Computational applications of nonextensive statistical mechanics

Journal of Computational and Applied Mathematics

Volumn 227, Issue 1, 2009, Pages 51-58

  Tsallis, Constantino ^a,b  

^a CENTRO BRASILEIRO DE PESQUISAS FÍSICAS   (Brazil)

^b SANTA FE INSTITUTE   (United States)

Author keywords

Entropy; Nonextensive statistical mechanics; Nonlinear dynamical systems; Numerical applications

Indexed keywords

APPLICATIONS; ENTROPY; NONLINEAR DYNAMICAL SYSTEMS; STATISTICAL MECHANICS;

BOLTZMANN; COMPUTATIONAL APPLICATIONS; NON-EXTENSIVE ENTROPIES; NONEXTENSIVE STATISTICAL MECHANICS; NUMERICAL APPLICATIONS;

DYNAMICAL SYSTEMS;

EID: 61849123634     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2008.07.030     Document Type: Article

References (217)

1. C. Tsallis, Entropy, in: Encyclopedia of Complexity and Systems Science, Springer, Berlin, 2008 (in press)
2. Tsallis C. Possible generalization of Boltzmann-Gibbs statistics. J. Stat. Phys. 52 (1988) 479
3. Penrose O. Foundations of Statistical Mechanics: A Deductive Treatment (1970), Pergamon, Oxford p. 167
4. Curado E.M.F., and Tsallis C. Generalized statistical mechanics: Connection with thermodynamics. J. Phys. A 24 (1991) L69
5. Curado E.M.F., and Tsallis C. Generalized statistical mechanics: Connection with thermodynamics. J. Phys. A 24 (1991) 3187 (corrigenda); 25 (1992) 1019
6. Tsallis C., Mendes R.S., and Plastino A.R. The role of constraints within generalized nonextensive statistics. Physica A 261 (1998) 534
7. C. Tsallis, Nonextensive statistical mechanics - An approach to complexity, in: Proceedings of the Conference on Chaos in Astronomy, Athens, 2007 (in press)
8. In: Gell-Mann M., and Tsallis C. (Eds). Nonextensive Entropy - Interdisciplinary Applications (2004), Oxford University Press, New York
9. In: Boon J.P., and Tsallis C. (Eds). Nonextensive statistical mechanics: New trends, new perspectives. Europhys. News 36 6 (2005)
10. Europhys. News 37 (2006) 25 (erratum)
11. C. Tsallis, Introduction to Nonextensive Statistical Mechanics - Approaching a Complex World, Springer, Berlin, 2008 (in press)
12. http://tsallis.cat.cbpf.br/biblio.htm. This is a long list which contains, at the date of 9 July 2008, 2485 articles (co)authored by 1897 scientists from 62 countries
13. q extensive. Proc. Natl. Acad. Sci. (USA) 102 (2005) 15377
14. F. Caruso, C. Tsallis, Extensive nonadditive entropy in quantum spin chains, in: S. Abe, H.J. Herrmann, P. Quarati, A. Rapisarda, C. Tsallis (Eds.), Complexity, Metastability and Nonextensivity, in: American Institute of Physics Conference Proceedings, vol. 965, New York, 2007, p. 51
15. F. Caruso, C. Tsallis, Nonadditive entropy reconciles the area law in quantum systems with classical thermodynamics, Phys. Rev. E 78 (2008) (in press)
16. Calabrese P., and Cardy J. Entanglement entropy and quantum field theory. J. Stat. Mech. Theory Exp. (2004) P06002
17. Ginsparg P., and Moore G. Lectures on 2D String Theory (1993), Cambridge Univ. Press, Cambridge
18. Tsallis C., Plastino A.R., and Zheng W.-M. Power-law sensitivity to initial conditions - New entropic representation. Chaos Solitons Fractals 8 (1997) 885
19. Baldovin F., and Robledo A. Sensitivity to initial conditions at bifurcations in one-dimensional nonlinear maps: Rigorous nonextensive solutions. Europhys. Lett. 60 (2002) 518
20. Baldovin F., and Robledo A. Universal renormalization-group dynamics at the onset of chaos in logistic maps and nonextensive statistical mechanics. Phys. Rev. E 66 (2002) R045104
