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Research Activities > Seminars > Spring 2010

Spring 2010 Seminars

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  • All talks are in the CSIC Bldg (#406) Room 4122 at 2.00pm (unless otherwise stated)
  • Directions can be found at: home.cscamm.umd.edu/directions
  • Refreshments will be served after the talk
  • Contact Email:




  • January 27

    2.00PM,
    4122 CSIC Bldg
     
    Prof Radu Balan, Department of Mathematics and CSCAMM, University of Maryland
    Signal Reconstruction From Its Spectrogram

    This paper presents a framework for discrete-time signal reconstruction from absolute values of its short-time Fourier coefficients. Our approach has two steps. In step one we reconstruct a band-diagonal matrix associated to the rank-one operator Kx=xx*. In step two we recover the signal x by solving an optimization problem. The two steps are somewhat independent, and one purpose of this talk is to present a framework that decouples the two problems. The solution to the first step is connected to the problem of constructing frames for spaces of Hilbert-Schmidt operators. The second step is somewhat more elusive. Due to inherent redundancy in recovering x from its associated rank-one operator Kx, the reconstruction problem allows for imposing supplemental conditions. In this paper we make one such choice that yields a fast and robust reconstruction. However this choice may not necessarily be optimal in other situations. It is worth mentioning that this second step is related to the problem of finding a rank-one approximation to a matrix with missing data.
     

    February 3

    2.00PM,
    4122 CSIC Bldg
     
    Dr Triet Le, Department of Mathematics, Yale University
    Local scales of oscillatory patterns

    In this talk, we study the problem of extracting local scales of oscillatory patterns in images. Given a multi-scale representation {u(t)} of an image f, we are interested in automatically picking out a few choices of t_i(x), which we call local scales, that better represent the multi-scale structure of f at x. We will characterize local scales coming from the Gaussian kernel. Non-linear type diffusions are also discussed.
     

    February 10

    2.00PM
    ,
    4122 CSIC Bldg
     
    Prof Brian Hunt, Inst for Physical Science & Technology, University of Maryland

    Ensemble Methods and Data Assimilation

    I will speak about ensemble methods that approximate and/or analyze a trajectory (or pseudotrajectory) of a chaotic dynamical system without linearizing the system, including a particular method ("Local Ensemble Transform Kalman Filter") developed at the University of Maryland for data assimilation in spatially extended systems. By "ensemble method" I mean an iterative procedure that alternately: (1) makes a short-term forecast from an ensemble of initial conditions; and then (2) adjusts the ensemble by some prescribed algorithm to determine initial conditions for the next forecast. The methods I consider seek to maintain an ensemble whose spread is reasonably small and that approximately spans the most unstable directions in its vicinity. For data assimilation, the method inputs a time series of observations of an otherwise unknown trajectory, and seeks to keep the ensemble close to that trajectory. I will discuss theoretical results for hyperbolic systems, and practical results for data assimilation in spatially extended systems, including weather forecast models.
     

    February 17

    2.00PM,
    4122 CSIC Bldg
     
    Joint CSCAMM/PDE Seminar

    Prof Helena Lopes-Nussenzveig, Departamento de Matemática, Universidade Estadual de Campinas

    Vortex sheets and conservation of circulation

    Vortex sheets are idealized models for flows with strong shears concentrated in a thin region, such as what occurs in the flow trailing an airfoil. In 1991 J.-M. Delort established the existence of a weak solution of the incompressible two-dimensional Euler equations with general vortex sheet initial data of distinguished sign, ie, in which the vorticity, which is the curl of velocity, is a bounded Radon measure with distinguished sign. The original result was proved for flows in the full plane, on a compact manifold and in a bounded domain.

    In this talk we revisit the case of a bounded domain and seek to understand the vortex dynamics point-of-view. In particular we note that, despite circulation (around boundary components) being a conserved quantity for smooth flows, it may cease to be conserved for vortex sheet flows. We extend Delort's proof to include exterior domain flows and show that the same issue arises. Finally, we discuss what is missing for conservation of circulation to hold. This is joint work with D. Iftimie (Lyon), M. C. Lopes Filho (UNICAMP) and F. Sueur (Paris VI).
     


