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Applied and Computational Mathematics Seminar, Fall 2006
MATH 891-A07 (04800)
Brought to you by the Department of Mathematics at Ohio University. For further information, or to volunteer to talk, contact Vardges Melkonian (vardges@math.ohiou.edu), Martin Mohlenkamp (mjm@math.ohiou.edu), or Annie Xiaoping Shen (shen@math.ohiou.edu). Regular meetings are Mondays 4:10-5pm in 320 Morton Hall.
Scope
Topics of significant mathematical content that either have direct application to a real-world problem or require computational techniques in their solution (or both).
Mission
To expose the participants (especially graduate students) to problems of current interest to members of the department; to provide a forum for interdisciplinary interaction with other departments; and to provide an incubator for student research projects.
Schedule
Monday 11/13,
Speaker: Martin Mohlenkamp,
Department of Mathematics,
Title: Helium and a bit of Lithium Hydride
Abstract: The multiparticle Schrodinger equation is the basic governing
equation in Quantum Mechanics. For a given molecule, the wavefunction
that solves this equation determines the molecule's energy and
other physical and chemical properties.
We have developed a method for computing an approximation to a
wavefunction with an unconstrained sum of Slater determinants. In this
talk I will formulate the multiparticle Schrodinger equation, sketch
our solution method, and present intitial numerical results for the
Helium atom and the Lithium Hydride molecule. We will also look at
lots of graphs of pieces of the wavefunctions and wonder what they
mean.
Tuesday 10/24,
Speaker: Gregory S. Springer,
Department of Geological Sciences,
Title: Stream Erosion As Accomplished By Vortices: What Math Can Tell Geologists
Abstract: Stream erosion is the process by which floodwaters pluck blocks of rock
off streambeds or abrade channel surfaces in a manner similar to
sandblasting. Thick, hard rock units resist plucking and favor abrasion.
Typically, abrasion occurs within depressions that contain high-velocity
vortices (eddies) during floods. Potholes are a common type of
depression and take the form of holes drilled into rock. Potholes are
self-sustaining. As they grow in size, potholes create more coherent
vortices that are highly effective at eroding rock. Analyses of pothole
geometries has led to recognition that regardless of locality, potholes
are formed by a small set of processes. The analyses also reveal how
erosion of adjacent channel surfaces affects potholes and how the
interiors of potholes are eroded. However, many questions remain to be
answered. The majority of these questions will require sophisticated
statistical analyses of pothole populations. The presenter will
discuss his work in potholes and identify some of the key questions at
hand.
See some photos of potholes.
Wednesday 10/18,
Speaker: Brandilyn Stigler, postdoctoral fellow, Mathematical Biosciences
Institute (MBI),
Title: Reverse Engineering of Network Topology
Abstract: Advances in bioinformatics technologies and computational
modeling methods are launching biology into a new paradigm of
quantitative, predictive science. The emerging field of systems biology
is focused on the
integration of biological information at multiple levels of living
organization into descriptive and predictive mathematical models. One
primary approach in the systems-biology framework is to build models from
time series of experimental data, often obtained by measuring the response
of a biological system to certain types of perturbations. This approach,
commonly referred to as reverse engineering, is an important step in
elucidating features of such systems, including network topology and
dynamics.
We consider the problem of reverse engineering network topology for
systems of interacting biochemicals. In this setting network topology is
encoded in a directed graph, called a wiring diagram, which represents the
causal relationships between system variables. We present an algorithm
which computes all possible minimal wiring diagrams for a given data set
of measurements from a biochemical network and scores the diagrams. The
algorithm uses computational algebra, namely primary decomposition of
monomial ideals, as the principal tool. An application to the
reverse-engineering of two gene regulatory networks is included.
Monday 10/9,
Speaker: Dr. Winfried
Just, Department
of Mathematics,
Title: Hard questions about simple
finite dynamical systems
Abstract: A Boolean dynamical system is a dynamical system whose state
space consists of vectors of fixed finite length of Boolean values 0 and
1. Such systems have important applications in mathematical biology as
models of gene regulatory networks. In studying these models, one would
like to have an efficient algorithm for deducing the dynamical properties
of the system from the formula for the updating function. In particular,
one would like to know if all attractors of the system are steady states.
Efficient algorithms for this problem are known if the updating function
is linear or each of its components is a monomial. In this talk we will
see that if the set of permissible updating functions is only slightly
broadened, the problem becomes computationally intractable, more
precisely, NP-hard.
In this talk we will present Boolean dynamical systems as models of gene
regulatory networks and will review the basics of NP-hardness. Then we
will state our main results and illustrate the technique of proving
NP-hardness of a given combinatorial problem with one of our proofs.
Monday 9/25,
Speaker: Dr. Wei
Lin, Department
of Mathematics,
Title: Error variance estimation for
single-index models
Abstract:
Single-index models (SIMs) provide one way of reducing the dimension in regression analysis. The statistical literature has mainly focused on estimating the index coefficients, the mean function, and their asymptotic properties. In this talk I will briefly talk about this class of models and then discuss the estimation for the error variance. Two estimators will be introduced, one is the traditional MSE-type estimator, and the other is similar to the difference-based error variance estimator in the literature of nonparametric regression. The asymptotic normality of both estimators is established, a test for the equlity of the error variances of two SIMs is proposed and an empirical study will be presented to show their finite sample performances. In addition to the above theoretical aspects of SIMs, I will also introduce how statistical simulations are carried out in general and then we will look into some computational issue that is related to this specific simulation study.
Spring
2005-2006 schedule