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Additional newsletters available at http://www.ima.umn.edu/newsletters
Additional newsletters available at http://www.ima.umn.edu/newsletters
IMA Newsletter #361
November 2006
2006-2007 Program
Applications of Algebraic Geometry
See http://www.ima.umn.edu/2006-2007 for a full description of the 2006-2007 program on Applications of Algebraic Geometry.
The Blackwell-Tapia Conference, the premier national event for underrepresented mathematical sciences researchers will take place on Friday and Saturday, Nov. 3 and 4 at the IMA. A high point of the meeting will be the awarding of 2006 Blackwell-Tapia prize to Massey for his outstanding achievements in queuing theory, stochastic networks, modeling of communications systems, and for increasing diversity in mathematical sciences. There are over 150 participants registered to attend this event. To kick off the conference, Tapia will inspire more than 100 area high school students with his Math is Cool presentation from 10-11 a.m. Friday, Nov. 3. This conference is already getting a lot of publicity and coverage by the local and national media. You can find more information about this event on the IMA Blackwell-Tapia conference web page.
Application deadlines: If you are interested in applying for one of the "IMA New Directions Professorship" or "Postdoctoral Fellowship" positions in connection with the 2007-2008 thematic program: Mathematics of Molecular and Cellular Biology, the deadline for applying for these positions is January 5, 2007. You can find the applications for these positions at our Applications site.
IMA Events
IMA Workshop
Blackwell-Tapia Conference
November 3-4, 2006
Organizers: Douglas N. Arnold (University of Minnesota Twin Cities), David Manderscheid (University of Iowa), Samuel Myers (University of Minnesota Twin Cities), Arlie O. Petters (Duke University)
Schedule
Wednesday, November 1
| 11:15a-12:15p | Algebraic geometry and applications seminar: Equations and degenerations of the moduli space of genus zero stable curves with n marked points | Diane Maclagan (Rutgers University) | Lind Hall 409 | AGS |
Thursday, November 2
| 10:00a-11:00a | Special talk: Computer assisted mathematics: Tools and tactics for solving hard problems | Daniel Lichtblau (Wolfram Research, Inc.) | Lind Hall 409 | |
| 11:15a-12:15p | Real algebraic geometry tutorial: Sturm's root counting theorem and Tarski's generalization (continued) | Kenneth R. Driessel (Iowa State University) | Lind Hall 409 | RAG |
| 7:00p-8:00p | Math matters - IMA public lecture: How hard can it be? | Margaret H. Wright (New York University) | Willey Hall 125 | PUB11.2.06 |
Friday, November 3
| 12:00p-2:00p | poster set-up | Lind Hall 400 | SW11.3-4.06 | |
| 1:30p-2:00p | Coffee and registration | EE/CS 3-176 | SW11.3-4.06 | |
| 2:00p-2:30p | Welcome and introduction | EE/CS 3-180 | SW11.3-4.06 | |
| 2:30p-3:00p | From Massey to Blackwell: A study of non-stationary queueing control via sensitive optimality criteria | Mark E. Lewis (Cornell University) | EE/CS 3-180 | SW11.3-4.06 |
| 3:00p-4:15p | Panel discussion: Best practices for recruitment and retention of under-represented minorities in the mathematical sciences | Farrah J. Chandler (University of North Carolina) Shirley M. Malcom (American Association for the Advancement of Science) David Manderscheid (University of Iowa) William Yslas Vélez (University of Arizona) | EE/CS 3-180 | SW11.3-4.06 |
| 4:15p-4:30p | coffee break | EE/CS 3-176 | SW11.3-4.06 | |
| 4:30p-5:00p | Branch decomposition techniques for discrete optimization | Illya V. Hicks (Texas A & M University) | EE/CS 3-180 | SW11.3-4.06 |
| 5:00p-5:15p | Conference photo | Lind Hall 400 | SW11.3-4.06 | |
| 5:15p-6:30p | Reception and poster session | Lind Hall 400 | SW11.3-4.06 | |
| Discriminant analysis based on statistical depth functions | Asheber Abebe (Auburn University) | |||
| Nonlinear interaction of light in disordered optical fiber arrays | Alejandro Aceves (University of New Mexico) | |||
| JHU Applied Physics Lab - Aviation systems engineering group overview | Javier Armendariz (Johns Hopkins University) | |||
| Modelling faculty teaching workload as a linear program | Kanadpriya Basu (University of South Carolina) Maria Cristina Villalobos (University of Texas Pan American) | |||
| Texas prefreshman engineering program: Closing the gap for minorities in science and engineering | Manuel Berriozábal (University of Texas) | |||
| Accurate computation of second order derivatives using complex variables | Nelson Butuk (Prairie View A&M University) | |||
| Research Institute of Mathematical Sciences | Luis Enrique Carrillo Díaz (Universidad Nacional Mayor de San Marcos) Roxana Lopez-Cruz (Universidad Nacional Mayor de San Marcos) | |||
| A new semifield of order 36 | Minerva Cordero-Epperson (University of Texas) | |||
| Clones in minors of matroids | Carla Cotwright (Wake Forest University) | |||
| Mathematics and its application to modeling the earth's surface | Diana Dalbotten (University of Minnesota Twin Cities) | |||
| The fixed charge network flow problem | Adewale Faparusi (Texas A & M University) | |||
| Allee effect in an open-access fishery model | Jose D. Flores (University of South Dakota) | |||
| Fourier restriction problem and its relation to PDE | Cristi Darley Guevara (Arizona State University) | |||
| Mathematical modelling at NIST: An example | Fern Y. Hunt (National Institute of Standards and Technology) | |||
| Statistical and Applied Mathematical Sciences Institute | Christopher Jones (University of North Carolina) | |||
| Spherical nilpotent orbits of reductive Lie groups: an overview | Donald King (Northeastern University) | |||
| American Institute of Mathematics | Rachel Kuske (University of British Columbia) | |||
| AWM Mentor Network | Rachel Kuske (University of British Columbia) | |||
| Thermal stability of a reactive third grade fluid in a cylindrical pipe: An exploitation of Hermite-Padé approximation technique | Oluwole Daniel Makinde (University of Limpopo) | |||
| Change in host behavior and its impact on the co-evolution of dengue | David Murillo (Arizona State University) | |||
| Error estimates between the stochastic simulation algorithm (SSA) and the tau-leap method | Josue C. Noyola-Martinez (Rice University) | |||
| Mathematical Sciences Research Institute | Kathleen O'Hara (Mathematical Sciences Research Institute) | |||
| 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) | |||
| Historical development of the secant method: from the Babylonians to Wolfe | Joanna Papakonstantinou (Rice University) | |||
| Automated parameter estimation and sensitivity analysis | Carlos Andrés Quintero Salazar (University of Texas) | |||
