• Participants:
  • Maia Averett, University of California, Santa Barbara.
    Brendan Creutz, Cal Poly, San Luis Obispo.
    Patricia Romano Cirilo, Universidade Federal de Minas Gerais.
    John Adrian DeIonno, University of California, Los Angeles.
    Lisa Helene Feigenbaum, Harvard University.
    Juliana Abrantes Freire, PUC - Rio de Janeiro.
    Jean Carlo P. Garcia, Universidade Federal do Rio Grande do Sul.
    William Jeck, Pomona College.
    Mikhail Lev, University of California, Los Angeles.
    Ives Jose A. Macedo Jr., Universidade Federal de Pernambuco.
    Rafael Kaufmann Nedal, PUC - Rio de Janeiro.
    Anna Shustrova, University of California, Berkeley.
    Renato R. V. Zanforlin, Universidade Federal de Minas Gerais.
  • Brazilian participants were supported by the Brazilian Federal Agency, CNPq.
  • Organizers and Faculty Advisors: M. Helena Noronha, California State University Northridge, and Carlos Tomei, PUC - Rio de Janeiro.
  • Other Faculty Advisors: Helio Lopes, Marco Grivet, and Carlos Frederico Borges Palmeira, PUC - Rio de Janeiro.

The focus of the 2003 program was Applied Mathematics. In the first week participants were introduced to possible research projects and were given the option to select the problem to work on. Towards the end of the program, students gave presentations describing their progress. They also wrote a preliminary paper describing their results. As the program was only one month long, participants didn't have much time to revise and polish their papers. These papers were seen as work in progress and after the summer, students continued to work with their advisors to prepare papers for publication. Below are the participants and faculty advisors. Click on the title of the papers for a pdf version.

Facebreaker: A Compression for Tetrahedral Meshes without Boundary.
John DeIonno, Ives Jose A. Macedo Jr., and Anna Shustrova.

Tetrahedral meshes used in applications such as volume visualization consume very large amounts of memory. Thus compression is essential for storage and transmission purposes. A lot of different schemes have been developed to address this problem. Our algorithm handles tetrahedral meshes that are connected oriented combinatorial 3-manifolds without boundaries. It extends the Edgebreaker algorithm on a Corner Table for triangular meshes to work with tetrahedral meshes.
Models and Algorithms for Hydrothermal Scheduling.
William Jeck and Rafael Kaufmann Nedal.

The purpose is to minimize the cost of operating a hydrothermal power system throughout a certain amount of time, while meeting market demand at every instant. We have considered three models and applied some mathematical programming techniques.
Functions from the plane to the plane
Patricia Romano Cirilio, Brendan Creutz, Jean Carlo Pech Garcia, and Renato Rocha Fierno Zanfolin.
The goal of this study is to develop a global sense of how functions from the plane to the plane behave. In the case of functions from the real line to the real line, the standard practice is to compute critical points (i.e. maxima and minima) then use these points to infer geometric information about the function as a whole. We extend this approach to functions from the plane to the plane. Using topological tools we combine local theory of the function at singularities and regular points to obtain a global picture of how the function behaves. The image of the critical set and the locations of its preimages are highly structured. This gives us detailed information concerning the number and location of all preimages of any given point. In particular, we provide a description of a method for finding the roots of such functions, which may be applied to solving solutions of two equations in two unknowns. We then compare the method described herein for obtaining roots to methods employed by such standard mathematical packages as Maple and Mathematica.
Multi-Channel Wireless Telecommunication Systems: An Algorithm for Optimal Channel and Power Allocation
Maia Averett, Lisa Feigenbaum, Juliana Freire, and Mikhail Lev.
Optimization of multi-channel wireless communication networks is a field of research, which strives to improve system capacity by appropriately allocating network resources. This overarching goal entails a balance between a number of individual goals, including: minimization of total power consumption, minimization of any individual's power consumption, and maintenance of a sufficient number of freely available channels. One current problem in the wireless telecom industry is the lack of an efficient algorithm for partitioning a set of links into subsets which can be grouped into various, shared communication resources. We have chosen to focus on two of the many aspects of this problem. The first is to find a quick way of determining whether or not a set of links can share a communication resource feasibility. The second is to create an efficient algorithm for exploring the possible link combinations and recording those of which are feasible. We use undergraduate linear algebra techniques to present and modify parts of an existing algorithm by Professor Marco Grivet, PUC-Rio.