# <span class=strong>Reception and poster session</span>

Friday, November 3, 2006 - 5:15pm - 6:30pm

Lind 400

**Undergraduate, graduate, and postdoctoral opportunities**

at New York University

Margaret Wright (New York University)

New York University, located in the heart of Greenwich

Village in New York City, offers outstanding undergraduate,

graduate, and postdoctoral opportunities. Material about

all of these, especially those involving the Courant Institute

of Mathematical Sciences, will be available, and the presenter

will be happy to answer questions.**The fixed charge network flow problem**

Adewale Faparusi (Texas A & M University)

The fixed charge network flow problem (FCNFP) is NP Hard and has

various practical applications including transportation, network design,

communication, and production scheduling. More work has been done on the

development of algorithms for specific variants of the FCNFP than the

generalized problem.

Various formulations and exact and heuristic methods for solving the FCNFP

are reviewed.**Modelling faculty teaching workload as a linear program**

Kanadpriya Basu (University of South Carolina)Maria Cristina Villalobos (University of Texas Pan American)

We present an assignment problem that distributes classes among instructors

in the Mathematics department. Currently, the Director of Scheduling assigns

about 190 classes 60 instructors using the manual process of trial-and-error

by considering, for example, an instructor's teaching workload and class

preferences. However, this process is quite time-consuming. Therefore, we

model the problem as a linear program with binary variables. The results are

presented for Fall'2006.**Mathematical modelling at NIST: An example**

Fern Hunt (National Institute of Standards and Technology)

Fluorescent stains and dyes are widely used to visualize biological structure

and function on the cellular and sub-cellular level. The photodegradation of

fluorescent particles (fluorophores) is an extremely important issue for

biomedical and biotechnology applications because the sensitivity and the

accuracy of the quantitative information conveyed by assays using them

depends on fluorophore photostability.

Recently the presenter and Dr. Adolfas Gaigalas of NIST developed a

mathematical model of an experimental method for measuring photodegradation.

The model is a set of coupled partial differential equations that describe

the kinetics of photodegradation and the flow of fluorophores through the

experimental apparatus. Using singular perturbation techniques, the

model is reduced to to a

dramatically simpler and experimentally accessible ordinary differential

equation. The latter can be used to interpret and fit the experimental

meausurements, thus providing a quantitative characterization of photostability.**Optimal product portfolio formulation: Merging predictive data mining**

with analytical target cascading

Conrad Tucker (University of Illinois at Urbana-Champaign)

This paper addresses two important fundamental areas in product

family

formulation that have recently begun to receive great

attention. First is the

incorporation of market demand that we address through a data

mining

approach where realistic customer survey data is translated

into performance

design targets. Second is platform architecture design that we

model as a

dynamic entity. The dynamic approach to product architecture

optimization

differs from conventional static approaches in that a

predefined architecture is

not present at the initial stage of product design, but rather

evolves with

fluctuations in customer performance preferences. The benefits

of direct

customer input in product family design will be realized

through our cell phone

product family example presented in this work. An optimal

family of cell phones

is created with modularity decisions made analytically at the

enterprise level that

maximize company profit.**Existence of traveling waves solution for a nonlocal**

reaction-diffusion model of influenza A

Joaquin Rivera (The University of Iowa)

In this paper we study the existence of traveling wave solutions

for an integro-differential system of equations. The system was proposed by

Lin et. al as a model for the spread for influenza A drift. The model uses

diffusion to simulate the mutation of the virus along a one dimensional

phenotype space. By considering the system under the traveling wave variable

*z=x-ct* the PDE system is transformed to a higher dimensional ODE

system. Applying

the theory of geometric singular perturbation we constructed a traveling

wave solution for the system.

Key words: traveling wave, reaction-diffusion, geometric singular

perturbation.**Large circuit pairs in matroids**

Bryan Williams (Hampton University)

Scott Smith conjectured in 1979 that two distinct longest

cycles of

a k-connected graph meet in at least k vertices when k is less

than or equal

to 2.

This conjecture is known to be true for k is less than or equal

to 10. Only

the case

k less than or equal to 6 appears in the literature, however.