    February 24

    2.00PM,
    4122 CSIC Bldg
     
    Prof Brian Hunt, Inst for Physical Science & Technology, University of Maryland

    Ensemble Methods and Data Assimilation

    I will speak about ensemble methods that approximate and/or analyze a trajectory (or pseudotrajectory) of a chaotic dynamical system without linearizing the system, including a particular method ("Local Ensemble Transform Kalman Filter") developed at the University of Maryland for data assimilation in spatially extended systems. By "ensemble method" I mean an iterative procedure that alternately: (1) makes a short-term forecast from an ensemble of initial conditions; and then (2) adjusts the ensemble by some prescribed algorithm to determine initial conditions for the next forecast. The methods I consider seek to maintain an ensemble whose spread is reasonably small and that approximately spans the most unstable directions in its vicinity. For data assimilation, the method inputs a time series of observations of an otherwise unknown trajectory, and seeks to keep the ensemble close to that trajectory. I will discuss theoretical results for hyperbolic systems, and practical results for data assimilation in spatially extended systems, including weather forecast models.
     

    March 3

    2.00PM,
    4122 CSIC Bldg
     
    Prof Alina Chertock, Department of Mathematics, North Carolina State University

    Particle Methods for Pressureless Gas Dynamics

    In this talk, I will consider one- and two-dimensional pressureless gas dynamics equations. These equations arise in different applications and, in particular, serve as a basic model of formation of large structures in the universe. The main feature of interest in this problem is the occurrence of strong singularities (delta-functions along the surface as well as at separate points) and the emergence of vacuum states. The same pressureless equations also arise in semiclassical approximations of highly oscillating solutions of the Schrodinger equation with high frequency initial data, in which case multivalued solutions -- not the single valued ones -- are physically relevant.

    Both the single and multivalued solutions of the pressureless gas dynamics equations can be accurately captured by low dissipative particle methods. In these methods, the solution is sought in the form of a linear combination of delta-functions, whose positions and coefficients are evolved in time according to a system of ODEs, obtained from a weak formulation of the system of PDEs.

    I will first introduce a new sticky particle method which is used for capturing the singular single valued solutions. The method is based on the idea of merging the particles that cluster at singularities and determining the particle velocities from the conservation requirements. This particle merger procedure results in the desired mass concentration.

    I will then discuss how to apply particle methods for computing the multivalued solutions. In this case, the particles do not interact and thus several particles are allowed to be located at exactly the same point (representing several branches of the computed solution) and to propagate with the velocities that are completely independent of the velocities of their neighbors. The main issue to be discussed here is how the point values of the computed solution can be recovered from its particle distribution.
     

    March 10

    Special Event

     
    Special Event:

    Quantum-Classical Modeling of Chemical Phenomena
    March 17 NO SEMINAR, UMD SPRING BREAK

    March 24

    2.00PM,
    4122 CSIC Bldg
     
    Prof Eric Carlen, Department of Mathematics, Rutgers University

    Analysis of the Boltzmann collision kernel via an N particle stochastic system

    In 1956, Mark Kac proposed a novel approach to the study of the Boltzmann equation via the large N limit of a stochastic system of N particle undergoing binary collisions. In the 1960's, Henry McKean and his students made many significant contributions to this program, particularly with regard to the problem of propagation of chaos. However, analysis of the rate of equilibration for this model remained an open problem for many years, and progress on this front was much more recent, and until now, had been made only for "Maxwellian molecules". Recent work of myself, Carvalho and Loss extends this progress to the physically significant hard-sphere case, as will be explained in this lecture.
     


