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IMA Postdoc Seminar 2003-2004
Tuesday : 11:15 - 12:15 at 409 Lind Hall

Complete List of Industrial Postdoc Seminar

The IMA Postdoc Seminar is intended for expository talks from the visitors on their current research interests. For the year 2003 - 2004 it is organized by Antar Bandyopadhyay and Gerard Awanou. The seminar meets at 409 Lind Hall on Tuesdays at 11:15 only on the weeks when there is no IMA workshop or tutorial. If you are interested to give a talk please contact the organizers at antar@ima.umn.edu or awanou@ima.umn.edu. Note that Balaji Gopalakrishnan was a co-organizer from October-December, 2003.

Spring 2004

May 18, 2004 (Tuesday) 11:15 am-12:15 pm, Room 409, Lind Hall
Speaker:Professor Scot Adams (IMA Associate Director)

Title: Some Remarks on Finite Element Method

April 20, 2004 (Tuesday) 11:15 am-12:15 pm, Room 409, Lind Hall
Speaker: Professor Yuhong Yang (Iowa State University)

Title: Multi-armed Bandits with Covariates

Abstract: Suppose that there are K (K>1) possibly biased coins available for play. At each time, you can choose one and only one coin to flip, and win a dollar if you get a head and receive nothing otherwise. Your goal is to obtain as much money as possible. Such a problem is called a multi-armed bandit problem.

Bandit problems have applications in clinical trials, scheduling, and automated problem-solving in machine learning. In the literature, covariates, while available in most applications, are rarely considered. In this talk, I will present a non-parametric approach with a randomization technique for effectively utilizing the information in the covariates. A consistency property of the proposed approach is established.

April 6, 2004 (Tuesday) 11:15 am-12:15 pm, Room 409, Lind Hall
Speaker: Professor Peter Bank (Humboldt University of Berlin, Germany)

Title: American Options, Finite-Fuel Problems, and the Multi-Armed Bandit

Abstract: We show how the optimal stopping, certain singular control problems, and dynamic allocation problems all can be reduced to the same kind of stochastic representation problem. This unifying approach allows for some new (and comparably easy) proofs for classical results such as Gittins' index theorem, and also offers some new insights into the common structure of these optimization problems.

March 23, 2004 (Tuesday) 11:15 am-12:15 pm, Room 409, Lind Hall
Speaker: Dr. Noam Berger (California Institute of Technology)

Title: Non-uniqueness for Specifications in 12+epsilon
Slides:   pdf

Abstract: Keane, Berbee and others have studied the question of which specifications (aka g-functions) admit a unique Gibbs measure. Bramson and Kalikow constructed the first example of a regular and continuous specification which admits multiple measures. For every p > 2, we construct a regular and continuous specification, whose variation is in ell p, that admits multiple Gibbs measures. This shows that a recent condition of Oberg and Johansson is tight. Joint work with Christopher Hoffman and Vladas Sidoravicius.

Winter 2004

March 16, 2004 (Tuesday) 11:15 am-12:15 pm, Room 409, Lind Hall
Speaker: Professor Ilze Ziedins (Department of Statistics, University of Auckland, New Zealand, ilze@stat.auckland.ac.nz)

Title: Optimal Routing in Parallel Tandem Queues with Loss

Abstract: In many queueing systems, individually optimal and socially optimal polices (whether for admission or routing) can be very different. This talk will look at a system of parallel finite tandem queues with loss. For this system, when customers choose routes that minimize their individual loss probability it can sometimes be optimal to choose queues with more customers already present and/or with greater residual service requirements (where preceding customers are further from their final destination). These individually optimal policies will be compared with socially optimal routing policies obtained in the limit as the number of possible routes becomes large. This is joint work with Ru-Shuo Sheu and Scott Spicer.

February 24, 2004 (Tuesday) [Joint with the Random Matrix Seminar]
12:45 - 2:15 at 570 Vincent Hall
Speaker: Dr. Tim Garoni (IMA Postdoc)

Title: Absolute Moments of Products of Characteristic Polynomials, and Impenetrable Bosons - II

Abstract: I will discuss the links between the moments of products of characteristic polynomials of random matrices, with the asymptotics of a certain class of Hankel determinants, and also with certain 1D quantum models. Some exact results from the literature will be discussed, as well as some interesting and as yet unproven conjectures.

February 17, 2004 (Tuesday) [Special meeting jointly with Random Matrix Seminar]
12:45 - 2:15 at 570 Vincent Hall
Speaker: Dr. Tim Garoni (IMA Postdoc)

Title: Absolute Moments of Products of Characteristic Polynomials, and Impenetrable Bosons - I

Abstract: I will discuss the links between the moments of products of characteristic polynomials of random matrices, with the asymptotics of a certain class of Hankel determinants, and also with certain 1D quantum models. Some exact results from the literature will be discussed, as well as some interesting and as yet unproven conjectures.

