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Stanislaw M. Ulam's contributions to theoretical theory

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S. M. Ulam's contributions to biology are surveyed. The survey covers cellular automata theory, population biology, Fermi-Pasta-Ulam results, pattern recognition, and sequence similarity.

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References

  1. VonNeumannJ., Theory of Self-Reproducing Automata, Univ. of Illinois Press, Urbana, 1966.

    Google Scholar 

  2. UlamS. M., ‘Random Processes and Transformations’, Proc. International Congress of Mathematicians, Cambridge, MA, 1950, Vol. 2, pp. 264–275, 1952.

    Google Scholar 

  3. UlamS. M., ‘On Some Mathematical Problems Connected with Patterns of Growth of Figures’, Proc. Symp. Appl. Math. 14, 215–224 (1962); also in A. W. Burks (ed.), Cellular Automata, Univ. of Illinois Press, Urbana, 1970, pp. 219–231.

    Google Scholar 

  4. Schrandt, R. G. and Ulam, S. M., ‘On Recursively Defined Geometrical Objects and Patterns of Growth’, Los Alamos Scientific Laboratory, LA-3762, 19 pp., 1967, also in A. W. Burks (ed.), Cellular Automata, Univ. of Illinois Press, Urbana, 1970, pp. 232–243.

  5. ButlerJ. T. and NtafosS. C., ‘The Vector String Descriptor as a Tool in the Analysis of Cellular Automata Systems’, Math. Biosci. 35, 55–84 (1977).

    Google Scholar 

  6. Moore, E. F., ‘Machine Models of Self Reproduction’, Proc. Symp. Appl. Math. 14 (1962).

  7. FarmerD., ToffoliT., and WolframS. (eds.), Cellular Automata, Proceedings of an Interdisciplinary Workshop, Los Alamos, New Mexico, U.S.A., North-Holland, Amsterdam, 1983.

    Google Scholar 

  8. Hawkins, D. and Ulam, S. M., ‘Theory of Multiplicative Processes’, Los Alamos Scientific Laboratory, LA-171, 1944, declass. 1946; Everett, C. J. and Ulam, S. M., ‘Multiplicative Systems. Part I.’, Proc. Nat. Acad. Sci. 34, 403–405 (1948); Everett, C. J. and Ulam, S. M., ‘Multiplicative Systems in Several Variables’, Los Alamos Scientific Laboratory, Part I, LA-683, 1948, Part II, LA-690, 1948, Part III, LA-707, 1948.

  9. HarrisT. E., The Theory of Branching Processes, Springer-Verlag, Berlin, 1963.

    Google Scholar 

  10. Ulam, S. M., ‘How to Formulate Mathematically Problems of the Rate of Evolution’, in Mathematical Challenges to the Neo-Darwinian Interpretation of Evolution, A Wistar Institute Monograph No. 5, 21–33 (1967).

  11. Schradt, R. and Ulam, S. M., ‘Some Elementary Attempts at Numerical Modeling of Problems Concerning Rates of Evolutionary Processes’, Los Alamos Scientific Laboratory, LA-4573-MS, 1971.

  12. BeyerW., SmithT. F., SteinM. L., and UlamS. M., ‘A Molecular Sequence Metric and Evolutionary Trees’, Math. Biosci. 19, 9–25 (1974).

    Google Scholar 

  13. Beyer, W. A., Smith, T. F., Stein, M. L., and Ulam, S. M., ‘Metrics in Biology, An Introduction’, Los Alamos Scientific Laboratory, LA-4973, 1972.

  14. UlamS. M., ‘On the Operations of Pair Production, Transmutations and Generalized Random Walks’, Adv. Appl. Math. 1, 7–21 (1980).

    Google Scholar 

  15. MycielskiJ. and UlamS. M., ‘On the Pairing Process and the Notion of Genealogical Distance’, J. Comb. Theory 6, 227–234 (1969).

    Google Scholar 

  16. KahaneJ. and MarrR., ‘On a Class of Stochastic Pairing Processes and the Mycielski-Ulam Notions of Genealogical Distance’, J. Comb. Theory A 13, 383–400 (1973).

    Google Scholar 

  17. Menzel, M., Stein, P. R., and Ulam, S. M., ‘Quadratic Transformations, Part I’, Los Alamos Scientific Laboratory, LA-2503, 158 pp. (1959).

