Colloquiums 2009- 2010
Please see the Colloquium Calendar for more information
DATE: Friday, February 5, 2010
TIME: : 2:00--3:00 pm.
LOCATION: Paul Erdos Room, 796 COE
Speaker: Dr. Vladimir Belykh, University of Nizhny Novgorod
Title: "Controlled oscillations of Huygens-type pendula"
Abstract: In this lecture, we will discuss the problem of controlled cooperative motion of two pendula hanging from a common support. This problem is directly related to the experiment carried out by C. Huygens in 1665. We use a system of two Van der Pol-Duffing oscillators with speeding up coupling as an appropriate model for the Huygens experiment. We examine the main regimes of the cooperative motion and their multistability. In particular, we reveal the co-existence of phase-locked chaotic modes, corresponding to the chaotic motion of the Huygens pendula.
Hosts: Vladimir Bondarenko and Andrey Shilnikov
DATE: Friday, January 22, 2009
TIME: : 2:00--3:00 pm.
LOCATION: Paul Erdos Room, 796 COE
Speaker: Dr. Arkadii Arinstein, Technion – Israel Institute of Technology.
Title: "Longitudinal oscillations and flights of the string pendulum driven by a periodic force"
Abstract: The longitudinal oscillations of a string pendulum are discussed. The regime in which the oscillating bob executes free flight under gravity is studied. This regime arises if, during the motion in the upward direction, the bob reaches a height at which no elastic force acts on the bob, and its further motion occurs only under gravity. Thus, the string pendulum executes a motion of two types: the harmonic oscillations under the action of elastic force, and free flights under gravity. In doing so, the height of flights can considerably exceed the amplitude of the forced oscillations, i.e. noticeable amplitude amplification in the longitudinal oscillations of a string pendulum takes place. A novel mechanism of a resonance phenomenon related to the excitation of free oscillations is described. These free oscillations arising after each bob flight are the channel for energy pumping into the system in question. It turns out that the frequency of the above resonance is equal to the fundamental frequency of the string; and the resonance amplitude of the flights is proportional to the square of amplitude of regular forced oscillations.
Hosts: Alexandra Smirnova and Mark Grinshpon.
DATE: Friday, December 11, 2009
TIME: : 2:00--3:00 pm.
LOCATION: Paul Erdos Room, 796 COE
Speaker: Grant Zhang, Department of Mathematical Sciences, University of Alabama in Huntsville
Title: "Edge Partitions of Graphs by Trees"
Abstract: PDF
Host: G. Chen
DATE: Friday, December 4, 2009
TIME: : 11:00--12::00 pm. Note the unusual time!
LOCATION: Paul Erdos Room, 796 COE
Speaker: Carlos D'Andrea, University of Barcelona
Title: "Effective Hilbert's Nullstellensatz"
Abstract: Hilbert Nullstellensatz is a cornerstone of Algebraic Geometry and Commutative Algebra. As for many central results in these areas, it is an existential noneffective statement. The estimation of both the degree and the height of polynomials involved in the Nullstellensatz became an important and widely considered question in the last century. Effective versions of Hilbert Nullstellensatz apply to a wide range of situations in Number Theory and Theoretical Computer Science. In this talk, we will survey the history of this problem and show the sharpest results obtained so far.
Host: F. Enescu
DATE: Tuesday, December 1, 2009
TIME: 2:30--3:30 pm.
LOCATION: Paul Erdos Room, 796 COE
Speaker: Genghua Fan, Center for Discrete Mathematics, Fuzhou University, China
Title: "Covering Graphs by Paths and Circuits"
Abstract: A graph G is covered by a set of its subgraphs if each edge of G is contained in at least one of the subgraphs. In this talk, we consider the case where the subgraphs are paths and circuits.
DATE: Firday, November 20, 2009
TIME: 2:00--3:00 pm.
