**COLLOQUIA 2013 -- 2014**

Refreshments are served in Parker Hall, Room 244, beginning at 3:30.

**Friday, April 11, 2014**

Speaker: Dr. Weixing Song, Kansas State University

Title: Simulation Extrapolation Estimation in Parametric Models with Laplace Measurement Error

Abstract: The N-SIMEX procedure proposed by Cook and Stefanski (1994) provides an easy-to-implement simulation-based method to remove or reduce the bias in parametric models with normal measurement error. In N-SIMEX, the estimates are obtained by first adding an additional normal measurement error to the contaminated data in a resampling stage, where the variability of the normal measurement error is controlled by the scale parameter; then some naive-like estimates are constructed based on the noise-enhanced data set, and a trend of measurement error-induced bias versus the variance of the added normal measurement error is established; finally, the trend is extrapolated back to the case of no measurement error case. As Cook and Stefanski (1994) described, the N-SIMEX procedure "... is completely general, it is also useful in applications when the particular model under consideration is novel and conventional approaches to estimation with the model have not been thoroughly studied and ! developed." In some simple cases, the N-SIMEX procedure does remove the bias completely, but in some other cases, in particular, if the true extrapolation function is not available, it only provides approximate solutions. Nevertheless, the N-SIMEX procedure certainly provides us a very useful exploratory tool for the model fitting in the measurement error context. In this talk, we will show that the N-SIMEX procedure only works for the normal measurement error and does not work for Laplace measurement error. A new L-SIMEX procedure is particularly designed to remove or reduce the Laplace measurement errors in parametric models. Different from the N-SIMEX, the proposed procedure will remove or reduce the Laplace measurement error by adding a noise variable which is a difference between the two independent gamma random variables, and where the noise level is governed by the shape parameter. Heuristic and rigorous arguments are provided to justify the proposed method and a Jackknife-type estimation procedure is provided to estimate the variance of the L-SIMEX estimate. Simulation studies and a real data example are presented to demonstrate the estimation procedures.

Faculty host: Xiaoyu Li

**Friday, April 18, 2014**

**Colloquium honoring Steve Stuckwisch on his retirement**

Speakers: Colleagues and friends of Steve

No dinner activity is organized because of Good Friday, per Steve’s request.

**Friday, April 25, 2014**

**Colloquium honoring Gary Gruenhage and Phil Zenor on their retirement**

Speaker: David Lutzer, College of William and Mary

Title: Baire space products, completeness, and Cp(X)

Abstract: Click here

**COMING** 2014 - 2015

September 5, 2014

Speaker: Jim Gleason, Department of Mathematics, University of Alabama, Tuscaloosa

Title: TBA

Faculty host: T.-Y. Tam

September 19, 2014

Speaker: Dr. Habib Najm, Sandia National Laboratories, Livermore, California

Title: TBA

Faculty host: Xiaoying Han

September 26, 2014

Speaker: Tomas Caraballo, University of Seville, Spain

Title: TBA

Faculty host: Georg Hetzer

November 7, 2014

Speaker: Dr. Kumer Pial Das ('05), Associate Professor of Mathematics at Lamar University, Beaumont, Texas

Dr. Das is one of three people from the U.S. and Canada to receive the 2013 Mathematical Association (MAA) of America's Henry L. Alder Award for Distinguished Teaching by a beginning College or University Mathematics faculty member.

Title: TBA

Faculty host: T.-Y. Tam

**Combined Colloquium and Stochastics Seminar TIME: 2:00 with refreshments at 1:30 in 244**

**Friday, April 4, 2014**

Speaker: Dr. Wenxuan Zhong, University of Georgia

Faculty host: Peng Zeng

**Friday, March 28, 2014 PLEASE NOTE: Colloquium will be held in ROOM 249**

Speaker: Richard A. Brualdi, UWF Beckwith Bascom Professor of Mathematics (emeritus) University of Wisconsin - Madison,

Editor-in-Chief of Linear Algebra and Its Applications,

Editor-in-Chief of the Electronic Journal of Combinatorics

Title: Permutations, X-rays, Tournaments, Partial Latin Squares, Transversals, and Skolem Sequences

Abstract: The title tells all. In this talk I will discuss some connections between these combinatorial notions.

Faculty hosts: Huajun Huang and Tin-Yau Tam

**Wednesday, March 26, 2014 PLEASE NOTE DAY (ROOM NUMBER 236) **

Speaker: Dongsheng Wu, University of Alabama Huntsville

Title: Regularity of Local Times of Gaussian Random Fields

Abstract available here

Faculty host: Erkan Nane

**Friday, March 21, 2014**

Speaker: Prof. Kui Ren, University of Texas at Austin

Title: Recent Developments in Quantitative Photoacoustic Imaging

Abstract: Quantitative photoacoustic imaging (QPAT) is a hybrid imaging technique that couples, through photoacoustic effect, the high-resolution ultrasound imaging with the high-contrast optical imaging techniques to achieve high resolution and high contrast in imaging applications. Image reconstruction problems in quantitative photoacoustic imaging can be formulated as inverse problems to certain partial differential equations. I will attempt to give an overview of some recent developments in the mathematical and computational aspects of QPAT.