| Existence of traveling waves solution for a nonlocal reaction-diffusion model of influenza A | Joaquin Rivera (University of Iowa) | |||
| An epidemiological approach to the spread of minor political parties | Daniel Romero (Arizona State University) | |||
| Mathematical aspects of dopamine's turnover | David Tello (Arizona State University) | |||
| Professional Science Masters programs | Sheila Tobias | |||
| Optimal product portfolio formulation: Merging predictive data mining with analytical target cascading | Conrad Tucker (University of Illinois at Urbana-Champaign) | |||
| Reduced basis simulation | Rachel E. Vincent-Finley (Rice University) | |||
| Large circuit pairs in matroids | Bryan Williams (Hampton University) | |||
| Algebraic characterizations of some classes of quasi-cyclic codes | Isaac Woungang (Ryerson Polytechnical University) | |||
| Undergraduate, graduate, and postdoctoral opportunities at New York University | Margaret H. Wright (New York University) | |||
| Differential elimination of PDEs by numerical algebraic geometry and numerical linear algebra | Wenyuan Wu (University of Western Ontario) |
Saturday, November 4
| 8:30a-9:00a | coffee | EE/CS 3-176 | SW11.3-4.06 | |
| 9:00a-9:30a | Computation of biological flows | Ricardo Cortez (Tulane University) | EE/CS 3-180 | SW11.3-4.06 |
| 9:30a-10:10a | short talks | EE/CS 3-180 | SW11.3-4.06 | |
| Formulating Fano's Method as an Optimization Problem to obtain Broadband Tuning Limits on UWB Antennas | Maria Cristina Villalobos (University of Texas Pan American) | |||
| Generalized hyperbolic functions to find soliton-like solutions of the inhomogeneous higher-order nonlinear Schrödinger equation | Emmanuel Yomba (University of Minnesota Twin Cities) | |||
| 9:30a-10:10a | short talks | EE/CS 3-230 | SW11.3-4.06 | |
| EL algorithm for linear models with missing data | Nancy Glenn (University of South Carolina) | |||
| Why should I care about Lie groups? | Edray Goins (Purdue University) | |||
| 10:20a-10:40a | coffee break | EE/CS 3-176 | SW11.3-4.06 | |
| 10:40a-11:40a | short talks | EE/CS 3-180 | SW11.3-4.06 | |
| Registration of 4D CT lung images | Edward Castillo (Rice University) | |||
| Transmission and control of seasonal and pandemic influenza | Gerardo Chowell (Los Alamos National Laboratory) | |||
| Epidemic spread in populations at demographic equilibrium | Karen Rios-Soto (Cornell University) | |||
| 10:40a-11:40a | short talks | EE/CS 3-230 | SW11.3-4.06 | |
| Probabilistic and stochastic modeling of turbulent flows | Sean C. Garrick (University of Minnesota Twin Cities) | |||
| Asymptotics of eigenvalue clusters for Schroedinger operators on the Sierpinski gasket | Kasso Okoudjou (University of Maryland) | |||
| Option pricing with memory | Flavia Sancier-Barbosa (Southern Illinois University) | |||
| 11:50a-12:20p | Opportunities at the IMA and other institutes | Douglas N. Arnold (University of Minnesota Twin Cities) | EE/CS 3-180 | SW11.3-4.06 |
| 12:20p-2:00p | lunch break | SW11.3-4.06 | ||
| 2:00p-3:15p | Panel discussion on career opportunities in the mathematical sciences | Francisco Barahona (IBM Thomas J. Watson Research Center) Raymond Beaulieu (National Security Agency) Fern Y. Hunt (National Institute of Standards and Technology) Overtoun Jenda (Auburn University) | EE/CS 3-180 | SW11.3-4.06 |
| 3:15p-3:45p | coffee break | EE/CS 3-176 | SW11.3-4.06 | |
| 3:45p-4:15p | Jump-diffusions | Erhan Cinlar (Princeton University) | EE/CS 3-180 | SW11.3-4.06 |
| 4:15p-5:00p | Dynamical queueing systems | William A. Massey (Princeton University) | EE/CS 3-180 | SW11.3-4.06 |
| 5:00p-6:00p | break | SW11.3-4.06 | ||
| 6:00p-9:00p | Conference reception and banquet | Coffman Memorial Union | SW11.3-4.06 | |
| Banquet talk | Tony F. Chan (National Science Foundation) |
Tuesday, November 7
| 11:15a-12:15p | IMA postdoc seminar: Algebraic torus-based cryptography | Jason E. Gower (University of Minnesota Twin Cities) | Lind Hall 409 | PS |
Wednesday, November 8
| 11:15a-12:15p | Algebraic geometry and applications seminar: Excess intersection theory and homotopy continuation methods | Sorin Popescu (SUNY) | Lind Hall 409 | AGS |
Thursday, November 9
| 11:15a-12:15p | Real algebraic geometry tutorial: Elimination of quantifiers | Kenneth R. Driessel (Iowa State University) | Lind Hall 409 | RAG |
Tuesday, November 14
| 11:15a-12:15p | IMA postdoc seminar: TBA | John Voight (University of Minnesota Twin Cities) | Lind Hall 409 | PS |
| 11:15a-12:15p | Applied math seminar:
Loewner chains and a problem in H∞ optimal control Talk Material | Farhad Jafari (University of Wyoming) | Vincent Hall 1 |
Wednesday, November 15
| 11:15a-12:15p | Algebraic geometry and applications seminar: Tropical celestial mechanics | Richard Moeckel (University of Minnesota Twin Cities) | Lind Hall 409 | AGS |
Tuesday, November 21
| 11:15a-12:15p | IMA postdoc seminar: TBA | Daniel J. Bates (University of Minnesota Twin Cities) | Lind Hall 409 | PS |
Tuesday, November 28
| 11:15a-12:15p | IMA postdoc seminar: TBA | Anton Leykin (University of Minnesota Twin Cities) | Lind Hall 409 | PS |
Wednesday, November 29
| 11:15a-12:15p | Algebraic geometry and applications seminar: | Niels Lauritzen (Aarhus University) | Lind Hall 409 | AGS |
Event Legend: |
|
| AGS | Algebraic Geometry and Applications Seminar |
| PS | IMA Postdoc Seminar |
| PUB11.2.06 | Dr. Margaret H. Wright |
| RAG | Weekly Tutorial: Real Algebraic Geometry |
| SW11.3-4.06 | Blackwell-Tapia Conference |
Abstracts
| Asheber Abebe (Auburn University) | Discriminant analysis based on statistical depth functions | ||
| Abstract: 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. | |||
| Alejandro Aceves (University of New Mexico) | Nonlinear interaction of light in disordered optical fiber arrays | ||
| Abstract: 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. | |||
| Javier Armendariz (Johns Hopkins University) | JHU Applied Physics Lab - Aviation systems engineering group overview | ||
| Abstract: 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. | |||
| Kanadpriya Basu (University of South Carolina), Maria Cristina Villalobos (University of Texas Pan American) | Modelling faculty teaching workload as a linear program | ||
| Abstract: 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. | |||
| Manuel Berriozábal (University of Texas) | Texas prefreshman engineering program: Closing the gap for minorities in science and engineering | ||
Abstract: 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:
|
|||
| Nelson Butuk (Prairie View A&M University) | Accurate computation of second order derivatives using complex variables | ||
| Abstract: 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. | |||