LOCATION: Paul Erdos Room, 796 COE
Speaker: Lijian Yang Department of Statistics and Probability Michigan State University
Title: "Simultaneous Confidence Band for Sparse Longitudinal Regression"
Abstract: Recently functional data analysis has received considerable attention in statistics research and a number of successful applications have been reported, but there have been no results on the inference of the global shape of the mean regression curve. In this paper, asymptotically simultaneous confidence band is obtained for the mean trajectory curve based on sparse longitudinal data, using piecewise constant spline estimation. Simulation experiments corroborate the asymptotic theory.
Host: Yichuan Zhao
DATE: Friday, November 13, 2009
TIME: 2:00--3:00 pm.
LOCATION: Paul Erdos Room, 796 COE
Speaker: Junhui Wang, Department of Mathematics, Statistics,
and Computer Science, University of Illinois at Chicago
Title: "On Margin Based Semisupervised Learning"
Abstract: In classiffication, semi-supervised learning occurs when a large amount of unlabeled data is available with only a small number of labeled data. This imposes a great challenge in that it is di±cult to achieve good classiffication performance through labeled data alone. To leverage unlabeled data for enhancing classi¯cation, we introduces a margin based semisupervised learning method within the framework of regularization, based on an efficient margin loss for unlabeled data, which seeks efficient extraction of the information from unlabeled data for estimating the Bayes rule for classiffication. In particular, I will discuss three aspects: (1) the idea and methodology development; (2) computational tools; (3) a statistical learning theory. Numerical examples will be provided to demonstrate the advantage of our proposed methodology against other existing competitors. An application to gene function prediction will be discussed.
Host: Y. Fang
DATE: Friday, November 6, 2009
TIME: : 2:00--3:00 pm.
LOCATION: Paul Erdos Room, 796 COE
Speaker: Vitaly Voloshin, Troy University
Title: "Graph Coloring: history, generalizations, algorithms and open problems"
Abstract: For the last 50 years, Computer Science became a major provider of problems to Graph Theory and, simultaneously, it became a major consumer of the solutions to such problems. Graph Coloring is the core of Graph Theory with many fundamental results and open problems. Especially rapidly are developing research related to hypergraph generalizations of graph coloring. Hypergraph is a collection of subsets of a given vertex set. Subsets are called hyperedges. Hypergraph coloring is a partition of the vertex set of a hypergraph satisfying some general constraints on hyperedges. I will give a survey talk on coloring of hypergraphs. I will discuss some models, algorithms and open problems concerning uncolorability, unique colorability, and perfection.
Some information related to my talk may be found on Mixed Hypergraph Coloring website maintained at http://spectrum.troy.edu/~voloshin/mh.html or by Google search for "mixed hypergraph".
Host: Guantao Chen
DATE: Friday, October 30, 2009
TIME: : 2:00--3:00 pm.
LOCATION: Paul Erdos Room, 796 COE
Speaker: Hongtu Zhu, University of North Carolina at Chapel Hill
Title: "Multiscale Adaptive Regression Models for Inference and Classification"
Abstract: Neuroimaging studies often aim to analyze imaging data with complex spatial correlation structures and activation patterns on a two-dimensional (2D) surface or in a 3D volume. The goal of this presentation is to develop a multiscale adaptive regression model (MARM) for spatial and adaptive analysis of neuroimaging data. Compared with the existing voxel-wise approach, MARM has three unique features: being spatial, being hierarchical and being adaptive. MARM creates a small sphere with a given radius at each location (called voxel), analyzes all observations in the sphere of each voxel, and then uses these consecutively-connected spheres across all voxels to capture spatial dependence among imaging observations. MARM builds hierarchically nested spheres by increasing the radius of a spherical neighborhood around each voxel and utilizes information in each of the nested spheres at each voxel. Finally, MARM combines imaging observations with adaptive weights in the voxels within the sphere of the current voxel to adaptively calculate parameter estimates and test statistics. Theoretically, we establish consistency and asymptotic normality of the adaptive estimates and the asymptotic distributions of the adaptive test statistics under some mild conditions. Three sets of simulation studies are used to demonstrate the methodology and examine the finite sample performance of the adaptive estimates and test statistics in MARM. We apply MARM to quantify spatiotemporal white matter maturation patterns in early postnatal populations using diffusion tensor imaging. Our simulation studies and real data analysis confirm that MARM significantly outperforms voxel-wise methods.
