Digital biology: data-mining with a physical chemistry lens

Speaker: 

Ridgway Scott

Institution: 

Departments of Computer Sci. and Math. , U. of Chicago

Time: 

Thursday, February 9, 2006 - 4:00pm

Location: 

MSTB 254

The digital nature of biology is crucial to its functioning
as an information system. The hierarchical development of
biological components (translating DNA to proteins which form
complexes in cells that aggregate to make tissue which form
organs in different species) is discrete (or quantized) at
each step. It is important to understand what makes proteins
bind to other proteins predictably and not in a continuous
distribution of places, the way grease forms into blobs.

Data mining is a major technique in bioinformatics. It has been
used on both genomic and proteomic data bases with significant
success. One key issue in data mining is the type of lens that
is used to examine the data. At the simplest level, one can just
view the data as sequences of letters in some alphabet. However,
it is also possible to view the data in a more sophisticated
way using concepts and tools from physical chemistry. We will
give illustrations of the latter and also show how data mining
(in the PDB) has been used to derive new results in physical
chemistry. Thus there is a useful two-way interaction between
data mining and physical chemistry.

We will give a detailed description of how data mining in the
PDB can give clues to how proteins interact. This work makes
precise the notion of hydrophobic interaction in certain cases.
It provides an understanding of how molecular recognition and
signaling can evolve. This work also introduces a new model of
electrostatics for protein-solvent systems that presents
significant computational challenges.

Time Reversal in a finite cavity effect of ergodicity and randomness

Speaker: 

Professor Claude Bardos

Institution: 

Paris VII & Lab of J. L. Lions

Time: 

Thursday, November 10, 2005 - 4:00pm

Location: 

MSTB 254

This talk is devoted to a mathematical analysis of the time reversal
method which was promoted by Mathias Fink, his group and others.

It involves source and transductors. The challenge is to
understand how to use as few transductors as possible.

Emphasis is put on examples of problems in a closed bounded cavity In
this situation I will describe the effect of ergodicity both when the
transductors are in the media or when they are at the boundary.

Results and methods are compared with what has already been done for
random media. Some of the proof are very similar sharper results are
obtained but only in domains with no boundary.

Estimates for the tangential Cauchy-Riemann equations with minimal smoothness

Speaker: 

Professor Meichi Shaw

Institution: 

Notre Dame

Time: 

Thursday, September 29, 2005 - 4:00pm

Location: 

MSTB 254

We study the regularity for the tangential Cauchy-Riemann equations and the associated Laplacian on CR manifolds with minimal smoothness assumption. One application is to extend the embedding theorem of Boutet De Monvel
to strongly pseudoconvex CR manifolds of class C^2.

(Joint work with Lihe Wang).

One direction and one component regularity for the Navier-Stokes equations

Speaker: 

Professor Igor Kukavica

Institution: 

USC

Time: 

Thursday, November 17, 2005 - 4:00pm

Location: 

MSTB 254

We consider sufficient conditions for regularity of weak solutions of the Navier-Stokes equation. By a result of Neustupa and Panel, the weak solutions are regular provided a single component of the velocity is bounded. In this talk we will survey existing and present new results on one component and one direction regularity.

Multiscale analysis in micromagnetics: an example

Speaker: 

Professor Felix Otto

Institution: 

Univ Bonn

Time: 

Thursday, December 1, 2005 - 4:00pm

Location: 

MSTB 254

From the point of view of mathematics,
micromagnetics is an ideal playground for a pattern forming system in materials
science: There are abundant experiments on a wealth of visually
attractive phenomena and there is a well--accepted continuum model.

In this talk, I will focus on a specific
experimental observation for thin film ferromagnetic elements: Elements
with elongated rectangular cross--section are saturated along the longer
axis by a strong external field. Then the external field is slowly
reduced. At a certain field strength, the uniform magnetization buckles
into a quasiperiodic domain pattern which resembles a concertina.
Our hypothesis is that the period of this pattern is the
frozen--in period of the unstable mode at critical field.

Starting point for the analysis is the micromagnetic model which has three
length scales. We rigorously identify four scaling regimes for the
critical field. One of the regimes has been
overseen by the physics literature. It displays an
oscillatory unstable mode, which we identify asymptotically.
In this parameter regime, we identify
a scaling limit for the bifurcation.

The analysis amounts to the combination of an asymptotic
limit with a bifurcation argument. This is carried out by a suitable
``blow--up'' of the energy landscape in form of Gamma--convergence.
Numerical simulation of the normal form visualizes a homotopy
from a turning point to
the strongly nonlinear concertina pattern.
This is joint work with Ruben Cantero--Alvarez and Jutta Steiner.

Volatility surface estimation

Speaker: 

George Papanicolaou

Institution: 

Stanford

Time: 

Thursday, November 3, 2005 - 4:00pm

Location: 

MSTB 254

A central problem in modern mathematical
finance is that of estimating the volatility
of financial time series, whether they are
equity prices, exchange rates, interest rates
or something else, such as options. A recent trend is to try to
estimate the implied volatility of an asset from
the fluctuations in the price of derivatives
whose underlying it is. This is the volatility
surface estimation problem. I will review briefly the
background and status of this problem, including
computational issues, and I will present a variational
theory for volatility surface estimation within
stochastic volatilty models. I will show the form
this theory takes under a fast mean reverting hypothesis
and I will conclude with a calibration of the theoretical
framework using SP500 options data.

Local Discontinuous Galerkin Methods for Dispersive Wave Equations

Speaker: 

Chi-Wang Shu

Institution: 

Brown University

Time: 

Thursday, May 19, 2005 - 4:00pm

Location: 

MSTB 254

In this talk I will first give a general introduction to the discontinuous
Galerkin finite element method and the main technical issues in generalizing
this method to solve PDEs with higher spatial derivatives. I will then
introduce the recent research of designing stable and convergent local
discontinuous Galerkin methods for solving various nonlinear dispersive
wave equations, including the Kadomtsev-Petviashvili equations and the
Zakharov-Kuznetsov equations. Numerical results will be shown to demonstrate
the good qualities of such methods. This is a joint work with Jue Yan and
Yan Xu.

Geometry and analysis on fractals

Speaker: 

Alexandre Kirillov

Institution: 

UPenn

Time: 

Wednesday, February 23, 2005 - 4:00pm

Location: 

MSTB 254

We consider only two fractals: Sierpinski and Apollonian gaskets. The
idea is to show on these two examples how geometry, analysis, algebra and
number theory are tied together in the simplest problems, related to
fractal sets.

We start with definitions, speculate on the general matrix numerical
systems, consider the analytic properties and the p-adic behavior of
harmonic functions, analyse the spectrum of the Laplace operator on the
Sierpinski gasket. Then we describe the geometry, group-theoretic
structure and arithmetic properties of the Apollonian gasket.

The final idea is to draw a parallel between the two fractals - an
unfinished program.

Infinite Groups

Speaker: 

Zelmanov

Institution: 

UCSD

Time: 

Thursday, April 21, 2005 - 4:00pm

Location: 

MSTB 254

I will try to give a broad review of the amasing
developments in the theory of infinite groups during the last 25 years. These include the
emergence of Monsters and flourishing of the Asymptotic Theory of Finite Groups. We will focus on important examples and formulate some open problems.

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