| Luis Enrique Carrillo Díaz (Universidad Nacional Mayor de San Marcos), Roxana Lopez-Cruz (Universidad Nacional Mayor de San Marcos) | Research Institute of Mathematical Sciences | ||
| Abstract: 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/ | |||
| Edward Castillo (Rice University) | Registration of 4D CT lung images | ||
| Abstract: In collaboration with Guerrero et al from MD Anderson Cancer Center, we are developing a new method for accurate registration of 4D CT lung images which accounts for: (1) the compressible nature of the lungs, (2) noise in the images, (3) the high computational workload required to register 4D CT image sets. In order to account for lung compressibility, voxel displacement is modeled by the conservation of mass equation. Secondly, the effects of noise are alleviated by applying the local-global approach of Weickert et al. to the conservation of mass setting. Finally, the resulting large scale linear systems are solved using a parallelizable, preconditioned conjugate gradient algorithm. The new method has been implemented in serial and tested on two dimensional sythetic images with promising results. | |||
| Gerardo Chowell (Los Alamos National Laboratory) | Transmission and control of seasonal and pandemic influenza | ||
| Abstract: Recurrent epidemics of influenza are observed seasonally around the world with considerable health and economic consequences. Major changes in the influenza virus composition through antigenic shifts can give rise to pandemics. The reproduction number provides a measure of the transmissibility of influenza. We estimated the reproduction number across influenza seasons in the United States, France, and Australia for the last 3 decades. In regards to pandemic influenza, we estimated the reproduction number for the first two epidemic waves during the 1918 influenza pandemic in Geneva, Switzerland. I will discuss the public health implications of our findings in terms of controlling regular influenza epidemics and an influenza pandemic of comparable magnitude to that of 1918. | |||
| Erhan Cinlar (Princeton University) | Jump-diffusions | ||
| Abstract: For Hunt processes with jumps, we seek a treatment that concentrates on the jumps. The idea is to use a generalized version of the renewal theory (to which Blackwell was a seminal contributor). Embedded at the jump times, there are Markov renewal processes (with continuous state space) that decompose the original process into a sequence of diffusions. Then, the original resolvent can be written as the potential operator of a Markov chain acting on the resolvent of a diffusion. Similar decompositions are possible for hitting distributions and the transition semigroup. Theoretically, our method reduces a jump diffusion to a combination of diffusions and Markov chains. | |||
| Minerva Cordero-Epperson (University of Texas) | A new semifield of order 36 | ||
| Abstract: 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. | |||
| Ricardo Cortez (Tulane University) | Computation of biological flows | ||
| Abstract: Biological systems often include very interesting fluid flows that arise from the interaction of a fluid with an external source of force. Examples are the motion of micro-organisms, such as bacteria, that propel themselves by moving their flagella, the motion of cells, and the motion generated by cilia beating in the lungs. The common theme is the interaction between the fluid and an elastic membrane of filament. Numerical models of these motions must compute the motion of the membranes and the fluid simultaneously. This talk highlights the use of Regularizaton Methods for these problems, a methodology that has shown promising results and that continues to expand. Examples of the computations will be shown. | |||
| Carla Cotwright (Wake Forest University) | Clones in minors of matroids | ||
| Abstract: 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. | |||
| Diana Dalbotten (University of Minnesota Twin Cities) | Mathematics and its application to modeling the earth's surface | ||
| Abstract: 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. | |||
| Adewale Faparusi (Texas A & M University) | The fixed charge network flow problem | ||
| Abstract: 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. | |||
| Jose D. Flores (University of South Dakota) | Allee effect in an open-access fishery model | ||
| Abstract: We analyze the consequences of incorporating the phenomenon of depensation, also known as Allee effect, into the bio-economic model proposed by V. L. Smith in his research work on commercial fishing. The model proposed by Smith is one of the simplest bio-economic models used in the management of renewable resources, which related the biomass of the exploited resources and the nominal fishery's effort of open-access. | |||
| Sean C. Garrick (University of Minnesota Twin Cities) | Probabilistic and stochastic modeling of turbulent flows | ||
| Abstract: The transport of wide variety of phenomena in turbulent flows (heat, mass, momentum, species, etc.) is a significant challenge to computational scientists and engineers working in chemical processing, pharmaceuticals, materials synthesis, and atmospheric physics, to name a few. Capturing the variety of length and time scales manifest in these flows leads to compute times which are impractical at best and infeasible at worst. In this seminar, I will present some ideas and recent work in the modeling of multi-scale transport phenomena and the probabilistic and stochastic tools used in their description. | |||
| Nancy Glenn (University of South Carolina) | EL algorithm for linear models with missing data | ||
| Abstract: Linear regression is one of the most widely used statistical techniques. However, there is often a problem of missing response variables in practical applications. The expectation maximization (EM) algorithm is a general iterative algorithm for the analysis of missing data; but it relies on parametric assumptions that are usually not met. We present a nonparametric algorithm--the empirical likelihood (EL) algorithm for linear models with missing data. The EL algorithm's advantage is that it makes no assumptions regarding the form of the underlying distribution of the data. We construct confidence intervals for the mean response in the presence of missing responses. We also discuss the power and efficiency of confidence intervals constructed when using the EL algorithm to replace missing responses. | |||
| Edray Goins (Purdue University) | Why should I care about Lie groups? | ||
