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Industrial Programs
Abstracts for the 2004-2005 IMA/MCIM
Industrial Problems Seminar
1:25 pm
570 Vincent Hall
September
24, 2004, 1:25pm, 570 Vincent Hall
Viktoria Averina (MCIM, School
of Mathematics, University of Minnesota)
Stability of Linear Delay-Differential Equations
Dynamical systems with time delay describe many phenomena in science
- engineering, physics, biology, to name a few. In many applications inclusion
of the past history of the system is not only desirable but is necessary for
obtaining practical results.
The stability of the delay-differential equations (DDEs) with
linear constant coefficients has been thoroughly studied. However, there are
no general analytical methods for DDE systems with time-dependent coefficients.
The importance of this area is apparent in engineering fields such as machine
tool vibrations and optimal control, among others. We propose a numerical method
to study the parameter-dependent stability of this kind of systems with the
period of coefficients being rationally related to the delay.
It has been shown that an infinite-dimensional version of Floquet
theory can be applied to periodic DDEs, thus the stability of the system can
be determined by infinitely many eigenvalues. We construct an approximation
of the ''infinite-dimensional Floquet transition matrix'' by considering differentiation
and coefficient multiplication as operators on space of Chebyshev polynomials.
We show the stability boundaries of some well-known examples of DDEs in mathematics
and mechanics. We also consider application of the proposed method to the problem
of air-to-fuel ratio regulation in internal combustion engines.
October 8, 2004, 1:25pm,
570 Vincent Hall
Pam Binns (Honeywell Pam.Binns@honeywell.com)
A Statistical Verification Methodology and its Applications
Talks(A/V)
Slides: pdf
We present a versatile statistical verification methodology based
on Statistical Learning Theory. We illustrate different uses of this methodology
on two examples of non-linear real-time UAV (unmanned aerial vehicle) controllers.
The first example applies our statistical methodology to the verification of
a computation time property for a software implementation of a high-performance
controller as a function of controller state variable values. The second example
illustrates our statistical verification methodology applied to finding verifiably
safe flight envelopes for a class of maneuvers, again as a function of controller
state variable values. We compare our approach to verification with other statistical
techniques used for estimating execution times and controller performance.
October 15, 2004, 1:25pm,
570 Vincent Hall
Chai Wah Wu (IBM T. J. Watson
Research Center, Yorktown Heights, NY chaiwah@watson.ibm.com)
Halftoning, Watermarking and Scheduling: Some Applications
of the Error Diffusion Algorithm
Talks(A/V)
Slides: pdf
Since all modern printers use a small number of inks, halftoning
is needed to produce images with many colors. Error diffusion is a popular high
speed technique for producing high quality halftoned images. From a mathematical
point of view, error diffusion can be considered as a nonautonomous discrete-time
dynamical system. In the first part of this talk, I will describe some recent
stability results concerning this dynamical system. In particular, error diffusion
is shown to be bounded-input-bounded-state stable if and only if the input color
gamut is inside the convex hull of the output colors. In the second part of
this talk, I will describe several applications of error diffusion beyond digital
halftoning. In particular, I will discuss applications to digital watermarking
and steganography, enhancement of LCD displays and optimal online scheduling
of tasks on limited resources.
October 22, 2004,
1:25pm, 570 Vincent Hall
John R. Hoffman
(Tactical Systems, Lockheed Martin)
Several Problems of Interest to
Lockheed Martin Tactical
Systems
Talks(A/V)
Joint with
Ron Mahler also from Lockheed Martin Tactical
Systems.
They will talk about research at their company. Lockheed
Martin Tactical Systems is located in Eagan, MN, and the
particular group the speakers represent works on problems in
detection and tracking using very sophisticated mathematics.
The purpose of their presentation is to familiarize the
audience with the type of work they do, discuss possible
collaborations, and recruit students for off-campus summer
internships.
October 29, 2004,
1:25pm, 570 Vincent Hall
Todd Wittman (MCIM, School of
Mathematics, University of Minnesota) wittman@math.umn.edu
Decreasing Blur and Increasing Resolution in Barcode Scanning
A barcode is series of alternating black and white bars that encodes
information in the relative thickness of the bars. There are two major types
of electronic scanners in the market: laser and imaging scanners. The two limiting
factors of both laser and imaging scanner accuracy are signal blur and low signal
resolution. To solve the blurring problem, we present a deconvolution approach
based on the minimization of the Total Variation (TV) norm. To approach the
low resolution problem in imaging scanners, we discuss a projection that maps
the pixels in a 2D image to a 1D signal.
