Spring 2003 Seminars Organizer: Art Gorka
My Experiences with the Academic Job Search
Speaker
Kevin Hutson , Furman University
Abstract
Looking for a job in academics? The process of finding a (first
academic) job can be overwhelming and exhausting. In this talk, I describe my
recent experiences while on the job market. The topics I will discuss are:
how to prepare early, the interview process, juggling offers, and frequently
asked questions.
Here there are examples of the files you may need to send when applying for a job in academia:
Curriculum Vitae
Cover Letter
Research Statement
Teaching Statement
AG: and a useful link with some basic info about job hunting
What do you get when you cross a Swiss psychologist with 2 Dutch educators?
Speaker
Rachel Keller , Martin Hall E-6
Abstract
Are your students not understanding the material you present? Do you think
that your students are understanding you, but you find they disappoint you
come test day? Ever wonder who is to blame for this? Although many of us
blame our students, some of the experts would disagree. Piaget claims that
the students are not to blame for this problem because many of them have not
yet acquired crucial cognitive skills necessary for this level of math. The
van Hieles claim that the students are not to blame because with the proper
instruction, any student can achieve success at any level of mathematics.
Throughout this talk, we will examine Piaget's model of cognitive
development, as well as the van Hiele model of the development of geometric
thought. We will compare and contrast these two models, and also look at
suggestions for implementation in the classroom
What's Fair?
Speaker
Mark Liu , Martin Hall E-6
Abstract
Fairness has always been a topic of interest to mankind. (This applies to
other animals as well but we spare them of that spotlight at the moment.)
If Jack and Jill came up with $5 each and bought a $10 cake, what should be
the fair way of dividing the cake? If a bank rupts, what is a fair way to
divide the available money to its account holders? Or more applicably, if you
and your buddy decide to share an apartment here at the Clemson Metropolitan,
how much of the rent should each person pay? How about divorces? How about
dividing estate?
This talk will be somewhere at the intersection of simple Equity
Theory, Social Choice Theory, and Mechanism Design. The content
should be accessible enough for new undergrads. We will also talk
about the Talmud (a subset of the Jewish civil and canonical laws)
and one of its many wonders as well.
Dynamic Multi-Body Contact Problems with Friction
Speaker
Darek Wlodarczyk , Martin Hall O-4
Abstract
Dynamic multi-body contact problems arise in several research areas.
Modeling the dynamic behaviour of rigid bodies in contact is difficult, especially
when friction is present and the number of contacts is large.
In this talk we will formulate the problem as a linear complementarity problem
(LCP). We will introduce LCPs and discuss a few algorithms that solve LCPs. Simple
2-D simulations will be presented.
An Introduction to Multivariate Statistical Quality Control
Speaker
Thomas McCoy , Martin Hall E-6
Abstract
In this talk we will be discussing the advantages of introducing multivariate techniques to
traditional quality control tools, specifically, control charts for process average and
dispersion. When looking at process characteristics simultaneously, the region of control is
elliptical due to the correlation structure of the monitoring characteristics. A discussion
of univariate control charts will be provided, with their important connection with Process
Capability, and examples given. The motivation for the extension to the multivariate case
will be also given, noting the important considerations of controlling the accumulation of
Type I errors in monitoring many processes individually.
Multivariate control charts will be introduced by looking primarily at Hotelling's T2 charts
for process averages and dispersion. Connections with Mahalanobis distance and the
incorporation of correlation among process monitoring characteristics will be examined.
Mental Illness and the Mathematician
Speaker
Robert Beeler , Martin Hall O-5
Abstract
It is said that there is a thin line between genius and
insanity. In this talk, we will take a brief look at mathematicians who
stepped over this line and were plagued by schizophrenia, paranoia, and
emotional imbalance. Tragically , the lives and careers of several great
mathematicians were diminished due to their struggle with menal illness.
Mathematicians to be included are Blaise Pascal, Isaac Newton, Georg
Cantor, Kurt Godel, John Nash, and the infamous Unabomber, Theodore
Kaczynski. Other mathemaicians may be discussed if time permits.