Hosts: Y. Fang and G. Qin
DATE: Friday, September 25, 2009
TIME: : 2:00--3:00 pm.
LOCATION: Paul Erdos Room, 796 COE
Speaker: James L. Kepner, Ph.D.
Vice-President, Statistics and Evaluation American Cancer Society And Adjunct Professor, Department of Biostatistics Rollins School of Public Health Emory University
Title: "Survey of Exact Methods in Sample Size Determination"
Abstract:
Discussed are exact one-stage and group-sequential sample size determination methods for one- and two-sample binomial proportions testing problems, methods for the corresponding finite population tests, and simultaneous tests for correlated binomial proportions. Design properties are discussed and new/unpublished results are described. The exact group sequential methods allow early stops only for efficacy or only for futility or for either efficacy or futility. Sample sizes, levels of significance and power at fixed points in the research hypothesis parameter space are compared among competing designs including those derived using asymptotic normal theory methods. Documents provided will include
- a description of how sample points are placed in the rejection region,
- simple proofs for each of the 3 one-sample theorems,
- tables demonstrating the efficiency of the two-sample designs,
- a table showing how close the one-sample designs can get to the one-stage uniformly most powerful test in terms of significance and power,
- a table demonstrating the remarkable sample size savings if two or more binomial endpoints are tested simultaneously.
DATE: Wednesday, September 23, 2009
TIME: : 2:00--3:00 pm.
LOCATION: Paul Erdos Room, 796 COE
Speaker: Dr. Yufeng Liu, Department of Statistics & Operations Research Carolina Center for Genome Sciences, University of North Carolina Chapel Hill
Title: "Estimation of Multiple Noncrossing Quantile Regression Functions "
Abstract: Quantile regression is a very useful statistical tool to learn the relationship between the response variable and covariates. For many applications, one often needs to estimate multiple conditional quantile functions of the response variable given covariates. Although one can estimate multiple quantiles separately, it is of great interest to estimate them simultaneously. One advantage of simultaneous estimation is that multiple quantiles can share strength among them to gain better estimation accuracy than individually estimated quantile functions. Another important advantage of joint estimation is the feasibility to incorporate noncrossing constraints of quantile regression functions. In this talk, I will present a new multiple noncrossing quantile regression estimation technique. Both asymptotic properties and finite sample performance will be presented to illustrate usefulness of the proposed method.
Host: Yichuan Zhao
GSU Neurodynamics Seminar
Joint with Neuroscience
DATE: Thursday, May 7
TIME: 3:30 PM - 4:30 PM
LOCATION: South CB 500
Speaker: Maxim Bazhenov, Department of Cell Biology & Neuroscience
University of California, Riverside
http://cbns.ucr.edu/index.php?content=people/faculty/bazhenov/bazhenov.html
Title: "Extracellular Potassium Dynamics and Epileptogenesis"
Abstract: Extracellular ion concentrations change as a function of neuronal activity and also represent important factors influencing the dynamic state of a population of neurons. In particular, relatively small changes in extracellular potassium concentration mediate substantial changes in neuronal excitability and intrinsic firing patterns. While experimental approaches are limited in their ability to shed light on the dynamic feedback interaction between ion concentration and neural activity, computational models and dynamic system theory provide powerful tools to study activity-dependent modulation of intrinsic excitability mediated by extracellular ion concentration dynamics. Drawing on results obtained with biophysical network models of the thalamocortical system, I will discuss the potential role of extracellular potassium concentration dynamics in the generation of epileptoform activity in neocortical networks. Detailed bifurcation analysis of a model pyramidal cell revealed a bistability with hysteresis between two distinct firing modes (tonic firing and slow bursting) for mildly elevated extracellular potassium. In neocortical network models, this bistability gives rise to previously unexplained slow alternating epochs of fast runs and slow bursting as recorded in vivo during neocortical electrographic seizures in cats and in human patients with the Lennox-Gastaut syndrome. We conclude that extracellular potassium concentration dynamics may play an important role in the generation of seizures.
