Utah State University Department of Mathematics and National Science Foundation.

This is the third in a series of NSF sponsored workshops. The two day meeting will highlight research problems in industrial and interdisciplinary mathematics through talks by researchers in academia and industry and through a poster session. Additionally, the meeting will present a roundtable discussion on applied mathematics and a joint session with the Arizona Mathematics Undergraduate Conference on mathematical career choices in industry.

Dieter Armbruster [armbruster@asu.edu, phone: 480.965.5441]

Department of Mathematics,

Arizona State University,

Tempe, AZ 85287-1804

*Title:* Stochastic Modeling and the Theoretical Epidemic: Spatial Heterogeneity and Time to Extinction

*Abstract:*

*Title:* Linking Functional And Structural Brain Images With Multivariate Network Analyses: Description And
Application Using The Partial Least Square Method

*Abstract:*

*Title:* MANUFACTURING, ROBOTICS AND COMPUTATIONAL GEOMETRY

*Abstract:* This Lecture features examples of the dominating influence
of geometry in the automotive manufacturing process.
The lecture begins with the design and manufacture of sheetmetal
components that motivated advances in mathematical applications
for Computer Aided Design. After a discussing the mathematics
developed for the geometric aspects of this manufacturing
process, the lecture examines an application of the same
mathematics to robotics. The next topic relates the previous
geometric constructions with the analysis of automotive
components for fatigue, stress and strain. The lecture ends
with the award winning video tape "Ballet Robotique".

*Title:* Cross-shipping and Meeting Demand

*Abstract:* In this talk, results of simulations involving two manufacturing lines,
manufacturing similar products, will be presented. Two very similar manufacturing lines
with slightly different total manufacturing time will be considered. The main focus will
be on the need for cross-shipping at different levels of the manufacturing process to
meet short and long term demands.

*Title:* Computations of Multivalued Solutions of Nonlinear PDEs

*Abstract:*Many physical and industrial problems arising from high frequency waves,
dispersive waves, Hamiltonian systems, traffic models and supply chains
require the computations of multivalued solutions
which cannot be described by the viscosity methods. In this talk I will
review several recent numerical methods for such problems, including the
moment methods, kinetic equations and the new level set method with S.
Osher, H. Liu and R. Tsai.
Applications to the semiclassical Schroedinger equation and Euler-Piosson
equations with applications to modulated electron beams in Klystrons
will be discussed.

*Title:* Some Mathematical Ideas for Attacking the
Brain Computer Interface Problem

*Abstract:* The Brain Computer Interface (BCI) Problem has become a topic of
interest both to academic researchers and their industrial
counterparts. The ability to interpret or classify rational thought
from its measurements is, to say the least, intriguing. While there are
currently no BCI products available on the market many companies are
planning to introduce new devices and it appears that this is just the
beginning. It is unknown whether computers will ever be mind readers
and we will not attempt to answer this question! However, we will
describe the BCI research efforts at Colorado State University and some
mathematical ideas being considered.

*Title:* Modeling and control of manufacturing systems

*Abstract:*When considering the problem of supply chain management in semiconductor
industry, a prerequisite is to use the simplest model that still contains
sufficient information to answer all of the relevant questions. One of the
problems of interest is how to ramp from zero production to full production in
the shortest time possible.
Roughly three classes of models for manufacturing systems have been studied in
the literature so far: discrete event models, queueing theory and fluid
models. Each of these models have its shortcomings. Discrete event models
suffer from state explosion, queuing theory establishes only steady state
results, and fluid models do not incorporate flow times (also called
throughput times, cycle times or sojourn times). Therefore, we use a new class
of flow models in which we assume that the flow of products can be considered
as a compressible fluid flow. This new class of flow models yields
computationally feasible, dynamic models that incorporate both throughput and
cycle time.
Even though discrete event models suffer from state explosion, they can be
used for validation of the proposed PDE-models. Once the PDE-models have been
validated, the ramp-up control problem can be studied.

*Title:* Optimization-based design of multisine signals for "plant-friendly"
identification of highly interactive process systems

*Abstract:*Highly interactive systems are ill-conditioned and as a consequence
are very sensitive to model uncertainty; this imposes fundamental
limitations to achievable closed-loop performance.
We present an identification testing framework meaningful to
highly interactive process systems based on the application of
multivariable multisine input signals possessing specialized harmonic
characteristics. "Plant-friendliness" in the design procedure is
accomplished by using advanced optimization solvers that minimize an
objective function while imposing constraints on the overall span,
move size, and variability of both input and output signals.
Objective functions of interest include minimizing crest factor
(which results in signals that are evenly distributed at their high
and low limits) and maximizing the geometric distribution of the
output over a region in the state-space. The latter objective is
particularly meaningful for data-centric estimation techniques such
as Model-on-Demand. This signal design procedure is applied to a
2-by-2 multivariable model representing the simplified dynamics of
high-purity distillation, which represents a class of systems
exhibiting challenging interaction and gain directionality
properties. The signals obtained from this approach are shown to
possess significant fundamental and practical properties in
comparison to classical designs.

