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  Selected Publications

  Topics include: Optimization by Monte Carlo Methods, Computer Geometry,
Fractal Geometry, Mathematical Epidemiology, Neural Networks

    Optimization by Monte Carlo Methods
  • Limiting distribution and mixing time for genetic algorithms
    with S. Alwadani and F. Mendivil,   Nature Inspired Computing and Optimization: Theory and applications (2016)

  • Geometric Convergence of Genetic Algorithms under Tempered Random Restart
    with F. Mendivil and M.C. Spruill,   Applied Prob. Trust (2009)

  • Annealing a Genetic Algorithm for Constrainted Optimization
    with F. Mendivil,   J. Opt. Theory and App.(2009)

  • An Analysis of Random Restart and Iterated Improvement for Global Optimization with an Application to the Traveling Salesman Problem
    with F. Mendivil and M.C. Spruill,   J. Opt. Theory and App. (2005)

  • Restarting Search Algorithms with Applications to Simulated Annealing
    with F. Mendivil and M.C. Spruill,  Adv. in Applied Prob. (2001)

  • Estimating the convergence rate of a restarted search process
    with M.C. Spruill and Xiaohua Hu,   Int. J. Comput. Numer. Anal. Appl. (2002)

  • An Analysis of some Stochastic Optimization Methods   JCIS (1997)

  • Iterative Improvement plus Random Restart Stochastic Search
    with M.C. Spruill,   JCIS (1995)

  • Parallel Speedup of Monte Carlo Methods for Global Optimization
    with E. Van Vleck,   J. of Complexity (1994)

  • Parallel Genetic Algorithms   ICGA (1993)

    • Computer Geometry
  • Calculating the Hausdorff Distance Between Curves
    with C. Cabrelli, U. Molter and E. Belogay   Info. Proc. Letters (1997)

  • Computing the Hausdorff set distance in linear time for any L(p) point distance
      Info. Proc. Letters 30, 201-207 (1991)

  • An Image Algorithm for Computing the Hausdorff Distance Efficiently in Linear Time
      Info. Proc. Letters 30, 87-89 (1989)

    • Fractal Geometry
  • On the Hausdorff h-measure of Cantor sets
    with U. Molter, C. Cabrelli, and F. Mendivil,   Pacific J. Math. (2004)

  • Hausdorff measure of p-Cantor sets
    with Ursula Molter, Carlos Cabrelli, and Vygantas Paulauskas, Real Analysis Exchange (2002)

  • On the Inverse Fractal Problem for Two Dimensional Disjoint Polyhulled Attractors
    with A. Deliu and J. Geronimo,   Phil. Trans. of the Royal Soc. Lond. A, Physical Sciences and Engineering (1997)

  • Genetic Algorithms for the 1-D Inverse Fractal Problem
    with A. Deliu and F. Mendivil,   ICGA (1991)

  • Dimensions Associated with Recurrent Self-Similar Sets
    with A. Deliu, J. S. Geronimo, and D. Hardin   Math. Proc. Cambridge Philo. Soc. (1991)

    • Mathematical Epidemiology
  • Some Mathematical Models for Malaria
    with S. J. Aneke,   Int. J. Num. Math. (2008)

  • A Growth and Division Model for Retinoblastoma
    with M. Mistretta and V.J.Varma,   Math. Biosci. (2007)

  • A Gonorrhea Model Treating Sensitive and Resistant Strains in a Multigroup Population
    with Paul Pinsky,   Math. Biosciences (1990)

  • Common Source Epidemics II: Toxoplasmosis in Atlanta
    with M. Thompson   Bulletin of Math. Biol. (1982)

  • Common Source Epidemics I: A Stochastic Model
    with M. Thompson, Bulletin of Math. Biol. (1982)

    • Neural Networks
  • A Constructive Solution to the Two-Layer Perceptron Problem for Feed Forward Artificial Neural Networks
    with C. Cabrelli and U. Molter   IEEE Trans. on Neural Networks (2000)

  • Separating the Vertices of N-Cubes by Hyperplanes and its Application to Artificial Neural Networks
    Trans. on Neural Networks (1993)