21. Baldovin F., and Robledo A. Nonextensive Pesin identity. Exact renormalization group analytical results for the dynamics at the edge of chaos of the logistic map. Phys. Rev. E 69 (2004) 045202R
22. Tsallis C., Gell-Mann M., and Sato Y. Extensivity and entropy production. In: Boon J.P., and Tsallis C. (Eds). Nonextensive Statistical Mechanics: New Trends, New perspectives. Europhys. News 36 (2005) 186 European Physical Society
23. Plastino A.R., and Plastino A. Non-extensive statistical mechanics and generalized Fokker-Planck equation. Physica A 222 (1995) 347
24. Tsallis C., and Bukman D.J. Anomalous diffusion in the presence of external forces: Exact time-dependent solutions and their thermostatistical basis. Phys. Rev. E 54 (1996) R2197
25. Umarov S., Tsallis C., and Steinberg S. On a q-central limit theorem consistent with nonextensive statistical mechanics. Milan J. Math. 76 (2008) 10.1007/s00032-008-0087-y
26. S. Umarov, C. Tsallis, M. Gell-Mann, S. Steinberg, q-generalization of symmetric α-stable distributions. Part I. cond-mat/0606038, 2006
27. S. Umarov, C. Tsallis, M. Gell-Mann, S. Steinberg, q-generalization of symmetric α-stable distributions. Part II. cond-mat/0606040, 2006
28. S. Umarov, C. Tsallis, On multivariate generalizations of the q-central limit theorem consistent with nonextensive statistical mechanics, in: S. Abe, H.J. Herrmann, P. Quarati, A. Rapisarda, C. Tsallis (Eds.), Complexity, Metastability and Nonextensivity, in: American Institute of Physics Conference Proceedings, vol. 965, New York, 2007, p. 34
29. C. Tsallis, S.M.D. Queiros, Nonextensive statistical mechanics and central limit theorem I - Convolution of independent random variables and q-product, in: S. Abe, H.J. Herrmann, P. Quarati, A. Rapisarda, C. Tsallis (Eds.), Complexity, Metastability and Nonextensivity, in: American Institute of Physics Conference Proceedings, vol. 965, New York, 2007, p. 8
30. S.M.D. Queiros, C. Tsallis, Nonextensive statistical mechanics and central limit theorems II - Convolution of q-independent random variables, in: S. Abe, H.J. Herrmann, P. Quarati, A. Rapisarda, C. Tsallis (Eds.), Complexity, Metastability and Nonextensivity, in: American Institute of Physics Conference Proceedings, vol. 965, New York, 2007, p. 21
31. Vignat C., and Plastino A. Central limit theorem and deformed exponentials. J. Phys. A 40 (2007) F969
32. Upadhyaya A., Rieu J.-P., Glazier J.A., and Sawada Y. Anomalous diffusion and non-Gaussian velocity distribution of Hydra cells in cellular aggregates. Physica A 293 (2001) 549
33. Daniels K.E., Beck C., and Bodenschatz E. Defect turbulence and generalized statistical mechanics. Physica D 193 (2004) 208
34. Douglas P., Bergamini S., and Renzoni F. Tunable Tsallis distributions in dissipative optical lattices. Phys. Rev. Lett. 96 (2006) 110601
35. Tirnakli U., Beck C., and Tsallis C. Central limit behavior of deterministic dynamical systems. Phys. Rev. E 75 (2007) 040106R
36. U. Tirnakli, C. Tsallis, C. Beck, A closer look on the time-average attractor at the edge of chaos of the logistic map, arxiv:0802.1138 [cond-mat.stat-mech], 2008
37. Pluchino A., Rapisarda A., and Tsallis C. Nonergodicity and central limit behavior in long-range Hamiltonians. Europhys. Lett. 80 (2007) 26002
38. Pluchino A., Rapisarda A., and Tsallis C. A closer look at the indications of q-generalized Central Limit Theorem behavior in quasi-stationary states of the HMF model. Physica A 387 (2008) 3121