DATE: Friday, April 10, 2009
TIME: : 2:30 pm.
LOCATION: Paul Erdos Room, 796 COE
Speaker: Denish Shah, Ph.D. Assistant Professor of Marketing, Assistant Director - Center for Excellence in Brand & Customer Management, J. Mack Robinson College of Business, Georgia State University.
Title: "Expanding the Role of Marketing: From Customer Equity to Market Capitalization ?"
Abstract:
Can the marketer drive the stock price of the firm? Yes, it should be possible. Towards this endeavor, the authors develop a framework to link customer equity (as determined by the customer lifetime value metric) to market capitalization (as determined by the stock price of the firm). The authors test the framework through an empirical field experiment with two Fortune 1000 firms in the business-to-business and business-to-consumer context, respectively. The findings show that: (i) A customer equity - based framework can reliably predict the market capitalization of the firm, and (ii) Marketing strategies directed at increasing the customer equity not only increase the stock price of the firm, but also beat market expectations. Furthermore, the results indicate that the relationship between customer equity and market capitalization is moderated by risk factors in the form of volatility and vulnerability of cash flows from customers. By accounting for these factors, the association between customer equity and market capitalization is improved. The findings serve to broaden the scope and role of marketing while reinforcing the importance of the marketer to any organization.
Hosts: Yixin Fang and Jiawei Liu
DATE: Friday, February 27, 2009
TIME: : 2:30 pm.
LOCATION: Paul Erdos Room, 796 COE
Speaker: Craig Huneke, The Henry J. Bischoff Professor of Mathematics at the University of Kansas
Title: "How many times does a polynomial vanish along an algebraic subset of points?"
Abstract: This talk will discuss the title question. It is not too hard to figure out what it should mean for a polynomial f(X_1,...,X_n) to have an k-fold zero at a point (a_1,a_2,...,a_n) in complex n-space. One demands that f and all its partial derivatives up to k-1 st order vanish at that point. But there are several possibilities if one asks that f vanish along an algebraic subset X of complex n-space. (An algebraic set is the set of zeroes of some set of polynomials.) The differences between possible definitions leads to what are called symbolic powers of ideals. Many open questions pertain to symbolic powers. We will discuss some elementary ones.
Hosts: Florian Enescu and Yongwei Yao
DATE: Friday, February 20, 2009
TIME: : 2:00 pm--3:00pm.
LOCATION: Paul Erdos Room, 796 COE
Speaker: Jean M-S Lubuma (University of Pretoria, South Africa)
Title: "Non-standard finite difference schemes for impact oscillators with one degree or two degree of freedom"
Host: Dr. Hattingh
Colloquiums 2008
DATE: Friday, November 21, 2008
TIME: : 2:00 pm--3:00pm.
LOCATION: Paul Erdos Room, 796 COE
Speaker: Qi Long, Department of Biostatistics and Bioinformatics, Rollins School of Public Health, Emory University
Title: "A Double Robust Nearest Neighbor-Based Multiple Imputation Approach"
Abstract: In this talk, a nearest neighbor-based multiple imputation approach is proposed to recover information for missing observations. Under missing at random (MAR) mechanism, the proposed imputation approach has a double robustness property. Specifically, this imputation approach is robust to misspecification of either one of the two working models that are used to define imputing sets for missing observations. Asymptotic distributions for our proposed estimators are derived. Our simulation results show that the proposed approach is competitive or outperforms existing methods in a wide range of settings. The proposed imputation approach is illustrated using data from a colorectal adenoma study.
Host: Yichuan Zhao
DATE: Friday, November 7, 2008
TIME: : 2:00 pm--3:00pm.
