메뉴 건너뛰기




Volumn 107, Issue 2-4, 1997, Pages 240-254

Correlation length, isotropy and meta-stable states

Author keywords

Graph Laplacian; Isotropy; Meta stable states; Rugged landscapes; XY Hamiltonian

Indexed keywords


EID: 0001100941     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-2789(97)00091-2     Document Type: Article
Times cited : (30)

References (63)
  • 2
    • 0030596731 scopus 로고    scopus 로고
    • Approximate scaling properties of RNA free energy landscapes
    • S. Baskaran, P.F. Stadler and P. Schuster, Approximate scaling properties of RNA free energy landscapes, J. Theor. Biol. 181 (1996) 299-310.
    • (1996) J. Theor. Biol. , vol.181 , pp. 299-310
    • Baskaran, S.1    Stadler, P.F.2    Schuster, P.3
  • 3
    • 0000913755 scopus 로고
    • Spatial interactions and the statistical analysis of lattice systems
    • J. Besag, Spatial interactions and the statistical analysis of lattice systems, Am. Math. Monthly 81 (1974) 192-236.
    • (1974) Am. Math. Monthly , vol.81 , pp. 192-236
    • Besag, J.1
  • 5
    • 22244487312 scopus 로고
    • Potential Theory on Graphs
    • LSE-MPS-95, Centre for Discrete and Applicable Mathematics, London School of Economics
    • N.J. Biggs, Potential Theory on Graphs, CDAM Research report, LSE-MPS-95, Centre for Discrete and Applicable Mathematics, London School of Economics (1995).
    • (1995) CDAM Research Report
    • Biggs, N.J.1
  • 6
    • 36149042419 scopus 로고
    • Metastable states in spin glasses
    • A.J. Bray and M.A. Moore, Metastable states in spin glasses, J. Phys. C 13 (1980) L469-L476.
    • (1980) J. Phys. C , vol.13
    • Bray, A.J.1    Moore, M.A.2
  • 7
    • 0001569748 scopus 로고
    • Metastable states in spin glasses with short-ranged interactions
    • A.J. Bray and M.A. Moore, Metastable states in spin glasses with short-ranged interactions, J. Phys. C 14 (1981) 1313-1327.
    • (1981) J. Phys. C , vol.14 , pp. 1313-1327
    • Bray, A.J.1    Moore, M.A.2
  • 11
    • 0019061437 scopus 로고
    • White and weighted averages over solutions of Thouless Anderson Palmer equations for the Sherrington-Kirkpatrick spin glass
    • C. De Dominicis, M. Gabay, T. Garel and H. Orland, White and weighted averages over solutions of Thouless Anderson Palmer equations for the Sherrington-Kirkpatrick spin glass, J. Phys. 41 (1980) 923-930.
    • (1980) J. Phys. , vol.41 , pp. 923-930
    • De Dominicis, C.1    Gabay, M.2    Garel, T.3    Orland, H.4
  • 12
    • 0001128801 scopus 로고
    • Multiplicites des valeurs prores Laplaciens discrets et laplaciens continus
    • Y.C. De Verdiere, Multiplicites des valeurs prores Laplaciens discrets et laplaciens continus, Rend. Mat. Appl. 13 (1993) 433-460.
    • (1993) Rend. Mat. Appl. , vol.13 , pp. 433-460
    • De Verdiere, Y.C.1
  • 13
    • 35949021286 scopus 로고
    • Random energy model: Limit of a family of disordered models
    • B. Derrida, Random energy model: Limit of a family of disordered models, Phys. Rev. Lett. 45 (1980) 79-82.
    • (1980) Phys. Rev. Lett. , vol.45 , pp. 79-82
    • Derrida, B.1
  • 14
    • 0040678779 scopus 로고
    • The random energy model
    • B. Derrida, The random energy model, Phys. Rep. 67 (1980) 29-35.
    • (1980) Phys. Rep. , vol.67 , pp. 29-35
    • Derrida, B.1
  • 15
    • 4243861085 scopus 로고
    • Random-energy model: An exactly solvable model of disordered systems
    • B. Derrida, Random-energy model: An exactly solvable model of disordered systems, Phys. Rev. B 24 (5) (1981) 2613-2626.
