Equitable partitions, coherent algebras and random walks: Applications to the correlation structure of landscapes

Match

Volumn 40, Issue , 1999, Pages 215-261

  Stadler, P F ^a   Tinhofer, G ^b  

^a SANTA FE INSTITUTE   (United States)

^b NONE

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000697944     PISSN: 03406253     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (82)

1. Altenberg L.: Fitness distance correlation analysis: An instructive counterexample. Technical Report 97-05-037, Santa Fe Institute, Santa Fe, NM, 1997.
2. Babel L., Baumann S., Lüdecke M., Tinhofer G.: STABCOL: Graph isomorphism testing using the WL-algorithm. Technical University of Munich, 1997.
3. Babel L., Chuvaeva D.V., Klin K., Pasechnik D.V.: Algebraic combinatorics in mathematical chemistry. Methods and algorithms. II. Program implementation of the Weisfeiler-Leman algorithm. Technical Report, Technische Universität München, TUM-M9701 (1997).
4. Bannai E., Ito T.: Algebraic Combinatorics I. Association Schemes. Benjamin/Cummings, Menlo Park, 1984.
5. Bastert O.: New ideas for canonically computing graph algebras. Preprint. Technische Universität München, TUM-M9803, June 1998.
6. Biggs N.: Algebraic Graph Theory. Cambridge University Press, Cambridge UK, 2nd edition, 1994.
7. Binder K, Young A.P.: Spin glasses. Experimental facts, theoretical concepts, and open questions. Rev. Mod. Phys., 58, 1986, 801-976.
8. Bollobás B.: Graph Theory - An Introductory Course. Springer, New York, 1979.
9. Brouwer A.E., Cohen A.M., Neumaier A.: Distance-Regular Graphs. Springer, Berlin, 1989.
10. Chan A., Godsil Ch.D.: Symmetry and eigenvectors. In G. Hahn and G. Sabidussi, editors, Graph Symmetry: Algebraic Methods and Applications, volume 497 of NATO ASI Series C, 75-106. Kluwer, Dordrecht, 1997.
11. Chung F.R.K.: Spectral Graph Theory, volume 92 of CBMS. American Mathematical Society, 1997.
12. Codenotti B., Margara L.: Local properties of some NP-complete problems. Technical Report TR 92-021, International Computer Science Institute, Berkeley, CA, 1992.
13. Cvetković D., Doob M., Sachs H.: Spectra of Graphs. Academic Press, New York, 1980.
14. Cvetković D., Rowlinson P., Simić S.: Eigenspaces of Graphs. Encyclopedia of Mathematics and Its Applications, Cambridge University Press, 1997.
15. Dill K.A., Bromberg S., Yue K., Fiebig K.M., Yeo D.P., Thomas P.D., Chan H.S.: Principles of protein folding: a perspective from simple exact models. Prot. Sci. 4, 1995, 561-602.
16. Dress A.W.M., Rumschitzki D.S.: Evolution on sequence space and tensor products of representation spaces, Acta Appl.Math., 11, 1988, 103-111.
17. Eigen M. : Selforganization of matter and the evolution of biological macromolecules. Naturwissenschaften, 10, 1971, 465-523.
18. Eigen M., McCascill J., Schuster P.: The molecular quasi-species. Advances in Chemical Physics, 75, 1989, 149-263.
19. Faradžev I.A., Klin M.H.: Computer package for computations with coherent configurations. Proc. ISSAC-91, Bonn, ACM Press, 1991, 219-223.
20. Faradžev I.A., Klin M.H., Muzichuk M.E.: Cellular rings and groups of automorphisms of graphs. In: Faradžev I.A. et al. (eds.): Investigations in algebraic theory of combinatorial objects. Kluwer Acad. Publ., Dordrecht, 1994, 1-152.
21. Flamm C., Hofacker I.L., Stadler P.F.: RNA in silico: The computational biology of RNA secondary structures. Submitted to Adv. Complex Syst., 2, 1999, 65-90.
22. Fontana W., Schuster P.: A computer model of evolutionary optimization. Biophysical Chemistry, 26, 1987, 123-147.
23. Fontana W., Schnabl W., and Schuster P.: Physical aspects of evolutionary optimization and adaption. Physical Review A, 40, 1989, 3301-3321.
24. Fontana W., Stadler P.F., Bomberg-Bauer E.G., Griesmacher T., Hofacker I.L., Tacker M., Tarazona P., Weinberger E.D., and Schuster P.: RNA folding and combinatory landscapes. Phys. Rev. E, 47, 1993, 2083-2099.
25. García-Pelayo R., Stadler P.F.: Correlation length, isotropy, and meta-stable states. Physica D, 107, 1997, 240-254.
26. Garey M., Johnson D.: Computers and Intractability. A Guide to the Theory of NP Completeness. Freeman, San Francisco, 1979.