    March 30 *Tuesday*

    3:30pm
    ,
    Math 3206

    (note special day, time and place)

    Joint Numerical Analysis / CSCAMM Seminar

    Prof Coralia Cartis, School of Mathematics, University of Edinburgh

    Adaptive regularization methods for nonlinear optimization

    Nonlinear nonconvex optimization problems represent the bed-rock of numerous real-life applications, such as data assimilation for weather prediction, radiation therapy treatment planning, optimal design of energy transmission networks, and many more. Finding (local) solutions of these problems usually involves iteratively constructing easier-to-solve local models of the function to be optimized, with the optimizer of the model taken as an estimate of the sought-after solution. Linear or quadratic models are usually employed locally in this context, yielding the well-known steepest descent and Newton approaches, respectively. However, these approximations are often unsatisfactory either because they are unbounded in the presence of nonconvexity and hence cannot be meaningfully optimized, or they are accurate representations of the function only in a small neighbourhood, yielding only small or no iterative improvements. Hence such models require some form of regularization to improve algorithm performance and avoid failure; traditionally, linesearch and trust-region techniques have been employed for this purpose and represent the state-of-the-art. Here, we first show that the steepest descent and Newton's methods, even with the above-mentioned regularization strategies, may both require a similar number of iterations and function evaluations to reach within approximate first-order optimality, implying that the known bound for worst-case complexity of steepest descent is tight and that Newton's method may be as slow as steepest descent under standard assumptions. Then, a new class of methods will be presented that approximately globally minimize a quadratic model of the objective regularized by a cubic term, extending to practical large-scale problems earlier regularization approaches by Nesterov (2007) and Griewank (1982). Preliminary numerical experiments show our methods to perform better than a trust-region implementation, while our convergence results show them to be at least as reliable as the latter approach. Furthermore, their worst-case complexity is provably better than that of steepest descent, Newton's and trust-region methods. This is joint work with Nick Gould (Rutherford Appleton Laboratory, UK) and Philippe Toint (University of Namur, Belgium).
     


    March 31

    2.00PM,
    4122 CSIC Bldg
     
    Prof Jared Tanner, School of Mathematics, University of Edinburgh

    Phase transitions phenomenon in Compressed Sensing

    Compressed Sensing reconstruction algorithms typically exhibit a zeroth-order phase transition phenomenon for large problem sizes, where there is a domain of problem sizes for which successful recovery occurs with overwhelming probability, and there is a domain of problem sizes for which recovery failure occurs with overwhelming probability. The mathematics underlying this phenomenon will be outlined for 1 regularization, non-negative feasibility point regions, and bounded constraints. Both instances employ a large deviation analysis of the associated geometric probability event. These results give precise if and only if conditions on the number of samples needed in Compressed Sensing applications.

    Lower bounds on the phase transitions implied by the Restricted Isometry Property for Gaussian random matrices will also be presented for the following algorithms: q-regularization for q ∈ (0,1), CoSaMP, Subspace Pursuit, and Iterated Hard Thresholding.
     
    April 7

    Special Event

    Special Event:

    Nonlinear Dynamics of Networks

    April 14

    2.00PM,
    4122 CSIC Bldg
     
    Prof Howard Barnum, Perimeter Institute for Theoretical Physics in Ontario, Canada

    Quantum information processing in context: information processing in convex operational theories

    The rise of quantum information science has been paralleled by the development of a vigorous research program aimed at obtaining characterizations or reconstructions of the quantum formalism in terms the possibilities it makes available for information processing. This development has involved a variety of approaches; I will review results, primarily ones by me and my collaborators, in a broad framework for stochastic theories that encompasses quantum and classical theory, but also a wide variety of other theories that can serve as foils to them. One goal is an understanding of the conceptual features of quantum mechanics that account for its greater-than-classical information-processing power, an understanding which could perhaps help guide the search for new quantum algorithms and protocols.

    The main results reviewed are: (1) the fact that the only information that can be obtained in the framework without disturbance is inherently classical, no-cloning and no-broadcasting theorems in the generalized framework, (2) the existence of exponentially secure bit commitment in non-classical theories without entanglement, (3) the consequences for theories of the existence of a conclusive teleportation scheme, and (4) sufficient conditions for the existence of a deterministic teleportation scheme (5) sufficient conditions for what Schroedinger called "steering" of ensembles using entangled states of generalized theories, rendering insecure bit commitment protocols of the form shown to be secure in the unentangled case.

    If time permits, I may cover (6) some notions of entropy and mutual information in this framework, connecting properties of these (specifically, the equality of preparation and measurement entropy, and a data processing inequality for mutual information) to bounds on quantum, correlations via the "information causality" property, and (7) a generalized notion of interference in such theories, adapting Rafael Sorkin's notion of a hierarchy of "levels" of interference, of which quantum theory only exhibits the lowest order, may be adapted to this framework.

