Seminars > Spring 2013

Spring 2013 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: www.cscamm.umd.edu/directions
  • Refreshments will be served after the talk
  • Contact Email:



  • January 23

    2.00PM,
    4122 CSIC Bldg

     
    Prof. Bill Rand, Robert H. Smith School of Business, University of Maryland

    The Complex Network of Social Media

    The dramatic feature of social media is that it gives everyone a voice; anyone can speak out and express their opinion to a crowd of followers with little or no cost or effort, which creates a loud and potentially overwhelming marketplace of ideas. The good news is that the organizations have more data than ever about what their consumers are saying about their brand. The bad news is that this huge amount of data is difficult to sift through. We will look at developing methods that can help sift through this torrent of data and examine important questions, such as who do users trust to provide them with the information that they want? Which entities have the greatest influence on social media users? Using agent-based modeling, machine learning and network analysis we begin to examine and shed light on these questions and develop a deeper understanding of the complex system of social media.
     

    January 31

    3:30 PM

    Math 3206
    (note time + location)  
    Joint PDE/KI-Net Seminar

    Prof. Razvan Fetecau, Department of Pure Mathematics and Mathematical Statistics, University of Cambridge

    Swarm dynamics and equilibria for a nonlocal aggregation model

    We consider the aggregation equation ρt − ∇ • (ρ∇K ∗ ρ) = 0 in Rn, where the interaction potential K models short-range repulsion and long-range attraction. We study a family of interaction potentials with repulsion given by a Newtonian potential and attraction in the form of a power law. We show global well-posedness of solutions and investigate analytically and numerically the equilibria and their global stability. The equilibria have biologically relevant features, such as finite densities and compact support with sharp boundaries. This is joint work with Yanghong Huang and Theodore Kolokolnikov.
     

    February 6

    2.00PM,
    4122 CSIC Bldg

     
    Joint CSCAMM/KI-Net Seminar

    Dr. Carola-Bibiane Schönlieb, Department of Applied Mathematics and Theoretical Physics (DAMTP), University of Cambridge

    Noise estimation by PDE-constrained optimisation

    A key issue in image denoising is an adequate choice of the correct noise model. In a variational approach this amounts to the choice of the data fidelity and its weighting. Depending on this choice, different results are obtained.

    In this talk I will discuss a PDE-constrained optimization approach for the determination of the noise distribution in total variation (TV) image denoising. An optimization problem for the determination of the weights correspondent to different types of noise distributions is stated and existence of an optimal solution is proved. A tailored regularization approach for the approximation of the optimal parameter values is proposed thereafter and its consistency studied. Additionally, the differentiability of the solution operator is proved and an optimality system characterizing the optimal solutions of each regularized problem is derived. The optimal parameter values are numerically computed by using a quasi-Newton method, together with semismooth Newton type algorithms for the solution of the TV-subproblems. The talk is furnished with numerical examples computed on simulated data.

    This is joint work with Juan Carlos De Los Reyes
     

    February 13

    2.00PM,
    4122 CSIC Bldg

     
    Dr. Prashant Athavale, Department of Mathematics, University of Toronto

    Fast multiscale total variation flow with applications.

    Images consist of features of varying scales. Thus, multiscale image processing techniques are extremely valuable, especially for medical images. We will discuss multiscale image processing techniques based on variational methods, specifically (BV, L2) decompositions. We will discuss the applications to real time denoising, deblurring, inpainting and image registration.
     
    February 20   NO SEMINAR

    February 27

    2.00PM,
    4122 CSIC Bldg

     
    Prof. Anne Gelb, School of Mathematical and Statistical Sciences, Arizona State University

    Numerical Approximation Methods for Non-Uniform Fourier Data

    In this talk I discuss the reconstruction of compactly supported piecewise smooth functions from non-uniform samples of their Fourier transform. This problem is relevant in applications such as magnetic resonance imaging (MRI) and synthetic aperture radar (SAR).

    Two standard reconstruction techniques, convolutional gridding (the non-uniform FFT) and uniform resampling, are summarized, and some of the difficulties are discussed. It is then demonstrated how spectral reprojection can be used to mollify both the Gibbs phenomenon and the error due to the non-uniform sampling. It is further shown that incorporating prior information, such as the internal edges of the underlying function, can greatly improve the reconstruction quality. Finally, an alternative approach to the problem that uses Fourier frames is proposed.
     