Investigating fractional order diffusive processes: Analysis and numerics.
Speaker
John Paul Roop , Martin Hall O-2
Abstract
In this talk, we will discuss the physical implications of modeling
diffusive processes using fractional dimensional operators. We will
discuss analytic results which show the mapping properties of these
operators in a Hilbert space setting. We introduce a least-squares finite
element variational method which is used to solve the steady-state and
transient problems. Numerical results are included which show error
convergence as well as the differences between different sets of modeling
equations. Here
there are a few profiles for the same problem.
Implementation and Numerical Results for a massively parallel generalized Stokes solver.
Speaker
Kelly Waters , Martin Hall O-8
Abstract
The generalized Stokes problem often arises as an iterated subproblem in
solving time dependent flow problems. Glowinski & Pironneau developed a
means of decomposing the velocity and pressure variables for this problem.
In the FEM setting, the divergence-free condition is enforced by the
computation of an appropriate value for the pressure along the boundary of
the domain of the flow governing PDE. Phase one includes building two
large linear operators, U & P, and a relatively small but costly linear
operator, B, to calculate the boundary pressure directly. Once phase one
is accomplished, it need not be repeated. Phase two makes use of U, P,
and B, and produces solutions for successive input values - that is, phase
two is the iterated subproblem in the time dependent flow problem.
In this talk we briefly present the method of Glowinski and Pironneau, along with a discussion of our parallel implementation using a Peaceman Rachford linear solver that decomposes the U & P operators into two permuted block diagonal symmetric positive definite systems. We also present numerical results including FEM error estimates, a parameter study, and timing results from solving a few example problems on up to 32 nodes on a Beowulf Cluster.
Ya'll come - it'll be fun:)
Optimal Control For Polymer Process Modelling
Speaker
David Szurley , Martin Hall O-317
Abstract
![[Fibers are used in military applications]](tanks_sm.jpg)
The fibers and films industry provides a wealth of mathematical
modeling opportunities. For example, the processes by which the polymeric fibers
and films are manufactured can be formulated as a system of nonlinear partial
differential equations. Accurate simulation can significantly reduce
trial-and-error experiments needed to determine optimal operating conditions for
the process lines. The introduction of optimization techniques moves the
simulation effort from prediction to design, automating the search for optimal
process conditions. In this talk, optimization-based simulation is presented for
fiber melt spinning and film casting. A system of ordinary differential equations
governs the one-dimensional approximation under the assumption of steady-state
behavior. Both simple and advanced optimization strategies are demonstrated.
Here's an example where the fibers are used, and
here's another one.
Interpolating Points in Higher Dimensions
Speaker
Jeff Farr , Martin Hall O-7
Abstract
The well-known problem of polynomial interpolation involves
finding a suitable (usually small) polynomial f such that f(Pj)=0 for
a collection of points P1,..., Pn. There are many ways to find an
interpolating polynomial in the two-dimensional case, i.e., when
Pj=(aj,bj). Standard algorithms include Lagrange interpolation and
Newton interpolation. However, interpolating points in higher dimensions
presents more of a challenge. We discuss solutions to this problem,
including a new generalization of Newton interpolation. We also apply this
algorithm to a decoding problem for algebraic geometry codes.
Permutation Decoding
Speaker
Jira Limbupasiriporn , Martin Hall O-6
Abstract
Permutation decoding is a technique for decoding linear codes, which was
developed in 1964 by F.J. McWilliams. The decoding can be used when a
code has a large group of automorphisms to ensure the existence of a set
S of automorphisms that satisfies certain conditions. Thus a PD-set S for a
code C is a set of automorphisms of C such that if C can correct t errors,
then the non-zero entries in every possible error vector of weight <= t can be
moved by some member of S out of the information positions. The set S will
then be used to assist in decoding a received vector.
In this talk, we will introduce some basic concepts on coding theory that
are necessary for our purpose and then discuss the algorithm for permutation
decoding. We will also give some simple examples to explain the decoding.