LOCATION: Paul Erdos Room, 796 COE
Speaker: Lance A. Waller, Department of Biostatistics and Bioinformatics, Rollins School of Public Health, Emory University
Title: "Spatial Statistics in Disease Ecology: Patterns and Processes in Landscape Epidemiology"
Abstract: Inferring process from pattern is a long-standing goal in landscape ecology and epidemiology, but is limited by data availability and parameter identifiability. We will review a broad conceptual framework for the analysis of data associated with the spread of disease in time and space, illustrating a continuum of perspectives ranging from ecology to public health surveillance and identify areas needing further development. Using this framework, we explore expanded roles for statistical techniques in mathematical models of the spread of raccoon rabies in the northeastern United States, focusing on assessments of fit for mathematical models of disease dynamics and exploration of the phylogeography of pathogens in wildlife populations.
Host: Yichuan Zhao.
DATE: Friday, April 25, 2008
TIME: : 2:30 pm--3:30pm.
LOCATION: Paul Erdos Room, 796 COE
Speaker: Ian M. Aberbach, University of Missouri Columbia
Title: "Uniform bounds in Noetherian rings"
Abstract: Let R be a commutative ring (with unit). Then R is Noetherian if every ideal of R is finitely generated. In the words of Craig Huneke, "behind the obvious finiteness condition in Noetherian rings, . . ., there lie many deeper and hidden types of finiteness which come to light in terms of uniform behavior. . . . [by that] we mean statements which give some bounds (usually numerical) not just for one ideal, but for all ideals simultaneously." The talk will try to give a flavor of such results, touching on, for instance, uniform Artin-Rees theorems, uniform annihilation of local cohomology and the connection to uniform annihilators of homology in classes of free complexes, tight closure and its uniform annihilation (i.e., test elements), Briancon-Skoda type theorems, and uniform degrees of nilpotency for parameter ideals.
Prof. Aberbach is the main speaker of GSU-USC Commutative Algebra meeting in Atlanta April 25-April 27.
Hosts: Florian Enescu and Yongwei Yao.
DATE: Friday, April 18, 2008
TIME: : 2:00 pm--3:00pm.
LOCATION: Paul Erdos Room, 796 COE
Speaker:Mourad Tighiouart, Co-Director of the Winship Cancer Institute Department of Biostatistics at Emory University
Title: "Design Considerations in Cancer Phase I clinical Trials: Escalation with Overdose Control"
We describe a Bayesian adaptive design for cancer phase I clinical trials. The method makes use of all the information available at the time of each dose assignment, and directly addresses the ethical need to control the probability of overdosing. The design is Bayesian-feasible and the sequence of doses generated by this scheme is consistent. Performance of this design under a large class of prior distributions will be explored through simulations. In particular, joint prior distributions for the maximum tolerated dose (MTD) and probability of dose limiting toxicity (DLT) at the initial dose with negative a priori correlation structure are used to model the dose-response relationship. When patients' specific characteristics thought to be related to treatment susceptibility are available at the onset of the trial, we show how this adaptive design takes into account this information. The performance of this extended design is evaluated by comparing the following designs via extensive simulations: (1) Design using a covariate; patients are accrued to the trial sequentially and the dose given to a patient depends on his/her covariate value, (2) Design ignoring the covariate; patients are accrued to the trial sequentially and the dose given to a patient does not depend on his/her covariate value, and (3) Design using separate trials; In each group, patients are accrued to the trial sequentially and EWOC is implemented in each group. The above methodologies are illustrated with examples of phase I trials conducted at Fox Chase Cancer Center and Winship Cancer Institute.