Reid and Wu

generalized Smith's conjecture to k-connected matroids by

considering largest circuits. The case k=2 of the matroid

conjecture follows from a result of Seymour. In addition,

McMurray,

Reid, Sheppardson, Wei, and Wu established an extension of the

matroid conjecture for k=2 and proved it for cographic

matroids

when k ≤ 6. In his Ph.D. dissertation, McMurray established

the

matroid conjecture for matroids of circumference four. I

establish

Reid and Wu's conjecture for several classes of matroids which

include those that have connectivity three, circumference

five, and

spanning circuits, Along with some structured results for

connectivity four. I am also looking at extending the dual

result

of Grotschel and Nemhauser's established result of Smith's

conjecture for k less than or equal to 6, by considering

largest bonds in

graphs.**Automated parameter estimation and sensitivity analysis**

Carlos Quintero Salazar (University of Texas)

We present the computational issues that will be considered

for the implementation of hybrid optimization approaches oriented to

automated parameter estimation problems. The proposed hybrid

optimization approaches are based on the coupling of the Simultaneous

Perturbation Stochastic Approximation (SPSA) approach (a global and

derivative free optimization method) and a globalized Newton-Krylov

Interior Point algorithm (NKIP) (a global and derivative dependent

optimization method). The first coupling will imply the generation of

a metamodel that will allow to incorporate derivative information on a

simpler representation of the original problem. The second type of

coupling assumes that there is some derivative information available

but its utilization is postponed until the SPSA algorithm has made

sufficient progress toward the solution. We implement the hybrid optimization

approach on a simple testcase, and present some numerical results.**Historical development of the secant method: from the**

Babylonians to Wolfe

Joanna Papakonstantinou (Rice University)

Many believe the Secant Method arose out of the finite difference

approximation of the derivative in Newton's Method. However,

historical evidence reveals that the Secant Method predated Newton's

Method. It was originally referred to as the Rule of Double False

Position and dates back to the Babylonians. We present a historical

development of the Secant Method in 1-D. We introduce the definition

of general position, present the n+1 point interpolation idea, and

outline Wolfe's formulation to compute the basic secant

approximation. We explain how the method is numerically unstable,

because it leads to ill-conditioning due to the deterioration of

general positioning.**Reduced basis simulation**

Rachel Vincent-Finley (Rice University)

Molecular dynamics (MD) simulation provides a powerful tool to study

molecular motion with respect to classical mechanics. When considering

protein dynamics, local motions, such as bond stretching, occur within

femtoseconds, while rigid body and large-scale motions, occur within a

range of nanoseconds to seconds. Generally to capture motion at all

levels using standard numerical integration techniques to solve the

equations of motion requires time steps on the order of a femtosecond.

To date, literature reports simulations of solvated proteins on the

order of nanoseconds, however, simulations of this length do not provide

adequate sampling for the study of large-scale molecular motion.

In this presentation we will describe a method for performing molecular

simulations with respect to a reduced coordinate space. Given a standard

MD trajectory we use principal component analysis (PCA) to identify k

dominant characteristics of a trajectory and construct a k-dimensional

(k-D) representation of the atomic coordinates with respect to these k

characteristics. Using this model we define equations of motion and

perform simulations with respect to the constructed k-D representation.

We apply our method to test molecules and compare the simulations to

standard MD simulations of the molecules. Our method allows us to

efficiently simulate test molecules by reducing the storage and the

computation requirements. The results indicate that the molecular

activity with respect to our simulation method is comparable to that

observed in the standard MD simulations of these molecules.**An epidemiological approach to the spread of minor**

political parties

Daniel Romero (Arizona State University)

Third political parties are influential in shaping American politics. In this work

we study the spread of

third parties ideologies in a voting population where we assume that party members

are more

influential in recruiting new third party voters than non-member third party voters

