Conditions for rapid mixing of parallel and simulated tempering on multimodal distributions

We give conditions under which a Markov chain constructed via parallel or simulated tempering is guaranteed to be rapidly mixing, which are applicable to a wide range of multimodal distributions arising in Bayesian statistical inference and statistical mechanics. We provide lower bounds on the spectral gaps of parallel and simulated tempering. These bounds imply a single set of sufficient conditions for rapid mixing of both techniques. A direct consequence of our results is rapid mixing of parallel and simulated tempering for several normal mixture models, and for the mean-field Ising model.Comment: Published in at http://dx.doi.org/10.1214/08-AAP555 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Using TPA to count linear extensions

A linear extension of a poset $P$ is a permutation of the elements of the set that respects the partial order. Let $L(P)$ denote the number of linear extensions. It is a #P complete problem to determine $L(P)$ exactly for an arbitrary poset, and so randomized approximation algorithms that draw randomly from the set of linear extensions are used. In this work, the set of linear extensions is embedded in a larger state space with a continuous parameter ?. The introduction of a continuous parameter allows for the use of a more efficient method for approximating $L(P)$ called TPA. Our primary result is that it is possible to sample from this continuous embedding in time that as fast or faster than the best known methods for sampling uniformly from linear extensions. For a poset containing $n$ elements, this means we can approximate $L(P)$ to within a factor of $1 + \epsilon$ with probability at least $1 - \delta$ using an expected number of random bits and comparisons in the poset which is at most $O(n^3(ln n)(ln L(P))\epsilon^{-2}\ln \delta^{-1}).$Comment: 12 pages, 4 algorithm

Multi-rate, real time image compression for images dominated by point sources

An image compression system recently developed for compression of digital images dominated by point sources is presented. Encoding consists of minimum-mean removal, vector quantization, adaptive threshold truncation, and modified Huffman encoding. Simulations are presented showing that the peaks corresponding to point sources can be transmitted losslessly for low signal-to-noise ratios (SNR) and high point source densities while maintaining a reduced output bit rate. Encoding and decoding hardware has been built and tested which processes 552,960 12-bit pixels per second at compression rates of 10:1 and 4:1. Simulation results are presented for the 10:1 case only

Spectral line shape modeling and ion temperature fluctuations in tokamak edge plasmas

In this work, we use a passive advection model for ion temperature fluctuations, in order to investigate their effects on Doppler Spectral line shapes. The relevance of the model is discussed in the framework of the Braginskii equations, and the subsequent Probability Density Function evaluation relies on results obtained in neutral fluids. The resulting Doppler line profiles are shown to exhibit characteristic exponential tails.Comment: 6 pages, 2 figures, to be published in Contributions to Plasma Physic

Projection Pursuit through Φ\Phi-Divergence Minimisation

Consider a defined density on a set of very large dimension. It is quite difficult to find an estimate of this density from a data set. However, it is possible through a projection pursuit methodology to solve this problem. Touboul's article "Projection Pursuit Through Relative Entropy Minimization", 2009, demonstrates the interest of the author's method in a very simple given case. He considers the factorization of a density through an Elliptical component and some residual density. The above Touboul's work is based on minimizing relative entropy. In the present article, our proposal will aim at extending this very methodology to the $\Phi-$divergence. Furthermore, we will also consider the case when the density to be factorized is estimated from an i.i.d. sample. We will then propose a test for the factorization of the estimated density. Applications include a new test of fit pertaining to the Elliptical copulas.Comment: 32 pages, 4 figures, 5 tableaux, elsarticle clas

Mrub_2120, Mrub_2121, Mrub_2122, Mrub_2123 and Mrub_2124 are orthologs of \u3cem\u3eE. coli\u3c/em\u3e genes b3458, b3457, b3456, b3455 and b3454, respectively, and make up an operon that codes for the branched-chain amino acid ABC transporter in \u3cem\u3eMeiothermus ruber\u3c/em\u3e DSM 1279

In this project we investigated the biological function of the genes Mrub_2120, Mrub_2121, Mrub_2122, Mrub_2123 and Mrub_2124 (KEGG map number 02010). We predict these genes encode components of a branched-chain amino acid ATP Binding Cassette (ABC) transporter: 1) Mrub_2120 (DNA coordinates 2169247-2170416 on the reverse strand) encodes the branched-chain amino acid binding protein that is localized to the periplasm; 2) Mrub_2121 (DNA coordinates 2170433..2171353 on the reverse strand) encodes the first TMD; 3) Mrub_2122 (DNA coordinates 2171365..2172279 on the reverse strand) encodes the second TMD; 4) Mrub_2123 (DNA coordinates 2172276..2173028 on the reverse strand) encodes the first NBD; 5) Mrub_2124 (DNA coordinates 2173025…2173735 on the reverse strand) encodes the second NBD. This branched-chain amino acid transport system has been found in E. coli K-12 MG1655 which was used as the model organism in this study. The predicted homologs of Mrub_2120, Mrub_2121, Mrub_2122, Mrub_2123 and Mrub_2124, are livK, livH, livM, livG and livF, respectively. Together, these genes form an operon encoding for an ABC transporter that selectively transports branched-chain amino acids across the intracellular plasma membrane of bacteria. This project is part of the Meiothermus ruber genome analysis project, which predicts gene function using the bioinformatics tools collected under the umbrella of the Guiding Education through Novel Investigation–Annotation Collaboration Toolkit (GENI-ACT)

Efficient Algorithm for Two-Center Coulomb and Exchange Integrals of Electronic Prolate Spheroidal Orbitals

We present a fast algorithm to calculate Coulomb/exchange integrals of prolate spheroidal electronic orbitals, which are the exact solutions of the single-electron, two-center Schr\"odinger equation for diatomic molecules. Our approach employs Neumann's expansion of the Coulomb repulsion 1/|x-y|, solves the resulting integrals symbolically in closed form and subsequently performs a numeric Taylor expansion for efficiency. Thanks to the general form of the integrals, the obtained coefficients are independent of the particular wavefunctions and can thus be reused later. Key features of our algorithm include complete avoidance of numeric integration, drafting of the individual steps as fast matrix operations and high accuracy due to the exponential convergence of the expansions. Application to the diatomic molecules O2 and CO exemplifies the developed methods, which can be relevant for a quantitative understanding of chemical bonds in general.Comment: 27 pages, 9 figure