February 17, 2004 (Tuesday) [Joint with the Brown Bag Seminar]
11:15 am-12:15 pm, Room 409, Lind Hall
Speaker: Dr. Lili Ju (IMA Postdoc)

Title: Finite Volume Method on Spherical Voronoi Meshes

Abstract: We first develop and analyze a finite volume scheme for the discretization of partial differential equations on the sphere; the scheme uses Voronoi tessellation of the sphere. For a model convection-diffusion problem, the finite volume scheme is shown to produce first-order accurate approximations with respect to a mesh-dependent discrete first-derivative norm. Then, we introduce the notion of constrained centroidal Voronoi tessellation (CCVTs) of the sphere; these are special Voronoi tessellation of the sphere for which the generators of the Voronoi cells are also the constrained centers of mass, with respect to a prescribed density function, of the cells. After discussing an algorithm for determining CCVT meshes on the sphere, we discuss and illustrate several desirable properties possessed by these meshes. In particular, it is shown that CCVT meshes define very high quality uniform and nonuniform meshes on the sphere. Finally, we discuss, through some computational experiments, the performance of the CCVT meshes used in conjunction with the finite volume scheme for the solution of simple model PDEs on the sphere. The experiments show, for example, that the CCVT based finite volume approximations are second-order accurate if errors are measured in discrete L2-norms.

February 3, 2004 (Tuesday) 11:15 am-12:15 pm, Room 409, Lind Hall
Speaker: Professor Greg Rempala (University of Louisville, visiting IMA)

Title: Bootstrapping Parametric Models of Mortality

Abstract: We consider a general problem of modeling a mortality law of a population of failing units with some parametric function. In this setting we define a mortality table of crude rates as a statistical estimator with multinomial distribution and show its consistency as well as asymptotic normality. We further derive the statistical properties of parameter estimators in a parametric mortality model based on a weighted square loss function. We use the obtained results to study consistency and appropriateness of the parametric bootstrap method in our setting. We derive the conditions on the assumed parametric mortality law and the loss function, under which the bootstrap is consistent for estimating the model parameters, their standard errors and corresponding confidence intervals. We apply our results to a model of Aggregate US Mortality Table based on a so called mixture of extreme value distributions suggested by Carriere (1992).

January 27, 2004 (Tuesday) 11:15 am-12:15 pm, Room 409, Lind Hall
Speaker: Dr. Olga Brezhneva (IMA Postdoc)

Title: Modified Methods for Nonlinear Optimization and Complementarity Problems in the Absence of Strict Complementarity

Abstract: For nonlinear constrained optimization and complementarity problems, we consider the case when the strict complementarity condition does not hold. In this situation, only a linear rate of convergence can be guaranteed for most classical algorithms. In this talk, we consider a Lagrange-Newton method and the modified Lagrangian method for nonlinear constrained optimization, and propose an approach that allows us to obtain modifications of these methods. The obtained modifications attain super-linear convergence even when the strict complementarity condition does not hold and subsume the case when this condition holds. Moreover, the proposed approach to modifying the methods can be applied to a variety of problems with some kind of degeneracy. We illustrate this by constructing a method for nonlinear complementarity problems in the absence of strict complementarity.

January 20, 2004 (Tuesday) 11:15 am-12:15 pm, Room 409, Lind Hall
Speaker: Dr. Gerard Awanou (IMA Postdoc)

Title: Trivariate Spline Approximations of 3D Navier-Stokes Equations

Abstract: We present numerical approximations of the 3D steady state Navier-Stokes equations in velocity-pressure formulation. We use trivariate splines of arbitrary degree d and arbitrary smoothness r < d. Using functional arguments, we derive the discrete Navier-Stokes equations in terms of B-coefficients of trivariate splines over a tetrahedral partition of any given polygonal domain. Smoothness conditions, boundary conditions and the divergence-free conditions are enforced through Lagrange multipliers. The discrete equations are solved by a variant of the augmented Lagrangian algorithm for which we prove a linear algebraic convergence rate. We have implemented this approach in MATLAb and present numerical evidence of the convergence rate as well as experiments on the lid driven cavity flow problem.

Fall 2003

December 9, 2003 (Tuesday) 11:15 am-12:15 pm, Room 409, Lind Hall
Speaker: Dr. Soohan Ahn (Seoul National University (SRCCS), Visiting IMA)

Title: Transient Analysis of Fluid Flow Models via Stochastic Coupling to a Queue

Abstract: Markovian fluid flow models are used extensively in performance analysis of communication networks. They are also instances of Markov reward models that find applications in several areas like storage theory, insurance risk and financial models, and inventory control. This paper deals with the transient analysis of such models. Given a Markovian fluid flow, we construct on the same probability space a sequence of queues that are stochastically coupled to the fluid flow in the sense that at certain selected random epochs the distribution of the fluid level and the phase (the state of the modulating Markov chain) is identical to that of the work in the queue and the phase. The fluid flow is realized as a stochastic process limit of the processes of work in the system for the queues, and the latter are analyzed using the matrix-geometric method. These in turn provide the needed characterization of transient results for the fluid model.