November 12, 2004,
1:25pm, 570 Vincent Hall
James F. Greenleaf (Mayo Clinic
College of Medicine, http://www.mayo.edu/ultrasound
jfg@mayo.edu)
Quantitative Promise of Vibro-acoustography and Vibrometry
Talks(A/V)
Vibro-acoustography is a method of imaging and measurement that
uses ultrasound radiation force to vibrate objects. The radiation force is concentrated
laterally by focusing the ultrasound beam. The radiation force is limited in
depth by intersecting two beams at different frequencies so that there is interference
between the beams at the difference frequency only at their intersection. This
results in a cyclic radiation stress of limited spatial extent on or within
the object of interest. The resulting harmonic displacement of the object is
detected by its acoustic emission, with ultrasound Doppler measurement, with
a laser interferometer or the resulting acoustic emission is detected with a
hydrophone. The displacement is a complicated function of the object material
parameters. However, significant low speckle and high contrast images and measurements
can be made with this arrangement. Vibro-acoustography can produce images of
biologically relevant objects such as breast microcalcification, vessel calcifications,
heart valves, and normal arteries. In addition vibrations placed in specific
geometrically shaped tissues such as arteries can be used to induce modal responses
that can be used to solve for material properties. Specific examples of these
results will be described.
December 3, 2004, 1:25pm,
570 Vincent Hall
Douglas C. Allan (Corning Incorporated
AllanDC@Corning.com)
Adventures in Industrial Mathematics: Making Better Lenses
for Making Computer Chips
Talks(A/V)
This talk presents some real-life examples of mathematics and
numerical simulation used in a manufacturing industry. Examples include one
story with a mathematical moral.
The exponential improvement over time in computer speed and memory
relative to cost and size makes ever-increasing demands on the many technologies
that are part of computer chip manufacture. One strategy for shrinking the size
of computer chip features is to do photolithography with light sources of smaller
wavelength. At smaller (now ultraviolet) wavelengths, each photon carries more
energy. These energies are now high enough to slowly cause damage in the glass
lenses used in photolithography optics, destroying the optics over time. This
talk presents some aspects of the mathematical analysis of laser-induced damage
in glass and emphasizes how mathematical analysis and computer simulation play
a role in modern materials research and manufacturing.
December 10, 2004, 1:25pm,
570 Vincent Hall
Kevin R Vixie (Los Alamos National
Laboratories, Los Alamos, NM vixie@speakeasy.net)
Image Analysis as an Inverse Problem: Overview and Examples
Talks(A/V)
In this talk I present a viewpoint that makes many of the image
analysis and processing tasks look very similar to one another. This view --
that we are solving an inverse problem in which the tasks are the choice of
regularization and the modeling of the measurement operator -- carefully highlights
where effort and insight need to be focused. Since specification of regularization
is nothing more or less than the specification of the prior assumptions on what
ideal images are like, this task can be seen to take on great importance, especially
when -- as is often the case -- the data is sparse. The mathematical issues
and their practical impact will be discussed and illustrated with examples.
January 21, 2005, 1:25pm,
570 Vincent Hall
Yiju Chao (Morton Consulting Corporation,
Minnetonka, MN)
Algebraic-Topological Formulation and Distributed Control
of Packet-Switched Networks of General Topology
Talks(A/V)
Slides: pdf
This talk presents a novel algebraic-topological methodology to
formulate and design distributed control of traffic flows on packet-switched
networks. This formulation is a more natural way to model packet-switched networks
than traditional models using the multi-commodity network flow formulation or
the queuing network formulation. Using this new framework, we show how the local
boundary, coboundary, and Laplacian operators defined for a graph can be used
to design distributed control of traffic flows. Our distributed network control
design is a two-step paradigm based on the adjoint relation between the node
space (0-chains) and the link space (1-chains) of a network. The two-step paradigm
includes:
(1) A global outer-loop routing solution that is optimal on the
cycle space.
(2) A real-time inner-loop control to load-balance queues formulated
on the image of the coboundary operator.
According to the solution in each of these two steps, each network
node updates its routing table autonomously based on local information. Even
though the algorithm has a distributed implementation, the resulting routing
solution is an acyclic flow (no closed loops) that minimizes cost and ensures
network stability.
January 28 , 2005,
1:25pm, 570 Vincent Hall
Maria Ponomarenko (MCIM, School
of Mathematics, University of Minnesota)
Approximation of Functions by Artificial Neural Networks
Neural computing is a very powerful class of modelling techniques
capable of approximating extremely complex functional relationships. It has
been increasingly used as a practical approach in such problems as pattern recognition,
classification and function approximation. Within the broad range of different
networks, the most widely used ones are the sigmoidal and the radial basis function
ones. We discuss the use of these networks in function approximation problems,
making emphasis on the network structures, training processes and learning algorithms.