    • (1981) Phys. Rev. B , vol.24 , Issue.5 , pp. 2613-2626
    • Derrida, B.1
  • 16
    • 0022738867 scopus 로고
    • Metastable states of a spin glass chain at 0 temperature
    • B. Derrida and E. Gardner, Metastable states of a spin glass chain at 0 temperature, J. Phys. 47 (1986) 959-965.
    • (1986) J. Phys. , vol.47 , pp. 959-965
    • Derrida, B.1    Gardner, E.2
  • 17
    • 0000569632 scopus 로고
    • Evolution on sequence space and tensor products of representation spaces
    • A.W.M. Dress and D.S. Rumschitzki, Evolution on sequence space and tensor products of representation spaces, Acta Appl. Math. 11 (1988) 103-111.
    • (1988) Acta Appl. Math. , vol.11 , pp. 103-111
    • Dress, A.W.M.1    Rumschitzki, D.S.2
  • 19
    • 0017667182 scopus 로고
    • The Hypercycle A: A principle of natural self-organization: Emergence of the hypercycle
    • M. Eigen and P. Schuster, The Hypercycle A: A principle of natural self-organization: Emergence of the hypercycle, Naturwissenschaften 64 (1977) 541-565.
    • (1977) Naturwissenschaften , vol.64 , pp. 541-565
    • Eigen, M.1    Schuster, P.2
  • 20
    • 0000647969 scopus 로고
    • Statistics of landscapes based on free energies, Replication and degredation rate constants of RNA secondary structures
    • W. Fontana, T. Griesmacher, W. Schnabl, P.F. Stadler and P. Schuster, Statistics of landscapes based on free energies, Replication and degredation rate constants of RNA secondary structures, Monatsh. Chemie 122 (1991) 795-819.
    • (1991) Monatsh. Chemie , vol.122 , pp. 795-819
    • Fontana, W.1    Griesmacher, T.2    Schnabl, W.3    Stadler, P.F.4    Schuster, P.5
  • 21
    • 0000654132 scopus 로고
    • Physical aspects of evolutionary optimization and adaption
    • W. Fontana, W. Schnabl and P. Schuster, Physical aspects of evolutionary optimization and adaption, Phys. Rev. A 40 (1989) 3301-3321.
    • (1989) Phys. Rev. A , vol.40 , pp. 3301-3321
    • Fontana, W.1    Schnabl, W.2    Schuster, P.3
  • 22
    • 0023648965 scopus 로고
    • A computer model of evolutionary optimization
    • W. Fontana and P. Schuster, A computer model of evolutionary optimization, Biophys. Chem. 26 (1987) 123-147.
    • (1987) Biophys. Chem. , vol.26 , pp. 123-147
    • Fontana, W.1    Schuster, P.2
  • 24
    • 36149036022 scopus 로고
    • Application of statistical mechanics to NP-complete problems in combinatorial optimization
    • Y. Fu and P.W. Anderson, Application of statistical mechanics to NP-complete problems in combinatorial optimization, J. Phys. A 19 (1986) 1605-1620.
    • (1986) J. Phys. A , vol.19 , pp. 1605-1620
    • Fu, Y.1    Anderson, P.W.2
  • 25
    • 0004029110 scopus 로고
    • Pergamon Press, Oxford
    • L. Fuchs, Abelian Groups (Pergamon Press, Oxford, 1960).
    • (1960) Abelian Groups
    • Fuchs, L.1
  • 27
    • 13844303260 scopus 로고
    • Local search and the local structure of NP-complete problems
    • L.K. Grover, Local search and the local structure of NP-complete problems, Oper. Res. Lett. 12 (1992) 235-243.
    • (1992) Oper. Res. Lett. , vol.12 , pp. 235-243
    • Grover, L.K.1
  • 28
    • 0040085238 scopus 로고    scopus 로고
    • Canonical approximation of fitness landscapes
    • R. Happel and P.F. Stadler, Canonical approximation of fitness landscapes, Complexity 2 (1996) 53-58.