| Abstract: Sometimes differential equations have an obvious symmetry which leads to a natural guess for its solution. The Norwegian mathematician Marius Sophus Lie (1842-1899) spent most of his career attempting to generalize ideas of fellow Norwegian Niels Henrik Abel (1802-1829) from discrete groups of symmetries of algebraic objects to continuous groups of symmetries of topological objects. In the process, Lie created a new branch of mathematics which united differential geometry and abstract algebra. In this talk, we give a brief introduction to the pulchritude of Lie's ideas. From the geometric nature of manifolds to the analytic nature of differential equations, we discuss the natural group action of the space of vector fields of a manifold on itself. We conclude the talk with a discussion of the computation of Lie group of the real line. | |||
| Jason E. Gower (University of Minnesota Twin Cities) | IMA postdoc seminar: Algebraic torus-based cryptography | ||
| Abstract: In 2003, Karl Rubin and Alice Silverberg proposed using algebraic tori for use in public key cryptography. Their basic construction can be used for Diffie-Hellman key exchange and ElGamal encryption and authentication, as well as for improving pairing-based cryptographic protocols associated with elliptic curves, voting schemes, and sequential and parallel re-encrypting mix-nets. After describing the basic construction, we will sketch some of the cryptographic applications and discuss the efficiency/security considerations and related open problems. | |||
| Cristi Darley Guevara (Arizona State University) | Fourier restriction problem and its relation to PDE | ||
| Abstract: No Abstract | |||
| Illya V. Hicks (Texas A & M University) | Branch decomposition techniques for discrete optimization | ||
| Abstract: This talk gives a general overview of an emerging technique for discrete optimization that has footholds in mathematics, computer science, and operations research: branch decompositions. Branch decompositions along with its respective connectivity invariant, branchwidth, were first introduced to aid in proving the Graph Minors Theorem, a well known conjecture (Wagner's conjecture) in graph theory. The algorithmic importance of branch decompositions for solving NP-hard problems modeled on graphs was first realized by computer scientists. The dynamic programming techniques utilizing branch decompositions, called branch decomposition based algorithms, fall into a class of algorithms known as fixed-parameter tractable algorithms and this talk will highlight the computational effectiveness of these algorithms in a practical setting for NP-hard problems such as the travelling salesman problem, general minor containment, and the branchwidth problem. | |||
| Fern Y. Hunt (National Institute of Standards and Technology) | Mathematical modelling at NIST: An example | ||
| Abstract: 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. | |||
| Farhad Jafari (University of Wyoming) | Applied math seminar:
Loewner chains and a problem in H∞ optimal control Talk Material |
||
| Abstract: If f is a univalent function, Loewner chains are used to embed
the image
domain in a continuously increasing family of domains. This
family is then
described by a nonlinear differential equation. If
SM is the
class of
univalent funtions on the open unit disk bounded by M, we use
the
Loewner differential equation to solve the following:
Problem. Find an optimal nonnegative-valued function φ
such that for every z, w in the disk
|f(z)-f(w)| ≤ φ(z,w) for every f \in SM. |
|||
| Christopher Jones (University of North Carolina) | Statistical and Applied Mathematical Sciences Institute | ||
| Abstract: Come learn about opportunities at SAMSI. | |||
| Donald King (Northeastern University) | Spherical nilpotent orbits of reductive Lie groups: an overview | ||
| Abstract: 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. | |||
| Rachel Kuske (University of British Columbia) | American Institute of Mathematics | ||
| Abstract: 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. | |||
| Mark E. Lewis (Cornell University) | From Massey to Blackwell: A study of non-stationary queueing control via sensitive optimality criteria | ||
| Abstract: In this talk we explain how a single jump non-stationary queueing control problem can be solved via sensitive optimality criteria. In particular, the queueing problem is divided into a stationary infinite horizon problem and a non-stationary finite horizon problem with the appropriate terminal reward. The stationary problem leads to several results including the existence of a single bias optimal policy. Since the existence of a Blackwell optimal policy is known, this implies a similar result under this criterion. The search for an optimal policy in the non-stationary problem is shown to lie within the class of monotone (in time) control limit policies. The original problem was posed by Professor Massey and lead to an understanding of an application of Blackwell's sensitive optimality criterion, thereby drawing a connection between 2 (actually 3) generations of African-American scholars. | |||
| Daniel Lichtblau (Wolfram Research, Inc.) | Special talk: Computer assisted mathematics: Tools and tactics for solving hard problems | ||
| Abstract: In this talk I will present several problems that have caught my attention over the past few years. We will go over Mathematica formulations and solutions. Along the way we will meet with a branch-and-bound loop in its natural habitat, some rampaging Gr As the purpose is to illustrate a few of the many ways in which Mathematica can be used to advantage in tackling difficult problems, we will go into a bit of detail in selected examples. Do not let this deter you; there will be no exam, and it is the methods, not the problems, that are of importance. The examples are culled from problems I have seen on Usenet groups (primarily MathGroup), in articles, or have been asked in person. | |||
| Diane Maclagan (Rutgers University) | Algebraic geometry and applications seminar: Equations and degenerations of the moduli space of genus zero stable curves with n marked points | ||
| Abstract: Curves are one of the basic objects of algebraic geometry, and so much attention has been paid to the moduli space of all curves of a given genus. This talk will focus on the moduli space of genus zero stable curves with n marked points, which is a compactification of the space M0,n of isomorphism classes of n points on the projective line. After introducing this space, I will describe joint work with Angela Gibney on explicit equations for it, which lets us see degenerations to toric varieties. | |||
| Oluwole Daniel Makinde (University of Limpopo) | Thermal stability of a reactive third grade fluid in a cylindrical pipe: An exploitation of Hermite-Padé approximation technique | ||