    March 6

    2.00PM,
    4122 CSIC Bldg

     
    Joint CSCAMM/KI-Net Seminar

    Prof. Weizhu Bao, Department of Mathematics, Center for Computational Science & Engineering, National University of Singapore

    Ground states and dynamics of the nonlinear Schrodinger/Gross-Pitaevskii equations

    In this talk, I begin with a brief derivation of the nonlinear Schrodinger/Gross-Pitaevskii equations (NLSE/GPE) from Bose-Einstein condensates (BEC) and/or nonlinear optics. Then I will present some mathematical results on the existence and uniqueness as well as non-existence of the ground states of NLSE/GPE under different external potentials and parameter regimes. Dynamical properties of NLSE/GPE are then discussed, which include conservation laws, soliton solutions, well-posedness and/or finite time blowup. Efficient and accurate numerical methods will be presented for computing numerically the ground states and dynamics. Extension to NLSE/GPE with an angular momentum rotation term and/or non-local dipole-dipole interaction will be presented. Finally, applications to collapse and explosion of BEC, quantum transport and quantized vortex interaction will be investigated.
     
    March 13

    2.00PM,
    4122 CSIC Bldg

    Prof. Alex Mahalov, School of Mathematical & Statistical Sciences, Arizona State University

    Stochastic 3D Rotating Navier-Stokes Equations:
    Averaging, Convergence and Regularity


    We consider stochastic three-dimensional rotating Navier-Stokes equations and prove averaging theorems for stochastic problems in the case of strong rotation. Regularity results are established by bootstrapping from global regularity of the limit stochastic equations and convergence theorems. The energy injected in the system by the noise is large, the initial condition has large energy, and the regularization time horizon is long. Regularization is the consequence of precise mechanisms of relevant three-dimensional nonlinear dynamics. We prove multi-scale averaging theorems for the stochastic dynamics and describe its effective covariance operator.

    Reference
    F. Flandoli and A. Mahalov (2012), Stochastic 3D Rotating Navier-Stokes equations: averaging, convergence and regularity, Archive for Rational Mechanics and Analysis, vol. 205, Issue 1, p.195-237.
     
    March 20 NO SEMINAR, UMD SPRING BREAK  


    March 27

    2.00PM,
    4122 CSIC Bldg

    Prof. Siddhartha Mishra, Seminar für Angewandte Mathematik, ETH

    Arbitrarily high order numerical schemes that converge to entropy measure valued solutions of systems of hyperbolic conservation laws.

    We start by arguing through numerical examples as to why entropy measure valued solutions are the appropriate solution concept for systems of conservation laws in several space dimensions. Two classes of numerical schemes are presented that can be shown to converge to entropy measure valued solutions. The first class are finite volume schemes based on entropy conservative fluxes and numerical diffusion operators, using a ENO reconstruction. The second class are space-time shock capturing discontinuous Galerkin (STDG) schemes. The schemes are compared on a set of numerical experiments. The lecture concludes with a discussion of efficient ways to compute measure valued solutions using multi-level monte carlo methods, that were originally developed for uncertainty quantification in conservation laws.
     
    April 3

    2.00PM,
    4122 CSIC Bldg

    Prof. Joanna Wares, Department of Mathematics, University of Richmond

    Transmission of Antibiotic-Resistant Bacteria in the Health Care Setting

    Antibiotic-resistant bacteria present an enormous challenge in hospitals and other health care settings. Infection rates are high and new strains are constantly emerging. Mortality from nosocomial infections of certain gram-negative strains approaches 60%. Mathematical models consisting of systems of differential equations or computer simulations of agent-based models can be used to study interventions that can lessen transmission and infection rates. In this talk, I will discuss techniques for studying nosocomial infections and look at some results from our recent work.
     
    April 10

    2.00PM,
    4122 CSIC Bldg

    Prof. Chi-Wang Shu, Division of Applied Mathematics, Brown University

    Discontinuous Galerkin method for hyperbolic equations with singularities

    Discontinuous Galerkin (DG) methods are finite element methods with features from high resolution finite difference and finite volume methodologies and are suitable for solving hyperbolic equations with nonsmooth solutions. In this talk we will first give a survey on DG methods, then we will describe our recent work on the study of DG methods for solving hyperbolic equations with singularities in the initial condition, in the source term, or in the solutions. The type of singularities include both discontinuities and δ-functions. Especially for problems involving δ-singularities, many numerical techniques rely on modifications with smooth kernels and hence may severely smear such singularities, leading to large errors in the approximation. On the other hand, the DG methods are based on weak formulations and can be designed directly to solve such problems without modifications, leading to very accurate results. We will discuss both error estimates for model linear equations and applications to nonlinear systems including the rendez-vous systems and pressureless Euler equations involving δ-singularities in their solutions. This is joint work with Qiang Zhang, Yang Yang and Dongming Wei.
     
