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Proceedings of the 19th International Conference on Neural Information Processing Systems

作者： Boaz Nadler Stéphane Lafon Ronald R. Coifman Ioannis G. Kevrekidis Department of Mathematics Yale University New Haven CT Department of Chemical Engineering and Program in Applied Mathematics Princeton University Princeton NJ

This paper presents a diffusion based probabilistic interpretation of spectral clustering and dimensionality reduction algorithms that use the eigenvectors of the normalized graph Laplacian. Given the pairwise adjacency matrix of all points, we define a diffusion distance between any two data points and show that the low dimensional representation of the data by the first few eigenvectors of the corresponding Markov matrix is optimal under a certain mean squared error criterion. Furthermore, assuming that data points are random samples from a density p(x) = e-U(x) we identify these eigenvectors as discrete approximations of eigenfunctions of a Fokker-Planck operator in a potential 2U(x) with reflecting boundary conditions. Finally, applying known results regarding the eigenvalues and eigenfunctions of the continuous Fokker-Planck operator, we provide a mathematical justification for the success of spectral clustering and dimensional reduction algorithms based on these first few eigenvectors. This analysis elucidates, in terms of the characteristics of diffusion processes, many empirical findings regarding spectral clustering algorithms.

关键词： algorithms and architectures

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First-principles study of the interfacial adhesion between SiO2 and MoSi2

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Physical Review B 2005年第16期72卷 165410-165410页

作者： D. E. Jiang Emily A. Carter Department of Chemistry and Biochemistry Box 951569 University of California Los Angeles California 90095-1569 USA Department of Mechanical and Aerospace Engineering and Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544-5263 USA

Upon oxidation, a silica scale forms on MoSi2, a potential high-temperature coating material for metals. This silica scale protects MoSi2 against high-temperature corrosive gases or liquids. We use periodic density functional theory to examine the interface between SiO2 and MoSi2. The interfacial bonding is localized, as evidenced by an adhesion energy that changes only slightly with the thickness of the SiO2 layer. Moreover, the adhesion energy displays a relatively large (0.40J∕m2) variation with the relative lateral position of the SiO2 and MoSi2 lattices due to changes in Si−O bonding across the interface. The most stable interfacial structure yields an ideal work of adhesion of 5.75J∕m2 within the local density approximation (5.02J∕m2 within the generalized-gradient approximation) to electron exchange and correlation, indicating extremely strong adhesion. Local densities of states and electron density difference plots demonstrate that the interfacial Si−O bonds are covalent in character. Mo−O interactions are not found in the SiO2∕MoSi2 interface investigated here. Our work predicts that the SiO2 scale strongly adheres to MoSi2, and further supports the potential of MoSi2 as a high-temperature structural material and coating.

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Experiments on Random Packings of Ellipsoids

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Physical Review Letters 2005年第19期94卷 198001-198001页

作者： Weining Man Aleksandar Donev Frank H. Stillinger Matthew T. Sullivan William B. Russel David Heeger Souheil Inati Salvatore Torquato P. M. Chaikin Department of Physics and Princeton Institute for the Science and Technology of Materials Princeton University Princeton New Jersey 08544 USA Program in Applied and Computational Mathematics and Princeton Institute for the Science and Technology of Materials Princeton University Princeton New Jersey 08544 USA Department of Chemistry and Princeton Institute for the Science and Technology of Materials Princeton University Princeton New Jersey 08544 USA Department of Chemical Engineering and Princeton Institute for the Science and Technology of Materials Princeton University Princeton New Jersey 08544 USA Department of Psychology and Center for Neural Science New York University New York New York 10003 USA

Recent simulations indicate that ellipsoids can pack randomly more densely than spheres and, remarkably, for axes ratios near 1.25∶1∶0.8 can approach the densest crystal packing (fcc) of spheres, with a packing fraction of 74%. We demonstrate that such dense packings are realizable. We introduce a novel way of determining packing density for a finite sample that minimizes surface effects. We have fabricated ellipsoids and show that, in a sphere, the radial packing fraction ϕ(r) can be obtained from V(h), the volume of added fluid to fill the sphere to height h. We also obtain ϕ(r) from a magnetic resonance imaging scan. The measurements of the overall density ϕavr, ϕ(r) and the core density ϕ0=0.74±0.005 agree with simulations.

关键词： .ellipsoids Princeton New Jersey

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Stalactite Growth as a Free-Boundary Problem: A Geometric Law and Its Platonic Ideal

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Physical Review Letters 2005年第1期94卷 018501-018501页

作者： Martin B. Short James C. Baygents J. Warren Beck David A. Stone Rickard S. Toomey, III Raymond E. Goldstein Department of Physics University of Arizona Tucson Arizona 85721 USA Department of Chemical and Environmental Engineering University of Arizona Tucson Arizona 85721 USA Program in Applied Mathematics University of Arizona Tucson Arizona 85721 USA Accelerator Mass Spectrometry Facility University of Arizona Tucson Arizona 85721 USA Department of Soil Water and Environmental Science University of Arizona Tucson Arizona 85721 USA Kartchner Caverns State Park P.O. Box 1849 Benson Arizona 85602 USA

The chemical mechanisms underlying the growth of cave formations such as stalactites are well known, yet no theory has yet been proposed which successfully accounts for the dynamic evolution of their shapes. Here we consider the interplay of thin-film fluid dynamics, calcium carbonate chemistry, and CO2 transport in the cave to show that stalactites evolve according to a novel local geometric growth law which exhibits extreme amplification at the tip as a consequence of the locally-varying fluid layer thickness. Studies of this model show that a broad class of initial conditions is attracted to an ideal shape which is strikingly close to a statistical average of natural stalactites.

