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Annual Allerton Conference on Communication, Control, and Computing

作者： Tariq R. Qureshi Michael D. Zoltowski Robert Calderbank The School of Electrical and Computer Engineering Purdue University West Lafayette IN USA The Center of Applied and Computational Mathematics Engineering Quadrangle Princeton University Princeton NJ USA

ISBN: (纸本)9781424458707

In this paper, we present a method for detecting a point target using multiple antennas when the relative motion between the receivers and the target induces a non-negligible Doppler shift. As a key illustrative example, we consider a 4 × 4 system employing a unitary matrix waveform set, e.g., formed from Golay complementary sequences. When a non-negligible Doppler shift is induced by the target motion, the waveform matrix formed from the complementary sequences is no longer unitary, resulting in significantly degraded target range estimates. To solve this problem, we adopt a subspace based approach exploiting the observation that the receive matrix formed from matched filtering of the reflected waveforms has a (non-trivial) null-space. Through processing of the waveforms with the appropriate vector from the null-space, we can significantly improve the detection performance. We provide simulation results to confirm the theoretical analysis.

关键词： Object detection MIMO Doppler radar Doppler shift Radar antennas Radar detection Motion detection Receiving antennas Degradation Motion estimation

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On detection with partial information in the Gaussian setup

On detection with partial information in the Gaussian setup

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Annual Allerton Conference on Communication, Control, and Computing

作者： Onur Özyeşil M. Kivanç Mihçak Yğcel Altug PACM (the Program in Applied and Computational Mathematics) Princeton University Princeton NJ USA Electrical and Electronics Engineering Department Boğaziçi University Istanbul Turkey School of Electrical and Computer Engineering Cornell University Ithaca NY USA

We introduce the problem of communication with partial information, where there is an asymmetry between the transmitter and the receiver codebooks. Practical applications of the proposed setup include the robust signal hashing problem within the context of multimedia security and asymmetric communications with resource-lacking receivers. We study this setup in a binary detection theoretic context for the additive colored Gaussian noise channel. In our proposed setup, the partial information available at the detector consists of dimensionality-reduced versions of the transmitter codewords, where the dimensionality reduction is achieved via a linear transform. We first derive the corresponding MAP-optimal detection rule and the corresponding conditional probability of error (conditioned on the partial information the detector possesses). Then, we constructively quantify an optimal class of linear transforms, where the cost function is the expected Chernoff bound on the conditional probability of error of the MAP-optimal detector.

关键词： Transmitters Protection Context Detectors Noise robustness Information security Engineering profession Signal processing Privacy Bidirectional control

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Method for obtaining upper bounds on photonic band gaps

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Physical Review B 2009年第15期80卷 155126-155126页

作者： Mikael C. Rechtsman Salvatore Torquato Courant Institute of Mathematical Sciences 251 Mercer Street New York New York 10012 USA Department of Chemistry Princeton University Princeton New Jersey 08544 USA Princeton Center for Theoretical Physics Princeton New Jersey 08544 USA Program in Applied and Computational Mathematics Princeton Institute for the Science and Technology of Materials Princeton New Jersey 08544 USA School of Natural Sciences Institute for Advanced Study Princeton New Jersey 08544 USA

We present a method to calculate upper bounds on the photonic band gaps of two-component photonic crystals. The method involves calculating both upper and lower bounds on the frequency bands for a given structure, and then maximizing over all possible two-component structures. We apply this method to a number of examples, including a one-dimensional photonic crystal (or “Bragg grating”) and two-dimensional photonic crystals (in both the TM and TE polarizations) with both four and sixfold rotational symmetries. We compare the bounds to band gaps of numerically optimized structures and find that the bounds are extremely tight. We prove that the bounds are “sharp” in the limit of low dielectric contrast ratio between the two components. This method and the bounds derived here have important implications in the search for optimal photonic band-gap structures.