Faculty host: Yanzhao Cao

**Thursday, March 20, 2014 Please note DAY/DATE**

Speaker: Jan Boronski, National Supercomputing Center IT4Innovations Institute for Research and Applications of Fuzzy Modeling - Ostrava, Czech Republic

Title: On Birkhoff Attractors and Rotational Chaos

Abstract: An attractor in the 2-torus (or in an annulus) is called strange if it admits two orbits with distinct rotation vectors. The associated dynamics is then referred to as rotational chaos. Strange attractors were discovered by George D. Birkhoff in 1932 for dissipative maps with a twist, and then studied by P. Le Calvez, M. Casdagli, and others. It was an open question in rotation theory if there exist strange attractors other than those described by Birkhoff. I shall present a method of constructing new examples of strange attractors, and will show that R.H. Bing's pseudocircle is one such example, admitting rotational chaos. This is joint work with P. Oprocha (Institute of Mathematics, Polish Academy of Sciences).

Faculty host: Krystyna Kuperberg

**Friday, March 7, 2014**

Speaker: Dr. Zhongshan Li, Math Graduate Director, Georgia State University

Title: Minimum ranks of sign pattern matrices via sign vectors and duality

Abstract available here

Faculty host: Tin-Yau Tam

**Friday, February 28, 2014**

Speaker: Zhigen Zhao, Temple University

Title: Optimal Multiple Testing Methods

Abstract: When testing a large amount of hypotheses simultaneously, it is not only important to control a certain rate of type I error such as (marginal) False Discovery Rate (FDR/mFDR), but it is also important to minimize a certain rate of type II error, such as (marginal) False Non-discovery Rate (FNR/mFNR). We call a testing method optimal if it minimizes the mFNR among all the testing method which controls the mFDR at a designated level . When considering the two-group models, we will give a general approach in deriving the optimal testing method. We will further study the advantage and drawback of this method. This talk is based on the joint work with Li He, Sanat K. Sarkar, and Jiashun Jin.

Faculty host: Xiaoyu Li

**Friday, February 21, 2014**

Speaker: J. M. Landsberg, Texas A & M

Title: Title: Tensor decomposition, geometry, and matrix multiplication

Abstract: I will explain several uses of geometric methods in the study of problems originating in computer science, numerical analysis, and signal processing regarding tensors. Applications will be given to the matrix multiplication tensor, where computer scientists have made the astounding conjecture that as n goes to infinity, it becomes essentially just as easy to matrix multiply two n by n matrices together as it is to add them.

Faculty host: Luke Oeding

**Friday, February 7, 2014**

Speaker: Dr. Yichuan Zhao, Georgia State University, Atlanta

Title:Smoothed jackknife empirical likelihood inference for ROC curves with missing data

Abstract: In this paper, we apply smoothed jackknife empirical likelihood (JEL) method to construct confidence intervals for the receiver operating characteristic (ROC) curve with missing data. After using hot deck imputation, we generate pseudo-jackknife sample to develop jackknife empirical likelihood. Comparing to traditional empirical likelihood method, the smoothed JEL has a great advantage in saving computational cost. Under mild conditions, the smoothed jackknife empirical likelihood ratio converges to a scaled chi-square distribution. Furthermore, simulation studies in terms of coverage probability and average length of confidence intervals demonstrate this proposed method has the good performance in small sample sizes. A real data set is used to illustrate our proposed JEL method. This is joint work with Dr. Hanfang Yang.

Faculty host: Ash Abebe

**Friday, January 17, 2014**

Speaker: Ke Ye, L.E. Dickson Instructor, University of Chicago

Title: Matrix decompositions

PDF version available here

Abstract: Perhaps the most obvious motivation for the study of matrix decompositions is that one can use these decompositions to solve linear systems quickly. LU decomposition and QR decomposition are classical examples of matrix decompositions. We will discuss matrix decompositions for many other interesting matrices. For example, we will see that every matrix can be decomposed as the product of Toeplitz matrices and this result indicates that one has the hope to find a fast algorithm to solve linear systems. Tools we use are from algebraic geometry and algebraic group theory. (I will not assume audiences have backgrounds in algebraic geometry so I will review some basic facts first.)