    • (1996) Complexity , vol.2 , pp. 53-58
    • Happel, R.1    Stadler, P.F.2
  • 30
    • 0023647382 scopus 로고
    • Towards a general theory of adaptive walks on rugged landscapes
    • S.A. Kauffman and S. Levin, Towards a general theory of adaptive walks on rugged landscapes, J. Theor. Biol. 128 (1987) 11.
    • (1987) J. Theor. Biol. , vol.128 , pp. 11
    • Kauffman, S.A.1    Levin, S.2
  • 32
    • 0030552855 scopus 로고    scopus 로고
    • Local minima in the graph bipartitioning problem
    • B. Krakhofer and P.F. Stadler, Local minima in the graph bipartitioning problem, Europhys. Lett. 34 (1996) 85-90.
    • (1996) Europhys. Lett. , vol.34 , pp. 85-90
    • Krakhofer, B.1    Stadler, P.F.2
  • 33
    • 0001440813 scopus 로고
    • On the depth of combinatorial optimization problems
    • W. Kern, On the depth of combinatorial optimization problems, Discr. Appl. Math. 43 (1993) 115-129.
    • (1993) Discr. Appl. Math. , vol.43 , pp. 115-129
    • Kern, W.1
  • 34
    • 0007515578 scopus 로고
    • Spectra of graphs with transitive groups
    • L. Lovász, Spectra of graphs with transitive groups, Periodica Math. Hung. 6 (1975) 191-195.
    • (1975) Periodica Math. Hung. , vol.6 , pp. 191-195
    • Lovász, L.1
  • 36
    • 0012319913 scopus 로고
    • Evolution on fitness landscapes
    • 1993 Lectures in Complex Systems, eds. L. Nadel and D.L. Stein, Addison-Wesley, Reading, MA
    • C.A. Macken and P.F. Stadler, Evolution on fitness landscapes, in: 1993 Lectures in Complex Systems, eds. L. Nadel and D.L. Stein, SFI Studies in the Sciences of Complexity, Vol. VI (Addison-Wesley, Reading, MA, 1995) pp. 43-86.
    • (1995) SFI Studies in the Sciences of Complexity , vol.6 , pp. 43-86
    • Macken, C.A.1    Stadler, P.F.2
  • 37
    • 0002278290 scopus 로고
    • The genetic algorithm and the structure of the fitness landscape
    • eds. R.K. Belew and L.B. Booker Morgan Kaufmann, Los Altos, CA
    • B. Manderick, M. de Weger and P. Spiessen, The genetic algorithm and the structure of the fitness landscape, in: Proc. 4th Int. Conf. Genetic Algorithms, eds. R.K. Belew and L.B. Booker (Morgan Kaufmann, Los Altos, CA, 1991).
    • (1991) Proc. 4th Int. Conf. Genetic Algorithms
    • Manderick, B.1    De Weger, M.2    Spiessen, P.3
  • 38
    • 0001216057 scopus 로고
    • The laplacian spectrum of graphs
    • eds. Y. Alavi, G. Chartrand, O.R. Ollermann and A.J. Schwenk Wiley, New York
    • B. Mohar, The laplacian spectrum of graphs, in: Graph Theory, Combinatorics, and Applications, eds. Y. Alavi, G. Chartrand, O.R. Ollermann and A.J. Schwenk (Wiley, New York, 1991) pp. 871-897.
    • (1991) Graph Theory, Combinatorics, and Applications , pp. 871-897
    • Mohar, B.1
  • 39
    • 0001478211 scopus 로고
    • Eigenvalues in combinatorial optimization
    • Combinatorial and Graph-Theoretical Problems in Linear Algebra, eds. R.A. Brualdi, S. Friedland and V. Klee, Springer, Berlin
    • B. Mohar and S. Poljak, Eigenvalues in combinatorial optimization, in: Combinatorial and Graph-Theoretical Problems in Linear Algebra, eds. R.A. Brualdi, S. Friedland and V. Klee, IMA Volumes in Mathematics and Its Applications, Vol. 50 (Springer, Berlin, 1993) pp. 107-151.