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Extracting Kinetic and Stationary Distribution Information from Short MD Trajectories via a Collection of Surrogate Diffusion Models. (vol 5, pg 47, 2009)

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JOURNAL OF CHEMICAL THEORY AND COMPUTATION 2009年第8期5卷 2192-2192页

作者： Calderon, Christopher P. Arora, Karunesh Department of Computational and Applied Mathematics and Department of Statistics Rice University Houston Texas 77005-1892 and Department of Chemistry Biophysics Program University of Michigan 930 North University Avenue Ann Arbor Michigan 48109

Low-dimensional stochastic models can summarize dynamical information and make long time predictions associated with observables of complex atomistic systems. Maximum likelihood based techniques for estimating low-dimensional surrogate diffusion models from relatively short time series are presented. It is found that a heterogeneous population of slowly evolving conformational degrees of freedom modulates the dynamics. This underlying heterogeneity results in a collection of estimated low-dimensional diffusion models. Numerical techniques for exploiting this finding to approximate skewed histograms associated with the simulation are presented. In addition, statistical tests are used to assess the validity of the models and determine physically relevant sampling information, e.g. the maximum sampling frequency at which one can discretely sample from an atomistic time series and have a surrogate diffusion model pass goodness-of-fit tests. The information extracted from such analyses can possibly be used to assist umbrella sampling computations as well as help in approximating effective diffusion coefficients. The techniques are demonstrated on simulations of adenylate kinase.

关键词： Transport properties Diffusion Approximation computational chemistry Computer simulations

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Asymmetric profiles observed in the recombination of Bi79+: A benchmark for relativistic theories involving interference

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Physical Review A 2009年第1期80卷 014503-014503页

作者： Nobuyuki Nakamura Anthony P. Kavanagh Hirofumi Watanabe Hiroyuki A. Sakaue Yueming Li Daiji Kato Fred J. Currell Xiao-Min Tong Tsutomu Watanabe Shunsuke Ohtani Institute for Laser Science The University of Electro-Communications Chofu Tokyo 182-8585 Japan Queen’s University Belfast Belfast BT7 1NN United Kingdom Chubu University Kasugai-shi Aichi 487-8501 Japan National Institute for Fusion Science Toki Gifu 509-5292 Japan Institute of Applied Physics and Computational Mathematics P.O. Box 8009 Beijing 100088 China Doctoral Program in Materials Science Graduate School of Pure and Applied Sciences University of Tsukuba Tsukuba Ibaraki 305-8573 Japan Center for Computational Sciences University of Tsukuba Tsukuba Ibaraki 305-8577 Japan

Asymmetric profiles have been observed in the recombination cross section of Be-like Bi obtained by measuring the electron energy dependence of the ion abundance ratio in an electron-beam ion trap. In contrast to the previous x-ray measurements, the present measurement gives the integrated recombination cross section with higher statistical quality, which provides a benchmark to test the relativistic theory involving the interference between the resonant and continuum states. The comparison with our theoretical study shows that the Breit interaction plays an important role in this case.

关键词： Benchmarking

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Sequential Multiscale Modeling Using Sparse Representation

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Communications in computational Physics 2008年第10期4卷 1025-1033页

作者： Carlos J.Garcıa-Cervera Weiqing Ren Jianfeng Lu Weinan E Mathematics Department University of CaliforniaSanta BarbaraCA 93106USA Courant Institute of Mathematical Sciences New York UniversityNew YorkNY 10012USA Program in Applied and ComputationalMathematics Princeton UniversityPrincetonNJ 08544USA Department of Mathematics and PACM Princeton UniversityPrincetonNJ 08544USA

The main obstacle in sequential multiscale modeling is the pre-computation of the constitutive relationwhich often involvesmany independent *** constitutive relation of a polymeric fluid is a function of six variables,even after making the simplifying assumption that stress depends only on the rate of *** such a function is usually considered too *** the value of sequential multiscale modeling is often limited to“parameter passing”.Here we demonstrate that sparse representations can be used to drastically reduce the computational cost for precomputing functions of many *** strategy dramatically increases the efficiency of sequential multiscale modeling,making it very competitive in many situations.

关键词： Multiscale modeling sparse grids

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Locality and low-dimensions in the prediction of natural experience from fMRI

Locality and low-dimensions in the prediction of natural exp...