*Title:* A Constrained Filtered Least Squares Method Applied to a Problem in
Medical Imaging

*Abstract:*

*Title:* Computational Biosciences Masters at ASU

*Abstract:*

*Title:* An Introduction to Inverse Problems

*Abstract:*The scope of this talk is basic. I hope to introduce and make concrete
the concept and ideas that arise in the study of inverse problems.
Several simple examples will demonstrate common difficulties arising in
the study of inverse problems. These examples will be drawn from inverse
problems of elliptic, parabolic and hyperbolic PDEs.

*Title:* Applications of Wavelets in Signal Processing: Introduction to
Wavelets

*Abstract:*Abstract: This talk introduces
the audience to wavelets by describing what wavelets are (and are not),
what their properties are (and are not), and what you can do with them
(and can not). A brief history of the early development of wavelets is
given to provide motivation for their existence, i.e. they were created
on purpose as opposed to being discovered by accident.
Specific examples of how wavelets are
used in current applications and how they might be used in the future
are discussed.

*Title:* Overview of our effort in using computer simulation to understand
the turbulence in the stratosphere

*Abstract:*Understanding the turbulence in the stratosphere is important as it
affects aviation and light propagation. There are three major sources
of turbulence in the stratosphere : (1) turbulence may be generated at the
edge of the jet stream due to shear, (2) convection in the troposphere may
overshoot into the stratosphere, (3) gravity waves generated in the
troposphere may propagete upward and in turns create turbulence in the
middle or upper stratosphere. The dynamics of the turbulence is goverened
by the Navier-Stokes equation. Substituting different parameters and models
into the equation, we are able to simulate computationally
the turbulence generated from all three circumstances. Some
features of our results, e.g. separation of mechanical and thermal layers,
length scale of the turbulence, etc, will be presented.

USU

*Title:* Reverse engineering gene networks

*Abstract:* We present a scheme to reverse-engineer gene networks on a
genome-wide scale using a relatively small amount of gene
expression data from microarray experiments. It uses singular
value decomposition to construct a family of solutions and then
identify the unique solution by robust regression. Our
algorithm has $O(\log N)$ sampling complexity and $O(N^4)$
computational complexity. We test and validate our approach in
a series of numerical experiments on model gene networks.

USU

*Title:* Optimal Velocity Profiles for the Migration Flights of Swans

*Abstract:*
Members of the two swan species that are native to North America, Tundra and Trumpeter swans,
undertake long migratory journeys as long as 6,000 km twice yearly. These migrations are
carried out as a series of hops and stops. For Tundra swans, hops of approximately 500
kilometers are followed by stops of several days during which flight-depleted fat stores and
muscle mass are restored. In order to model migration flights it can be reasonably assumed
that a swan will choose a velocity profile that minimizes energy expenditure over the course
of the flight, and that its mass and frontal body area decrease during flight due to fat store
depletion. Utilizing an equation describing power requirements for level flight published by
Pennycuick (1989), optimal velocity profiles and resultant mass profiles were obtained by
solving a constrained optimization problem with the calculus of variations.
Swan mass over the course of migration can be described by a dynamical system that
when coupled with optimal mass profiles obtained from the model yields a tool for
predicting the length of a refueling stop based on the length of a preceding migratory hop.
The model predictions can then be tested using satellite tracking data.

Wageningen University, The Netherlands

*Title: Population movement of ladybeetles;
model evaluation of mechanisms causing ladybeetle aggregation in resource patches
*

*Abstract:*The presentation focuses on the analysis of an experiment in which
areas in an alfalfa crop were sprayed with sucrose solution. Sucrose (table sugar)
is a useful resource for ladybeetles (like for many insects), and it acts as an
indicator for the presence of aphids because aphids excrete a waste product, honeydew,
that is rich in sugars. Following sucrose application, it is observed that ladybeetle
densities increase by a factor of 10-20 within a couple of hours. It is unknown whether
this aggregation occurs by: (1) directional immigration by flight into sugar-sprayed areas
(presumably guided by volatile chemical cues) (2) decreased emigration by flight by beetles
who have (possibly by chance) entered the sugar sprayed area (3) decreased motility of walking
beetles in sugar sprayed canopy, compared to unsprayed canopy (area restricted search)
In the field experiment, strips of alfalfa of 2, 5 and 10 m width were sprayed with sugar,
and ladybeetle densities on transects across those plots were measured at three times after
sugar spray. Different spatially explicit models are fitted to the data to determine which
of the above three candidate explanations for aggregation are operating.