Research Activities > Seminars > Fall 2007

Fall 2007 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:
  • Refreshments will be served after the talk
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  • September 5

    2.00 PM,
    4122 CSIC Bldg
    Professor Uri Keich, Computer Science Department, Cornell University

    Estimating the Significance of Sequence Motifs

    Efficient and accurate statistical significance evaluation is an essential requirement of motif-finding tools. One such widely used significance criterion is the E-value of the motif's information content or entropy score. Current computation schemes used in popular motif-finding programs can unwittingly provide poor approximations. We present an approach to a fast and reliable estimation of this E-value that can be applied more generally.

    Unfortunately, this improvement did not completely solve the motif significance estimation problem. In particular, we more recently found that relying on these E-values when searching for relatively weak motifs can lead to undesirable results. This motivated our design of a novel, parametric approach for analyzing the significance of sequence motifs.
    September 12

    2.00 PM,
    4122 CSIC Bldg
    Dr. Siddhartha Mishra, Centre of Mathematics for Applications, University of Oslo

    Finite Volume Methods for Wave Propagation in Stratified Magneto-atmospheres

    We consider equations of Magneto-Hydro dynamics (MHD) along with gravitational source terms which serve as a model for the propagation of waves in the solar atmosphere. Numerical methods for this model involve the design of suitable finite volume schemes. Numerical issues addressed include handling the divergence constraint in the equations by a suitable upwind discretization of the Godunov-Powell source term.

    Approximate Riemann solvers of the HLL-type based on a splitting between the fluid and magnetic field parts of the equation has been developed and will be compared with other existing solvers. Non-reflecting characteristic type boundary conditions have been designed to treat wave propagation through the artificial top boundary. All the above issues will be described and a series of numerical examples will be presented during the lecture.
    September 19

    2.00 PM,
    4122 CSIC Bldg
    Dr. Arthur Cheng, CSCAMM, University of Maryland

    Free Boundary Problems: Viscous Fluids Interacting with Elastic Shells

    The moving boundary problem in continuum mechanics is one of the most beautiful problems in nature. It appears when considering the motion of two types of materials in liquid crystals, elastic solids, porous media, and etc. This seminar talk is concerned with a moving boundary value problem consisting of a viscous incompressible fluid moving and interacting with a elastic shell. Two types of elastic shells, a fluid-shell type of shell which is usually used to model bio-membrane, and a solid-shell type of shell which is widely used in solid mechanics, will be considered here. We will learn how to model these problems in terms of the PDEs, and the fundamental difficulties in both theoretic and numerical points of view. Finally, a brief presentation of the idea of solving the problem and a well-posedness result will be discussed.
    September 26

    2.00 PM,
    4122 CSIC Bldg
    Professor Luminita Vese, Department of Mathematics, UCLA

    Minimization Models and Algorithms for Image Segmentation, Image Decomposition, and Texture Modeling

    This talk is devoted to some computational methods for image segmentation, cartoon-texture separation and texture modeling, in a variational and partial differential equations approach. A multilayer curve evolution model will be presented for image segmentation that is well adapted for volumetric MRI brain data and is more efficient than previous models.

    Also, computational methods for modeling oscillations and image decomposition into cartoon and texture will be presented. Images and in particular oscillatory patterns are represented by more refined texture norms, such as dual norms or generalized functions. The difficulty arising in the minimization of such models will be addressed, and theoretical and experimental results will be presented.
    October 3

    2.00 PM,
    4122 CSIC Bldg
    Professor Richard James, Aerospace Engineering and Mechanics, University of Minnesota

    Lessons on Structure from the Structure of Viruses

    As the most primitive organisms, occupying the gray area between the living and nonliving, viruses are the least complex biological system. One can begin to think about them in a quantitative way, while still being at some level faithful to biochemical processes. We make some observations about their structure, formalizing in mathematical terms some rules-of-construction discovered by Watson and Crick and Caspar and Klug. We call the resulting structures objective structures. It is then seen that objective structures include many of the most important structures studied in science today: carbon nanotubes, the capsids, necks, tails and other parts of many viruses, the cilia of some bacteria, DNA octahedra, buckyballs, actin and collagen and many other common proteins, and certain severely bent and twisted beams. The rules defining them relate to the basic invariance group of quantum mechanics. We give simple formulas for all such structures. Some of the nonperiodic structures revealed by the formulas exhibit beautifully subtle relations of symmetry. This common mathematical structure paves the way toward many interesting calculations for such structures: simplified schemes for exact molecular dynamics of such structures (objective MD), phase transformations between them (as in bacteriophage T4), new x-ray methods for direct determination of structure not relying on crystallization, and a theory of their growth by self-assembly.
    October 10

    2.00 PM,
    4122 CSIC Bldg
    Dr. Amit Singer, Department of Mathematics, Yale University

    Geometric Inversion Problems with Case Studies in Structural Biology and Sensor Networks

    In many applications, the main goal is to obtain a global low dimensional representation of the data, given some local noisy geometric constraints. In this talk we will show how all (seemingly unrelated) problems listed below can be solved by constructing suitable operators on their data. Those operators are different from the graph Laplacian, and can be regarded as its extension. The solutions involve only the computation of a few eigenvectors of sparse matrices corresponding to the data operators.

