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IEEE Convention of the Electrical and ELectronic Engineers in Israel

作者： Daniel Sigalov Yaakov Oshman Interdepartmental Program for Applied Mathematics&Technion Technion-Israel Institute of Technology Israel Department of AeroSpace Engineering Technion-Israel Institute of Technology Israel

The problem of fault tolerant state estimation is considered. We propose a unified, general formulation of the problem in which two different types of faults affect the system's output simultaneously. This problem statement generalizes previously reported formulations that may be obtained as special cases. Three families of state estimation methods for fault-prone systems are presented, generalizing several classical estimation algorithms. These families include: one-step near-optimal filters, which are closely related to the GPB filter family, IMM-based filters, and linear optimal estimators.

关键词： Markov processes Mathematical model Equations Additives Approximation methods Estimation Joints

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Robust algorithm to generate a diverse class of dense disordered and ordered sphere packings via linear programming

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Physical Review E 2010年第6期82卷 061302-061302页

作者： S. Torquato Y. Jiao Department of Chemistry Department of Physics Princeton Center for Theoretical Science Princeton Institute for the Science and Technology of Materials Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA Department of Mechanical and Aerospace Engineering Princeton University Princeton New Jersey 08544 USA

We have formulated the problem of generating dense packings of nonoverlapping, nontiling nonspherical particles within an adaptive fundamental cell subject to periodic boundary conditions as an optimization problem called the adaptive-shrinking cell (ASC) formulation [S. Torquato and Y. Jiao, Phys. Rev. E 80, 041104 (2009)]. Because the objective function and impenetrability constraints can be exactly linearized for sphere packings with a size distribution in d-dimensional Euclidean space Rd, it is most suitable and natural to solve the corresponding ASC optimization problem using sequential-linear-programming (SLP) techniques. We implement an SLP solution to produce robustly a wide spectrum of jammed sphere packings in Rd for d=2, 3, 4, 5, and 6 with a diversity of disorder and densities up to the respective maximal densities. A novel feature of this deterministic algorithm is that it can produce a broad range of inherent structures (locally maximally dense and mechanically stable packings), besides the usual disordered ones (such as the maximally random jammed state), with very small computational cost compared to that of the best known packing algorithms by tuning the radius of the influence sphere. For example, in three dimensions, we show that it can produce with high probability a variety of strictly jammed packings with a packing density anywhere in the wide range [0.6, 0.7408…], where π/18=0.7408… corresponds to the density of the densest packing. We also apply the algorithm to generate various disordered packings as well as the maximally dense packings for d=2, 4, 5, and 6. Our jammed sphere packings are characterized and compared to the corresponding packings generated by the well-known Lubachevsky-Stillinger (LS) molecular-dynamics packing algorithm. Compared to the LS procedure, our SLP protocol is able to ensure that the final packings are truly jammed, produces disordered jammed packings with anomalously low densities, and is appreciably more robust an

关键词： Packing

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Two-way interaction analysis of obesity trait from Korean population using generalized MDR

Two-way interaction analysis of obesity trait from Korean po...

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IEEE International Conference on Bioinformatics and Biomedicine Workshops (BIBMW)

作者： Sungyoung Lee Sohee Oh Min-Seok Kwon Seungyeoun Lee Taesung Park Interdisciplinary Program in Bioinformatics Seoul National University Seoul South Korea Department of Statistics Seoul National University Seoul South Korea Department of Applied Mathematics Sejong University Seoul South Korea

Most common complex traits such as obesity, hypertension, diabetes, and cancers are known to be associated with multiple genes, environmental factors, and epistasis. Recently, the development of advanced genotyping technologies allows us to perform the genome-wide association studies (GWAS). For detecting the effects of multiple genes on complex traits, many approaches have been proposed for GWAS. Multifactor dimensionality reduction (MDR) proposed by Ritchie et al. (2001) is one of the powerful methods for detecting epistasis, which detects high order interactions among genes. However, MDR is computationally intensive due to its requirement of testing all possible n-way combinations. Thus, it is not practically feasible to apply MDR directly to analyzing large-scale GWAS data. We propose an efficient strategy to perform MDR analysis for GWAS data. First, select a subset of genetic factors such as SNPs with some marginal significance. Second, perform MDR analysis only for the selected genetic factors. Third, provide MDR summary results through network graph. Even for the MDR analysis for the selected SNPs, a fast computing system is required. We developed our own GPU based system for the large-scale GWAS data. We applied our strategy to Korean Association REsource (KARE) (8,838 individuals with 101,837 SNPs) for detecting two-way interactions of genetic factors associated with body mass index (BMI). We identified several genes and pathways which have been known to be associated with obesity.