Statistical properties of the Random Method of Feasible Directions
Speaker
Art Gorka , Martin Hall O-1
Abstract
In this talk we will be looking at the working of the Random Method of Feasible Directions.
The algorithm is considered to be a mapping transforming uniform distributions to some other
type (skewd normal, dychotomic, increasing or decreasing etc) distributions. We atempt to
describe these distributions and use the findings to improve the performance of the
algorithm.
A solution fiber
A bunch of solution fibers
Fall 2002 Seminars Organizer: Art Gorka
Mathematics Web Resources
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Art Gorka , Martin Hall O-1
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Solving the generalized Stokes problem is a major/expensive step in
producing flow solutions in a variety of applications. In this talk we
first discuss how the generalized Stokes problem arises in the
viscoelastic flow setting. Then we will review our use of the
Glowinski Pirroneau pressure decomposition coupled with a Peaceman
Rachford domain decomposition generalized Poisson solver. In conclusion
we breifly address the many opportunities the combination of two
techniques offer in terms of parallelization.
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Abstract In this presentation we introduce the basic commands and environments commonly used in
LATEX. Starting with the fundamentals we learn how to prepare an
input file, how to compile the input file (run latex on the input file), how to view the
compiled file, and how to print the final document.
In part two of the presentation, we explore some of the commonly used
environments in LATEX and how to typeset Mathematical formulas.
We look at the various ways in which formulas can be entered into your document and the
advantages and disadvantages of each environment for entering formulas. If time
permits we will explore some of the more advanced features of
LATEX like customizing some environments and giving your document
a professional touch.
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There are other variations of domination to be studied. If we return our
attention to the definitions of an independent set we can develop the definitions
of a dominating set and irredundant set using maximality and minimality
conditions. If instead of avoiding paths of length two, we avoid cycles then we
have what we call a cycle-independent set. Using maximality and minimality
conditions we can develop appropriate definitions for a cycle-dominating set and
a cycle-irredundant set.
In this presentation we assume no knowledge of graph theory, although some would
not hurt. We begin with a brief study of domination, domination parameters, and
the domination chain. We then turn our attention to defining a variation of
domination, cycle-domination. After which we examine cycle-domination and finish
with a few results regarding the parameters of cycle-domination.
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The basic facility loaction models assume that the parameters of the problem
are known with certainty. However, there is considerable uncertainty in most
real-world location problems. Uncertain parameters which have been addressed
in the literature include demand, travel time, the availability of the
facility for service, and number of facilities to be sited.
In this talk, we begin with a brief review of stochatic location models.
Then we will present a "bottle-neck" (with Minimax objective) M/G/1 queuing
facilty location model. Several results regarding solving the problem will be
derived.
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In the second half of the presentation we'll learn how to make up slide
presentations in LATEX using simple
commands.
For preparing Power Point type presentations we can use the
ifmslide package that will be presented at the seminar on
11/11/02 .
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Spring 2002 Seminars
Organizer: Jeff Farr
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Fall 2001
Seminars Organizer: Jeff Farr
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In our talk we present the main idea behind this iterative method and
the historical developement since its invention by Zoutendjik in 1960
till the most recent Random MFD.
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We also give an overview of several packages that use Latex to create slides
and slideshows for presentations. These would be very useful for master's
project presentations, thesis defenses, conference talks, job interviews, and
much more! These methods will be illustrated with some examples.
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Nonautonomous Dynamical Systems occur naturally in different problems, e.g.
as solutions of nonautonomous difference equations, nonautonomous ordinary
and partial differential equation, random and stochastic differential
equations, control systems, dynamic equations on time scales, etc.
We motivate and introduce this abstract notion with explicit examples. In
the second part of the talk we apply it to the problem of the numerical
computation of invariant manifolds for nonautonomous difference equations.
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Last update 8/26/02
In this talk we will be looking at the mathematical resources available on the Web
for research, reference, teaching, etc. The wealth of information on the Web is
so vast that it is impossible to list all of the resources but at least some
compilation would be very useful. We will present a list of links we use and
of others who shared their favourites. This itself makes up a valuable
resource.
