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)