    • (1993) IMA Volumes in Mathematics and Its Applications , vol.50 , pp. 107-151
    • Mohar, B.1    Poljak, S.2
  • 41
    • 0023123456 scopus 로고
    • Spectral properties of Eigen's evolution matrices
    • D.S. Rumschitzky, Spectral properties of Eigen's evolution matrices, J. Math. Biol. 24 (1987) 667-680.
    • (1987) J. Math. Biol. , vol.24 , pp. 667-680
    • Rumschitzky, D.S.1
  • 42
    • 0000855721 scopus 로고
    • The depth and width of local minima in discrete solution spaces
    • J. Ryan, The depth and width of local minima in discrete solution spaces, Discr. Appl. Math. 56 (1995) 75-82.
    • (1995) Discr. Appl. Math. , vol.56 , pp. 75-82
    • Ryan, J.1
  • 43
    • 0000036067 scopus 로고
    • Vertex transitive graphs
    • G. Sabidussi, Vertex transitive graphs, Mh. Math. 68 (1994) 426-438.
    • (1994) Mh. Math. , vol.68 , pp. 426-438
    • Sabidussi, G.1
  • 44
    • 0028502408 scopus 로고
    • Landscapes: Complex optimization problems and biopolymer structures
    • P. Schuster and P.F. Stadler, Landscapes: Complex optimization problems and biopolymer structures, Computers Chem. 18 (1994) 295-314.
    • (1994) Computers Chem. , vol.18 , pp. 295-314
    • Schuster, P.1    Stadler, P.F.2
  • 46
    • 4444384303 scopus 로고
    • Solvable model of a spin-glass
    • D. Sherrington and S. Kirkpatrick, Solvable model of a spin-glass, Phys. Rev. Lett. 35 (26) (1975) 1792-1795.
    • (1975) Phys. Rev. Lett. , vol.35 , Issue.26 , pp. 1792-1795
    • Sherrington, D.1    Kirkpatrick, S.2
  • 47
    • 0003690783 scopus 로고
    • Combinatorial optimization, simulated annealing, and fractals
    • No. 61253
    • G.B. Sorkin, Combinatorial optimization, simulated annealing, and fractals, IBM Research Report, RC13674 (No. 61253) (1988).
    • (1988) IBM Research Report , vol.RC13674
    • Sorkin, G.B.1
  • 49
    • 0001408990 scopus 로고
    • Correlation structure of the landscape of the graph-bipartitioning-problem
    • P.F. Stadler and R. Happel, Correlation structure of the landscape of the graph-bipartitioning-problem, J. Phys. A. 25 (1992) 3103-3110.
    • (1992) J. Phys. A , vol.25 , pp. 3103-3110
    • Stadler, P.F.1    Happel, R.2
  • 50
    • 0000856790 scopus 로고
    • The landscape of the traveling salesman problem
    • P.F. Stadler and W. Schnabl, The landscape of the traveling salesman problem, Phys. Lett. A 161 (1992) 337-344.
    • (1992) Phys. Lett. A , vol.161 , pp. 337-344
    • Stadler, P.F.1    Schnabl, W.2
  • 51
    • 84956266773 scopus 로고
    • Correlation in landscapes of combinatorial optimization problems
    • P.F. Stadler, Correlation in landscapes of combinatorial optimization problems, Europhys. Lett. 20 (1992) 479-482.
    • (1992) Europhys. Lett. , vol.20 , pp. 479-482
    • Stadler, P.F.1
  • 52
    • 0038900707 scopus 로고
    • Linear operators on correlated landscapes
    • P.F. Stadler, Linear operators on correlated landscapes, J. Phys. I France 4 (1994) 681-696.
    • (1994) J. Phys. I France , vol.4 , pp. 681-696
    • Stadler, P.F.1
  • 53
    • 0001420553 scopus 로고
    • Random walks and orthogonal functions associated with highly symmetric graphs
    • P.F. Stadler, Random walks and orthogonal functions associated with highly symmetric graphs, Disc. Math. 145 (1995) 229-238.