| Abstract: 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. | |||
| William A. Massey (Princeton University) | Dynamical queueing systems | ||
| Abstract: Technological innovations are creating new types of communication systems such as call centers, electronic commerce, and wireless communications. Communication services managers must make important business decisions to stay competitive and profitable. They have to maximize the communication resources that they are making available to the customer. However, managers must also minimize their costs for providing these resources, which results in maximizing profits for their companies. The mathematical field of queueing theory was successfully introduced in the first half of the 20th century to model voice communication networks. It has traditionally provided managers with a useful set of decision making formulas, algorithms and policies for designing communication systems and services. Another major triumph for queueing theory happened in the second half of the 20th century when it was applied to data communication systems and contributed to the design of the first prototype for the Internet. Both types of voice and data queueing models made significant use of the steady state theory for continuous time Markov chains. Given the new types of communication systems and services available in the 21st century, it is no longer possible to make many of the simplifying assumptions of classical queueing theory. One major theme of my research has been to move away from the static steady state analysis of the past and develop a theory of queues that captures more of the true dynamic behavior that is found in real communications operations. My talk will discuss the types of mathematical tools needed to create a dynamical queueing theory. This involves new types of perturbation analysis applied to the differential equations of the transition probabilities for the underlying, time-inhomogeneous Markov chain, queueing model. Moreover, we also use the theory of strong approximations to apply this asymptotic analysis directly to the random sample paths of these stochastic processes. We can also relax these Markovian assumptions by using the theory of Poisson random measures. Finally, we can establish fundamental limit theorems that approximate many of these random processes by dynamical systems. From these results, we can then apply the dynamic optimization techniques of variational calculus and classical mechanics to the efficient design of these queueing models. | |||
| Richard Moeckel (University of Minnesota Twin Cities) | Algebraic geometry and applications seminar: Tropical celestial mechanics | ||
| Abstract: Some interesting problems in mechanics can be reduced to solving systems of algebraic equations. A good example is finding relative equilibria of the gravitational n-body problem. These are special configurations of the n point masses which can rotate rigidly such that the outward centrifugal forces exactly cancel the gravitational attractions. The algebraic equations are complicated enough that it is a long-standing open problem even to show that the number of solutions is finite. I will describe a solution to this question for n=4 which makes use of some ideas from what is now called tropical algebraic geometry – Puiseux series solutions, initial ideals, etc. The problem is open for larger n. | |||
| David Murillo (Arizona State University) | Change in host behavior and its impact on the co-evolution of dengue | ||
| Abstract: 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 | |||
| Josue C. Noyola-Martinez (Rice University) | Error estimates between the stochastic simulation algorithm (SSA) and the tau-leap method | ||
| Abstract: 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. | |||
| Kathleen O'Hara (Mathematical Sciences Research Institute) | Mathematical Sciences Research Institute | ||
| Abstract: Come learn about opportunities at MSRI. | |||
| Kasso Okoudjou (University of Maryland) | Asymptotics of eigenvalue clusters for Schroedinger operators on the Sierpinski gasket | ||
| Abstract: In this talk we shall present some results on the asymptotic behavior of spectra of Schrodinger operators with continuous potential on the Sierpinski gasket SG. In particular, using the extence of localized eigenfunctions for the Laplacian on SG we show that the eigenvalues of the Schrodinger opeartor break into clusters around certain eigenvalue of the Laplacian. Moreover, we prove that the characteristic measure of these clusters converges to a measure. | |||
| Janis Oldham (North Carolina Agricultural and Technical State University) | Progress report on the NSA mathematics enhancement grant: Developing a mathematics culture among undergraduate mathematics majors at North Carolina A&T State University | ||
| Abstract: 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. | |||
| Joanna Papakonstantinou (Rice University) | Historical development of the secant method: from the Babylonians to Wolfe | ||
| Abstract: 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. | |||
| Sorin Popescu (SUNY) | Algebraic geometry and applications seminar: Excess intersection theory and homotopy continuation methods | ||
| Abstract: I will recall first basic techniques and results in (excess) intersection theory in algebraic geometry and then discuss their implications and also applications toward a numerical approach to primary decomposition for ideals in polynomial rings. | |||
| Carlos Andrés Quintero Salazar (University of Texas) | Automated parameter estimation and sensitivity analysis | ||
| Abstract: 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. | |||
| Karen Rios-Soto (Cornell University) | Epidemic spread in populations at demographic equilibrium | ||
| Abstract: We introduce an integrodifference equation model to study the spatial spread of epidemics through populations with overlapping and non- overlapping epidemiological generations. Our focus is on the existence of travelling wave solutions and their minimum asymptotic speed of propagation c*. We contrast the results here with similar work carried out in the context of ecological invasions. We illustrate the theoretical results numerically in the context of SI (susceptible-infected) and SIS (susceptible-infected-susceptible) epidemic models. | |||
| Joaquin Rivera (University of Iowa) | Existence of traveling waves solution for a nonlocal reaction-diffusion model of influenza A | ||
| Abstract: 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. | |||
| Daniel Romero (Arizona State University) | An epidemiological approach to the spread of minor political parties | ||
| Abstract: 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. | |||
