fourier extension of the discrete cosine transform and its multidimensional generalization

A versatile method is described for the practical computation of the discrete Fourier transforms (DFT) of a continuous function $g(t)$ given by its values $g_{j}$ at the points of a uniform grid $F_{N}$ generated by conjugacy classes of elements of finite adjoint order $N$ in the fundamental region $F$ of compact semisimple Lie groups. The present implementation of the method is for the groups SU(2), when $F$ is reduced to a one-dimensional segment, and for $SU(2)\times ... \times SU(2)$ in multidimensional cases. This simplest case turns out to result in a transform known as discrete cosine transform (DCT), which is often considered to be simply a specific type of the standard DFT. Here we show that the DCT is very different from the standard DFT when the properties of the continuous extensions of these two discrete transforms from the discrete grid points $t_j; j=0,1, ... N$ to all points $t \in F$ are considered. (A) Unlike the continuous extension of the DFT, the continuous extension of (the inverse) DCT, called CEDCT, closely approximates $g(t)$ between the grid points $t_j$. (B) For increasing $N$, the derivative of CEDCT converges to the derivative of $g(t)$. And (C), for CEDCT the principle of locality is valid. Finally, we use the continuous extension of 2-dimensional DCT to illustrate its potential for interpolation, as well as for the data compression of 2D images.Comment: submitted to JMP on April 3, 2003; still waiting for the referee's Repor

Quality Assessment and Data Analysis for microRNA Expression Arrays

MicroRNAs are small (∼22 nt) RNAs that regulate gene expression and play important roles in both normal and disease physiology. The use of microarrays for global characterization of microRNA expression is becoming increasingly popular and has the potential to be a widely used and valuable research tool. However, microarray profiling of microRNA expression raises a number of data analytic challenges that must be addressed in order to obtain reliable results. We introduce here a universal reference microRNA reagent set as well as a series of nonhuman spiked-in synthetic microRNA controls, and demonstrate their use for quality control and between-array normalization of microRNA expression data. We also introduce diagnostic plots designed to assess and compare various normalization methods. We anticipate that the reagents and analytic approach presented here will be useful for improving the reliability of microRNA microarray experiments

EBImage—an R package for image processing with applications to cellular phenotypes

Summary: EBImage provides general purpose functionality for reading, writing, processing and analysis of images. Furthermore, in the context of microscopy-based cellular assays, EBImage offers tools to segment cells and extract quantitative cellular descriptors. This allows the automation of such tasks using the R programming language and use of existing tools in the R environment for signal processing, statistical modeling, machine learning and data visualization

SAFEGUI: resampling-based tests of categorical significance in gene expression data made easy

Summary: A large number of websites and applications perform significance testing for gene categories/pathways in microarray data. Many of these packages fail to account for expression correlation between transcripts, with a resultant inflation in Type I error. Array permutation and other resampling-based approaches have been proposed as solutions to this problem. SAFEGUI provides a user-friendly graphical interface for the assessment of categorical significance in microarray studies, while properly accounting for the effects of correlations among genes. SAFEGUI incorporates both permutation and more recently proposed bootstrap algorithms that are demonstrated to be more powerful in detecting differential expression across categories of genes

Identifying functional modules in protein–protein interaction networks: an integrated exact approach

Motivation: With the exponential growth of expression and protein–protein interaction (PPI) data, the frontier of research in systems biology shifts more and more to the integrated analysis of these large datasets. Of particular interest is the identification of functional modules in PPI networks, sharing common cellular function beyond the scope of classical pathways, by means of detecting differentially expressed regions in PPI networks. This requires on the one hand an adequate scoring of the nodes in the network to be identified and on the other hand the availability of an effective algorithm to find the maximally scoring network regions. Various heuristic approaches have been proposed in the literature

Using Markov chain Monte Carlo methods for estimating parameters with gravitational radiation data

We present a Bayesian approach to the problem of determining parameters for coalescing binary systems observed with laser interferometric detectors. By applying a Markov Chain Monte Carlo (MCMC) algorithm, specifically the Gibbs sampler, we demonstrate the potential that MCMC techniques may hold for the computation of posterior distributions of parameters of the binary system that created the gravity radiation signal. We describe the use of the Gibbs sampler method, and present examples whereby signals are detected and analyzed from within noisy data.Comment: 21 pages, 10 figure