(i.e., those who vote

but do not pay party dues, officiate, campaign). The study is conducted using a

‘Susceptible-Infected’

epidemiological model with a system of nonlinear ordinary differential equations as

applied to a case

study, the Green Party. Through the analysis of our system we obtain the party-free

and member-free

equilibria as well as two endemic equilibria, one of which is stable. We consider

the conditions for

existence and stability (if applicable) of all equilibria and we identify two

threshold parameters in our

model that describe the different possible scenarios for a third political party and

its spread. Of the

two possible endemic states for the voting population we posit ideal threshold

ranges for which the

stable endemic equilibrium exists. Interestingly enough, our system produces a

backward bifurcation

that identifies parameter values under which a third party can either thrive or die

depending on the

initial number of members in the voting system. We then perform sensitivity

analysis to the threshold

conditions to isolate those parameters to which our model is most sensitive. We

explore all results

through numerical simulations and refer to data from the Green Party in the state of

Pennsylvania as a

case study for parameter estimation.**Fourier restriction problem and its relation to PDE**

No Abstract**Mathematical Sciences Research Institute**

Kathleen O'Hara (Mathematical Sciences Research Institute)

Come learn about opportunities at MSRI.**Thermal stability of a reactive third grade fluid in a cylindrical pipe: An**

exploitation of Hermite-Padé approximation technique

Oluwole Makinde (University of Limpopo)

A large class of real fluids used in industries is chemically reactive and

exhibit non-Newtonian characteristics e.g. coal slurries, polymer solutions or

melts, drilling mud, hydrocarbon oils, grease, etc. Because of the non-linear

relationship between stress and the rate of strain, the analysis of the behavior of

such fluids tends to be more complicated and subtle in comparison with that of

Newtonian fluids. In this paper, we investigate the thermal stability of a reactive

third-grade fluid flowing steadily through a cylindrical pipe with isothermal wall.

It is assumed that the reaction is exothermic under Arrhenius kinetics, neglecting

the consumption of the material. Approximate solutions are constructed for the

governing nonlinear boundary value problem using regular perturbation techniques

together with a special type of Hermite-Padé approximants and important properties

of the flow structure including bifurcations and thermal criticality conditions are

discussed.**Change in host behavior and its impact on the co-evolution of**

dengue

David Murillo (Arizona State University)

The joint evolutionary dynamics of dengue strains are poorly understood

despite its high prevalence around the world. Two dengue strains are put in

competition in a population where behavioral changes can affect the

probability of infection. The destabilizing dynamic effect of even minor

behavioral changes are discussed and their role in dengue control is explained**Texas prefreshman engineering program: Closing the**

gap for minorities in science and engineering

Manuel Berriozábal (University of Texas)

The Texas Prefreshman Engineering Program (TexPREP) started in

the summer of 1979 at the University of Texas at San Antonio.

It is a seven-to eight week summer mathematics-based academic

enrichment program designed to prepare middle school and high

school students for college studies in science and engineering.

The program focuses on the development of abstract reasoning

and problem solving skills through the mastery of academic

content. Since the program started, over 24,000 students have

completed at least one summer component of PREP. At least 75%

of the students have come from minority groups underrepresented

in science and engineering and over 50% have been women. Of

the 11,000 students former students who are of college age,

6,500 responded to the 2005 annual survey. The following is a

summary of the results:- 99.9% graduated from high school;
- 97 % are college

students (3,300) or senior college graduates (3,000); - The senior college graduation rate is 80%;
- 78% of the

college graduates are underrepresented minorities; - 50% of the college graduates are science, mathematics, or

engineering majors; - 74% of the science, mathematics, and engineering graduates

are underrepresented minorities.

The 2006 Program served over 2600 students in 21 Texas college

campuses and 6 college campuses in other states and Puerto

Rico.**Differential elimination of PDEs by numerical algebraic**

geometry and numerical linear algebra

Wenyuan Wu (University of Western Ontario)

The computational difficulty of completing nonlinear PDE to involutive form by

differential elimination algorithms is a significant obstacle in applications.

We apply numerical methods to this problem which, unlike existing symbolic

methods for exact systems, can be applied to approximate systems arising in

applications.

We use Numerical Algebraic Geometry to process the lower order leading

nonlinear parts of such PDE systems to obtain their witness sets. To check the

conditions for involutivity Numerical Linear Algebra techniques are applied to

constant matrices which are the leading linear parts of such systems evaluated

at the generic points. Representations for the constraints result from applying

a method based on Polynomial Matrix Theory. Examples to illustrate the new

approach are given.