27. Gillespie J.H.: The Causes of Molecular Evolution. Oxford University Press, New York, Oxford, 1991.
28. Godsil C.D.: Algebraic Combinatorics. Chapman & Hall, 1993.
29. Goldberg D.E.: Genetic algorithms and Walsh functions. Part I: a gentle introduction. Complex Systems, 3, 1989, 129-152.
30. Grover L.: Local search and the local structure of NP-complete problems. Operations Res. Lett. 12, 1992, 235-243.
31. Hansch C., Leo A., Hoekman D.: Exploring QSAR. American Chemical Society, Washington, 1995.
32. Heidrich D., Kliesch W., Quapp W.: Properties of Chemically Interesting Potential Energy Surfaces, volume 56 of Lecture Notes in Chemistry. Springer-Verlag, Berlin, 1991.
33. Higman D.G.: Coherent configurations. Part I: Ordinary representation theory. Geom. Dedic. 4, 1975, 1-32.
34. Higman D.G.: Coherent configurations. Part II: Weights. Geom. Dedic. 5, 1976, 209-239.
35. Higman D.G.: Coherent algebras. Linear Algebra Appl. 93, 1987, 209-239.
36. Holland J.H.: Adaptation in Natural and Artificial Systems. MIT Press, Cambridge, MA, 1993.
37. Hordijk W., Stadler P.F.: Amplitude spectra of fitness landscapes. Adv. Complex Systems, 1, 1998, 39-66.
38. Huynen M.A., Stadler P.F., and Fontana W.: Smoothness within ruggedness: the role of neutrality in adaptation. Proc. Natl. Acad. Sci. (USA), 93, 1996, 397-401.
39. Jones T.: Evolutionary algorithms, fitness landscapes, and search. PhD thesis, Univ. of New Mexico, Albuquerque, NM, 1995.
40. Jones T.: One operator, one landscape. Technical Report #95-02-025, Santa Fe Institute, 1995.
41. Kauffman S.A. Levin S.: Towards a general theory of adaptive walks on rugged landscapes. J. Theor. Biol., 128, 1987, 11-45.
42. Kauffman S.A.: The Origin of Order. Oxford University Press, New York, Oxford, 1993.
43. M. Klin, C. Rücker, G. Rücker, G. Tinhofer, Algebraic combinatorics in mathematical chemistry. Methods and algorithms. I. Permutation Groups and coherent (cellular) algebras. This issue.
44. Koza J.R.: Genetic Programming: On the Programming of Computers by Means of Natural Selection. MIT Press, Cambridge, MA, 1992.
45. Kubinyi, H.: QSAR: Hansch analysis and related approaches, Vol. 1 of Methods and Principles in Medicinal Chemistry, Mannhold, R. et al., Eds., VCH, Weinheim.
46. Lafferty J., Rockmore D.: Numerical Investigation of the Spectrum for Certain Families of Cayley Graphs. In: J. Friedman, ed.: DIMACS Series in Disc. Math. and Theor. Comp. Sci. 10, 1993, 63-73.
47. Lovász L.: Random walks on graphs: A survey. Combinatorics, Paul Erdös is Eighty, Bolyai Society Mathematical Studies 2, Keszthely (Hungary), 1993, 353-398.
48. Maslen D., Rockmore D. Generalized FFTs - a survey of some recent results. In: L. Finkelstein and W. Kantor, editors: Groups and Computation II, DIMACS Series in Discrete Math. and Theor. Comp. Sci. 28, 1996, 183-238.
49. McKay B.D.: Practical graph isomorphism. Congressus Numerantium 30, 1981, 45-87.
50. McKay B.D.: Nauty user's guide (Version 1.5). Technical Report TR-CS-90-02. Dept. Comput. Sci., Australian National University, 1990.
51. Mézard M., Parisi G., and Virasoro M.A.: Spin Glass Theory and Beyond. World Scientific, Singapore, 1987.
52. Mezey P.G.: Potential Energy Hypersurfaces. Elsevier, Amsterdam, 1987.
53. Mohar B.: The Laplacian spectrum of graphs. In Y. Alavi, G. Chartrand, O. Ollermann, and A. Schwenk, editors, Graph Theory, Combinatorics, and Applications, pages 871-898, New York, 1991. John Wiley and Sons, Inc.
54. Mohar B.: Some applications of Laplace eigenvalues of graphs. In G. Hahn and G. Sabidussi, editors, Graph Symmetry: Algebraic Methods and Applications, volume 497 of NATO ASI Series C, pages 227-275. Kluwer, Dordrecht, 1997.
55. Muzychuk M., Klin M.: On graphs with three eigenvalues. Discrete Mathematics, 53, 1998, 123-133.
56. Palmer R. Optimization on rugged landscapes. In A. S. Perelson and S. A. Kauffman, editors, Molecular Evolution on Rugged Landscapes: Proteins, RNA, and the Immune System, pages 3-25. Addison Wesley, Redwood City, CA, 1991.