| Flavia Sancier-Barbosa (Southern Illinois University) | Option pricing with memory | ||
| Abstract: In this talk we introduce an option pricing model with delayed memory. The memory is introduced in the stock dynamics, which is described by a stochastic functional differential equation. The model has the following key features: 1. Volatility depends on a (delayed) history, i.e., its value at time t is a deterministic functional of the history of the stock from time t-L up to time t-l, where l is positive and less than or equal to L. Hence, due to this past-dependence on the stock price, the volatility is necessarily stochastic. 2. The randomness in the volatility is intrinsic, since it is generated by past values of the stock price. 3. The stock dynamics is driven by a single one-dimensional Brownian motion, and the model is one dimensional. 4. The market is complete. 5. For large delays (or at times relatively close to maturity) we obtain a closed-form representation for the fair price of the option, as well as for the hedging strategy. 6. The option price can be expressed in terms of the exact solution of a one-dimensional partial differential equation (PDE). 7. The classical Black-scholes model is a particular case of the delayed memory model. 8. We believe that our model is sufficiently flexible to fit real market data, in particular to account for observed "smiles" and "frowns". | |||
| David Tello (Arizona State University) | Mathematical aspects of dopamine's turnover | ||
| Abstract: 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. | |||
| Sheila Tobias | Professional Science Masters programs | ||
| Abstract: 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 | Conrad Tucker (University of Illinois at Urbana-Champaign) | Optimal product portfolio formulation: Merging predictive data mining with analytical target cascading | |
| Abstract: 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. | |||
| Maria Cristina Villalobos (University of Texas Pan American) | Formulating Fano's Method as an Optimization Problem to obtain Broadband Tuning Limits on UWB Antennas | ||
| Abstract: Modern broadband communications requires antennas with greatly improved frequency range and reduced size. It has been known since 1948 that there are basic physical limitations on the bandwidth that can be obtained for a given size antenna; however, the numerical results that have been available were until recently based entirely on a second-order model for the antenna that was (a) an approximation, and (b) only strictly applicable to relatively narrowband cases. In the last few years, a new approach based on "Fano's formulation" has been used which can apply over any bandwidth. We have reformulated Fano's method as an optimization problem and as a result have been able to obtain fundamental bandwidth limits that can in principle be calculated for any radiation mode. This means that one can now find the ultimate possible bandwidth performance for directional antennas, a result with immediate practical significance for designers of ultra-wideband antennas. Graphs of numerical limits on the in-band reflection coefficient tolerance versus electrical size for high-pass and band-pass tuning are presented. This is joint work with H.D. Foltz and J.S. McLean | |||
| Rachel E. Vincent-Finley (Rice University) | Reduced basis simulation | ||
| Abstract: 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. | |||
| Bryan Williams (Hampton University) | Large circuit pairs in matroids | ||
| Abstract: 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. | |||
| Isaac Woungang (Ryerson Polytechnical University) | Algebraic characterizations of some classes of quasi-cyclic codes | ||
| Abstract: 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 qm-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. | |||
| Margaret H. Wright (New York University) | Undergraduate, graduate, and postdoctoral opportunities at New York University | ||
| Abstract: 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. | |||
| Wenyuan Wu (University of Western Ontario) | Differential elimination of PDEs by numerical algebraic geometry and numerical linear algebra | ||
| Abstract: 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 | |||
| Emmanuel Yomba (University of Minnesota Twin Cities) | Generalized hyperbolic functions to find soliton-like solutions of the inhomogeneous higher-order nonlinear Schrödinger equation | ||
| Abstract: The inhomogeneous higher-order nonlinear Schrödinger (IHONLS) equation is studied by the use of generalized hyperbolic functions and the complex amplitude method. The results reveal that for the new bright soliton-type and dark soliton-type solutions obtained, one can control the velocity, the phase shift (by managing the distributed parameters of the system) and the shape (by choosing appropriately the two parameters introduced in the generalized hyperbolic functions). | |||
Visitors in Residence
| Kobi Abayomi | Columbia University | 11/3/2006 - 11/5/2006 |
| Asheber Abebe | Auburn University | 11/3/2006 - 11/5/2006 |
| Alejandro Aceves | University of New Mexico | 11/2/2006 - 11/5/2006 |
| Evans Afenya | Elmhurst College | 11/3/2006 - 11/5/2006 |
| Jung-Ha An | University of Minnesota Twin Cities | 9/1/2005 - 8/31/2007 |
| Issareeya Anunyaporn | University of Texas Pan American | 11/3/2006 - 11/5/2006 |
| Miguel Argaez | University of Texas | 11/3/2006 - 11/5/2006 |
| Javier Armendariz | Johns Hopkins University | 11/3/2006 - 11/5/2006 |
| Douglas N. Arnold | University of Minnesota Twin Cities | 7/15/2001 - 8/31/2007 |
| Donald G. Aronson | University of Minnesota Twin Cities | 9/1/2002 - 8/31/2007 |
| Rodrigo Bañuelos | Purdue University | 11/2/2006 - 11/5/2006 |
| Francisco Barahona | IBM Thomas J. Watson Research Center | 11/3/2006 - 11/5/2006 |
| Earl Barnes | Georgia Institute of Technology | 11/3/2006 - 11/5/2006 |
| Kanadpriya Basu | University of South Carolina | 11/2/2006 - 11/5/2006 |
| Daniel J. Bates | University of Minnesota Twin Cities | 9/1/2006 - 8/31/2007 |
| Raymond Beaulieu | National Security Agency | 11/3/2006 - 11/5/2006 |
| Keith Berrier | Law Offices of Mark L. Berrier | 11/3/2006 - 11/4/2006 |
| Manuel Berriozábal | University of Texas | 11/3/2006 - 11/5/2006 |
| Yermal Sujeet Bhat | University of Minnesota Twin Cities | 9/1/2006 - 8/31/2007 |
| Sean Brooks | Coppin State University | 11/2/2006 - 11/5/2006 |
| Javier Burgos | Universidad Nacional de Colombia | 11/3/2006 - 11/5/2006 |
| Nelson Butuk | Prairie View A&M University | 11/2/2006 - 11/5/2006 |
| Maria-Carme T. Calderer | University of Minnesota Twin Cities | 11/3/2006 - 11/4/2006 |
| Rodrigo Carraminana | University of Illinois | 11/3/2006 - 11/5/2006 |