This is joint work with Greg Reid. The paper is available at

publish.uwo.ca/~wwu26**Mathematics and its application to modeling the earth's surface**

Diana Dalbotten (University of Minnesota, Twin Cities)

Students with a Mathematics or Physics degree who wish to

apply their abstract skills in a concrete way are invited to

investigate the National Center for Earth-surface Dynamics. This

multidisciplinary center examines the Earth's surface

quantitatively, using computer models, field studies, and laboratory

experiments to investigate channels and channel dynamics.**AWM Mentor Network**

Rachel Kuske (University of British Columbia)

At present, the goal of the Association for Women in Mathematics (AWM)

Mentor Network is to match mentors, both men and women, with girls and women who are interested in mathematics or are pursuing careers in mathematics. The network is intended to link mentors with a variety of groups: recent PhD's, graduate students, undergraduates, high school and grade school students, and teachers. Matching is based on common interests in careers in academics or industry, math education, balance of career and family, or general mathematical interests. Following increased support from the math institutes, we are considering the possibility to expand the Mentor Network to other under-represented groups in mathematics. All who are interested in participating in this expansion are encouraged to discuss this possibility at the conference.**A new semifield of order 3**^{6}

Minerva Cordero-Epperson (University of Texas)

A (finite) semifield is a non-associative division ring; the associated projective

plane is called a semifield plane. The first semifields were defined by Dixon in the

early 1900s; in the 1960s several new classes were introduced including the twisted

fields defined by Albert. In this poster we will give a historical development of

finite semifields. We will present the development in the last decade including a

new semifield recently constructed by the author.**Professional Science Masters programs**

Sheila Tobias (NONE)*Why Industry should be interested in PSM*

Companies are transforming their cultures and reshaping their business models to focus on high-impact innovation. This business strategy requires a skill set very different from the old Six Sigma. Universities have responded to this challenge by creating a new business and industry-oriented Professional Science (Mathematics) Masters degree (PSM).

PSM degree holders are trained to work productively at what Business Week calls the sweet spot where design, customer understanding, and emerging technologies come together.

PSM graduates have expertise in science, mathematics, and computational skills PLUS business basics, project management, regulatory affairs, technology transfer, teamwork, and communication.*Why Students should be interested in PSM*

A two-year post-graduate terminal degree for mathematics/computational science majors, in areas of applied mathematics, including financial mathematics, industrial mathematics, computational science and at the intersection of disciplines including bioinformatics, proteomics, environmental decision making, biostatistics, statistics for entrepreneurship, and applications of GIS.

For more information, see www.sciencemasters.com.**Error estimates between the stochastic simulation algorithm (SSA) and**

the tau-leap method

Josue Noyola-Martinez (Rice University)

The use of the relatively new tau-leap algorithm to model the kinematics of

genetic regulatory systems is of great interest, however, the algorithm's

accuracy is not known. We introduce a new method which enables us to establish

the accuracy of the tau-leap method effectively. Gillespie introduced both the

Stochastic Simulation Algorithm (SSA) and the tau-leap method to simulate

chemical systems which can model the dynamics of cellular processes. The SSA

is an exact method but is computationally inefficient. The tau-leap is an

approximate method which has computational advantages over the SSA. There have

been some efforts to quantify the error between the SSA and the tau-leap

method, but the accuracy of these efforts is questionable. We propose an

adaptation of a non-homogeneous Poisson process to couple the SSA and tau-leap

so that we can make direct comparisons between individual realizations of their

simulations. Our method has not been attempted in the literature and we

demonstrate that it gives far better error estimates than anything proposed

previously.**JHU Applied Physics Lab - Aviation systems engineering group overview**

Javier Armendariz (Johns Hopkins University)

The Aviation Systems Engineering Group at JHU/APL conducts systems

engineering and analysis to support the development and operational

employment of military aviation systems. In this endeavor technical

requirements and enabling technologies are identified that relate to

operational requirements and operational concepts. The group strives to

maintain expertise in air defense threat characterization and analyze

the survivability and effectiveness of current and future military

aviation systems. To this end we are involved in a wide array of

projects encompassing many technical disciplines.**American Institute of Mathematics**