Go to Math Resources
Approximation of Time-Dependent, Multicomponent, Viscoelastic Fluid Flow
Will Miles , Martin Hall O-8
This presentation will discuss some of the fundamental issues when modeling
fluid flows. While Newtonian fluids have been studied in detail, the study
of viscoelastic fluids leave us with a wealth of unanswered questions. In
this talk, we present an existence theorem as well as an apriori error
estimate for viscoelastic flows. The discussion will also allow a second
fluid to be included in the flow field. Some of the complications will be
discussed and numerical results will be presented.
A Massively Parallel Generalized Stokes Solver
Kelly Waters , Martin Hall O-8
The generalized Stokes problem is the PDE
![[the PDE]](kellys_pdf2.jpg)
An Introduction to
Louis Ntasin , Martin Hall O-4
Since its introduction in 1985, LATEX
has made it possible for authors of
scientific papers, especially mathematicians, to typeset their own documents.
Just like any programming language one needs to learn its syntax,
commands and environments to effectively use it for document processing.
Parameters of Cycle-Domination
John Villalpando , Martin Hall O-2
Domination is one of the most studied aspects of graph theory. There are many
variations of domination such as total domination, connected domination, and
acyclic domination just to name a few. However, these variations are created by
placing conditions on the dominating sets.
The History of e
Robert Beeler , Martin Hall O-5
While e is not as famous as its geometric cousin, pi, it has an
interesting history of its own. The acceptance of the infinite which allowed
for the development of calculus also allowed for the discovery of e, the first
number defined by a limiting process. The importance of the constant was
emphasized by Jakob Bernoulli, who showed why it should be considered as the
"natural" base for the logarithms, and Leonard Euler, who showed the
relationship between the trigonometric and the exponential. The impact of
other mathematicians such as Napier, Briggs, DeMoivre, Hermite, and Cantor may
also be discussed with regard to their contributions to the history of e.
The Facility Location Problems with Uncertainty
Minsang Chan , Martin Hall M-303
Facility location problems are concerned with the location of one or more
facilities in a way that optimizes a certain objective such as minimizing
transportation cost, providing equitable service to customers, capturing
the largest market share, etc.
Intermediate
Art Gorka , Martin Hall O-1
Virginia Rodrigues , Martin Hall O-1
This is a second part of the LATEX
presentation. In this part we will be looking at the
article style document: the environments for abstract, formulae, arrays, tables,
lists, figures, bibliography, etc. We'll look at ways we can customize some environments
and create our own commands.
An example article file and
the article's source
An example of slide presentation and
the slides source
the presentation source
Anomalous Diffusion, the Levy-Gnedenko Generalized Central Limit Theorem, Fractional
Differential Equations, and the Finite Element Method
John Paul Roop , Martin Hall O-3
![[fractional derivatives]](derbasis.jpg)
In this talk, we review the connection
between Brownian motion, Gaussian random
variables, the central limit theorem,
and the diffusion equation. Noting that
a diffusive process involves a jump p.d.f.
and a waiting-time p.d.f. we investigate
what happens when the requirement that
the variance of the jump probability be
finite is dropped. We show through the Levy-Gnedenko
generalized central limit theorem how this
gives rise to a Levy random variable,
and leads to a partial differential equation
with fractional derivative components.
The concept of a fractional derivative
is introduced. Finally, FEM results for
fractional versions of Poisson's equation
are presented as a first step towards
solving the fractional advection-dispersion
equation numerically.
Power Point type presentations using
Louis Ntasin , Martin Hall O-4
In this instalment on LaTeX we'll look at the ways for preparing Power Point type
presentations using the ifmslide package. Examples will be given on using
some of the commands of the package to prepare fully featured presentations. This will be a hands
on seminar at the computer.