| Jamylle Laurice Carter | San Francisco State University | 11/2/2006 - 11/4/2006 |
| Edward Castillo | Rice University | 11/3/2006 - 11/5/2006 |
| Carlos Castillo-Chavez | Arizona State University | 11/3/2006 - 11/5/2006 |
| Ximena Catepillan | Millersville University | 11/3/2006 - 11/5/2006 |
| Tony F. Chan | National Science Foundation | 11/3/2006 - 11/5/2006 |
| Farrah J. Chandler | University of North Carolina | 11/2/2006 - 11/5/2006 |
| Gerardo Chowell | Los Alamos National Laboratory | 11/2/2006 - 11/5/2006 |
| Erhan Cinlar | Princeton University | 11/3/2006 - 11/5/2006 |
| Ionut Ciocan-Fontanine | University of Minnesota Twin Cities | 9/1/2006 - 6/30/2007 |
| Barry Cipra | St. Olaf College | 11/3/2006 - 11/5/2006 |
| Jon Cline | Case Western Reserve University | 11/3/2006 - 11/5/2006 |
| Olga Cordero-Brana | University of Hawaii at Manoa | 11/2/2006 - 11/5/2006 |
| Minerva Cordero-Epperson | University of Texas | 11/3/2006 - 11/5/2006 |
| Ricardo Cortez | Tulane University | 11/3/2006 - 11/5/2006 |
| Carla Cotwright | Wake Forest University | 11/3/2006 - 11/5/2006 |
| Cyndy Crist | Minnesota State Colleges and Universities | 11/3/2006 - 11/4/2006 |
| Diana Dalbotten | University of Minnesota Twin Cities | 11/3/2006 - 11/3/2006 |
| Alicia Dickenstein | University of Buenos Aires | 9/1/2006 - 11/30/2006 |
| Kenneth R. Driessel | Iowa State University | 9/1/2006 - 5/31/2007 |
| Kossi Delali Edoh | North Carolina Agricultural and Technical State University | 11/3/2006 - 11/5/2006 |
| Marco Enriquez | Rice University | 11/3/2006 - 11/5/2006 |
| Adewale Faparusi | Texas A & M University | 11/2/2006 - 11/5/2006 |
| Makan Fardad | University of Minnesota Twin Cities | 8/26/2006 - 8/13/2007 |
| Jose D. Flores | University of South Dakota | 11/3/2006 - 11/5/2006 |
| Dennis Frank | North Carolina State University | 11/3/2006 - 11/5/2006 |
| Joe Gallian | University of Minnesota | 11/3/2006 - 11/4/2006 |
| Shuhong Gao | Clemson University | 9/3/2006 - 12/20/2006 |
| Sean C. Garrick | University of Minnesota Twin Cities | 11/3/2006 - 11/4/2006 |
| Tepper Gill | Howard University | 11/2/2006 - 11/6/2006 |
| Nancy Glenn | University of South Carolina | 11/2/2006 - 11/5/2006 |
| Edray Goins | Purdue University | 11/3/2006 - 11/5/2006 |
| Jason E. Gower | University of Minnesota Twin Cities | 9/1/2006 - 8/31/2007 |
| Arthur D. Grainger | Morgan State University | 11/3/2006 - 11/5/2006 |
| Angela Grant | Northwestern University | 11/3/2006 - 11/5/2006 |
| Lawrence Gray | University of Minnesota Twin Cities | 11/3/2006 - 11/4/2006 |
| Michael Green | Metropolitan State University | 11/3/2006 - 11/4/2006 |
| Alvaro Guevara | Louisiana State University | 11/2/2006 - 11/5/2006 |
| Cristi Darley Guevara | Arizona State University | 11/3/2006 - 11/5/2006 |
| Abba Gumel | University of Manitoba | 11/3/2006 - 11/5/2006 |
| Robert C. Hampshire | Princeton University | 11/3/2006 - 11/5/2006 |
| Gloria Haro Ortega | University of Minnesota Twin Cities | 9/1/2005 - 8/31/2007 |
| Milena Hering | University of Minnesota Twin Cities | 9/1/2006 - 8/31/2007 |
| Illya V. Hicks | Texas A & M University | 11/2/2006 - 11/5/2006 |
| Benjamin J. Howard | University of Minnesota Twin Cities | 9/1/2006 - 8/31/2007 |
| Evelyne Hubert | Institut National de Recherche en Informatique Automatique (INRIA) | 9/1/2006 - 6/30/2007 |
| Fern Y. Hunt | National Institute of Standards and Technology | 11/3/2006 - 11/5/2006 |
| Monica Jackson | American University | 11/3/2006 - 11/5/2006 |
| Trachette L. Jackson | University of Michigan | 11/3/2006 - 11/5/2006 |
| Farhad Jafari | University of Wyoming | 9/1/2006 - 6/30/2007 |
| Overtoun Jenda | Auburn University | 11/2/2006 - 11/5/2006 |
| Otis B. Jennings | Duke University | 11/3/2006 - 11/5/2006 |
| Anders Nedergaard Jensen | Aarhus University | 9/6/2006 - 6/30/2007 |
| Silvia Jimenez | Louisiana State University | 11/2/2006 - 11/5/2006 |
| Cynthia Johnson | Rice University | 11/2/2006 - 11/5/2006 |
| Christopher Jones | University of North Carolina | 11/3/2006 - 11/5/2006 |
| Donald Kahn | University of Minnesota Twin Cities | 11/3/2006 - 11/4/2006 |
| Hans Kaper | National Science Foundation | 11/3/2006 - 11/5/2006 |
| John Kemper | University of St. Thomas | 11/3/2006 - 11/4/2006 |
| Harvey Keynes | University of Minnesota Twin Cities | 11/3/2006 - 11/4/2006 |
| Nkem Khumbah | University of Michigan | 11/3/2006 - 11/5/2006 |
| Donald King | Northeastern University | 11/3/2006 - 11/5/2006 |
| Genevieve Knight | Fayetteville State University | 11/3/2006 - 11/5/2006 |
| Teresa Krick | University of Buenos Aires | 11/27/2006 - 11/29/2006 |
| Teresa Krick | University of Buenos Aires | 11/1/2006 - 11/3/2006 |
| Aderemi Kuku | Abdus Salam International Centre for Theoretical Physics | 11/2/2006 - 11/5/2006 |
| Rachel Kuske | University of British Columbia | 11/2/2006 - 11/5/2006 |
| Song-Hwa Kwon | University of Minnesota Twin Cities | 8/30/2005 - 8/31/2007 |
| Niels Lauritzen | Aarhus University | 8/28/2006 - 6/30/2007 |
| Steven L. Lee | Lawrence Livermore National Laboratory | 11/2/2006 - 11/5/2006 |
| Delia Letang | University of Minnesota Twin Cities | 11/3/2006 - 11/5/2006 |
| Mark E. Lewis | Cornell University | 11/2/2006 - 11/5/2006 |
| Anton Leykin | University of Minnesota Twin Cities | 8/16/2006 - 8/15/2007 |
| Ruifang Li | University of Texas Pan American | 11/3/2006 - 11/5/2006 |
| Hstau Liao | University of Minnesota Twin Cities | 9/2/2005 - 8/31/2007 |
| Daniel Lichtblau | Wolfram Research, Inc. | 11/1/2006 - 11/3/2006 |
| Roxana Lopez-Cruz | Universidad Nacional Mayor de San Marcos | 11/2/2006 - 11/6/2006 |
| Laura Lurati | University of Minnesota Twin Cities | 9/1/2006 - 8/31/2007 |
| Gennady Lyubeznik | University of Minnesota Twin Cities | 9/1/2006 - 6/30/2007 |
| Diane Maclagan | Rutgers University | 9/5/2006 - 11/30/2006 |
| Oluwole Daniel Makinde | University of Limpopo | 10/31/2006 - 11/5/2006 |
| Shirley M. Malcom | American Association for the Advancement of Science | 11/3/2006 - 11/3/2006 |
| David Manderscheid | University of Iowa | 11/2/2006 - 11/5/2006 |
| Hannah Markwig | University of Minnesota Twin Cities | 9/1/2006 - 8/31/2007 |
| Thomas Markwig | Universität Kaiserslautern | 9/1/2006 - 6/30/2007 |
| Geoffrey Maruyama | University of Minnesota Twin Cities | 11/3/2006 - 11/4/2006 |
| Juliette Massey | NONE | 11/3/2006 - 11/5/2006 |
| Richard Massey Jr. | NONE | 11/3/2006 - 11/5/2006 |
| William A. Massey | Princeton University | 11/2/2006 - 11/5/2006 |
| Douglas McWilliams | Purdue University | 11/3/2006 - 11/5/2006 |
| Willard Miller Jr. | University of Minnesota Twin Cities | 11/3/2006 - 11/4/2006 |
| Richard Moeckel | University of Minnesota Twin Cities | 9/1/2006 - 6/30/2007 |