关键词： Obesity Bioinformatics Genomics Graphics processing unit Diabetes

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Jammed hard-particle packings: From Kepler to Bernal and beyond

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Reviews of Modern Physics 2010年第3期82卷 2633-2633页

作者： S. Torquato F. H. Stillinger []Department of Chemistry Department of Physics Princeton Center for Theoretical Science Princeton Institute for the Science and Technology of Materials and Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA and School of Natural Sciences Institute of Advanced Study Princeton New Jersey 08540 USA

Understanding the characteristics of jammed particle packings provides basic insights into the structure and bulk properties of crystals, glasses, and granular media and into selected aspects of biological systems. This review describes the diversity of jammed configurations attainable by frictionless convex nonoverlapping (hard) particles in Euclidean spaces and for that purpose it stresses individual-packing geometric analysis. A fundamental feature of that diversity is the necessity to classify individual jammed configurations according to whether they are locally, collectively, or strictly jammed. Each of these categories contains a multitude of jammed configurations spanning a wide and (in the large system limit) continuous range of intensive properties, including packing fraction ϕ, mean contact number Z, and several scalar order metrics. Application of these analytical tools to spheres in three dimensions (an analog to the venerable Ising model) covers a myriad of jammed states, including maximally dense packings (as Kepler conjectured), low-density strictly jammed tunneled crystals, and a substantial family of amorphous packings. With respect to the last of these, the current approach displaces the historically prominent but ambiguous idea of “random close packing” with the precise concept of “maximally random jamming.” Both laboratory procedures and numerical simulation protocols can and, frequently, have been used for creation of ensembles of jammed states. But while the resulting distributions of intensive properties may individually approach narrow distributions in the large system limit, the distinguishing varieties of possible operational details in these procedures and protocols lead to substantial variability among the resulting distributions, some examples of which are presented here. This review also covers recent advances in understanding jammed packings of polydisperse sphere mixtures, as well as convex nonspherical particles, e.g., ellipsoids, “

关键词： Spheres Euclidean space laboratory procedure jammed state Kepler

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Densest local sphere-packing diversity: General concepts and application to two dimensions

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Physical Review E 2010年第4期81卷 041305-041305页

作者： Adam B. Hopkins Frank H. Stillinger Salvatore Torquato Department of Chemistry Department of Physics Princeton Institute for the Science and Technology of Materials Program in Applied and Computational Mathematics Princeton Center for Theoretical Science Princeton University Princeton New Jersey 08544 USA and School of Natural Sciences Institute for Advanced Study Princeton New Jersey 08544 USA

The densest local packings of N identical nonoverlapping spheres within a radius Rmin(N) of a fixed central sphere of the same size are obtained using a nonlinear programming method operating in conjunction with a stochastic search of configuration space. The knowledge of Rmin(N) in d-dimensional Euclidean space Rd allows for the construction both of a realizability condition for pair-correlation functions of sphere packings and an upper bound on the maximal density of infinite sphere packings in Rd. In this paper, we focus on the two-dimensional circular disk problem. We find and present the putative densest packings and corresponding Rmin(N) for selected values of N up to N=348 and use this knowledge to construct such a realizability condition and an upper bound. We additionally analyze the properties and characteristics of the maximally dense packings, finding significant variability in their symmetries and contact networks, and that the vast majority differ substantially from the triangular lattice even for large N. Our work has implications for packaging problems, nucleation theory, and surface physics.

关键词： Spheres

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Displaced Path Integral Formulation for the Momentum Distribution of Quantum Particles

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Physical Review Letters 2010年第11期105卷 110602-110602页

作者： Lin Lin Joseph A. Morrone Roberto Car Michele Parrinello Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA Department of Chemistry Princeton University Princeton New Jersey 08544 USA Department of Physics Princeton University Princeton New Jersey 08544 USA Computational Science Department of Chemistry and Applied Biosciences ETH Zurich USI Campus Via Giuseppe Buffi 12 CH-6900 Lugano Switzerland

The proton momentum distribution, accessible by deep inelastic neutron scattering, is a very sensitive probe of the potential of mean force experienced by the protons in hydrogen-bonded systems. In this work we introduce a novel estimator for the end-to-end distribution of the Feynman paths, i.e., the Fourier transform of the momentum distribution. In this formulation, free particle and environmental contributions factorize. Moreover, the environmental contribution has a natural analogy to a free energy surface in statistical mechanics, facilitating the interpretation of experiments. The new formulation is not only conceptually but also computationally advantageous. We illustrate the method with applications to an empirical water model, ab initio ice, and one dimensional model systems.

关键词： Statistical mechanics

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Systematic Reduction of Combustion Reaction Mechanisms of common Hydrocarbons and Oxygenated Fuels

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AIP Conference Proceedings 2010年第1期1281卷 558-561页

作者： A. L. De Bortoli F. A. Vaz G. S. Lorenzzetti I. Martins aUFRGS‐IM/DMPA‐Department of Pure and Applied Mathematics Bento Gonçalves 9500 P.O. Box 15080 Porto Alegre Brazil bUFRGS‐PPGMAp—Graduate Program in Applied Mathematics Bento Gonçalves 9500 91509‐900 Porto Alegre‐RS Brazil cUFRGS‐PPGEQ‐Graduate Program in Chemical Engineering Engenheiro Luiz Englert s/no 90040‐040 Porto Alegre‐RS Brazil dUFRGS‐PPGEQ‐Graduate Program in Chemical Engineering Engenheiro Luiz Englert s/no 90040‐040 Porto Alegre‐RS Brazil

The aim of this work is the development of a numerical technique for the reduction of reaction mechanisms of common hydrocarbon and oxygenated fuels, such as methane, ethylene, propane, methanol and ethanol, using steady‐state and partial equilibrium assumptions. Numerical tests are carried to establish the basic chain for each fuel as well as to determine the amount of small products of combustion, whose concentration depends on the turbulent mixing and needs to be controlled due to environmental restrictions. The results are in agreement with data in the literature.