    Cryo Electron Microscopy for protein structuring: reconstructing the three-dimensional structure of a molecule from projection images taken at random unknown orientations (unlike classical tomography, where orientations are known).

    NMR spectroscopy for protein structuring: finding the global positioning of all hydrogen atoms in a molecule from their local distances.  Distances between neighboring hydrogen atoms are estimated from the spectral lines corresponding to the short ranged spin-spin interaction.

    Sensor networks: finding the global positioning from local distances.

    Detecting the slow manifold in stochastic chemical reactions:
    finding the slow coordinates in large multi-scaled dynamical systems
    from experimental or simulation data.

    Non linear independent component analysis: de-mixing statistically independent processes that were mixed by an unknown smooth non-linear functions.

    Joint work with Ronald Coifman, Yoel Shkolnisky and Fred Sigworth.
    October 12

    3206 Math Bldg
    note special
    place & time
    Joint Seminar with Mathematics Department.

    Professor Nira Dyn, School of Mathematical Sciences, Tel-Aviv University

    Subdivision Schemes for the Refinement of Geometric Objects

    Subdivision schemes are efficient computational methods for the design,
    representation and approximation of surfaces of arbitrary topology in 3D.
    Subdivision schemes generate curves/surfaces from discrete data by repeated
    refinements. This talk is mainly concerned with ”classical” schemes refining
    control points, and their applications in geometric modeling. The relation of
    subdivision schemes to the construction of wavelets is also discussed. The last part of the talk reviews subdivision schemes refining other objects, such as compact sets and nets of curves. Examples of various schemes are presented
    October 17

    1.00 PM,
    note special time

    4122 CSIC Bldg
    Dr. Istvan Szunyogh, Institute for Physical Science and Technology, University of Maryland

    Development of a Data Assimilation System to Estimate the State of Large Spatio-temporally Chaotic Systems

    This talk is an overview of the research that led to the current algorithmic and code design of the Local Ensemble Transform Kalman Filter (LETKF) data assimilation system. The LETKF estimates the time evolving state of the system based on observations and a numerical model of the system. To the best of our knowledge, the LETKF is the computationally most efficient ensemble-based data assimilation system for large observational data sets. The LETKF has been successfully tested on models of the atmosphere, the oceans and a laboratory system to simulate coupled convective cells. In this talk, we demonstrate the potentials of the LETKF with an implementation on a state-of-the-art numerical model of the atmospheric global circulation. We pay special attention to the role the process of data assimilation plays in the predictability of the system.
    October 24

    2.00 PM,
    4122 CSIC Bldg
    Professor David Jacobs, Computer Science, University of Maryland

    Modeling Lighting to Capture the Variability of Images

    Variations in lighting can have a significant impact on the appearance of an object. Because the set of possible lighting conditions is high-dimensional, it is a challenge to represent this variability in a computationally tractable way. We will discuss three ways of doing this for the problem of determining the lighting that best fits a known, 3D model to a new image. First, we show that we can model the reflection of light by diffuse (non-shiny) objects as a low-pass filter. This implies that the set of images produced by such objects is well represented by a low-dimensional, linear subspace. This is not the case for specular (shiny objects); high frequency components of the lighting significantly affect their appearance. In this case, it is important to also enforce the constraint that lighting is everywhere non-negative, meaning that we must model the set of images of an object as a convex subspace of a higher-dimensional space. Using an extension of Szego’s eigenvalue distribution theorem to spherical harmonics, we show that we can enforce this non-negative lighting constraint using semi-definite programming. Finally, we consider the set of images produced in scenes with cast shadows. We show that these images can be captured when we represent lighting as a combination of a low-dimensional subspace and a sparse subset of the set of all images produced by point sources of light. This provides a compact and computationally tractable representation. We will discuss applications of these results to face recognition, 3D reconstruction, and lighting recovery for computer graphics.

    Collaborators: Ronen Basri, The Weizmann Institute
    Xue Mei, the University of Maryland
    Margarita Osadchy, NEC Labs
    Ravi Ramamoorthi, Columbia University
    Sameer Shirdhonkar, the University of Maryland

    October 31

    2.00 PM,
    4122 CSIC Bldg


    November 7

    2.00 PM,
    4122 CSIC Bldg
    Professor Bala Balachandran, Department of Mechanical Engineering, University of Maryland

    Microsystems: Mechanics and Nonlinear Phenomena

    Analytical, numerical, and experimental efforts carried out to understand nonlinear phenomena exhibited by micro-resonator and micro-resonator arrays will be presented in this talk. The nonlinear phenomena considered include jumps, oscillations about non-flat positions caused by buckling, and intrinsic localized modes. The distributed-parameter systems used to model the oscillators and the weakly nonlinear analysis undertaken to explain buckling influenced oscillations will be discussed. The phenomenon of intrinsic localized modes in coupled oscillator arrays will also be explored, and it is discussed as to how one can take advantage of them for different applications.

