[Sem-coll] IIT Applied Math Seminars & Colloquium Next Week

Joe Millham jmillham at iit.edu
Fri Mar 12 12:15:45 CST 2010


Please join the Applied Math department for the following Seminars and
Colloquia.  All are welcome to attend, and refreshments will be served
at some events.  For a complete and updated listing of the
department's seminars, please visit the seminar webpage:
http://www.iit.edu/csl/am/colloquia/

Department Colloquium
Monday, March 15  4:40 pm  E1 106
Patrick Cheridito, Princeton University
"Equilibrium Pricing in Incomplete Markets Under Translation Invariant
Preferences"
See abstract below

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Department Colloquium
Tuesday, March 16  4:40 pm  E1 121
Seo Young Park, University of North Carolina, Chapel Hill
"Flexible Margin-Based Classification Techniques"
See abstract below

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Department Colloquium
Wednesday, March 17   4:40 pm  E1 106
Junhui Wang, University of Illinois - Chicago
"On Margin Based Semisupervised Learning"
See abstract below

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Stochastic & Multiscale Modeling and Computation Seminar
Monday, March 15  E1 244  11:30 am
Jinqiao Duan, IIT-Applied Math
"Random Dynamical Systems with Non-Gaussian Noises"
See abstract below

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Meshfree Methods Seminar
Monday, March 15   AM222 1:50 pm
Greg Fasshauer, IIT-Applied Math
"Green's Functions: Taking Another Look at Kernel Approximation,
Radial Basis Functions, and Splines"
See abstract below

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Department Colloquium
Monday, March 15  4:40 pm  E1 106
Patrick Cheridito, Princeton University
"Equilibrium Pricing in Incomplete Markets Under Translation Invariant
Preferences"
Abstract:
Conditions are given for the existence and uniqueness of equilibria in
incomplete dynamic market models when agents have translation
invariant preferences. This includes mean-variance type preferences
and expected exponential utility. General results are provided in
discrete time. Then a special case is discussed where equilibrium
prices can be calculated as solutions to a system of backward
stochastic difference equations. In the continuous-time limit, a
system of coupled backward stochastic differential equations with
drivers of quadratic growth appears.


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Department Colloquium
Tuesday, March 16  4:40 pm  E1 121
Seo Young Park, University of North Carolina, Chapel Hill
"Flexible Margin-Based Classification Techniques"
Abstract:
Classification is a very useful statistical tool for information
extraction. Among numerous classification methods, margin-based
classification techniques have attracted a lot of attention. In this
talk, I will present several new margin-based  classifiers, via
modifying loss functions of two well-known classifiers, Penalized
Logistic Regression (PLR) and the Support Vector Machine (SVM). For
binary classification, we propose three new classification techniques,
Robust Penalized Logistic Regression (RPLR), Bounded Contraint Machine
(BCM), and the Balancing Support Vector Machine (BSVM). For
multicategory classification, we propose the efficient multicategory
Combined Least Squares (CLS) classifier. We study properties of the
new methods and provide efficient computational algorithms. Simulated
and microarray gene expression data analysis examples are used to
demonstrate competitive performance of the proposed methods.

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Department Colloquium
Wednesday, March 17   4:40 pm  E1 106
Junhui Wang, University of Illinois - Chicago
"On Margin Based Semisupervised Learning"
Abstract:
In classification, 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 difficult to
achieve good classification performance through labeled data alone. To
leverage unlabeled data for enhancing classification, 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 classification. 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.

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Stochastic & Multiscale Modeling and Computation Seminar
Monday, March 15  E1 244  11:30 am
Jinqiao Duan, IIT-Applied Math
"Random Dynamical Systems with Non-Gaussian Noises"
Abstract:
Gaussian processes, such as Brownian motion, have been widely used in
modeling fluctuations, while some complex phenomena in engineering and
science involve non-Gaussian Levy motions. Thus dynamical systems
driven by non-Gaussian noises have attracted considerable attention
recently.

The speaker first reviews dynamical issues for nonlinear systems with
non-Gaussian Levy noises, and then presents recent work on the exit
phenomenon, bifurcation and random invariant manifolds. The
differences in dynamics under Gaussian and non-Gaussian noises are
highlighted, theoretically or numerically.

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Meshfree Methods Seminar
Monday, March 15   AM222 1:50 pm
Greg Fasshauer, IIT-Applied Math
"Green's Functions: Taking Another Look at Kernel Approximation,
Radial Basis Functions, and Splines"
Abstract:
The theories for radial basis functions (RBFs) as well as piecewise
polynomial splines have now reached a stage of relative maturity as is
demonstrated by the recent publication of a number of monographs in
either field. However, there remain a number of issues that deserve to
be investigated further. For instance, it is well known that both
splines and radial basis functions yield “optimal” interpolants, which
in the case of radial basis functions are discussed within the
so-called native space setting. It is also known that the theory of
reproducing kernels provides a common framework for the interpretation
of both RBFs and splines. However, the associated reproducing kernel
Hilbert spaces (or native spaces) are often not that well understood —
especially in the case of radial basis functions.  By linking
(conditionally) positive definite kernels to Green’s functions of
differential operators we obtain new insights that enable us to better
understand the nature of the native space as a generalized Sobolev
space. An additional feature of our new perspective is the notion of
scale built into the definition of these function spaces. Furthermore,
we are able to use eigenfunction expansions of our kernels (Mercer’s
theorem) to make progress on such important questions as stable
computation with flat radial basis functions and dimension independent
error bounds.


see you there,

Joe Millham

Administrative Assistant
Department of Applied Mathematics
Illinois Institute of Technology
Engineering-1 Room 208
10 W. 32rd St.
Chicago IL 60616
312.567.8984 (Phone)
312.567.3135 (Fax)




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