Department of Mathematics and Statistics

Graduate Seminar Series — Spring 2014

Location: Haag Hall, room 312 (Unless otherwise noted)
Day & Time: Fridays, 3:00-4:00 pm
(Unless otherwise noted)

Campus Map for Talks (PDF Format)

Organizer: Dr. Naveen Vaidya , (816) 235-2847

Previous Semesters 

Dates, Titles, Speakers (with Abstracts as available)

Spring 2014

Anisotropic Mesh Adaptation in Image Representation and Scaling

Dr.  Xianping Li [UMKC]

Triangular mesh has gained much interest in image representation and has been widely used in image processing. Currently available content-based adaptive sampling methods are lack of clear mathematic framework. This paper introduces a particular anisotropic mesh adaptation (AMA) method for triangular meshes, which has been successfully applied in solving partial differential equations, to image representation and image scaling. The AMA method is based on metricspecified mesh adaptation and finite element interpolation for Delaunay triangles. An initial triangular mesh is generated using the amount of sample points that is much less than the original image points. Then the mesh is adapted based on a computed metric tensor that controls the size, shape and orientation of the triangles in the mesh. Finally, the image is reconstructed from the mesh using finite element interpolation. This AMA method has clear mathematical framework and can improve computational efficiency and accuracy.


Dr. Xiaoming He [Missouri University of Science and Technology]

Multi-physics domain decomposition methods for Stokes-Darcy model

The Stokes-Darcy model arises in many interesting real world applications, including groundwater flows in karst aquifers, interaction between surface and subsurface flows, industrial filtrations, oil reservoir in vuggy porous medium, and so on. This model describes the free flow of a liquid by the Stokes or Navier-Stokes equation and the confined flow in a porous media by the Darcy equation; the two flows are coupled through interface conditions. For the problems mentioned, the resulting coupled Stokes-Darcy model has higher fidelity than either the Darcy or Stokes systems on their own. However, coupling the two constituent models leads to a very complex system.

This presentation discusses multi-physics domain decomposition methods for solving the coupled Stokes-Darcy system. Robin boundary conditions based on the physical interface conditions are utilized to decouple the Stokes and Darcy parts of the system. A parallel iterative domain decomposition method is first constructed for the steady state Stokes-Darcy model with the Beavers-Joseph interface condition. Then two parallel non-iterative domain decomposition methods are proposed for the time-dependent Stokes-Darcy model with the Beavers-Joseph-Saffman interface condition. Numerical examples are presented to illustrate the features of these methods and verify the theoretical results.


Borrowing information across genes and experiments for improved error variance estimation in microarray data analysis

Dr. Tieming Ji [University of Missouri - Columbia]

Statistical inference for microarray experiments usually involves the estimation of error variance for each gene. Because the sample size available for each gene is
often low, the usual unbiased estimator of the error variance can be unreliable.
Shrinkage methods, including empirical Bayes approaches that borrow information across genes to produce more stable estimates, have been developed in recent years. Because the same microarray platform is often used for at least several experiments to study similar biological systems, there is an opportunity to improve variance estimation further by borrowing information not only across genes but also across experiments. We propose a lognormal model for error variances that involves random gene effects and random experiment effects. Based on the model, we develop an empirical Bayes estimator of the error variance for each combination of gene and experiment and call this estimator BAGE because information is Borrowed Across Genes and Experiments. A permutation strategy is used to make inference about the differential expression status of each gene. Simulation studies with data generated from different probability models and real microarray data show that our method outperforms existing approaches. A similar idea can also be adopted for analyzing RNA sequencing experiment data, which is an on-going research.

Boris Rubinstein, Stowers Institute for Medical Research

Mathematical model of cell polarization

Cell polarization is critical stage in cell cycle preceding the cell division and the understanding of its mechanism is important for the analysis of many morphological processes. We consider a minimalistic mass-conserved model in which the polarization emerges as the result of symmetry breaking of the nonpolarized state. We discuss the general approach to the description of the Turing instability and apply its results to a specific model of polarization in budding yeast cells. The predictions of the model were tested against the experiment showing a qualitative correspondence to the observed behavior.

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