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Departmental ColloquiaFall 2009 & Spring 2010 |
September 11, 2009
Dr. Elmas Irmak, Bowling Green State University
Title : Superinjective Simplicial Maps of the Complexes of Curves on Nonorientable Surfaces
Abstract : We prove that each superinjective simplicial map of the complex of curves of a compact, connected, nonorientable surface is induced by a homeomorphism of the surface, if $g + n \leq 3$ or $g + n \geq 5$, where $g$ is the genus of the surface and $n$ is the number of the boundary components.
September 18, 2009
Dr. Yao Lu, University of Michigan at Ann Arbor
Title : Integral Equation Models for Image Restoration: High Accuracy Methods and Fast Algorithms
Abstract : Discrete models are consistently used as practical models for image restoration. They are piecewise constant approximations of the true physical (continuous) model, and hence, inevitably impose bottleneck model errors. We propose to work directly with the continuous model for image restoration aiming at suppressing the model errors caused by the discrete models. A systematic study is introduced in this talk for the continuous out-of-focus image models which can be formulated as an integral equation of the first kind. The resulting integral equation is regularized by the Lavrentiev method and the Tikhonov method. We develop fast multiscale algorithms having high accuracy to solve the regularized integral equations of the second kind. Numerical experiments show that the methods based on the continuous model perform much better than those based on discrete models, in terms of PSNR values and visual quality of the reconstructed images.
September 25, 2009
Dr. Nan Bin, University of Michigan at Ann Arbor
Title : Semiparametric Accelerated Failure Time Model with Missing Data
Abstract : We consider a class of doubly weighted rank based estimating methods for the transformation (or accelerated failure time) model with missing data as arise, for example, in case-cohort studies. The weights considered may not be predictable as required in a martingale stochastic process formulation. We treat the general problem as a semiparametric estimating equation problem and show asymptotic properties for the weighted estimators, with either true weights or estimated weights, by using empirical process theory where martingale theory may fail. Simulations show that the outcome-dependent weighted method works well for finite samples in case-cohort studies and improves efficiency compared to methods based on predictable weights. Further, it is seen that the method is even more efficient when estimated weights are used, as is commonly the case in the missing data literature. The Gehan censored data Wilcoxon weights are found to be surprisingly efficient in a wide class of problems.
October 02, 2009
Dr. Mark lewis, Kent State University
Title : Some graphs associated with the character degrees of finite groups
Abstract : We will show how to associate graphs with the set of character degrees of a finite group. Two obvious questions to ask are (1) what graphs arise this way and (2) if the graph $\Gamma$ is associated to the group $G$, what can be said about the structure of $G$? We will survey the known results and open questions regarding these questions. We will also show how these graphs can be applied to other results regarding character degrees.
October 09, 2009
Dr. Nan Lin, Washington University at St. Louis
Title : An information criterion for order-restricted inference and its application to clustering short time-course microarray data
Abstract : Techniques of statistical inference under order restrictions have been successfully used in many areas in statistics. We consider the problem of selecting an order restriction profile out of a set of candidate profiles. Existing information criteria can only be used with simple ordering, such as monotone increasing or decreasing profiles. We developed a new information criterion for order-resticted inference applicable to general order restrictions, and showed its consistency in selecting the correct order restriction profile. This new information criterion is also successfully applied to clustering short time-course microarray data. We first define candiate gene clusters using the order restriction profile over the mean expression across time. A gene is then assigned to the best matched profile/cluster determined by our new information criterion. Compared to other existing clustering algorithms for short time-course microarray data, the information criterion-based clustering provides competitive clustering accuracy and is computationally more efficient.
October 16, 2009
Dr. Rohit Deo, New York University
Title : The Restricted Likelihood (REML) in Econometrics: Estimation and Likelihood based Inference in Autoregressive Models, Predictive Regressions, Dynamic Panel Data and Co-integrated Sytems
Abstract :We will discuss the various applications of the Restricted Likelihood (REML) in Econometrics, covering univariate and vector autoregressive models, predictive regressions and dynamic panel data. The Restricted Likelihood is found to yield not only point estimates with significantly reduced bias in such models, but also likelihood ratio tests with excellent finite sample properties due to its small curvature. For example, in AR(1) models the Restricted Likelihood Ratio Tests is second order pivotal for the asymptotic chi-square distribution. Least squares approximations to the Restricted Likelihood estimates will be presented with the accompanying theory.
October 23, 2009
Dr. Maria Isabel Garrido, Universidad Complutense de Madrid, Spain.