关键词： Limestone

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Time-frequency and time-scale canonical representations of doubly spread channels 12

Time-frequency and time-scale canonical representations of d...

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12th European Signal Processing Conference, EUSIPCO 2004

作者： Balan, Radu Vincent Poor, H. Rickard, Scott Verdú, Sergio Program in Applied and Computational Mathematics Princeton University PrincetonNJ United States Siemens Corporate Research PrincetonNJ United States Electronic and Electrical Engineering Department University College Dublin Ireland

ISBN: (纸本)9783200001657

A general technique for the generation of canonical channel models and demonstrate the application of the technique to time-frequency and time-scale integral kernel operators is developed. As an example, the derivation of Sayeed/Aazhang's time-frequency canonical channel characterization that forms the basis for the time-frequency RAKE receiver is shown. Then, a canonical time-scale channel model for wideband communication is developed. © 2004 EUSIPCO.

关键词： Time measurement

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Eulerian method for computing multivalued solutions of the Euler-Poisson equations and applications to wave breaking in klystrons

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Physical Review E 2004年第1期70卷 016502-016502页

作者： Xiantao Li John G. Wöhlbier Shi Jin John H. Booske The Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA Department of Electrical and Computer Engineering University of Wisconsin Madison Wisconsin 53706 USA Department of Mathematics University of Wisconsin Madison Wisconsin 53706 USA

We provide methods of computing multivalued solutions to the Euler-Poisson system and test them in the context of a klystron amplifier. An Eulerian formulation capable of computing multivalued solutions is derived from a kinetic description of the Euler-Poisson system and a moment closure. The system of the moment equations may be closed due to the special structure of the solution in phase space. The Eulerian moment equations are computed for a velocity modulated electron beam, which has been shown by prior Lagrangian theories to break in a finite time and form multivalued solutions. The results of the Eulerian moment equations are compared to direct computation of the kinetic equations and a Lagrangian method also developed in the paper. We use the Lagrangian formulation for the explicit computation of wave breaking time and location for typical velocity modulation boundary conditions.

关键词： Klystrons

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Time-frequency and time-scale canonical representations of doubly spread channels

Time-frequency and time-scale canonical representations of d...

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European Signal Processing Conference (EUSIPCO)

作者： Radu Balan H. Vincent Poor Scott Rickard Sergio Verdú Siemens Corporate Research Princeton New Jersey Program in Applied and Computational Mathematics Princeton University Princeton New Jersey U.S.A Electronic and Electrical Engineering Department University College Dublin Ireland

关键词： Abstracts Generators

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Space-time signaling based on Kerdock and Delsafte-Goethals codes

Space-time signaling based on Kerdock and Delsafte-Goethals ...

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IEEE International Conference on Communications (ICC)

作者： A.R. Calderbank S.N. Diggavi N. Al-Dhahir Program in Applied and Computational Mathematics Princeton University Princeton NJ USA School of Computer and Communication Sciences Swiss Federal Institute of Technology Lausanne Switzerland Department of Electrical Engineering University of Technology Dallas TX USA

This paper designs space-time codes for standard PSK and QAM signal constellations that have flexible rate, diversity and require no constellation expansion. Central to this construction are binary partitions of the PSK and QAM constellations that appear in codes designed for the Gaussian channel. The space-time codes presented here are designed by separately specifying the different levels of the binary partition in the space-time array. The individual levels are addressed by either the binary symmetric matrices associated with codewords in a Kerdock code or other families of binary matrices. Binary properties of these sets are sufficient to verify the diversity property of the codewords in the complex domain. Larger sets of binary symmetric matrices (such as the set used in Delsarte-Goethals codes) are used to trade diversity protection for increased rate.

关键词： Space time codes Phase shift keying Quadrature amplitude modulation Constellation diagram Symmetric matrices Binary phase shift keying Quadrature phase shift keying Transmitting antennas Fading mathematics

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Distributed nonlinear control of diffusion-reaction processes

Distributed nonlinear control of diffusion-reaction processe...

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American Control Conference (ACC)

作者： S. Dubljevic P.D. Christofides I.G. Kevrekidis Department of Chemical Eagineering University of California Los Angeles CA USA Department of Chemical Engineering and the Program in Applied and Computational Mathematics Princeton University Princeton NJ USA

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Diversity-embedded space-time codes

Diversity-embedded space-time codes

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IEEE Conference and Exhibition on Global Telecommunications (GLOBECOM)

作者： S.N. Diggavi N. Al-Dhahir A.R. Calderbank School of Computer and Communication Sciences Swiss Federal Institute of Technology Lausanne Switzerland Department of Electrical Engineering University of Technology Dallas TX USA Program in Applied and Computational Mathematics Princeton University Princeton NJ USA

Rate and diversity impose a fundamental trade-off in space-time coding. High-rate space-time codes come at a cost of lower diversity, and high reliability (diversity) implies a lower rate. We explore a different point of view where we design high-rate space-time codes that have a high-diversity code embedded within them. This allows a form of communication where the high-rate code opportunistically takes advantage of good channel realizations whereas the embedded high-diversity code ensures that at least part of the information is received reliably. We explore this point of view with design issues, along with some preliminary progress on code constructions and some information-theoretic considerations.

关键词： Space time codes Rayleigh channels Costs Transmitting antennas Transmitters Space technology mathematics Wireless communication Error probability Time division multiplexing

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