57. Papadimitrou C.H., Steiglitz K.: Combinatorial Optimization: Algorithms and Complexity. Prentice-Hall, Englewood Cliffs NJ, 1982.
58. Pardalos P., Rendl F., and Wolkowicz H.: The quadratic assignment problem: A survey and recent developments. In Proceedings of the DIMACS Workshop on Quadratic Assignment Problems, volume 16 of DIMACS Series in Discrete Math, and Theor. Comp. Sci., pages 1-41. American Mathematical Society, 1994.
59. Pearl J.: Heuristics: Intelligent search strategies for computer problem solving. Addison-Wesley, Reading MA, 1984.
60. Rogers D., Hopfinger A.J.: Application of genetic function approximation to quantitative structure activity relationships and quantitative structure property relationships. J. Chem. Inf. Comp. Sci., 34, 854-866, 1994.
61. Rockmore D.: Some applications of generalized FFTs. In: L. Finkelstein and W. Kantor, editors: Groups and Computation II,DIMACS Series in Discrete Math. and Theor. Comp. Sci. 28, 1995, 329-370.
62. Sachs, H.: Über Teiler, Faktoren und charakteristische Polynome von Graphen. Teil I. Wiss. Z., T.H. Ilmenau, 12, 1966, 7-12.
63. Sachs, H.: Über Teiler, Faktoren und charakteristische Polynome von Graphen. Teil II. Wiss. Z., T.H. Ilmenau, 13, 1967, 405-412.
64. Sherrington D., Kirkpatrick S.: Solvable model of a spin-glass. Physical Review Letters, 35(26), 1075, 1792-1795.
65. Schuster P., Stadler P.F.: Landscapes: Complex optimization problems and biopolymer structures. Computers & Chem., 18, 1995, 295-314.
66. Schwenk A.J.: Computing the characteristic polynomial of a graph. In: Bari R., Harary F. (ed.): Graphs and Combinatorics. Springer, Berlin, 1974, 153-172.
67. Sorkin G.B.: Combinatorial optimization, simulated annealing, and fractals. Technical Report RC13674 (No.61253), IBM Research Report, 1988.
68. Stadler P.F.: Fitness landscapes arising from the sequence-structure maps of biopolymers. J. Mol. Struct. (THEOCHEM) 463, 1999, 7-19.
69. Stadler P.F., Seitz R., Wagner G.P.: Evolvability of complex characters: Population dependent Fourier decomposition of fitness landscapes over recombination spaces. Bull. Math. Biol. in press 1999. Santa Fe Institute Preprint 99-01-001.
70. Stadler P.F., Schnabl W.: The landscape of the traveling salesman problem. Phys. Letters A 161, 1992, 337-344.
71. Stadler P.F.: Random walks and orthogonal functions associated with highly symmetric graphs. Discr. Math. 145, 1995, 229-237.
72. Stadler P.F.: Landscapes and their correlation functions. J. Math. Chem. 20, 1996, 1-45.
73. Stadler P.F., Happel R.: Random field models for fitness landscapes. J. Math. Biol., 38, 1999, 435-478.
74. Stadler P.F., Wagner G.P.: The algebraic theory of recombination spaces. Evol. Comp., 5, 1998, 241-275.
75. Tinhofer G., Klin M.: Algebraic Combinatorics in Mathematical Chemistry. Methods and Algorithms. III Graph Invariants and Stabilization Methods. Technical Report TUM-M9902, München, 1999, 1-64.
76. Vose M.D., Wright A.H.: The simple genetic algorithm and the Walsh transform. Part I: Theory. Evol. Comp., 6, 1998, 253-274.
77. Wagner G.P, Stadler P.F.: Complex adaptations and the structure of recombination spaces. In C. Nehaniv and M. Ito, editors, Algebraic Engineering, pages 151-170, Singapore, 1998. World Scientific. Proceedings of the Conference on Semi-Groups and Algebraic Engineering, University of Aizu, Japan.
78. Weinberger E. D.: Correlated and uncorrelated fitness landscapes and how to tell the difference. Biol. Cybernetics 63, 1990, 325-336.
79. Weinberger E.D.: Fourier and Taylor series on fitness landscapes. Biol. Cybernetics, 65, 1991, 321-330.
80. Weisfeiler B.Y., Leman A.A.: Reduction of a graph to a canonical form and an algebra arising during this reduction. Naucho - Technicksagy Informatsia 9, Seria 2, 1968, 12-16 (Russian).
81. Weisfeiler B. Y. (ed.): On construction and identification of graphs. Lecture Notes in Math. 558, Springer, Berlin, 1976.
82. Wright S.: The roles of mutation, inbreeding, crossbreeeding and selection in evolution. In D. F. Jones, editor, Int. Proceedings of the Sixth International Congress on Genetics, volume 1, 1932, 356-366.