College of Liberal Arts and Sciences
Department of Mathematics
Search Close Search
Give
Toggle Menu
Back to Directory

Stephen Willson

  • University Professor Emeritus

Contact

swillson@iastate.edu

Bio

Stephen Willson

University Professor and Professor of Mathematics Emeritus

Research Interests

Computational biology, especially building phylogenetic trees and networks. Supertrees. Game theory and fair division problems. Cellular automata. Fractals and chaotic dynamics.

Education

A.B., Mathematics, Harvard, 1968

M.A., Mathematics, University of Michigan (Ann Arbor), 1970

Ph.D., Mathematics, University of Michigan (Ann Arbor), 1973

Selected Publications

  • Equivariant maps between representation spheres. Pacific J. Math 56 (1975): 291-296.
  • The converse to the Smith theorem for Zp-homology spheres. Pacific J. Math 56 (1975): 597-605.
  • On the ergodic theory of cellular automata. Math. Systems Theory 9 (1975): 132-141.
  • Equivariant homology theories on G-complexes. Trans. Amer. Math. Soc. 212 (1975): 155-171.
  • Homological dimensions of the isotropy ring. Duke Math. J. 43 (1976): 159-170.
  • The orbit space of a sphere by an action of Zps. Proc. Amer. Math. Soc. 59 (1976): 361-365.
  • The growth of configurations. Math. Systems Theory 10 (1977): 387-400.
  • Limiting shapes for configurations, J. Comput. System Sci. 15 (1977): 243-261.
  • On convergence of configurations. Discrete Math. 23 (1978): 279-300.
  • A semigroup on the space of compact convex bodies. SIAM J. Math. Anal. 11 (1980): 448-457.
  • Growth patterns of ordered cellular automata. J. Comput. System Sci. 22 (1981): 29-41.
  • Cellular automata can generate fractals. Discrete Applied Mathematics 8 (1984): 91-99.
  • Growth rates and fractional dimensions. Physica 10D (1984): 69-74.
  • On coherent growth of configurations. SIAM J. Math. Anal. 16 (1985): 316-330.
  • A use of cellular automata to obtain families of fractals, in M.F. Barnsley and S.G. Demko, eds., "Chaotic Dynamics and Fractals," Academic Press, Orlando, 1986, 123-140.
  • The equality of fractional dimensions for certain cellular automata. Physica 24D (1987): 179-189.
  • Computing fractal dimensions for additive cellular automata. Physica 24D (1987): 190-206.
  • Convergence of iterated median rules. Computer Vision, Graphics, and Image Processing 47 (1989): 105-110.
  • Decision procedures for openness and local injectivity. Complex Systems 5 (1991): 497-508
  • Calculating growth rates and moments for additive cellular automata. Discrete Applied Mathematics 35 (1992): 47-65.
  • Iterating maps on cellular complexes. Trans. A.M.S. 332 (1992): 225-240.
  • A value for partially defined cooperative games. International Journal of Game Theory 21 (1993): 371-384.
  • Long-term behavior in the theory of moves. Theory and Decision 45 (1998): 201-240.
  • Measuring inconsistency in phylogenetic trees. Journal of Theoretical Biology 190 (1998) 15-36.
  • Suranjan Panigrahi, Manjit K. Misra, and Stephen Willson. Evaluations of fractal geometry and invariant moments for shape classification of corn germplasm. Computers and electronics in agriculture 20 (1998) 1-20.
  • Building phylogenetic trees from quartets by using local inconsistency measures. Molecular Biology and Evolution 16 (1999): 685-693.
  • A higher-order parsimony method to reduce long-branch attraction. Molecular Biology and Evolution 16 (1999): 694-705.
  • Axioms for the outcomes of negotiation in matrix games. Mathematical Social Sciences 39 (2000): 323-348.
  • An error correcting map for quartets can improve the signals for phylogenetic trees. Molecular Biology and Evolution 18 (2001): 344-351.
  • Money-egalitarian-equivalent and gain-maximin allocations of indivisible items with monetary compensation. Social Choice and Welfare 20 (2003): 247-259.
  • Constructing rooted supertrees using distances. Bulletin of Mathematical Biology 66 no 6 (2004): 1755-1783.
  • Dan Ashlock, Stephen Willson, and Nicole Leahy. Coevolution and Tartarus. Proceedings of CEC 2004 (Congress on Evolutionary Computation).
  • Dan Ashlock, Kenneth Bryden, Steven Corns, and Stephen Willson. An improved taxonomy of evolutionary computation problems. Conference proceedings for ANNIE 2004 (Artificial Neural Networks in Engineering).
  • Minimum evolution using ordinary least squares is less robust than neighbor-joining. Bulletin of Mathematical Biology 67 (2005): 261-279.
  • Kenneth M. Bryden, Daniel A. Ashlock, Steven Corns, and Stephen J. Willson. Graph Based Evolutionary Algorithms. IEEE Transactions on Evolutionary Computation 10 (2006): 550-567.
  • Consistent formulas for estimating the total lengths of trees. Discrete Applied Mathematics 148 (2005): 214-239.
  • Unique solvability of certain hybrid networks from their distances. Annals of Combinatorics 10 (2006): 165-178.
  • Unique reconstruction of tree-like phylogenetic networks from distances between leaves. Bulletin of Mathematical Biology 68 (2006): 919-944.
  • Unique determination of some homoplasies at hybridization events. Bulletin of Mathematical Biology 69 (2007): 1709-1725.
  • Reconstruction of some hybrid phylogenetic networks with homoplasies from distances. Bulletin of Mathematical Biology 69 (2007): 2561-2590.
  • Reconstruction of certain phylogenetic networks from the genomes at their leaves. Journal of Theoretical Biology 252 (2008): 338-349.
  • Robustness of topological supertree methods for reconciling dense incompatible data. IEEE/ACM Transactions on Computational Biology and Bioinformatics 6 (2009): 62-75.
  • Properties of normal phylogenetic networks. Bulletin of Mathematical Biology 72 (2010): 340-358.
  • Regular networks are determined by their trees. IEEE/ACM Transactions on Computational Biology and Bioinformatics 8 (2011): 785-796.
  • Restricted trees: simplifying networks with bottlenecks. Bulletin of Mathematical Biology 73 (2011): 2322-2338.
  • CSD Homomorphisms Between Phylogenetic Networks. IEEE/ACM Transactions on Computational Biology and Bioinformatics 9 (2012): 1128-1138.
  • Tree-average distances on certain phylogenetic networks have their weights uniquely determined. Algorithms for Molecular Biology (2012) 7:13.
  • Reconstruction of certain phylogenetic networks from their tree-average distances. Bulletin of Mathematical Biology (2013) 75(10): 1840-1878.
  • Comparing and simplifying distinct-cluster phylogenetic networks. Annals of Combinatorics (2016) 20(4), 917-938. https://doi.org/10.1007/s00026-016-0324-y
  • Merging Arcs to Produce Acyclic Phylogenetic Networks and Normal Networks. Bulletin of Mathematical Biology (2022) 84:26. https://doi.org/10.1007/s11538-021-00986-1
  • Distinct-Cluster Tree-Child Phylogenetic Networks and Possible Uses to Study Polyploidy. Bulletin of Mathematical Biology 84, 125 (2022). https://doi.org/10.1007/s11538-022-01084-6

Department