An example presentation and
the presentation's source
Continued Fractions in Physics
Suman Balasubramanian , Martin Hall O-6
Mathematics and Physics are two branches of Science that are interlinked in a
major way. While the Physicists established the basis for the relationship
between mathematics and physics,the Mathematicians developed the theory and
foundation of mathematics that would help the Physicists in a big way. One such
field is "Continued Fractions", where a continued fraction is an expression of
the form
b
a +- -------------- 1
d --------------
c +- --------- a
f z +- ---------
e +- ----- OR b
. 1 +- ------
. c
. z +- ----
d
1 +- ---
.
.
.
Prompted by a query raised by Dwight E. Neuenschwander(1994) "Is there a physics
application that is best analyzed in terms of continued fractions?", a few
applications of continued fractions to physics are studied.
John Villalpando , Martin Hall O-2
Digital television, cell phones, and other wireless communications are
changing the way we live. While discussing the Steelers' win on the cell phone
and watching ESPN highlights over satellite television you must have asked, how
does this information get to me? Wireless communication flows through the air
waves which are quickly becoming saturated. Your cell phone company must avoid
the frequencies used by your satellite company.
The channel assignment problem is the problem of assigning frequencies to
radio transmitters in such a way that the communications do not interfere. Two
transmitters are considered to interfere with each other if they share similar
frequencies and are at a prescribed distance from one another.
In this presentation we will begin by discussing the channel assignment
problem. We will introduce some concepts of graph theory, primarily colorings.
We will then discuss L(2,1) colorings and its relationship to the channel
assignment problem. We will finish by studying certain parameters of L(2,1)
colorings on paths, cycles, trees, and various other types of graphs.
pdf file
Jeff Farr , Martin Hall O-7
Alliances play important roles in ecology, in the military, in society, and
in many other applications. Of course, many networks and relationships may be
modelled using graphs. In this talk we introduce the brand new study of
offensive and defensive alliances in graphs. Vertices which are allied agree to
support each other in the case of an ``attack" by vertices that are not part of
the alliance. An alliance in which every member is important is called a
critical alliance. We will study the mathematical properties of alliances,
paying special attention to critical alliances.
![[a critical alliance]](alliance.jpg)
pdf file
Brian Hunt , Martin Hall O-2![[no clear max to both objective functions]](02_3.jpg)
Abstract
Many problems involve finding a preferred solution in the presence of
multiple objective functions or criteria. Most often some (or possibly all)
of these criteria are in conflict with each other, especially as the number
of criteria increases. A solution that is very good with respect to one
criterion may be poor with respect to one or more of the other criteria. The
presence of this conflict makes it impossible to find an optimal solution
that optimizes all objective functions simultaneously. This requires
introducing the concept of a nondominated solution. In this talk,
nondominated solutions will be defined and solution methodologies for finding
the nondominated solution set will be discussed. Examples will be presented
for bi-criteria problems for ease of graphical representation. Preference
cones and the role they play in multicriteria optimization problems will also
be discussed.
pdf file
Suman Balasubramanian , Martin Hall O-6
In 1959 Gallai showed that the vertex independence number and the vertex
covering number of a graph G=(V,E) sum to V. Over the last twenty years,
many results similar to Gallai's Theorem have been observed . These theorems
are referred to as ``Gallai Theorems," and usually have the form: a + b =n,
where a and b are integer-valued minimum or maximum functions corresponding to
some property of a graph on n vertices.
Slater described several graph subset parameters using linear programs
(LP) and integer programs (IP). Graph theoretic minimization (maximization)
problems can be modelled in terms of LP/IP problems using the adjacency matrix,
A, the (closed) neighborhood matrix, N, and the vertex-edge incidence matrix, H.
Gallai Theorems for the resulting parameters may be obtained by using the
concepts of LP-duality and complementarity. Slater defines several of the
parameters generated by the above matrices, but leaves other parameters
unstudied. In this talk, we take a closer look at some of those unstudied
parameters.