We give an overview of the most important theoretical developments in this field
and outline the relevant practical open problems. Finally, we present our results
on error bounds for function approximation by sigmoidal and radial basis function
networks.
February 18 , 2005,
1:25pm, 570 Vincent Hall
John Dodson (American Express)
Selections from an Applied Mathematics Research Agenda
for the Finance & Investments Industry
Talks(A/V)
Slides: pdf
The speakers will present and discuss a selection of open problems
from finance and investments, including: investment decisions under information
asymmetry, risk in a world of Levy stable processes, bubbles as emergent phenomena,
measuring investment breadth, pro-cyclicality, practical multi-period coherent
definitions of risk, and challenges with inverse problems.
March 4, 2005,
1:25pm, 570 Vincent Hall
Chenyang Xu (Imaging and Visualization
Department, Siemens Corporate Research, Inc.)
Medical Image Segmentation Using Deformable Models
Talks(A/V)
In the past four decades, computerized image segmentation has
played an increasingly important role in medical imaging. Segmented images are
now used routinely in a multitude of different applications, such as the quantification
of tissue volumes, diagnosis, localization of pathology, study of anatomical
structure, treatment planning, partial volume correction of functional imaging
data, and computer-assisted surgery. Image segmentation remains a difficult
task, however, due to both the tremendous variability of object shapes and the
variation in image quality. In particular, medical images are often corrupted
by noise and sampling artifacts, which can cause considerable difficulties when
applying classical segmentation techniques such as edge detection and thresholding.
As a result, these techniques either fail completely or require some kind of
postprocessing step to remove invalid object boundaries in the segmentation
results.
To address these difficulties, deformable models have been extensively
studied and widely used in medical image segmentation, with promising results.
Deformable models are curves or surfaces defined within an image domain that
can move under the influence of internal forces, which are defined within the
curve or surface itself, and external forces, which are computed from the image
data. By constraining extracted boundaries to be smooth and incorporating other
prior information about the object shape, deformable models offer robustness
to both image noise and boundary gaps and allow integrating boundary elements
into a coherent and consistent mathematical description. Such a boundary description
can then be readily used by subsequent applications. Since its introduction
15 years ago, deformable models have grown to be one of the most active and
successful research areas in image segmentation.
There are basically two types of deformable models: parametric
deformable models and geometric deformable models. Parametric deformable models
represent curves and surfaces explicitly in their parametric forms during deformation.
This representation allows direct interaction with the model and can lead to
a compact representation for fast real-time implementation. Adaptation of the
model topology, however, such as splitting or merging parts during the deformation,
can be difficult using parametric models. Geometric deformable models, on the
other hand, can handle topological changes naturally. These models, based on
the theory of curve evolution and the level set method, represent curves and
surfaces implicitly as a level set of a higher-dimensional scalar function.
Their parameterizations are computed only after complete deformation, thereby
allowing topological adaptivity to be easily accommodated. Despite this fundamental
difference, the underlying principles of both methods are very similar.
In this talk, I will present an overall description of the development
in deformable models research and their applications in medical imaging. I will
first introduce parametric deformable models, and then describe geometric deformable
models. Next, I will present an explicit mathematical relationship between parametric
deformable models and geometric deformable models. Finally, I will present several
extensions to these deformable models by various researchers and point out future
research directions.
March
25, 2005, 1:25pm, 570 Vincent Hall
Jan H. Vandenbrande (Boeing)
Solid Modeling: Math at Work in Design
Talks(A/V)
Design is the art of creating something new and predicting how
it will perform before it is ever build. One of the major breakthroughs in the
last 25 years is the ability to describe a design as a virtual artifact in a
computer, and simulate its physical characteristics accurately to enable designers
to make better decisions. The core technology that underlies these mechanical
Computer Aided Design and Manufacturing (CAD/CAM) systems is solid modeling,
whose theoretical underpinnings are grounded in mathematics.
This talk will cover some of these mathematical concepts, including
point set topology, regularized set operations, Constructive Solid Geometry
(CSG), representation schemes, algorithms and geometry.
We will cover the impact of solid modeling in industry, and discuss
some of the remaining open issues such as the ambiguity between the topological
representation and the computed geometric boundary.
April
1, 2005, 1:25pm, 570 Vincent Hall
Miroslav Trajkovic (Advanced Development Symbol
Technologies Inc.)