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SCOUT: A fast Monte-Carlo modeling tool of scintillation camera output

SCOUT: A fast Monte-Carlo modeling tool of scintillation cam...

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IEEE Symposium on Nuclear Science (NSS/MIC)

作者： William C. J. Hunter Harrison H. Barrett Thomas K. Lewellen Robert S. Miyaoka John P. Muzi Xiaoli Li Wendy McDougald Lawrence R. MacDonald Department of Radiology University of Washington Seattle WA USA Department of Radiology College of Optical Sciences the Applied Mathematics Program and the Biomedical Engineering Program University of Arizona Tucson Tucson AZ USA Departments of Radiology and Electrical Engineering University of Washington Seattle WA USA

We have developed a Monte-Carlo photon-tracking and readout simulator called SCOUT to study the stochastic behavior of signals output from a simplified rectangular scintillation-camera design. SCOUT models the salient processes affecting signal generation, transport, and readout. Presently, we compare output signal statistics from SCOUT to experimental results for both a discrete and a monolithic camera. We also benchmark the speed of this simulation tool and compare it to existing simulation tools. We find this modeling tool to be relatively fast and predictive of experimental results. Depending on the modeled camera geometry, we found SCOUT to be 4 to 140 times faster than other modeling tools.

关键词： Optical scattering Detectors Photonics Optical attenuators Crystals Photodetectors Cameras

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$H(\mathrm {div})$ preconditioning for a mixed finite element formulation of the diffusion problem with random data

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mathematics of Computation 2010年第270期79卷 733-760页

作者： Elman, Howard Furnival, Darran Powell, Catherine Department of Computer Science and Institute for Advanced Computer Studies University of Maryland College Park Maryland 20742 Applied Mathematics and Scientific Computing Program University of Maryland College Park Maryland 20742 National Oceanographic Centre Southampton S014 32H School of Mathematics University of Manchester Oxford Road Manchester M13 9PL United Kingdom

Abstract: We study $H(\mathrm {div})$ preconditioning for the saddle-point systems that arise in a stochastic Galerkin mixed formulation of the steady-state diffusion problem with random data. The key ingredient is a multigrid V-cycle for an $H(\mathrm {div})$ operator with random weight function acting on a certain tensor product space of random fields with finite variance. We build on the Arnold-Falk-Winther multigrid algorithm presented in 1997 by varying the spatial discretization from grid to grid whilst keeping the stochastic discretization fixed. We extend the deterministic analysis to accommodate the modified $H(\mathrm {div})$ operator and establish spectral equivalence bounds with a new multigrid V-cycle operator that are independent of the spatial and stochastic discretization parameters. We implement multigrid within a block-diagonal preconditioner for the full saddle-point problem, derive eigenvalue bounds for the preconditioned system matrices and investigate the impact of all the discretization parameters on the convergence rate of preconditioned minres.

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Modeling of Interference from Cooperative Cognitive Radios for Low Power Primary Users

Modeling of Interference from Cooperative Cognitive Radios f...

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2010 IEEE Global Telecommunications Conference GLOBECOM 2010

作者： Prasanna Madhusudhanan Juan G. Restrepo Youjian Liu Timothy X. Brown Kenneth Baker Department of Electrical Computer and Energy Engineering University of Colorado Boulder CO USA Department of Applied Mathematics University of Colorado Boulder CO USA Department of Electrical Computer and Energy Engineering Interdisciplinary Telecommunications Program University of Colorado Boulder CO USA Interdisciplinary Telecommunications Program University of Colorado Boulder CO USA

Cognitive radios (CR) must ensure that their transmissions do not cause harmful interference to the primary users that operate in the same band. Primary users with short communication range transmitters, such as wireless microphone systems, are considered. The CR network is distributed according to a Poisson process. The CRs detect the primary user either through primary transmitter signals or through beacons collocated with the primary receiver. Three levels of cooperative sensing by CRs are analyzed, namely, no cooperation, full cooperation and partial cooperation. The characteristic function of the interference at the primary receiver for all combinations of primary user detection and cooperative sensing schemes are derived for the system modeled along a line (1-D) and about a plane (2-D). The analysis in 1-D corresponds to a highway scenario and 2-D corresponds to a planar system. The carrier-to-interference ratio (C/I) at the primary receiver is evaluated using the characteristic function. The analysis clearly shows the need for cooperative spectrum sensing when the density of the CRs is high. It is shown that the effect of shadowing, small scale fading, and power control at the CRs can be captured into the density of the CR network. The results hold for the CRs that are wide-band devices as well as narrow-band devices.

关键词： Interference Microphones Wireless communication Wireless sensor networks Sensors Reliability Random variables

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