Tom Macdonald , MIT - Lincoln Lab
The ambiguity function provides a description of a finite-energy waveform (i.e., a square-integrable function) in both the time and frequency
domains. This function has been used extensively to characterize radar and sonar
applications. In this talk the definition of the ambiguity function is
given, and a number of salient properties of the function are discussed. The
application of the ambiguity function as a tool to analyze satellite
communications is presented. Particular attention is paid to the
development of the relationship between the ambiguity function and the performance of a
communications system. Finally, the talk concludes with the introduction
of the synthesis problem for ambiguity functions, which is a non-trivial
mathematical exercise.
pdf file
Shannon Purvis , Martin Hall M-303
Consider an n by k chessboard. Our task is to place non-attacking kings
on the board. We want to know how many possible boards we can get with no two
kings in adjacent squares. This number turns out to be hard to find. In this
talk, we discuss a matrix representation for the legal configurations of kings
on the board and use these matrices to find the number of possible n by k
boards where n is fixed. We will also discuss approaches to solving the
problem asymptotically for any n and k.
pdf file
Jon Edds , Martin Hall O-6
Many young kids take an interest in collecting football and baseball cards.
The goal is to collect the whole set of n cards by purchasing packs that
contain k cards. Provided that the cards in each pack are uniformly
distributed without repetition, we are able to represent this situation by a
stochastic matrix. By raising this matrix to the power t, we are able to
express the probability of collecting all the cards by purchasing t packs of
cards. We develop an asymptotic formula as n, k, and t go to infinity.
pdf file
Ron Scott , Martin Hall E-8
After a brief introduction describing how points on elliptic curves
behave like an abstract algebra group, a special curve is introduced which has a
point of order 5. The goal of the study is to find out how many of these curves
are distinct and how many are just isomorphisms of another curve. Answering this
question requires a journey through an interesting application of Maple's
algebra abilities, the factoring of polynomials over finite fields, some simple
Galois theory, and a little probability theory at the end. Certain regular
isomorphism patterns are found, together with more surprising and random-seeming
results.
pdf file
Jeff Farr , Martin Hall O-7
We consider a sequence, p_n, defined by
p_0=0,
This is a simple example of a sequence in which the nth term is a weighted
average of the preceding terms and the weights for p_n are heavily
concentrated at two previous elements in the sequence. It is known that if the
weights for the nth therm of a sequence are sharply concentrated around a
single
previous element and if the sequence appears to be oscillating at the
beginning,
then the sequence will continue to oscillate, and, hence, will not converge.
Although the double-biased sequence which we consider appears to be oscillating
at the beginning, we show that it does, in fact, slowly converge. Specifically,
we prove that p_n converges to 2/(1 + log_2(3)).
This talk will focus on various estimation techniques that were needed to show
that the sequence converges.
p_1=1,
p_n= 1/2 * p_{n/3} + 1/2*p_{n/2}, n > 1.
pdf file
Kelly Waters , Martin Hall O-8
We present the Finite Element Method (FEM) applied to a simple one-dimentional problem:
u" = f,
The intent is to give the audience a general idea of what FEM means. In much
less detail we present our current application of the Glowinski-Pironneau
pressure decomposition to the modified Stokes problem.
u(0) = 0,
u'(1) = 0,
pdf file
Art Gorka , Martin Hall O-1
The Methods of Feasible Directions (MFD) are used for solving
inequality constrained Nonlinear Programming problems .
pdf file
Jeff Farr &
Louis Ntasin
Latex is an excellent typesetting system that is designed to produce high
quality scientific and mathematical documents. We provide a brief introduction
for those who have limited experience with Latex. The introduction will
include
preparing document layout for papers and quizzes, typesetting mathematical
formulae, and importing graphics.
pdf file
Will Miles , Martin Hall O-8
In the field of multi-component fluid flow, the interface between two fluids
plays a crucial role in the development of the flow. This interface causes
the
introduction of a different force into the balance of momentum. Hence, the
ability to track the interface is of paramount importance.