Industrial Applications of Scene Change Detection Algorithms
Talks(A/V)
In this presentation I am going to discuss different approaches
to scene change detection and its various industrial applications. I will give
several examples of different scene change detection algorithms I developed
including: motion detection from a moving camera, with application to video
surveillance; building background model in the presence of moving objects; detection
of the foreground objects with fixed background, and it’s application in automotive
industry; and illumination invariant motion detection based on frame differencing;
and its application in bar code reading industry.
April 8, 2005, 1:25pm,
570 Vincent Hall
Kevin Ellwood (Materials Science Department, Ford Research & Advanced Engineering)
A Model for the Oxidative Ageing of Tires
Talks(A/V)
Joint work with John Baldwin and David Bauer.
A simple kinetic model has been developed to interpret issues
related to accelerated aging of tires. The finite-element model is based on
the Basic Autoxidation Scheme and incorporates mass transport limitations related
to diffusion of oxygen into the layered elastomer system. The effect of aging
on transport properties, such as diffusivity, due to changes in cross-link density
is also considered in the model. The extent of oxidation is calculated at different
locations within the tire as functions of time, temperature, and inflation media.
Approximate changes to physical properties were derived from oxidation histories
predicted by the model and compared to experimentally measured data which includes
crosslink density and elongation-to-break. Finally, we will examine the effect
of temperature on accelerated ageing in the context of accelerated testing.
April 22, 2005, 1:25pm,
570 Vincent Hall
David Trebotich (Lawrence
Livermore National Laboratory, Center for Applied Scientific
Computing)
Big Physics in Small Spaces: Numerical
Algorithms for Biological Flow at the Microscale
Biological flow is complex, not well-understood and inherently
multiscale due to the presence of macromolecules whose
molecular weights are comparable to length scales in the
typical flow geometries of microfluidic devices or critical
anatomies. Modeling these types of flows such as DNA in
solution or blood is a challenge because their constitutive
behavior is not easily represented. For example, a highly
concentrated solution of suspended polymer molecules may be
represented at the system level with a continuum viscoelastic
constitutive model. However, when geometry length scales are
comparable to the inter-polymer spacing, a continuum
approximation is no longer appropriate, but, rather, a discrete
particle representation coupled to the continuum fluid is
needed. Furthermore, fluid-particle methods are not without
their issues as stochastic, diffusive and advective processes
can result in disparate time scales which make stability
difficult to determine while capturing all the relevant
physics.
At Lawrence Livermore National Laboratory we have developed
advanced numerical algorithms to model particle-laden fluids at
the microscale. We will discuss a new stable and convergent
method for flow of an Oldroyd-B fluid which captures the full
range of elastic flows including the benchmark high Weissenberg
number problem. We have also fully coupled the Newtonian
continuum method to a discrete polymer representation with
constrained and unconstrained particle dynamics in order to
predict the fate of individual DNA molecules in post
microarrays. Our methods are based on higher-order finite
difference methods in complex geometry with adaptivity. Our
Cartesian grid embedded boundary approach to treating irregular
geometries has also been interfaced to a fast and accurate
level-set method for extracting surfaces from volume renderings
of medical image data and used to simulate cardio-vascular and
pulmonary flows in critical anatomies.
April 29, 2005, 1:25pm,
570 Vincent Hall
Howard Karloff (AT&T Labs--Research)
Optimization and Approximation at AT&T Labs and Beyond
I will speak on some practical projects at AT&T Labs in which
I've been involved. These include multiprocessor scheduling, voice switch "deloading,"
and FCC spectrum auctions; only the multiprocessor scheduling section will be
technical.
May 6, 2005, 1:25pm,
570 Vincent Hall
Geoffrey W. Burr (IBM Almaden
Research Center, San Jose, California)
Finite-Difference Simulation of Nanoscopic Devices
In its simplest manifestation, a finite-difference scheme
discretizes a
system of partial differential equations directly onto a
regular,
Cartesian mesh. Since such finite-difference schemes can
readily scale to
simulations with millions of elements, they have become popular
for
addressing complex physical simulations. Here we discuss two
applications
of finite-difference techniques. The first is the use of the
Finite-Difference Time-Domain (FDTD) algorithm for simulating
Maxwell's
Equations in nanophotonic devices such as photonic crystals;
the second is
a customized multi-physics simulator for non-volatile
electronic
phase-change memory. The latter solves the diffusion equation
by
finite-difference techniques in order to simulate heat
diffusion as well
as to compute the steady--state potentials satisfying Laplace's
equation.
The tight relationship between the choices of spatial and
temporal steps
("Courant stability"), and the resulting impact on the two
different
finite-difference schemes, will be discussed.
Industrial Programs
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