39. Arevalo R., Garcimartin A., and Maza D. Anomalous diffusion in silo drainage. Eur. Phys. J. E 23 (2007) 191
40. Arevalo R., Garcimartin A., and Maza D. A non-standard statistical approach to the silo discharge. In: Wio H.S., Rodriguez M.A., and Pesquera L. (Eds). Complex Systems - New Trends and Expectations. Eur. Phys. J.-Special Topics 143 (2007)
41. Liu B., and Goree J. Superdiffusion and non-Gaussian statistics in a driven-dissipative 2D dusty plasma. Phys. Rev. Lett. 100 (2008) 055003
42. C. Tsallis, D.A. Stariolo, Generalized simulated annealing (preliminary version), Notas de Fisica/CBPF 026, June 1994
43. Tsallis C., and Stariolo D.A. Generalized simulated annealing. Physica A 233 (1996) 395
44. Stariolo D.A., and Tsallis C. Optimization by simulated annealing: Recent progress. In: Stauffer D. (Ed). Ann. Rev. Comp. Phys. vol. II (1995), World Scientific, Singapore 343
45. Penna T.J.P. Fitting curves by simulated annealing. Comput. Phys. 9 (1995) 341
46. Mundim K.C., and Tsallis C. Geometry optimization and conformational analysis through generalized simulated annealing. Int. J. Quantum Chem. 58 (1996) 373
47. Andricioaei I., and Straub J.E. Generalized simulated annealing algorithms using Tsallis statistics: Application to conformational optimization of a tetrapeptide. Phys. Rev. E 53 (1996) R3055
48. Andricioaei I., and Straub J.E. On Monte Carlo and molecular dynamics inspired by Tsallis statistics: Methodology, optimization and applications to atomic clusters. J. Chem. Phys. 107 (1997) 9117
49. Hansmann U.H.E. Simulated annealing with Tsallis weights: A numerical comparison. Physica A 242 (1997) 250
50. Hansmann U.H.E., and Okamoto Y. Generalized-ensemble Monte Carlo method for systems with rough energy landscape. Phys. Rev. E 56 (1997) 2228
51. Hansmann U.H.E., Masuya M., and Okamoto Y. Characteristic temperatures of folding of a small peptide. Proc. Natl. Acad. Sci. USA 94 (1997) 10652
52. Hansmann U.H.E. Parallel tempering algorithm for conformational studies of biological molecules. Chem. Phys. Lett. 281 (1997) 140
53. Serra P., Stanton A.F., and Kais S. Pivot method for global optimization. Phys. Rev. E 55 (1997) 1162
54. Serra P., Stanton A.F., Kais S., and Bleil R.E. Comparison study of pivot methods for global optimization. J. Chem. Phys. 106 (1997) 7170
55. Xiang Y., Sun D.Y., Fan W., and Gong X.G. Generalized simulated annealing algorithm and its application to the Thomson model. Phys. Lett. A 233 (1997) 216
56. Lemes M.R., Zacharias C.R., and Dal Pino Jr. A. Generalized simulated annealing: Application to silicon clusters. Phys. Rev. B 56 (1997) 9279
57. Serra P., and Kais S. Symmetry breaking and stability of binary clusters. Chem. Phys. Lett. 275 (1997) 211
58. Berne B.J., and Straub J.E. Novel methods of sampling phase space in the simulation of biological systems. Current Opinion Struct. Biol. 7 (1997) 181
59. Andricioaei I., and Straub J.E. An efficient Monte Carlo algorithm for overcoming broken ergodicity in the simulation of spin systems. Physica A 247 (1997) 553
60. Hansmann U.H.E., Eisenmenger F., and Okamoto Y. Stochastic dynamics in a new generalized ensemble. Chem. Phys. Lett. 297 (1998) 374
61. Okamoto Y. Protein folding problem as studied by new simulation algorithms. Recent Res. Devel. Pure Appl. Chem. 2 (1998) 1
62. Linhares A., and Torreao J.R.A. Microcanonical optimization applied to the traveling salesman problem. Internat. J. Modern Phys. C 9 (1998) 133
