TUESDAY, February 5, 2008
MATHEMATICS AND COGNITION SEMINAR PSA 206 12:15 p.m.
Abdul Ahmed III, Fulton School of Engineering
"Complex Systems Robustness and the Role of Participatory
Decision Making Processes"
ABSTRACT: The speaker will discuss Complex Systems Robustness,
systems characteristics for coping with stress and the
disturbances. The speaker will present a preliminary model of
the effect participatory decision making processes using
stochastic games and discuss extension of the model,
scalability and number of other factors. Examples from various
areas will also be discussed.
Cookies and coffee will be served at 12:00 p.m.
APPLIED ANALYSIS AND PDE READING SEMINAR PSA 546 3:00 p.m.
For more information, contact Svetlana Roudenko.
COLLOQUIUM (FACULTY CANDIDATE) PSA 206 3:00 p.m.
Wenbo Tang, Massachusetts Institute of Technology
"Anatomy of Chaotic Mixing and Locating Clear-Air-Turbulence"
ABSTRACT: Quantifying the mixing and transport that occurs
within turbulent flows remains a difficult, multi-scale problem.
Mathematical tools have recently been developed based upon
dynamical systems theory that regards turbulence as being
organized by Lagrangian Coherent Structures. While mixing and
transport are inhibited in elliptic structures, they are
enhanced by the flow's hyperbolic structures.
In this presentation, I will discuss the application of one
of these tools to extract Lagrangian Coherent Structures in a
large-scale atmospheric data set, as an effort to locate
regions of Clear-Air-Turbulence. The extracted coherent
structures objectively describe regions of different flow
behavior and act as templates for chaotic mixing within the
domain of interest. I will analyze the type and evolution of
several important structures that exist in the data set. This
atmospheric simulation matches a series of balloon experiments
near Hawaii in Dec, 2002. The extracted hyperbolic structures
are in good agreement with turbulent motions from these balloon
measurements.
The extension of this methodology to various other problems
(e.g. the fluid transport in a rotationally constrained
Rayleigh-Benard Convection and mesozooplankton swimming in a
heterogeneous turbulent field) will also be discussed.
Refreshments will be served in PSA 206 at 2:45 p.m.
WEDNESDAY, February 6, 2008
FIRST YEAR MATHEMATICS SEMINAR ECA 225 1:40 p.m.
Igor Fulman, Department of Mathematics and Statistics
"Randomly Generated Paper Exams"
ABSTRACT: I will talk about a Latex/Tex program producing
randomly generated paper exams in a fashion similar to WeBWorK.
This way each student will get a unique form of the exam. The
exams can be either write-up or multiple choice. The same
program also produces answer keys. This is work in progress.
The program has not yet been tested in real tests.
THURSDAY, February 7, 2008
COLLOQUIUM (FACULTY CANDIDATE) PSA 206 11:00 a.m.
X. San Liang, Courant Institute, New York University
"Understanding the Nonlinear Internal Atmosphere-Ocean
Processes"
ABSTRACT: Understanding the internal dynamical processes within
atmospheric/oceanic flows, which are in nature highly
nonlinear, multiscale interactive, and intermittent in space
and time, is a very important and continuing challenging
problem in geophysical and environmental fluid dynamics. During
the past few years, a system of theories and analysis
methodologies has been rigorously developed to address this
kind of challenge. In this talk I will give a brief
presentation of these theories and methodologies, together with
several real problem applications. Of particular focus are the
interactions among large-scale, meso-scale, and sub-mesoscale
processes in the ocean, or the interactions among the mean, low
frequency variability, and synoptic eddies in the atmosphere. I
will first introduce the concept of scale window, and a new
mathematical apparatus called multiscale window transform
(MWT). Established on the MWT is a theory of canonical transfer
and multiscale transport, which leads to a novel localized
hydrodynamic instability analysis, and the formalism of a new
diagnostic methodology called localized multiscale energy and
vorticity analysis (MS-EVA). This system has been validated
with benchmark fluid processes, and applied with success to a
variety of complicated atmosphere-ocean problems, which
otherwise would be very difficult, if not impossible, to
study. Problems investigated include the dynamics that governs
a highly variable ocean front, the nonlinear processes
underlying the complex Monterey Bay circulation and upwelling,
the shedding of the Gulf Stream eddies, the variability of the
North Adriatic circulation, wake dynamics and control, and the
challenging two-way interactions among the chaotic transients,
the North Atlantic Oscillation, and the slower manifold of the
climate system.
Refreshments will be served in PSA 206 at 10:45 a.m.
FRIDAY, February 8, 2008
COMPUTATIONAL AND APPLIED MATHEMATICS PROSEMINAR
PSA 206 3:15 p.m.
Aaron Luttman, Bethany Lutheran College
"Inverse Problems for Botanical and Astronomical Image
Analysis"
ABSTRACT: Many image analysis problems are formulated as
inverse problems, where the goal is to minimize a particular
energy functional over some set of allowable functions. Two
such problems are image segmentation and image deblurring. In
botany it is useful to capture image data of leaves as they
fluoresce in the infra-red, and the goal is to segment the
videos or images into regions of fluorescence and non-
fluorescence. The botanical problem will be described as well
a variational technique with numerical methods for video
segmentation in this context.
Astronomical data measured from the ground is blurred as it
passes through the atmosphere, and this effect must be reversed
in order to analyze the data. This deblurring is formulated as
an inverse problem, and we present theoretical analysis and
numerical results demonstrating that Poisson negative log-
likelihood estimation can be used to reconstruct such
astronomical data when regularized using the total variation of
the reconstruction.