December 2, 2003 (Tuesday) 11:15 am-12:15 pm, Room 409, Lind Hall
Speaker: Dr. Amir Niknejad (University of Illinois at Chicago, visiting IMA)

Title: Missing Data Imputation for Gene Expression Arrays : An Algebraic Approach

Abstract: We introduce an algebraic framework for missing data imputation through Fixed Rank Approximation Algorithm(FRAA). Preliminary test indicates that FRAA is Robust and might be a feasible alternative in cases when the number of columns are small in Genome - Wide Matrix.

November 25, 2003 (Tuesday) 11:15 am-12:15 pm, Room 409, Lind Hall
Speaker: Dr. Karen Ball (IMA Postdoc)

Title: Factors of Processes on Groups and Graphs
Slides:   pdf

Abstract: Let X be a set with a group G acting on it. We will consider the question of when there exists a G-homomorphism between two i.i.d. processes which are indexed by X. In the case where X=G, we will see that amenable and nonamenable groups are characterized by very different behavior with respect to this question. We will also consider the case where X is a graph. The proofs involve applications of interesting ideas from percolation theory.

November 11, 2003 (Tuesday) 11:15 am-12:15 pm, Room 409, Lind Hall
Speaker: Professor Thomas G. Kurtz (Center for Mathematical Sciences, University of Wisconsin-Madison)  kurtz@math.wisc.edu

Title: Introduction to Martingale Problems
Slides:   pdf

Abstract: The generator for a Markov process is a linear operator that characterizes infinitesimally the evolution of the distribution of the process. Classically, the Hille-Yosida theory of operator semigroups was used to connect the Markov process to its generator. In the context of diffusion processes, Stroock and Varadhan showed that Markov processes can be characterized by the requirement that certain functionals of the process, determined by the generator, must be martingales, that is, the Markov process can be characterized as the unique solution of a martingale problem. For example, Brownian motion is the unique solution of the martingale problem for the Laplacian.

Martingale problems provide a powerful approach to the study of Markov processes. The basic theory of martingale problems will be reviewed and several illustrative examples of its application will be given.

NOTE: This talk is intended to give some useful background for the November 12 talk in the Complex Systems Seminar.

October 28, 2003 (Tuesday) 11:15 am-12:15 pm, Room 409, Lind Hall
Speaker: Professor Mohammad Kazim Khan (Kent State University)

Title: On SPRT and CUSUM Procedures and Some Open Problems     Slides:   pdf

Abstract: Let Y1, Y1, ··· , Ynu-1 be iid random variables with a distribution function (df) F0(y), and let Ynu , Ynu+1 , ··· be iid random variables with a df F1(y), where nu is an unknown time index of a change in distribution with the change in parametric value. For a suitable function psi let Xj = psi (Yj) denote some convenient data reduction or it may be defined by certain optimality consideration such as the Sequential Probability Ratio Test. For detecting a change-point in the distribution, Page (1954) defined his famous cusum (cumulative sum) procedure. From the inherent renewal property of the cusum, Page noted that EN = EM/P(SM geq h), where N is the cusum stopping rule and M is the SPRT and Sn represents the partial sum of the information X1, X2,... . The constant h is the trigering constant for the cusum. This link between the SPRT and the cusum is quite useful in approximating and/or evaluating EN. However, a deeper connection between N and M is known that I will try to present. The purpose of this exposition is to further exploit such a relationship between N and M to study the properties of some one sided and two sided cusums with several applicable examples. We will see how exact results can be computed in discrete time settings. There are some open problems which I will outline.

October 14, 2003 (Tuesday) 11:15 am-12:15 pm, Room 409, Lind Hall
Speaker: Professor Simon Morgan (Visiting Assistant Professor, Department of Mathematics, University of Minnesota)

Title: Applications of Geometric Measure Theory to Variational Problems with Surfaces

Abstract: Geometric measure theory offers compactness theorems for candidate objects in variational problems, giving existence results in variational problems. Additionally it offers regularity information about limits of regular objects.

I will introduce the objects of geometric measure theory; rectifiable sets, currents and varifolds. Key examples of each and their associated topologies will be given.

The primary application of geometric measure theory was minimal surface theory, but I will also explain my own research into geometric measure theory techniques and my motivating applications.

October 7, 2003 (Tuesday) 11:15 am- 12:15 pm, Room 409, Lind Hall
Speaker: Professor Taerim Lee (Korea National Open University)

Title: Tree Structured Prognostic Model for Hepatocellular Carcinoma
Slides:   html   pdf   ps    ppt

Abstract: Recent progress in both diagnostic and therapeutic technique of hepatocellular carcinoma appears to improve the prognosis. The purpose of this study was designed to evaluate the prognosis of HCC in relation to treatment methods and their affecting factors by the tree- structured model. This paper attempt to identify and quantify the effect of prognostic factors namely, patient characteristics that related to the prognosis of Hepatocellular Carcinoma. Our proposed survival tree model uses statistical tests for the modified Cox-Snell residuals derived from fitting a Cox proportional hazards model, and therefore it can detect curvature of covariates and interactions among them. As a result, split covariate selection bias is negligible. Furthermore, our proposed piecewise constant modeling can be generalized with piecewise multiple linear modeling without much computational burden.

 

Complete List of Industrial Postdoc Seminar

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