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Complete
List of Industrial Postdoc Seminar
IMA
Postdoc Seminar 2003-2004
Tuesday
: 11:15 - 12:15 at 409 Lind Hall
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.
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+
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 
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.
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.
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, ··· , Y -1
be iid random variables with a distribution function (df)
F0(y), and let Y
, Y+1
, ··· be iid random variables with a
df F1(y), where
is an unknown time index of a change in distribution with
the change in parametric value. For a suitable function 
let Xj =
(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 
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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