Title : Lipschitz-type functions on metric space
Abstract :We present an analogue to the Banach-Stone theorem in the context of Lipschitz functions. Namely, we show that the unital vector lattice structure of the space Lip(X) of all real Lipschitz functions on a complete metric space X, characterizes the Lipschitz structure of X. In order to find metric spaces X for which the algebra Lip*(X), of bounded Lipschitz functions X, also determines its Lipschitz structure, we introduce the class of "small-determined" spaces. We show that this class includes precompact and quasi-convex metric spaces. We obtain several metric characterizations of this property, as well as some other characterizations given in terms of the uniform approximation and the extension of uniformly continuous functions. In particular we show that X is small-determined if and only if every uniformly continuous real function on X can be uniformly approximated by Lipschitz functions.
October 30, 2009
Dr. Lili Zhao, University of Michigan at Ann Arbor
Title :Bayesian Hierarchical Changepoint Methods in Modeling the Tumor Growth Profiles in Xenograft Experiments
Abstract : In tumor xenograft experiments, the mice are grafted with cancer cells and then are treated and monitored for changes in tumor growth. The primary goal is to compare antitumor activities between treatments. We propose a Bayesian hierarchical changepoint method to model the growth profiles. Each tumor growth profile follows a simple, “broken stick” changepoint model, with random tumor-specific parameters, including the changepoint. Informative missing data are efficiently incorporated in the model as well. Clinical meaningful estimates will be obtained from the model, including tumor growth delay and growth rate. Estimations are implemented via Markov chain Monte Carlo methods in the WinBUGS software, and 90% high density probability intervals were calculated to compare different treatments. A real xenograft study on a novel targeted agent, AZD7762, combined with gemcitabine and radiation in pancreatic cancer is analyzed by the proposed method.
November 6, 2009
Dr. Feng Shui, McMaster University
Title : Asymptotic Behavior of Poisson-Dirichlet Distribution
Abstract : Poisson-Dirichlet distribution, introduced by Kingman in 1975, is a probability defined the infinite dimensional simplex. It arises in many areas including Bayesian statistics, combinatorics, ecology, economics, physics, random number theory, and population genetics. In this talk, we will give three constructions of the distribution. Asymptotic behavior such as law of large numbers, fluctuation theorems, and large deviations will be discussed for the distribution and its random samples.
November 13, 2009
Dr. Steve Vardeman, Iowa State University
Title : Some New Modeling and (Mostly Bayes) Inference for 3-D Orientations/Rotations
Abstract: We summarize some recent joint work with Melissa Bingham (UW La Crosse) and Dan Nordman (Iowa State) on modeling and inference for data that are 3-D orientations. We identify a tractable class of families of symmetric distributions on orientations that (importantly) have interpretable parameterizations. The class includes the well-known symmetric Matrix Fisher von Mises distributions and most other symmetric distributions in the current literature, and many others besides. Bayes methods for the one-sample model involving these distributions are easy to implement, and non-informative priors produce inferences with frequentist properties matching the posterior probability levels used to define the methods. In regular sub-classes of these models, credible set size is comparable to (to slightly better than) set size produced by inversion of likelihood ratio tests. In non-regular cases, set size can be not only strikingly better than set size produced using a sensible quasi-likelihood, but can decrease with sample size at a (perhaps unexpected) super-efficient rate. A virtue of the modeling and MCMC-based Bayes analysis is that it has obvious extensions to a variety of more complicated contexts beyond the simple one-sample situation. We will discuss a one-way random effects model and analysis for orientation data, and note that extensions to problems like clustering, regression, and time series with model components in our class of distributions are clearly possible. We close with some comments about potential extensions of the modeling and inference to non-symmetric cases and to problems where orientations are only partially distinguishable.
November 20, 2009
Dr. Xiaoping Shen, Ohio University
Title : The Solution of Energy Concentration Problem and Associated Wavelet Systems
Abstract : In the context of harmonic analysis, the uncertainty principle implies that a nonzero signal cannot possess finite duration in time domain and finite bandwidth in frequency domain simultaneously. However, among all possible functions with a given finite bandwidth, one can ask which function maximizes the energy over the prescribed time interval. Prolate spheroidal wave functions (PSWFs) are special functions that lead to the optimal solutions of this energy concentration problem. In this talk, we will recall the energy concentration problem and then focus on the construction of wavelet-like systems associated with PSWFs. The new system retains not only multiscale structure of wavelets but also preserve the high energy concentration property inherited from PSWFs.
December 4, 2009
Dr. Steve Gagola, Kent State University
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January 15, 2010
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January 22, 2010
Dr. Maosheng Xiong, The Pennsylvania State University
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January 29, 2010
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February 5, 2010
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February 12, 2010
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February 19, 2010
Dr. Tong Li, Iowa State University
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February 26, 2010
Dr. Jiquan Chen, University of Toledo
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March 19, 2010
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March 26, 2010
Professor Subal Kumbhakar, SUNY at Binghamton
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April 2, 2010
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April 9, 2010
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April 16, 2010
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April 23, 2010
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April 30, 2010
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