Institute for Mathematical Sciences                                        Programs & Activities

 

~ ABSTRACTS ~


Some Future Directions of White Noise Analysis
Takeyuki Hida, Nagoya University and Meijo University, Japan

 

We will discuss the following future directions of white noise analysis.
(1) Feynman's path integral. Following the idea of Dirac and Feynman we can form a quantum mechanical propagator starting from the Lagrangian, where generalized white noise functionals will play the key role. We will discuss its relations with the Chern-Simons action integrals in the abelian case.
(2) Infinite dimensional differential calculus. Because of the natural introduction of the class of generalized white noise functionals, we may discuss essentially infinite dimensional analysis. Note that it looks like a continuously many dimensional calculus, but separability is always behind. Stochastic integral is discussed in this general framework, where the integrands are not necessarily non-anticipating.
(3) If time permits, we will choose interesting subgroups of the infinite dimensional rotation group and discover their probabilistic meanings. A good example is a subgroup isomorphic to the conformal group. We may also discuss the duality between white noise (which is Gaussian) and Poisson noise.

 

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Analysis of Least Absolute Deviation
Zhiliang Ying, Columbia University, USA

 

In this talk, I will describe a least absolute deviation-based method for testing linear hypothesis. Like ANOVA, this method is coordinate-free, and admits singular design matrices. A simple approximation using stochastic perturbation is developed to obtain cut-off values for the resulting tests. Theoretical justification, computer implementation and simulation will be presented. Focus will be given to the special cases of one- and multi-way layouts.

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What is Mathematical Biology and How Useful is it?
Avner Friedman, Director, Mathematical Biosciences Institute
Ohio State University

 

Biological processes are very complex, and mathematical models of such processes are at best just a crude approximation. Nevertheless one can gain some useful knowledge from the models. In this talk, I shall give examples of biological and biomedical problems that have been addressed by mathematical models. The examples will be from areas as diverse as wound healing, hemodialysis, tuberculosis, and cancer.

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