    April 17

    2.00PM,
    4122 CSIC Bldg

    Joint CSCAMM/KI-Net Seminar

    Prof. Yann Brenier, Centre de Mathématiques Laurent Schwartz, Ecole Polytechnique

    The relative entropy method for geophysical flows

    The "relative entropy method" is well-known in several fields of mathematical physics, PDEs and probabilities (systems of hyperbolic conservation laws, systems of particles, kinetic equations...). It typically leads to the rigorous derivation of some asymptotic models having smooth enough solutions.

    Here, we report on examples of geophysical fluid dynamics (with rotation and convection effects, at different aspect ratio and time scales), for which the relative entropy method applies in a non-standard way because the entropy functional depends on the asymptotic solution itself.
     

    April 24

    2.00PM,
    4122 CSIC Bldg

     
    Prof. Donatella Donatelli, Department of Mathematics, Università degli Studi L'Aquila

    Analysis of Oscillations and Defect Measures in Plasma Physics

    We perform a rigorous analysis of the quasineutral limit for a hydrodynamical model of a viscous plasma represented by the Navier Stokes Poisson system in 3 − D. We show that as the Debye length goes to zero the velocity field strongly converges towards an incompressible velocity vector field and the density fluctuation weakly converges to zero. In general the limit velocity field cannot be expected to satisfy the incompressible Navier Stokes equation, indeed the presence of high frequency oscillations strongly affects the quadratic nonlinearities and we have to take care of self interacting wave packets. We shall provide a detailed mathematical description of the convergence process by using microlocal defect measures and by developing an explicit correctors analysis.
     

    May 1

    2.00PM,
    4122 CSIC Bldg

     
    Prof. Andrea Bertozzi, Department of Mathematics, University of California Los Angeles

    Swarming by Nature and by Design

    The cohesive movement of a biological population is a commonly observed natural phenomenon. With the advent of platforms of unmanned vehicles, such phenomena have attracted a renewed interest from the engineering community. This talk will cover a survey of the speaker’s research and related work in this area ranging from aggregation models in nonlinear partial differential equations to control algorithms and robotic testbed experiments. We conclude with a discussion of some interesting problems for the applied mathematics community.
     

    May 8

    2.00PM,
    4122 CSIC Bldg

     
    Joint CSCAMM/KI-Net Seminar

    Prof. Laurent Desvillettes, École Normale Supérieure de Cachan

    Coupling kinetic and fluid equations in the context of the study of sprays

    Sprays are complex flows consisting of an underlying gas and a large quantity of small liquid droplets. They appear in many industrial devices (engines, nuclear industry) and natural phenomena (clouds, lungs). Their modeling, first proposed by Williams in the 70s, can be performed through the coupling of a kinetic equation of Vlasov type (for the droplets) and a fluid equation (viscous or inviscid, compressible or incompressible) for the gas. The mathematical theory for this coupling mixes the kinetic theory (control of moments as in the Vlasov-Poisson equation) and the Euler/Navier-Stokes theory (strong local solutions, weak solutions). We wish to present during the seminar some of the latest results obtained for sprays.
     

    May 15

    2.00PM,
    4122 CSIC Bldg

     
    Joint KI-Net/CSCAMM Seminar

    Prof. Alexis Vasseur, University of Texas at Austin

    Relative entropy applied to the study of stability of shocks for conservation laws, and application to asymptotic analysis

    The relative entropy method is a powerful tool for the study of conservation laws. It provides, for example, the weak/strong uniqueness principle, and has been used in different context for the study of asymptotic limits. Up to now, the method was restricted to the comparison to Lipschitz solutions. This is because the method is based on the strong stability in L2 of such solutions. Shocks are known to not be strongly L2 stable. We show, however that their profiles are strongly L2 stable up to a drift. We provide a first application of this stability result to the study of asymptotic limits.
     

    June 11

    3.45PM,
    4122 CSIC Bldg

    Live Webcast
     
    Dr. Reza Malek-Madani, Mathematical, Computer and Information Sciences Division, Office of Naval Research

    A Guide for Proposal Writing


    June 17

    3.00PM,
    4122 CSIC Bldg

    Live Webcast
     
    KI-Net Seminar

    Prof. Gianluca Crippa, Universitaet Basel, Department Mathematik und Informatik

    Ordinary Differential Equations and Singular Integrals

    Given a Lipschitz vector field, the classical Cauchy-Lipschitz theory gives existence, uniqueness and regularity of the associated ODE flow. In recent years, much attention has been devoted to extensions of such theory to cases in which the vector field is less regular than Lipschitz, but still belongs to some "weak differentiability classes". In this talk, I will review the main points of an approach involving quantitative estimates for flows of Sobolev vector fields (joint work with Camillo De Lellis) and describe a further extension to a case involving singular integrals of L^1 functions (joint work with Francois Bouchut).
    University of Maryland    

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