    Joint work with various groups of collaborators including Jonathan Barrett, Matthew Leifer, Alexander Wilce, Oscar Dahlsten, Ben Toner, Cozmin Ududec, Joe Emerson, Rob Spekkens, Lisa Orloff-Clark, Phillip Gaebler, Nicholas Stepanik, Robin Wilke.
     

    April 21

    2.00PM,
    4122 CSIC Bldg
     
    Prof Edriss Titi, The Weizmann Institute of Science and The University of California - Irvine

    Alpha Sub-grid Scale Models of Turbulence and Inviscid Regularization

    In recent years many analytical sub-grid scale models of turbulence were introduced based on the Navier--Stokes-alpha model (also known as a viscous Camassa--Holm equations or the Lagrangian Averaged Navier--Stokes-alpha (LANS-alpha)). Some of these are the Leray-alpha, the modified Leray-alpha, the simplified Bardina-alpha and the Clark-alpha models. In this talk I will show the global well-posedness of these models and provide estimates for the dimension of their global attractors, and relate these estimates to the relevant physical parameters. Furthermore, I will show that up to certain wave number in the inertial range the energy power spectra of these models obey the Kolmogorov -5/3 power law, however, for the rest the inertial range the energy spectra are much steeper.

    In addition, I will show that by using these alpha models as closure models to the Reynolds averaged equations of the Navier--Stokes one gets very good agreement with empirical and numerical data of turbulent flows for a wide range of huge Reynolds numbers in infinite pipes and channels.

    It will also be observed that, unlike the three-dimensional Euler equations and other inviscid alpha models, the inviscid simplified Bardina model has global regular solutions for all initial data. Inspired by this observation I will introduce new inviscid regularizing schemes for the three-dimensional Euler, Navier--Stokes and MHD equations, which does not require, in the viscous case, any additional boundary conditions. This same kind of inviscid regularization is also used to regularize the Surface Quasi-Geostrophic model.

    Finally, and based on the alpha regularization I will present, if time allows, some error estimates for the rate of convergence of the alpha models to the Navier-Stokes equations, and will also present new approximation of vortex sheets dynamics.
     

    April 28

    2.00PM,
    4122 CSIC Bldg
     
    Prof. Michael Evans, Department of Geology and ESSIC, University of Maryland

    Applications of proxy system modeling in high resolution paleoclimatology

    Paleoclimatic reconstructions are generally based on robust multivariate linear regression of indirect climate measures ("proxies") on contemporaneous direct climate observations. Mechanistic models of proxy systems may be multivariate and/or nonlinear. We explore the extent to which such a model for the environmental controls on the tree-ring width climate proxy explains ring width observations, and discuss the potential to use proxy system models as data level constraints on Bayesian hierarchical reconstructions of recent paleoclimates.
     

    May 5

    2.00PM,
    4122 CSIC Bldg
     
    Prof Sennur Ulukus, Electrical and Computer Engineering, University of Maryland

    Securing Wireless Communications in the Physical Layer using Signal Processing

    The last couple of decades have witnessed an amazing growth in wireless communications and networking applications. More and more subscribers are relying solely on their wireless communication and computing devices for communicating sensitive information. Ensuring secure transfer of information is thus essential. This important issue is currently dealt with at the higher layers of the protocol hierarchies using cryptographic algorithms, which provide useful protection against computationally-limited adversaries.

    Our research explores providing security in the physical layer using techniques from information theory, communication theory and signal processing. This approach is a fundamental departure from the currently available cryptographic solutions in that the security we provide is unbreakable, provable and quantifiable (in bits/sec). We use unique characteristics of the wireless medium, such as the inherent random fluctuations in the wireless channels (that enable opportunistic transmissions), overheard information (that enables cooperation), and the use of multiple antennas (that provides spatial diversity and multiplexing gains) to secure wireless communications in the physical layer. In this talk, we will demonstrate how opportunistic transmissions in fading channels, cooperation (with trusted or untrusted relays), multiple antennas, and signal alignment can be used to enhance security of wireless communications. We will also present results on secure data compression.
     

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