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21st Annual Conference on Neural Information Processing Systems, NIPS 2007

作者： Meyer, François G. Stephens, Greg J. Center for the Study of Brain Mind and Behavior Program in Applied and Computational Mathematics Princeton University United States Center for the Study of Brain Mind and Behavior Department of Physics Princeton University United States

ISBN: (纸本)160560352X

Functional Magnetic Resonance Imaging (fMRI) provides dynamical access into the complex functioning of the human brain, detailing the hemodynamic activity of thousands of voxels during hundreds of sequential time points. One approach towards illuminating the connection between fMRI and cognitive function is through decoding;how do the time series of voxel activities combine to provide information about internal and external experience? Here we seek models of fMRI decoding which are balanced between the simplicity of their interpretation and the effectiveness of their prediction. We use signals from a subject immersed in virtual reality to compare global and local methods of prediction applying both linear and nonlinear techniques of dimensionality reduction. We find that the prediction of complex stimuli is remarkably low-dimensional, saturating with less than 100 features. In particular, we build effective models based on the decorrelated components of cognitive activity in the classically-defined Brodmann areas. For some of the stimuli, the top predictive areas were surprisingly transparent, including Wernicke's area for verbal instructions, visual cortex for facial and body features, and visual-temporal regions for velocity. Direct sensory experience resulted in the most robust predictions, with the highest correlation (c ∼ 0:8) between the predicted and experienced time series of verbal instructions. Techniques based on non-linear dimensionality reduction (Laplacian eigenmaps) performed similarly. The interpretability and relative simplicity of our approach provides a conceptual basis upon which to build more sophisticated techniques for fMRI decoding and offers a window into cognitive function during dynamic, natural experience.

关键词： Forecasting

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Diffusion maps - A probabilistic interpretation for spectral embedding and clustering algorithms

Diffusion maps - A probabilistic interpretation for spectral...

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作者： Nadler, Boaz Lafon, Stephane Coifman, Ronald Kevrekidis, Ioannis G. Department of Computer Science and Applied Mathematics Weizmann Institute of Science Rehovot 76100 Israel Google Inc. United States Department of Mathematics Yale University New Haven CT 06520-8283 United States Department of Chemical Engineering Program in Applied and Computational Mathematics Princeton University Princeton NJ 08544 United States

ISBN: (纸本)9783540737490

Spectral embedding and spectral clustering are common methods for non-linear dimensionality reduction and clustering of complex high dimensional datasets. In this paper we provide a diffusion based probabilistic analysis of algorithms that use the normalized graph Laplacian. Given the pairwise adjacency matrix of all points in a dataset, we define a random walk on the graph of points and a diffusion distance between any two points. We show that the diffusion distance is equal to the Euclidean distance in the embedded space with all eigenvectors of the normalized graph Laplacian. This identity shows that characteristic relaxation times and processes of the random walk on the graph are the key concept that governs the properties of these spectral clustering and spectral embedding algorithms. Specifically, for spectral clustering to succeed, a necessary condition is that the mean exit times from each cluster need to be significantly larger than the largest (slowest) of all relaxation times inside all of the individual clusters. For complex, multiscale data, this condition may not hold and multiscale methods need to be developed to handle such situations.

关键词： Relaxation time

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Domain Formation in the Plasma Membrane: Roles of Nonequilibrium Lipid Transport and Membrane Proteins

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Physical Review Letters 2008年第17期100卷 178102-178102页

作者： Jun Fan Maria Sammalkorpi Mikko Haataja Department of Mechanical and Aerospace Engineering Princeton Institute for the Science and Technology of Materials (PRISM) and Program in Applied and Computational Mathematics (PACM) Princeton University Princeton New Jersey 08544 USA

Compositional lipid domains (“lipid rafts”) in plasma membranes are believed to be important components of many cellular processes. The mechanisms by which cells regulate the sizes and lifetimes of these spatially extended domains are poorly understood at the moment. Here we show that the competition between phase separation in an immiscible lipid system and active cellular lipid transport processes naturally leads to the formation of such domains. Furthermore, we demonstrate that local interactions with immobile membrane proteins can spatially localize the rafts and lead to further clustering.

关键词： Lipids

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Analytic form for a nonlocal kinetic energy functional with a density-dependent kernel for orbital-free density functional theory under periodic and Dirichlet boundary conditions

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Physical Review B 2008年第4期78卷 045105-045105页

作者： Gregory S. Ho Vincent L. Lignères Emily A. Carter Department of Chemistry Princeton University Princeton New Jersey 08544 USA Department of Mechanical and Aerospace Engineering and Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544-5263 USA

We derive an analytic form of the Wang-Govind-Carter (WGC) [Wang et al., Phys. Rev. B 60, 16350 (1999)] kinetic energy density functional (KEDF) with the density-dependent response kernel. A real-space aperiodic implementation of the WGC KEDF is then described and used in linear scaling orbital-free density functional theory (OF-DFT) calculations.

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