Rachel Kuske (University of British Columbia)

AIM, the American Institute of Mathematics, would like to bring to your attention opportunities at its conference center, AIM Research Conference Center (ARCC). Located in Palo Alto, California, AIM has been hosting fully-funded, week-long workshops at ARCC in all areas of the mathematical sciences since 2002. Through ARCC, AIM supports and develops an innovative style of workshop that encourages interactive research as part of the workshop, fosters new connections, and builds productive and lasting collaborations. Several proactive approaches are used to attract a diverse groups of participants, including women and under-represented minorities as well as junior mathematicians. All 32 participants receive full funding to attend the week-long workshop.**Research Institute of Mathematical Sciences**

Luis Enrique Carrillo Díaz (Universidad Nacional Mayor de San Marcos)Roxana Lopez-Cruz (Universidad Nacional Mayor de San Marcos)

The Research Institute of Mathematical Sciences develops

research in pure and applied mathematics, statistics,

computer science and research operations. One of the goals

of the Institute is to promote means of international

cooperation to support the research among the members of

our institute and other insitutions of the world.

PESQUIMAT is the review of the Institute in charge to spread

the research of our members.

http://matematicas.unmsm.edu.pe/**Mathematical aspects of dopamine's turnover**

David Tello (Arizona State University)

What do the world's champion Muhammad Ali and A Beautiful Mind's John

F. Nash have in common? They both suffer from dopamine malfunction

in one of the major dopaminegic pathways. It is believed that loss

of dopamine activity in the nigrostriatal pathway is associated with

Parkinson's Disease and that an imbalance of dopamine activity in the

mesocortical\mesolimbic pathway is the cause of (positive\negative)

symptoms of Schizophrenia.

I have assembled a collection of available literature concerning

dopamine turnover (the cascade chemical process that takes place in

the terminal button) and some of the available mathematical models

describing the dopamine process. This collection constitutes a

foundation of future work. I plan to develop a stochastic model

describing the dopamine cascade in the different major dopaminergic pathways.**Discriminant analysis based on statistical depth**

functions

Asheber Abebe (Auburn University)

We will consider the problem of identifying the most likely source

of a multivariate data point from among several multivariate

populations. The use of statistical depth functions for solving

this classification problem will be discussed. Statistical depth functions

provide a center-outward ordering of points in a multivariate data

cloud and hence can be considered to be multivariate analogues of ranks.

Specifically, classification through maximizing the estimated

transvariation probability of statistical depths is proposed. Considering

elliptically

symmetric populations, it will be illustrated that these new

classification techniques provide lower misclassification error rates in

the case of heavy tailed distributions.

This is joint work with Nedret Billor, Asuman Turkmen and Sai Nudurupati.**Accurate computation of second order derivatives using complex**

variables

Nelson Butuk (Prairie View A&M University)

In this presentation, the complex variables method of computing accurate

first derivatives is combined with an approximation method to calculate

second order derivatives efficiently. The complex variables method, is some

what similar to the automatic differentiation technique using the popular

software tool ADIFOR, to obtain sensitivities (derivatives) from source

codes. Application of automatic differentiation to an existing source code,

(that evaluates output functions) automatically generates another source

code that can be used to evaluate both output functions and derivatives of

those functions with respect to specified code input or internal

parameters. The pre-compiler software tool, ADIFOR is usually used to

obtain derivatives from CFD and grid generation codes. On the other hand,

the complex variables (CV) approach is simpler and easier to implement. The

current implementation of CV method only computes first order derivatives

accurately. The current methods of computing 2nd order derivatives using

different approaches are based on construction of appropriate meshes in a

given domain. Then some form of Taylor expansion scheme is applied to these

meshes to obtain the desired derivatives. The problem with this approach is

that only the function is continuous across meshes, but not its partial

derivatives. Because of this, the computed 2nd order derivatives are

usually inaccurate. The new method to be presented will address this issue

by combining the CV method with an accurate efficient approximation method.**Progress report on the NSA mathematics enhancement grant:**

