Seminars and Colloquia by Series

Monday, October 4, 2010 - 13:00 , Location: Skiles 002 , Michael Burkhart , Gatech, Math , Organizer: Luca Dieci
The over-abundance of remotely sensed data has resulted inthe realization that we do not have nor could ever acquire asufficient number of highly trained image analysts to parse theavailable data.  Automated techniques are needed to perform low levelfunctions, identifying scenarios of importance from the availabledata, so that analysts may be reserved for higher level interpretativeroles. Data fusion has been an important topic in intelligence sincethe mid-1980s and continues to be a necessary concept in thedevelopment of these automated low-level functions. We propose anapproach to multimodal data fusion to combine images of varyingspatial and spectral resolutions with digital elevation models.Furthermore, our objective is to perform this fusion at the imagefeature level, specifically utilizing Gabor filters because of theirresemblance to the human visual system.
Monday, September 20, 2010 - 13:00 , Location: Skiles 002 , Christopher Rorden , Center for Advanced Brain Imaging (Gatech/GSU) , Organizer: Sung Ha Kang
This talk showcases how we can use emerging methods to understand brainfunction. Many of the techniques described could be optimized usingtechniques being developed by researchers in the GT Mathematicsdepartment. A primary tenet of neuroscience is that the left frontal lobeis crucial for speech production and the posterior regions of the lefthemisphere play a critical role in language comprehension and wordretrieval. However, recent work shows suggests the left frontal lobe mayalso aid in tasks classically associated with posterior regions, such asvisual speech perception. We provide new evidence for this notion based onthe use brain imaging (structural and functional MRI) and brainstimulation techniques (TMS and tDCS) in both healthy individuals andpeople with chronic stroke. Our work takes these theoretical findings andtests them in a clinical setting. Specifically, our recent work suggeststhat stimulation of the frontal cortex may complement speech therapy inchronic stroke. Our recent brain stimulation work using transcranialdirect current stimulation supports this hypothesis, illustrating smallbut statistically significant benefits in anomia following brainstimulation.
Monday, August 23, 2010 - 13:00 , Location: Skiles 002 , Maria Cameron , U Maryland , Organizer:

I will propose two numerical approaches for minimizing the MFF. Approach
I is good for high-dimensional systems and fixed endpoints. It is
based on temperature relaxation strategy and Broyden's method. Approach
II is good for low-dimensional systems and only one fixed endpoint. It
is based on Sethian's Fast Marching Method.I will show the
application of Approaches I and II to the problems of rearrangement of
Lennard-Jones cluster of 38 atoms and of CO escape from the Myoglobin protein
respectively.