This presentation will introduce the idea of interface tracking. We will discuss such inherent
difficulties
as maintaining the sharpness of the interface and preventing spurious
oscillations. We also compare several tracking methods.
pdf file
Vijay Singh , Martin Hall O-3
Decision making for simple objective optimization is well-studied. The problem
becomes more difficult when a designer has to consider several conflicting
criteria, and no design simultaneously optimizes all the criteria. In this
discussion we illustrate some of the well known solution methods of
Multi-Criteria Optimization (MCO) problems, and we discuss the ways in which
these methods aid the designer in deciding which problems are worth
studying. We also highlight some issues related to the MCO problem when the designer
wants a "common best" design for a set of criteria under different scenarios.
pdf file
Louis Ntasin , Martin Hall O-4
Digital signal processing is a vital part of communication today with
applications in image/video processing, audio compression, denoising
and feature detection, etc. Two problems in this area are the storage
and bandwidth requirements of digital signals. In this talk we introduce
wavelets and filter banks and then move forward to discuss how wavelets
can be used in digital signal processing. In particular, we discuss how
wavelets are used in compression and decompression of digital signals. A few
specific areas in which applications are currently being developed are also
mentioned.
pdf file
Stefan Siegmund , Georgia Tech.
The notion of a Nonautonomous Dynamical System is a relatively new notion
which generalises Dynamical Systems. Whereas Dynamical Systems Theory is
very well established, a general theory for Nonautonomous Dynamical Systems
does not exist yet.
Abdul-Baasit Shaibu , Martin Hall M-304
In statistical parameter estimation problems, how well the parameters
are estimated largely depends on the sampling algorithm used. In this talk, we
consider estimating the parameters of the normal, exponential and gamma
distributions using median and extreme ranked set sampling. We will briefly
touch on ranked set sampling (McIntyre, 1952), which was modified to obtain the
median (Muttlak, 1997) and the extreme (Samawi, 1996) sampling algorithms.
Basic statistical concepts that are required for easy comprehension of the
entire talk would be explained at the beginning of the talk.
pdf file
Kevin Hutson, Martin Hall O-312
The Minimum Spanning Tree Problem is a classical network optimization problem
defined as follows: given a connected undirected graph each of whose edges
has a
real-valued cost, find a spanning tree of the graph whose total edge cost is
minimum. Minimum spanning trees are widely used in the design of physical
systems such as computer chips and communication systems in providing the
necessary infrastructure to connect geographically dispersed elements. In
general, however, links in a physical system degrade over time or the costs
associated with constructing such links are not known with certainty. In this
talk we present an algorithm for computing the distribution of the weight of a
minimum spanning tree of a given network where the edge weights are determined
by a discrete random variable.
pdf file
Brian Hunt , Martin Hall O-2
Baseball and mathematics are inextricably linked because baseball is a game
of probability and statistics. Around 1960, the idea to model the game of baseball
as a Markov chain first appeared in the mathematical literature. A Markov chain is a
special type of stochastic process that lends itself quite nicely to the analysis of
baseball. This talk will describe a Markov chain model for baseball and discuss ways
that the model can be used to evaluate team and player performance. The beginning of
this talk will include a general overview of stochastic processes and Markov chains
as well as a general description of the game of baseball to familiarize the audience
with key concepts used in the model.
pdf file
Erin McNelis, Martin Hall O-5
Along with the unusual hours associated with rotating shift work, comes a
battery of problems, both physiological and social, for the shift worker. As
shift work itself can't be eliminated, one aim is to develop schedules that
require workers to be on duty during the times that they are most naturally
alert and awake. This is where biological modeling and optimization come in.
A person's alertness is closely tied to his circadian rhythms, the body's
rhythms that innately maintain a 24-hour cycle. By modifying a mathematical
model for the body's core temperature, the most stable of the human circadian
rhythms, it is possible to represent the rhythms of a shift worker on a
parameterized shift work schedule. Denoting an ``optimal'' shift schedule as
one that leads to rhythms most like those of the naturally occurring
(free-run)
rhythms, identification of an optimal shift work schedule results
from minimizing the difference between the work-induced temperature rhythms
and the free-run temperature rhythms over the shift work parameter.
pdf file
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