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)
Modeling the influence of social interactions and
disease-related mortality during epidemics in small
communities: an agent-based approach
Dr. Lisa Sattenspiel [University of Missouri, Columbia]
When populations are very small, it is difficult to design and analyze appropriate mathematical models to address important questions about the spread of disease at the population level. One relatively new approach to this problem is to develop agent-based computer simulation models that can incorporate the most essential characteristics of the population as well as the stochasticity that is an essential feature in small populations. This talk describes the structure of an agent-based model designed to study the spread of the 1918-19 influenza pandemic in a fishing community in the Canadian province of Newfoundland and Labrador. Selected results from sensitivity analyses of the model are presented, including how different assumptions about the nature of social mixing, aggregation of the population during events such as church services, or social characteristics of the initial case may influence epidemic patterns.
Friday, Feb. 7
A plea for adaptive data analysis
Dr. Norden E. Huang [National Central University, Zhongli, Taiwan]
Data analysis is indispensable to every scientific endeavor. The existing data analysis methods are all developed by mathematicians based on their rigorous rules. In pursue of the rigor, we are forced to make idealized assumptions and live in a pseudo-real linear and stationary world, in which data analysis is relegated to data processing. But the world we live in is neither stationary nor linear. As scientific research getting increasingly sophistic, the inadequacy of mere processing data becomes glaringly obvious. In fact, the frequency defined from the traditional Fourier analysis can be proved to lack mathematical and physical meanings. To get the truth containing in the data, we have to break away from these limitations; we should let data speak for themselves so that the results could reveal the full range of consequences of nonlinearity and nonstationarity. To do so, we need new paradigm of data analysis methodology without a priori basis to fully accommodating the variations of the underlying driving mechanisms. The solution lies in adaptive data analysis approach. One example is the Empirical Mode Decomposition method and the associated extensions of timefrequency representation. We will show that, with the adaptive method, we can also determine trend objectively. In fact, we can only define true frequency with adaptive method, which would lead to quantify nonstationarity and nonlinearity. Examples from classic nonlinear system and recent climate change data will be used to illustrate the prowess of the new approach.
Friday, Feb. 14
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.
Friday, Feb. 21
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.
Friday, Feb. 28
A New Semiparametric Quantile Panel Data Model with Estimating the Growth Effect of FDI
Dr. Zongwu Cai [Department of Economics, University of Kansas]
In this paper, we propose a new semiparametric quantile panel data model with correlated random effects in which some of the coefficients are allowed to depend on some smooth economic variables while other coefficients remain constant. A three stage estimation procedure is proposed to estimate both constant and functional coefficients and their asymptotic properties are investigated. We show that the estimator of constant coefficients is root-N consistent and the estimator of varying coefficients converges in a nonparametric rate. A Monte Carlo simulation is conducted to examine the finite sample performance of the proposed estimators. Finally, the proposed semiparametric quantile panel data model is applied to estimating the impact of foreign direct investment (FDI) on economic growth using the cross-country data from 1970 to 1999. This is a join work with Linna Chen and Ying Fang.
Friday, March 7
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.
Friday, March 14
A Numerical Method for Calculating Minimum Distance to Near Earth Objects
Dr. Rhee [UMKC]
In the Calculus book written by Anton, Bivens
and Davis there is a
project called “Comet Collision.” They began their project as follows: “The
Earth lives in a cosmic gallery of comets and asteroids. Although the
probability that the Earth will be hit by a comet or asteroid in any given year
is small, the consequences of such a collision are so catastrophic that the
international community is now beginning to track near Earth objects.” In
this talk we discuss the problem of calculating minimum distance between
the Earth and a coplanar comet or asteroid.
Friday, April 4
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.