    • (1995) Disc. Math. , vol.145 , pp. 229-238
    • Stadler, P.F.1
  • 54
    • 0002196313 scopus 로고
    • Towards a theory of landscapes
    • eds. R. Lopéz-Peña, R. Capovilla, R. García-Pelayo, H. Waelbroeck and F. Zertuche Springer, Berlin
    • P.F. Stadler, Towards a theory of landscapes, in: Complex Systems and Binary Networks, eds. R. Lopéz-Peña, R. Capovilla, R. García-Pelayo, H. Waelbroeck and F. Zertuche (Springer, Berlin, 1995) pp. 77-163.
    • (1995) Complex Systems and Binary Networks , pp. 77-163
    • Stadler, P.F.1
  • 55
    • 0030371056 scopus 로고    scopus 로고
    • Landscapes and their correlation functions
    • P.F. Stadler, Landscapes and their correlation functions, J. Math. Chem. 20 (1996) 1-45.
    • (1996) J. Math. Chem. , vol.20 , pp. 1-45
    • Stadler, P.F.1
  • 56
    • 0012230357 scopus 로고    scopus 로고
    • Random field models for fitness landscapes
    • SFI preprint 95-07-069, in press
    • P.F. Stadler and R. Happel, Random field models for fitness landscapes, J. Math. Biol. (1997), SFI preprint 95-07-069, in press.
    • (1997) J. Math. Biol.
    • Stadler, P.F.1    Happel, R.2
  • 57
    • 0030536319 scopus 로고    scopus 로고
    • Local minima of p-spin models
    • P.F. Stadler and B. Krakhofer, Local minima of p-spin models, Rev. Mex. Fis. 42 (1996) 355-363.
    • (1996) Rev. Mex. Fis. , vol.42 , pp. 355-363
    • Stadler, P.F.1    Krakhofer, B.2
  • 58
    • 36149046562 scopus 로고
    • Analytic theory of ground state properties of a spin glass: I. Ising spin glass
    • F. Tanaka and S.F. Edwards, Analytic theory of ground state properties of a spin glass: I. Ising spin glass, J. Phys. F 10 (1980) 2769-2778.
    • (1980) J. Phys. F , vol.10 , pp. 2769-2778
    • Tanaka, F.1    Edwards, S.F.2
  • 59
    • 0542429631 scopus 로고
    • Analytic theory of ground state properties of a spin glass: II. XY spin glass
    • F. Tanaka and S.F. Edwards, Analytic theory of ground state properties of a spin glass: II. XY spin glass, J. Phys. F 10 (1980) 2779-2792.
    • (1980) J. Phys. F , vol.10 , pp. 2779-2792
    • Tanaka, F.1    Edwards, S.F.2
  • 60
    • 0024991769 scopus 로고
    • Correlated and uncorrelated fitness landscapes and how to tell the difference
    • E.D. Weinberger, Correlated and uncorrelated fitness landscapes and how to tell the difference, Biol. Cybern. 63 (1990) 325-336.
    • (1990) Biol. Cybern. , vol.63 , pp. 325-336
    • Weinberger, E.D.1
  • 61
    • 0000839719 scopus 로고
    • Fourier and Taylor series on fitness landscapes
    • E.D. Weinberger, Fourier and Taylor series on fitness landscapes, Biol. Cybern. 65 (1991) 321-330.
    • (1991) Biol. Cybern. , vol.65 , pp. 321-330
    • Weinberger, E.D.1
  • 62
    • 0027921902 scopus 로고
    • Why some fitness landscapes are fractal
    • E.D. Weinberger and P.F. Stadler, Why some fitness landscapes are fractal, J. Theoret. Biol. 163 (1993) 255-275.
    • (1993) J. Theoret. Biol. , vol.163 , pp. 255-275
    • Weinberger, E.D.1    Stadler, P.F.2
  • 63
    • 0000907353 scopus 로고
    • The roles of mutation, inbreeding, crossbreeeding and selection in evolution
    • ed. D.F. Jones
    • S. Wright, The roles of mutation, inbreeding, crossbreeeding and selection in evolution, in: Proc. 6th Int. Cong. on Genetics, ed. D.F. Jones, Vol. 1 (1932) pp. 356-366.
    • (1932) Proc. 6th Int. Cong. on Genetics , vol.1 , pp. 356-366
    • Wright, S.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.