Sergio A. Alvarez
Ph.D., University of Maryland at College Park

Research

Combination functions for integration of information sources

I have developed a methodology for the systematic generation of "combination functions" that allow the integration of two or more numerical measures (representing disparate information sources) into a single combined measure. There is a need for such combination functions in database integration, in management of uncertainty in knowledge-based systems, and in various experimental studies in biology and psychology. My approach uses a single canonical combination function to generate a multitude of combination functions by choosing appropriate "reference frames" in the space in which the measures take their values. Most recently, my work in this area has been presented at the 6th International Symposium on Artificial Intelligence and Mathematics, Ft. Lauderdale, FL, Jan. 2000, and at the Workshop on Soft Computing, Marianska u Jachymova, Czech Republic, Nov. 1999.

Performance trade-off in information retrieval and filtering

A trade-off between the measures known as recall and precision has been widely observed by researchers in information retrieval. The mechanisms underlying such a trade-off are less well understood. Recent work involving the application of machine learning techniques to information retrieval problems require the use of slightly different measures of performance, including the classification accuracy. I have obtained results that rigorously establish a trade-off between recall and precision in this context.

Computational modeling and analysis

I am interested in combining analytical and computational techniques to understand natural and engineering systems. My work in this direction includes optimization applied to orbital dynamics, computational metrics for neurobiological data, and analysis of mathematical models of phase transitions. My papers in this area have been accepted for publication in the following refereed journals: Journal of Guidance, Control, and Dynamics, Bulletin of Mathematical Biology, and Differential and Integral Equations.

Publications

  1. Lin, W.-Y., Alvarez, S.A., Ruiz, C.,
    "Collaborative Recommendation via Adaptive Asociation Rule Mining", KDD-2000 Workshop on Web Mining for E-Commerce, Boston, MA, Aug. 2000

  2. Alvarez, S.A.,
    "Web Metasearch as Belief Aggregation", AAAI-2000 Workshop on AI for Web Search, Austin, TX, July 2000

  3. Alvarez, S. A.,
    "Belief Combination by means of Frame Transformations", 6th International Symposium on Artificial Intelligence and Mathematics, Ft. Lauderdale, FL, Jan. 2000

  4. Lin, W.-Y., Ruiz, C., Alvarez, S.A.,
    "A New Adaptive-Support Algorithm for Asociation Rule Mining", Technical Report WPI-CS-TR-00-13, Department of Computer Science, Worcester Polytechnic Institute, May 2000

  5. Streeter, M.J., Ward, M.O., Alvarez, S.A.,
    "N2VIS: An Interactive Visualization Tool for Neural Networks", Technical Report WPI-CS-TR-00-11, Department of Computer Science, Worcester Polytechnic Institute, March 2000

  6. Carter, T., Alvarez, S. A.,
    "Quadratic-based Computation of Optimal Four-Impulse Rendezvous Near a Circular Orbit", Journal of Guidance, Control, and Dynamics, vol. 23, no. 1, Jan.-Feb. 2000, 109-117
    abstract (HTML)

  7. Alvarez, S. A.,
    "A Geometric Theory of Knowledge Aggregation", Workshop on Soft Computing, Marianska u Jachymova, Czech Republic, Nov. 1999

  8. Alvarez, S. A., Levitan, S.L., Reggia, J.A.,
    "Metrics for Cortical Map Organization and Asymmetry", Bulletin of Mathematical Biology, vol. 60 (1998), 27-47;

  9. Carter, T., Alvarez, S. A.,
    "Four-Impulse Rendezvous near Circular Orbit", AIAA/AAS Astrodynamics Specialist Conference, Session 84-ASD-10, Rendezvous and Orbit Transfer, Boston, MA, Aug. 1998

  10. Alvarez, S.A.
    "Rational comparison of probabilities via a blow-up conjugacy", Research Report No. 97-NA-010, Center for Nonlinear Analysis, Carnegie Mellon U., Aug. 1997
    abstract (HTML)

  11. Alvarez, S.A., Liu, C.
    "Initial Data Dependence for Motion by Minus the Surface Laplacian of Curvature", Differential and Integral Equations, accepted; also see Research Report No. 97-NA-009, Center for Nonlinear Analysis, Carnegie Mellon U., Aug. 1997
    abstract (HTML)

  12. "Measuring Organization and Symmetry in Topographic Map Formation" Technical Report UMCP-CSD CS-TR-3668, Department of Computer Science, University of Maryland College Park, Sept. 1996
    abstract (HTML)

  13. Alvarez, S.A.
    Interface Motion Driven by Curvature and Diffusion: Analytic Dependence on the Initial Data for the Mullins-Sekerka Equation", Ph.D. Thesis, University of Maryland at College Park, 1996
    abstract (HTML)

  14. Alvarez, S. A.,
    "Homothetic Invariance of the Space L0(\mu)", J. of Math. Analysis and Appl., vol. 179, no. 1, 260-274, Oct. 1993
    abstract (DVI)

  15. Alvarez, S. A.,
    "Lp Arithmetic", Am. Math. Monthly, vol. 99, no. 7, 656-662, Aug.-Sept. 1992
    abstract (DVI)

  16. Alvarez, S. A., Maddocks, J.H.,
    "Dynamics and Optimal Control of Wheeled Mobile Robots"

  17. Alvarez, S. A.,
    "Lattices Generated by Collections of Lp Spaces"
    Rev. Col. Mat., vol. XXII, 1988

  18. Alvarez, S. A., Noreña, D., Ramos, E.,
    ``Automated Recognition of Handprinted Alphanumeric Characters'', Sistemas, No. 23, Apr.-Jun. 1985
    abstract (DVI)

Research according to Hollywood

"Do you have any idea how easy this stuff is for me ?!?"

Exasperated 20 year old janitor/genius Will Hunting trying to explain a mathematical proof to a struggling Fields Medalist in Good Will Hunting, Miramax Films, 1997