  18. Stein, P. R. and Ulam, S. M., ‘Non-Linear Transformation Studies on Electronic Computers’, Los Alamos Scientific Laboratory, LA-DC 5688, 128 pp., 1963, also in Rozprawy Mathematyczne (Warsaw) 39, 1–66, (1964) and in A. W. Burks (ed.), Cellular Automata, Univ. of Illinois Press, Urbana, 1970, pp. 244–263.

  19. Fermi, E., Pasta, J., and Ulam, S. M., ‘Studies of Non-Linear Problems’, Los Alamos Scientific Laboratory, LA-1940, 20 pp., 1955, also in Enrico Fermi Collected Papers, Univ. of Chicago Press, Illinois, 1965, pp. 978–988.

  20. LambG. L.Jr., Elements of Soliton Theory, Wiley, New York, 1980.

    Google Scholar 

  21. Scott, A. C., ‘Solitons in Biological Molecules’, to appear.

  22. Pohl, H. A., ‘Do Cells in a Reproductial State Exhibit a Fermi-Pasta-Ulam-Frohlich Resonance and Limit Electromagnetic Radiation’, J. Biol. Phys. 8, 45–75.

  23. Ulam, S. M., ‘Speculations About the Mechanisms of Recognition and Discrimination’, Los Alamos National Laboratory, Preprint, LA-UR 82-62, 1981.

  24. Ulam, S. M., ‘Reflexions on the Brain's Attempts to Understand Itself’, Gamow Memorial Lecture, Univ. of Colorado, 3 October 1982, Preprint.

  25. UlamS. M., ‘Some Ideas and Prospects in Biomathematics’, Ann. Rev. Biophys. Bioeng. 1, 277–292 (1972).

    Google Scholar 

  26. UlamS. M., ‘Some Combinatorial Problems Studied Experimentally on Computing Machines’, in S. K.Zaremba (ed.), Applications of Number Theory to Numerical Analysis, Academic Press, New York, 1972, pp. 1–10.

    Google Scholar 

  27. NeedlemanS. B. and WunschC. D., ‘A General Method Applicable to the Search for Similarities in the Amino Acid Sequences of Two Proteins’, J. Mol. Biol. 48, 443–453 (1970).

    Google Scholar 

  28. SellersP. H., ‘An Algorithm for the Distance Between Two Finite Sequences’, J. Comb. Theory. 16, 253–258 (1974).

    Google Scholar 

  29. WatermanM. S., ‘General Methods of Sequence Comparison’, Bull. Math. Biology 46, 473–500 (1984).

    Google Scholar 

  30. SellersP. H., ‘The Theory and Computation of Evolutionary Distances: Pattern Recognition’, J. Algor. 1, 359–373 (1980).

    Google Scholar 

  31. ChvatalV. and SankoffD., ‘Longest Common Subsequence of Two Random Sequences’, J. App. Prob. 12, 306–315 (1975).

    Google Scholar 

  32. DekenJ., ‘Some Limit Results for Longest Common Subsequences’, Discrete Math. 26, 17–31 (1979).

    Google Scholar 

  33. SteeleM. J., ‘Long Common Subsequences and the Proximity of Two Random Strings’, SIAM J. Appl. Math. 42, 731–737 (1982).

    Google Scholar 

  34. ErdosP. and RenyiA., ‘On a New Law of Large Numbers’, J. Anal. Math. 22, 103–111 (1970). Reprinted in Selected Papers of Alfred Renyi, Vol. 3, Akademiai Kiado, Budapest, 1976; pp. 1962–1970.

    Google Scholar 

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Authors and Affiliations

  1. Los Alamos National Laboratory, 87545, Los Alamos, NM, USA

    William A. Beyer

  2. Rockefeller University, New York, New York, USA

    Peter H. Sellers

  3. Department of Mathematics, University of Southern California, 90089-1113, Los Angeles, CA, USA

    Michael S. Waterman

  4. Department of Biological Sciences, University of Southern California, 90089-1113, Los Angeles, CA, USA

    Michael S. Waterman

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  1. William A. Beyer
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  2. Peter H. Sellers
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  3. Michael S. Waterman
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Beyer, W.A., Sellers, P.H. & Waterman, M.S. Stanislaw M. Ulam's contributions to theoretical theory. Lett Math Phys 10, 231–242 (1985). https://doi.org/10.1007/BF00398163

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