Host: Dr. Yichuan Zhao
DATE:
Wednesday, January 16, 2008
TIME: 2:15 PM, Refreshments at 2 PM
LOCATION: Paul Erdos Room,
796 COE
Speaker: Tom Bella, University of Connecticut
Title: "Quasiseparable matrices and polynomials"
Abstract: The interplay between polynomials and dense structured matrices is a classical topic. Structure in this sense is interpreted to mean their $n 2 $ entries can be ``compressed'' to a smaller number ${\mathcal O}(n)$ of parameters. Operating directly on these parameters allows one to design efficient {\em fast algorithms} for these matrices and for the related applied problems. In the past decades matrices with structures such as DFT/DCT/DST, Toeplitz, Hankel, Vandermonde or Cauchy structure were the focus of attention. In this talk, some results that demonstrate that a relatively new {\em quasiseparable} structure enables substantial generalizations of a number of different algorithms will be presented.
Host: Mihaly Bakonyi
DATE: Friday, November 16, 2007
TIME: 2:00 PM - 3:00 PM
LOCATION: Paul Erdos Room
Speaker: Vladimir Koltchinskii, School of Mathematics Georgia Institute of Technology
Title: "Sparse Recovery in Function Estimation"
Abstract: A problem of learning of a target function based on its noisy observations at random points via penalized empirical risk minimization with convex loss function and convex complexity penalty will be discussed. This includes a number of regression and large margin classification problems. It is assumed that the target function belongs to the linear span of a very large dictionary of given functions and that it has a "sparse representation" in the "dictionary". The goal is to recover the function with an error that depends mainly on the "sparsity" of the problem (even if the size of the "dictionary" is very large). An approach based on $\ell_1$-type complexity penalization will be discussed. We prove several probabilistic bounds showing the relationship between the sparsity of the empirical solution and the sparsity of the target function and provide oracle inequalities on the excess risk and the L_2-error that depend on the sparsity of the problem.
Host: Yichuan Zhao
DATE: Tuesday, November 13, 2007
TIME: 3:00 PM - 4:00 PM
LOCATION: Paul Erdos Room
Speaker: Xingxing Yu, School of Mathematics, Georgia Insitute of Technology
Title: " Judicious partitions of graphs"
Abstract: Judicious partition problems ask for partitions of the vertex set of a graph so that several quantities are optimized simultaneously. I will discuss several judicious partition problems of Bollob\'{a}s and Scott, and present our recent results on these problems (joint work with Baogang Xu).
DATE: Friday, October 26, 2007
TIME: 2:00 PM - 3:00 PM
LOCATION: Paul Erdos Room
Speaker: Charles Wells, Case Western University and Oberlin College
Title: "Category Theory and Mathematical Discourse"
Abstract: Category theory provides a new way of thinking and talking about mathematical structures. Some categorical concepts will be introduced that exhibit this new point of view. Much goes on in mathematical discourse that mathematicians may not be aware of. The discourse the author uses to introduce the categorical ideas will be used to provide examples of some of the subtleties of math discourse. The two topics of the talk are related: Category theory clarifies some of the difficulties involved in communicating math.
Host: Mariana Montiel
Joint GSU Mathematics/GA Tech colloquium
DATE: Wednesday, April 18, 2007
TIME: 4:30 PM
LOCATION: Skiles 255, Skiles Classroom Building, School of Mathematics, GaTech
Speaker: Leonid Shilnikov (Institute for Applied Mathematics & Cybernetics, Russia)
Title: "Quasihyperbolicity and strange attractors"
Abstract: We propose an effective criterion of dynamical chaos that is based on a quasihyperbolicity condition. The latter means the phase space of the system has an absorbing domain with such unstable trajectory behavior that lets us find a factor-system expanding volumes. We will give examples of quasihyperbolic attractors of both structurally stable, like Smale-William solenoids, and unstable types such as Lorenz and spiral ones. We single out a class of quasihyperbolic systems with a single saddle equilibrium state having a 1D unstable manifold. The periodic perturbations on an attractor of Lorenz type are also discussed.
Hosts: Igor Belykh and Shui-Nee Chow (GaTech)
DATE: March 30, 2007
TIME: 2:00-3:00 PM
LOCATION: COE 796
Speaker: Graham Leuskchke (Syracuse University)
Title: "Factoring the Adjoint and Maximal Cohen-Macaulay Modules"