63. Straub J.E., and Andricioaei I. Exploiting Tsallis statistics. In: Deuflhard P., Hermans J., Leimkuhler B., Mark A., Reich S., and Skeel R.D. (Eds). Algorithms for Macromolecular Modeling. Lecture Notes in Computational Science and Engineering 4 (1998), Springer-Verlag, Berlin 189
64. Mundim K.C., Lemaire T., and Bassrei A. Optimization of nonlinear gravity models through generalized simulated annealing. Physica A 252 (1998) 405
65. Moret M.A., Pascutti P.G., Bisch P.M., and Mundim K.C. Stochastic molecular optimization using generalized simulated annealing. J. Comput. Chem. 19 (1998) 647
66. Moret M.A., Bisch P.M., and Vieira F.M.C. Algorithm for multiple minima search. Phys. Rev. E 57 (1998) R2535
67. Nishimori H., and Inoue J. Convergence of simulated annealing using the generalized transition probability. J. Phys. A 31 (1998) 5661
68. Straub J.E. Protein folding and optimization algorithms. In: Schleyer P.V.R., Allinger N.L., Clark T., Gasteiger J., Kollman P.A., Schaefer III H.F., and Schreiner P.R. (Eds). The Encyclopedia of Computational Chemistry vol. 3 (1998), John Wiley and Sons, Chichester 2184
69. Hansmann U.H.E., Okamoto Y., and Onuchic J.N. The folding funnel landscape of the peptide met-enkephalin. Proteins 34 (1999) 472
70. Hansmann U.H.E., and Okamoto Y. New Monte Carlo algorithms for protein folding. Current Opinion Struct. Biol. 9 (1999) 177
71. Ellis D.E., Mundim K.C., Dravid V.P., and Rylander J.W. Hybrid classical and quantum modeling of defects, interfaces and surfaces. Computer Aided-design of High-temperature Materials (1999), Oxford University Press, Oxford 350
72. Mundim K.C., and Ellis D.E. Stochastic classical molecular dynamics coupled to functional density theory: Applications to large molecular systems. In: Salinas S.R.A., and Tsallis C. (Eds). Nonextensive Statistical Mechanics and Thermodynamics. Braz. J. Phys. 29 (1999) 199
73. Berner A., Mundim K.C., Ellis D.E., Dorfman S., Fuks D., and Evenhaim R. Microstructure of Cu-C interface in Cu-based metal matrix composite. Sensors Actuators 74 (1999) 86
74. Ellis D.E., Mundim K.C., Fuks D., Dorfman S., and Berner A. Interstitial carbon in copper: Electronic and mechanical properties. Philos. Magazine B 79 (1999) 1615
75. Guo L., Ellis D.E., and Mundim K.C. Macrocycle-macrocycle interactions within one-dimensional Cu phthalocyanine chains. J. Porphyrins Phthalocyanines 3 (1999) 196
76. Salazar R., and Toral R. Hybrid simulated annealing using Tsallis statistics. Comput. Phys. Commun. 121-122 (1999) 40
77. Straub J.E., and Andricioaei I. Computational methods inspired by Tsallis statistics: Monte Carlo and molecular dynamics algorithms for the simulation of classical and quantum systems. In: Salinas S.R.A., and Tsallis C. (Eds). Nonextensive Statistical Mechanics and Thermodynamics. Braz. J. Phys. 29 (1999) 179
78. Berner A., Fuks D., Ellis D.E., Mundim K.C., and Dorfman S. Formation of nano-crystalline structure at the interface in Cu-C composite. Appl. Surface Sci. 144-145 (1999) 677
79. Gutterres R.F., de Menezes M.A., Fellows C.E., and Dulieu O. Generalized simulated annealing method in the analysis of atom-atom interaction. Chem. Phys. Lett. 300 (1999) 131
80. Hansmann U.H.E., and Okamoto Y. Tackling the protein folding problem by a generalized-ensemble approach with Tsallis statistics. In: Salinas S.R.A., and Tsallis C. (Eds). Nonextensive Statistical Mechanics and Thermodynamics. Braz. J. Phys. 29 (1999) 187
81. Pak Y., and Wang S.M. Folding of a 16-residue helical peptide using molecular dynamics simulation with Tsallis effective potential. J. Chem. Phys. 111 (1999) 4359