Developing a mathematics culture among undergraduate

mathematics majors at North Carolina A&T State University

Janis Oldham (North Carolina Agricultural and Technical State University)

From July 1, 1998 - September 30, 2001 North Carolina A&T's Math Department conducted a project, funded through the National Security Agency. The project was designed to produce a core of undergraduate students having a “mathematics culture”, that is, a depth in proof based higher mathematics, the ability to articulate ideas, solve problems, and conduct inquiry and research. It was hoped this core would communicate its knowledge and experience on to successive classes of students, maintaining this newly developed culture. It was also originally hoped that the Math department would go on to develop an Honors program from this program, or at least incorporate the main program elements, especially the required problem sessions. Students not having developed in such a 'culture' meant not being prepared to do well in graduate school or have the expertise to work in government or industry.

The current state of affairs is that the culture did not persist. While the department did adopt 2 program elements, namely a freshman / new math major orientation course, and a required problem session with the Logic/Proof transitions course, university administrative edicts and university curriculum changes, impeded or gutted the effectiveness of those program elements. Nevertheless 72% of those who were in the program for 1, 2, or 3 years graduated with a degree in mathematics, applied mathematics, or mathematics education from an accredited institution. This included 3 who went on to earn Ph.D.'s, and many more who earned masters degrees. These students had gpa's from 2.5 through just under 4.0. Students who currently hold these gpa's are not developing as the students did during the period of the NSA grant. What we believe is that the specific intervention and high amount of contact hours with students, with the purpose of compelling, guiding, and developing the appropriate study discipline, made the difference. For such results to persist, designing methods to maintain the intervention until a math culture actually takes hold, is necessary.**Statistical and Applied Mathematical Sciences Institute**

Christopher Jones (University of North Carolina, Chapel Hill)

Come learn about opportunities at SAMSI.**Lawrence Livermore National Laboratory**

Steven Lee (Lawrence Livermore National Laboratory)

Come learn about the exciting opportunities in the Computation Directorate

at LLNL.**Nonlinear interaction of light in disordered optical fiber arrays**

Alejandro Aceves (University of New Mexico)

Light propagation in coupled fiber arrays is described by a balanced of

diffraction and nonlinearity. At

high intensities, light is localized as a nonlinear mode propagating in a

few fibers. The imperfections

in the manufacturing of such fiber arrays account for multiplicative noise

in the governing equations.

Here we analyze how this noise affects the phenomenon of linear

(Anderson-like) and nonlinear localization.**Algebraic characterizations of some classes of quasi-cyclic**

codes

Isaac Woungang (Ryerson Polytechnical University)

The so-called Jensen's concatenation function has been found to be a

powerful tool for the study of quasi-cyclic (QC) codes, and in general,

of codes invariant under a permutation. In this paper, we introduce two

novel applications of the aforementioned tool. First, we provide a trace

description of a 1-generator QC code, which generalizes the well-known

trace description of a cyclic code. Second, we provide an algebraic

characterization of QC codes obtained as q-ary images of q^{m}-ary

irreducible cyclic codes. These QC codes are shown to be decomposable

into the direct sum of a fixed number of irreducible components. Based upon

this decomposition, we obtain some lower bounds on the minimum distances

of some classes of such codes. Our numerical results show that our technique

can yield optimal linear codes.**Spherical nilpotent orbits of reductive Lie groups: an overview**

Donald King (Northeastern University)

The vector space of complex symmetric n×n matrices is preserved by

conjugation with complex n×n orthogonal matrices. Conjugacy classes

(orbits) of height two nilpotent symmetric matrices have many pleasant

properties, and give insights into the structure of interesting

irreducible unitary representations of SL(n, R), the group of real n×n

matrices of determinant one. If we replace SL(n, R) by a general reductive

Lie group G, then its spherical nilpotent orbits have similar properties,

and carry similar information about some of the irreducible unitary

representations of G.**Clones in minors of matroids**

Carla Cotwright (Wake Forest University)

Results that relate clones in a matroid to minors of that matroid are given. Also,

matroids that contain few clonal-classes are characterized. These results are

related to several results from the literature such as Tutte's Excluded-Minor

characterization of the binary matroids.

Joint work with T. James Reid.