At low temperatures, a system evolving according to the overdamped Langevin equation spends most of the time near the potential minima and performs rare transitions between them. A number of methods have been developed to study the most likely transition paths.  I will focus on one of them: the MaxFlux Functional (MFF), introduced by Berkowitz in 1983.I will reintepret the MFF  from the point of view of the Transition Path Theory (W. E & E. V.-E.) and show that the  MaxFlux approximation is equivalent to the Eikonal Approximation of the Backward Kolmogorov Equation for the committor function.
Friday, August 20, 2010 - 13:00 , Location: Skiles 154 , Xiao-Ping Wang , Hong Kong University of Science and Technology , Organizer: Haomin Zhou
In this talk, I will  describe a newly developed phase field model for two phase fluid flow based on Cahn Hilliard  Navier Stokes equation with generalized Navier boundary condition.  Homogenization method is used to derive  the Wenzel's and Cassie's equations for two phase flow on rough surfaces. Efficient numerical method for the model will also be discussed. We then present some numerical results on two phase flow on rough and patterned surfaces.
Monday, April 26, 2010 - 13:00 , Location: Skiles 255 , Elena Kartaschova , Johannes Kepler University , Organizer:
Nonlinear Resonance Analysis (NRA) is a natural next step after Fourieranalysis developed for linear PDEs. The main subject of NRA isevolutionary nonlinear PDEs, possessing resonant solutions. Importance ofNRA is due to its wide application area -- from climatepredictability to cancer diagnostic to breaking of the wing of an aircraft.In my talk I plan to give a brief overview of the methods and resultsavailable in NRA, and illustrate it with some examples from fluid mechanics.In particular, it will be shown how1) to use a general method of q-class decomposition for computing resonantmodes for a variety of physically relevant dispersion functions;2) to construct NR-reduced models for numerical simulations basing on theresonance clustering; theoretical comparision with Galerkin-like models willbe made and illustrated by the results of some numerical simulations withnonlinear PDE.3) to employ NR-reduced models for interpreting of real-life phenomena (inthe Earth`s atmosphere) and results of laboratory experiments with watertanks.A short presentation of the software available in this area will be given.
Monday, April 26, 2010 - 13:00 , Location: Skiles 255 , Luca Dieci , School of Mathematics, Georgia Tech , Organizer:
In this seminar we consider piecewise smooth differential systems of Filippov type, in which the vector field varies discontinuously as solution trajectories reach one or more surfaces. Emphasis is on the fundamental matrix solution associated to these systems. We consider the cases of transversal intersection and of sliding motion on a co-dimension one surface and when sliding motion takes place on a co-dimension two surface (the intersection of two co-dimension one surfaces). [Joint work with L.Lopez, Univ. of Bari]
Monday, April 19, 2010 - 13:00 , Location: Skiles 255 , Jae-Hun Jung , Mathematics, SUNY Buffalo , Organizer: Sung Ha Kang
Solutions of differential equations with singular source terms easily becomenon-smooth or even discontinuous. High order approximations of suchsolutions yield the Gibbs phenomenon. This results in the deterioration ofhigh order accuracy. If the problem is nonlinear and time-dependent it mayalso destroy the stability. In this presentation, we focus on thedevelopment of high order methods to obtain high order accuracy rather thanregularization methods. Regularization yields a good stability condition,but may lose the desired accuracy. We explain how high order collocationmethods can be used to enhance accuracy, for which we will adopt severalmethods including the Green’s function approach and the polynomial chaosmethod. We also present numerical issues associated with the collocationmethods. Numerical results will be presented for some differential equationsincluding the nonlinear sine-Gordon equation and the Zerilli equation.
Monday, April 12, 2010 - 13:00 , Location: Skiles 255 , Samuel Isaacson , Boston University Mathematics Dept. , Organizer:
We will give an overview of our recent work investigating the influence of incorporating cellular substructure into stochastic reaction-diffusion models of gene regulation and expression. Extensions to the reaction-diffusion master equation that incorporate effects due to the chromatin fiber matrix are introduced. These new mathematical models are then used to study the role of nuclear substructure on the motion of individual proteins and mRNAs within nuclei. We show for certain distributions of binding sites that volume exclusion due to chromatin may reduce the time needed for a regulatory protein to locate a binding site.
Monday, April 5, 2010 - 13:00 , Location: Skiles 255 , Jianfeng Cai , Dep. of Math. UCLA , Organizer: Haomin Zhou
 Tight frame is a generalization of orthonormal basis. It  inherits most good properties of orthonormal basis but gains more  robustness to represent signals of intrests due to the redundancy. One can  construct tight frame systems under which signals of interests have sparse  representations. Such tight frames include translation invariant wavelet,  framelet, curvelet, and etc. The sparsity of a signal under tight frame systems has three different formulations, namely, the analysis-based sparsity, the synthesis-based one, and the balanced one between them. In this talk, we discuss Bregman algorithms for finding signals that are sparse under tight frame systems with the above three different formulations. Applications of our algorithms include image inpainting, deblurring, blind deconvolution, and cartoon-texture decomposition. Finally, we apply the linearized Bregman, one of the Bregman algorithms, to solve the problem of matrix completion, where we want to find a low-rank matrix from its incomplete entries. We view the low-rank matrix as a sparse vector under an adaptive linear transformation which depends on its singular vectors. It leads to a singular value thresholding (SVT) algorithm.
Friday, April 2, 2010 - 13:00 , Location: Skiles 269 , Sookkyung Lim , Department of Mathematical Sciences, University of Cincinnati , Organizer: Sung Ha Kang
We investigate the effects of electrostatic and steric repulsion on thedynamics of pre-twisted charged elastic rod, representing a DNA molecule,immersed in a viscous incompressible fluid. Equations of motion of the rod, whichinclude the fluid-structure interaction, rod elasticity, and electrostatic interaction, are solved by the generalized immersed boundary method. Electrostatic interaction is treated using a modified Debye-Huckel repulsive force in which the electrostatic force depends on the salt concentration and the distance between base pairs, and a close range steric repulsion force to prevent self-penetration. After perturbation a pretwisted DNA circle collapses into a compact supercoiled configuration.  The collapse proceeds along a complex trajectory that may pass near several equilibrium configurations of saddle type, before it settles in a locally stable equilibrium. We find that both the final configuration and the transition path are sensitive to the initial excess link, ionic stregth of the solvent, and the initial perturbation.

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