Faculty host: Luke Oeding

**Friday, November 15, 2013**

Speaker: Udayan(Dario) Darji, Department of Mathematics, University of Louisville

Title: Dynamics on the Cantor space

For abstract, click here

Faculty host: Jack Brown and Gary Gruenhage

**Thursday, November 14, 2013**

(Refreshments to be served at the customary time: 3:30 - 4:00)

from 2:30 to 3:30 ROOM 236

Speaker: Alejandro Illanes, Universidad Nacional Autónoma de México and Department of Mathematics, Texas Tech University

Title: Models for hyperspaces

For abstract, click here

from 4:00 to 5:00 ROOM 250

Speaker: Verónica Martínez de la Vega, Universidad Nacional Autónoma de México and Department of Mathematics, Tulane University

Title: Dendroids: Examples, Results and Problems

For abstract, click here

Faculty host: Piotr Minc

**Friday, November 8, 2013**

Speaker: Dr. Lily Wang, University of Georgia

Title: Estimation and Variable Selection for Single-Index Prediction Models with Diverging Number of Index Parameters

Abstract: Single-index models are useful and fundamental tools for handling “curse of dimensionality” problems in nonparametric regression. Along with that, variable selection also plays an important role in such model building process when the index vectors are high-dimensional. Several procedures have been developed for estimation and variable selection for single-index models when the number of index parameters is fixed. In many high-dimensional model selection problems, the number of parameters is increasing along with the sample size. In this work, we consider weakly dependent data and propose a class of variable selection procedures for single-index prediction models, which are robust against model misspecifications. We apply polynomial spline basis function expansion and smoothly clipped absolute deviation penalty to perform estimation and variable selection in the framework of a diverging number of index parameters. Under stationary and strong mixing conditions, the proposed variable selection method is shown to have the “oracle” property when the number of index parameters tends to infinity as the sample size increases. A fast and efficient iterative algorithm is developed to estimate parameters and select significant variables simultaneously. The finite sample behavior of the proposed method is evaluated with simulation studies and illustrated by the river flow data of Iceland.

Faculty host: Guanqun Cao

**Friday, November 1, 2013**

Speaker: Xiaobing H. Feng, Department of Mathematics, University of Tennessee, Knoxville

Title: Numerical Differential Calculus: A New Paradigm for Developing Numerical Methods for PDEs

Abstract: In this talk I shall first present a newly developed (discontinuous Galerkin finite element) numerical differential calculus theory for approximating weak (or distributional) derivatives of broken Sobolev functions. Various properties and calculus rules (such as product and chain rules, integration by parts formula and divergence theorem) for the proposed numerical derivatives will be discussed. I shall then discuss how this numerical differential calculus framework can be conveniently used to systematically construct numerical methods for various linear and nonlinear (including fully nonlinear) PDEs and how these new numerical methods are related to the existing numerical PDE methods. The material of this talk is based on a joint work with Michael Neilan of University of Pittsburgh and Tom Lewis of the University of North Carolina at Greensboro.

Faculty host: Yanzhao Cao

**Friday, October 25, 2013**

Speaker: Zoltan Furedi, Alfred Renyi Institute of Mathematics, Hungarian Academy of Sciences, Budapest and Emory University, Atlanta

Title: Superimposed Codes

For abstract, click here

Faculty host: Andras Bezdek

**Friday, October 18, 2013** (Refreshments for both speakers at 3:30)

NOTE TIME: 2:30

Speaker: Tomas Caraballo, University of Sevilla

Title: Effects of noise on the asymptotic behavior of dynamical systems

Abstract: The aim of this talk is to present some features concerning the effects of noise on the asymptotic behavior of dynamical systems. It is well-known now the stabilizing and destabilizing effects which the appearance of different kinds of noise (e.g. Ito or Stratonovich) may have on the stationary solutions (equilibria) of deterministic dynamical systems. Now we will report some results on the appearance of exponentially stable stationary (in the stochastic sense) solutions when some noise is added to the model, as well as, the analysis of the existence of random attractor when the deterministic model is not known to have (or does not have) a global attractor. These results will show some kind of stabilization on global attractors instead of only on equilibria.

Faculty host: Xiaoying Han

**Friday, October 18, 2013 (Regular Time)**

Speaker: Ping Ma, (UIUC, will move to UGA)

Title: Leveraging in Big Data Regression

Abstract: Advances in science and technology in the past a few decades have led to big data challenges across a variety of fields. Extraction of useful information and knowledge from big data has become a daunting challenge to both the science community and entire society. To tackle this challenge requires major breakthroughs in efficient computational and statistical approaches to big data analysis.

In this talk, I will present some leveraging algorithms, which make a key contribution to resolving the grand challenge. In these algorithms, by sampling a very small representative sub-dataset using smart algorithms, one can effectively extract relevant information of vast data sets from the small sub-dataset. Such algorithms are scalable to big data. These efforts allow pervasive access to big data analytics especially for those who cannot directly use supercomputers. More importantly, these algorithms enable massive ordinary users to analyze big data using tablet computers.

Faculty host: Peng Zeng

**Friday, August 30, 2013**

Speaker: Professor Wacław Marzantowicz, Adam Mickiewicz University, Poznań, Poland

Vice President of the Polish Mathematical Society

Title: Bourgin-Yang version of the Borsuk-Ulam theorem

Abstract: Click here

Faculty host: Wlodzimierz Kuperberg

**2014 - 2015**

**September 19, 2014**

**RESERVED**