| Salah Mohammed | Southern Illinois University | 11/3/2006 - 11/5/2006 |
| David Morrison | University of California | 11/3/2006 - 11/5/2006 |
| David Murillo | Arizona State University | 11/3/2006 - 11/5/2006 |
| Samuel Myers | University of Minnesota Twin Cities | 11/2/2006 - 11/4/2006 |
| Uwe Nagel | University of Kentucky | 9/1/2006 - 6/1/2007 |
| Jiawang Nie | University of Minnesota Twin Cities | 9/1/2006 - 8/31/2007 |
| Mechie Nkengla | University of Illinois | 11/3/2006 - 11/5/2006 |
| Josue C. Noyola-Martinez | Rice University | 11/2/2006 - 11/5/2006 |
| Kathleen O'Hara | Mathematical Sciences Research Institute | 11/3/2006 - 11/5/2006 |
| Kasso Okoudjou | University of Maryland | 11/3/2006 - 11/5/2006 |
| Janis Oldham | North Carolina Agricultural and Technical State University | 11/3/2006 - 11/5/2006 |
| Broderick Oluyede | Georgia Southern University | 11/3/2006 - 11/5/2006 |
| Omayra Ortega | Arizona State University | 11/2/2006 - 11/5/2006 |
| Juan Ariel Ortiz-Navarro | University of Iowa | 11/3/2006 - 11/5/2006 |
| Victor Padron | Normandale Community College | 11/3/2006 - 11/4/2006 |
| Joanna Papakonstantinou | Rice University | 11/2/2006 - 11/5/2006 |
| Chris Peterson | Colorado State University | 9/1/2006 - 12/31/2006 |
| Arlie O. Petters | Duke University | 11/3/2006 - 11/5/2006 |
| Sorin Popescu | SUNY | 9/1/2006 - 12/31/2006 |
| Carl Lindell Prather | Virginia Polytechnic Institute and State University | 11/3/2006 - 11/5/2006 |
| Carlos Andrés Quintero Salazar | University of Texas | 11/3/2006 - 11/5/2006 |
| Bharath Rangarajan | University of Minnesota Twin Cities | 11/3/2006 - 11/4/2006 |
| Gregory J. Reid | University of Western Ontario | 9/6/2006 - 12/1/2006 |
| Victor Reiner | University of Minnesota Twin Cities | 9/1/2006 - 6/30/2007 |
| Karen Rios-Soto | Cornell University | 11/2/2006 - 11/5/2006 |
| Joaquin Rivera | University of Iowa | 11/3/2006 - 11/5/2006 |
| Joel Roberts | University of Minnesota Twin Cities | 9/1/2006 - 6/30/2007 |
| Eliana Rojas | University of Connecticut | 11/3/2006 - 11/5/2006 |
| Daniel Romero | Arizona State University | 11/3/2006 - 11/5/2006 |
| Bjarke Hammersholt Roune | Aarhus University | 9/12/2006 - 6/30/2007 |
| Philippe Rukimbira | Florida International University | 11/3/2006 - 11/5/2006 |
| David Rusin | Northern Illinois University | 9/1/2006 - 12/31/2006 |
| Flavia Sancier-Barbosa | Southern Illinois University | 11/3/2006 - 11/5/2006 |
| Arnd Scheel | University of Minnesota Twin Cities | 7/15/2004 - 8/31/2007 |
| Abdulalim A. Shabazz | Lincoln University | 11/3/2006 - 11/5/2006 |
| Chehrzad Shakiban | University of Minnesota Twin Cities | 9/1/2006 - 8/31/2007 |
| Josef Aaron Sifuentes | Rice University | 11/2/2006 - 11/5/2006 |
| Michel Smith | Auburn University | 11/2/2006 - 11/5/2006 |
| Stephanie Somersille | University of California | 11/2/2006 - 11/5/2006 |
| Andrew Sommese | University of Notre Dame | 9/1/2006 - 12/31/2006 |
| Michelle Sowemimo | Duke University | 11/3/2006 - 11/5/2006 |
| Steven Sperber | University of Minnesota Twin Cities | 9/1/2006 - 6/30/2007 |
| Luke Stewart | Duke University | 11/3/2006 - 11/5/2006 |
| Jean Tapia | NONE | 11/2/2006 - 11/5/2006 |
| Rebecca Tapia | NONE | 11/2/2006 - 11/5/2006 |
| Richard Tapia Jr. | NONE | 11/2/2006 - 11/5/2006 |
| Richard Tapia | Rice University | 11/2/2006 - 11/5/2006 |
| Alberto Mokak Teguia | Duke University | 11/3/2006 - 11/5/2006 |
| David Tello | Arizona State University | 11/3/2006 - 11/5/2006 |
| Mohammed Tesemma | Spelman College | 11/3/2006 - 11/5/2006 |
| Gikiri Thuo | University of Maryland | 11/3/2006 - 11/5/2006 |
| Sheila Tobias | NONE | 11/2/2006 - 11/5/2006 |
| Enrique Augusto Tobis | University of Buenos Aires | 10/15/2006 - 11/11/2006 |
| Carl Toews | University of Minnesota Twin Cities | 9/1/2005 - 8/31/2007 |
| Conrad Tucker | University of Illinois at Urbana-Champaign | 11/2/2006 - 11/5/2006 |
| Jesse Turner | Rice University | 11/3/2006 - 11/5/2006 |
| Michael Turnley | University of Illinois at Urbana-Champaign | 11/3/2006 - 11/5/2006 |
| Leticia Velazquez | University of Texas | 11/3/2006 - 11/5/2006 |
| William Yslas Vélez | University of Arizona | 11/3/2006 - 11/4/2006 |
| Jan Verschelde | University of Illinois | 9/6/2006 - 11/30/2006 |
| Maria Cristina Villalobos | University of Texas Pan American | 11/3/2006 - 11/5/2006 |
| Alfredo Villanueva | University of Iowa | 11/3/2006 - 11/5/2006 |
| Rachel E. Vincent-Finley | Rice University | 11/3/2006 - 11/5/2006 |
| John Voight | University of Minnesota Twin Cities | 8/15/2006 - 8/31/2007 |
| Aissa Wade | Pennsylvania State University | 11/3/2006 - 11/5/2006 |
| Mingsheng Wang | Chinese Academy of Sciences | 9/15/2006 - 11/15/2006 |
| Esther R. Widiasih | University of Minnesota Twin Cities | 11/3/2006 - 11/4/2006 |
| Bryan Williams | Hampton University | 11/2/2006 - 11/5/2006 |
| Kyron Williams | Princeton University | 11/3/2006 - 11/5/2006 |
| Ulrica Wilson | University of California, San Diego | 11/3/2006 - 11/5/2006 |
| Isaac Woungang | Ryerson Polytechnical University | 11/2/2006 - 11/5/2006 |
| Margaret H. Wright | New York University | 11/1/2006 - 11/4/2006 |
| Wenyuan Wu | University of Western Ontario | 9/6/2006 - 12/1/2006 |
| Emmanuel Yomba | University of Minnesota Twin Cities | 11/3/2006 - 11/5/2006 |
| Joseph Young | Rice University | 11/3/2006 - 11/5/2006 |
| Hongchao Zhang | University of Minnesota Twin Cities | 9/1/2006 - 8/31/2007 |
| Yan Zhuang | University of Illinois | 9/1/2006 - 12/1/2006 |
Legend:
Postdoc or Industrial Postdoc
Long-term Visitor
IMA Affiliates:
3M, Boeing, Carnegie-Mellon University, Consiglio Nazionale delle Ricerche (CNR), Corning, ExxonMobil, Ford, General Electric, General Motors, Georgia Institute of Technology, Honeywell, IBM, Indiana University, Iowa State University, Johnson & Johnson, Kent State University, Lawrence Livermore National Laboratory, Lockheed Martin, Los Alamos National Laboratory, Medtronic, Michigan State University, Michigan Technological University, Mississippi State University, Motorola, Northern Illinois University, Ohio State University, Pennsylvania State University, Purdue University, Rice University, Rutgers University, Sandia National Laboratories, Schlumberger-Doll, Seoul National University, Siemens, Telcordia, Texas A & M University, University of Chicago, University of Cincinnati, University of Delaware, University of Houston, University of Illinois at Urbana-Champaign, University of Iowa, University of Kentucky, University of Maryland, University of Michigan, University of Minnesota, University of Notre Dame, University of Pittsburgh, University of Texas, University of Wisconsin, University of Wyoming, US Air Force Research Laboratory, Wayne State University, Worcester Polytechnic Institute