    November 14

    2.00 PM,
    4122 CSIC Bldg
    Professor Michelle Girvan, Department of Physics and IPST, University of Maryland

    Finding, Evaluating, and Generating Community Structure in Complex Networks

    will discuss a set of algorithms for discovering community structure in networks— natural divisions of network nodes into densely connected subgroups. These algorithms all share two definitive features: first, they involve iterative removal of edges from the network to split it into communities, the edges removed being identified using one of a number of possible “betweenness” measures, and second, these measures are, crucially, recalculated after each removal. I will also discuss a measure for the strength of the community structure found by the algorithms, which gives an objective metric for choosing the number of communities into which a network should be divided.

    I'll demonstrate that the algorithms are highly effective at discovering community structure in both computer-generated and real-world network data, and show how they can be used to shed light on the sometimes dauntingly complex structure of networked systems. Finally, I will discuss a simple model for the formation of community structure in social networks.
    November 21

    2.00 PM,
    4122 CSIC Bldg
    NO SEMINAR - Thanksgiving Break
    November 28

    2.00 PM,
    4122 CSIC Bldg
    Professor Kenneth Karlsen, Centre of Mathematics for Applications, University of Oslo

    Convergent Numerical Schemes for the Camassa-Holm Equation

    The Korteweg-de Vries (KdV) equation models weakly nonlinear unidirectional long waves, and arises in various physical contexts. For example, it models surface waves of small amplitude and long wavelength on shallow water. The Camassa-Holm equation entered the arena in the early 1990s. In one interpretation, it models the propagation of unidirectional shallow water waves on a flat bottom. The Camassa-Holm equation is a water wave equation of quadratic order in an asymptotic expansion for unidirectional shallow water waves described by the incompressible Euler equations, while the KdV equation appears as first order in this expansion. In another interpretation it describes finite length, small amplitude radial deformation waves in cylindrical compressible hyperelastic rods, and in this context the equation is often referred to as the hyperelastic-rod wave equation. The Camassa-Holm equation possesses many interesting properties, like its bi-Hamiltonian structure and complete integrability. Moreover, it has an infinite number of non-smooth solitary wave solutions called peakons. Related equations are the Hunter-Saxton, variational wave, and Degasperis-Procesi equations.

    From a mathematical analysis point of view, the Camassa-Holm equation is rather well understood. However, much less is known when it comes to the design and analysis of numerical schemes. In particular, it has been rather difficult to construct numerical schemes for which one can prove the convergence to a (non-smooth) solution of the Camassa-Holm equation. This statement is particularly accurate in the case of general H^1 initial data and peakon-antipeakon interactions. In this talk we present finite dfference schemes for the Camassa-Holm equation that can handle general H^1 initial data. The form of the difference schemes are judiciously chosen to ensure that they satisfy a total energy inequality. We prove that the difference schemes converge strongly in H^1 towards a dissipative weak solution of the Camassa-Holm equation. Similar results hold for the Hunter-Saxton, variational wave, and Degasperis-Procesi equations.

    This is joint work with Giuseppe Maria Coclite (Bari) and Nils Henrik Risebro (Oslo).

    December 5

    2.00 PM,
    4122 CSIC Bldg
    Professor Alexander Vladimirsky, Department of Mathematics, Cornell University

    Causality and Efficiency: Non-Iterative Numerical Methods

    Our knowledge of the direction of information flow is fundamental for many efficient numerical methods (e.g., time-marching for evolutionary PDEs). However, for many problems (including first-order static nonlinear PDEs) the direction of information flow might be a priori unknown even if it is otherwise well-defined. This leads to a common use of iterative methods, which can be unnecessarily inefficient.

    For certain systems of nonlinear equations, the "causality" present in the problem can be used to uncover the direction of information flow at runtime. Exploiting causality to effectively de-couple nonlinear systems is the fundamental idea behind Dijkstra's classical method for finding shortest paths on graphs.

    We will use a continuous analogue of this principle to build efficient methods for a wide class of causal problems. We will consider examples in continuous and hybrid optimal control (e.g., optimal traveling on foot and using the buses), in anisotropic front propagation (e.g., first-arrivals and multiple-arrivals in seismic imaging), in optimal control under uncertainty (e.g., optimal traveling when the map is not quite known), in Markov decision processes (e.g., stochastic shortest paths on graphs), and in dynamical systems (e.g., approximation of "geometrically stiff" invariant manifolds).

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