82. Gielis G., and Maes C. A simple approach to time-inhomogeneous dynamics and applications to (fast) simulated annealing. J. Phys. A 32 (1999) 5389
83. Iwamatsu M., and Okabe Y. Reducing quasi-ergodicity in a double well potential by Tsallis Monte Carlo simulation. Physica A 278 (2000) 414
84. Iwamatsu M. Generalized evolutionary programming with Levy-type mutation. Comput. Phys. Commun. 147 (2002) 729
85. n (n =2-55) clusters. J. Phys. Chem. A 104 (2000) 2746
86. Xiang Y., and Gong X.G. Efficiency of generalized simulated annealing. Phys. Rev. E 62 (2000) 4473
87. Calvo F., and Spiegelmann F. Mechanisms of phase transitions in sodium clusters: From molecular to bulk behavior. J. Chem. Phys. 112 (2000) 2888
88. Ahon V.R., Tavares F.W., and Castier M. A comparison of simulated annealing algorithms in the scheduling of multiproduct serial batch plants. Braz. J. Chem. Eng. 17 (2000) 199
89. Fachat A., Hoffmann K.H., and Franz A. Simulated annealing with threshold accepting or Tsallis statistics. Comput. Phys. Commun. 132 (2000) 232
90. Franz A., and Hoffmann K.H. Best possible strategy for finding ground states. Phys. Rev. Lett. 86 (2001) 5219
91. Fuks D., Mundim K.C., Malbouisson L.A.C., Berner A., Dorfman S., and Ellis D.E. Carbon in copper and silver: Diffusion and mechanical properties. J. Mol. Struct. 539 (2001) 199
92. Klos J., and Kobe S. Generalized simulated annealing algorithms using Tsallis statistics: Application to ± J spin glass model. In: Abe S., and Okamoto Y. (Eds). Nonextensive Statistical Mechanics and Its Applications. Lecture Notes in Physics (2001), Springer-Verlag, Heidelberg. 3-540-41208-5
93. Andricioaei I., and Straub J.E. Computational methods for the simulation of classical and quantum many body systems sprung from the non-extensive thermostatistics. In: Abe S., and Okamoto Y. (Eds). Nonextensive Statistical Mechanics and Its Applications. Lecture Notes in Physics (2001), Springer-Verlag, Heidelberg. 3-540-41208-5
94. Andricioaei I., Straub J., and Karplus M. Simulation of quantum systems using path integrals in a generalized ensemble. Chem. Phys. Lett. 346 (2001) 274
95. Fuks D., Dorfman S., Mundim K.C., and Ellis D.E. Stochastic molecular dynamics in simulations of metalloid impurities in metals. Internat. J. Quantum Chem. 85 (2001) 354
96. 3 〈 111 〉 grain boundary in tungsten with non-empirically derived interatomic potentials: The influence of boron interstitials. J. Phys.: Condens. Matter 13 (2001) 6719
97. Okamoto Y., and Hansmann U.H.E. Protein folding simulations by a generalized-ensemble algorithm based on Tsallis statistics. In: Abe S., and Okamoto Y. (Eds). Nonextensive Statistical Mechanics and Its Applications. Lecture Notes in Physics (2001), Springer-Verlag, Heidelberg. 3-540-41208-5
98. Munakata T., and Nakamura Y. Temperature control for simulated annealing. Phys. Rev. E 64 (2001) 046127
99. Takaishi T. Generalized ensemble algorithm for U (1) gauge theory. Nucl. Phys. B (Proc. Suppl.) 106 (2002) 1091
100. Hansmann U.H.E. Protein energy landscapes as studied by a generalized-ensemble approach with Tsallis statistics. In: Grigolini P., Tsallis C., and West B.J. (Eds). Classical and Quantum Complexity and Nonextensive Thermodynamics. Chaos Solitons Fractals 13 3 (2002) 507 Pergamon-Elsevier, Amsterdam
101. Franz A., and Hoffmann K.H. Optimal annealing schedules for a modified Tsallis statistics. J. Comput. Phys. 176 (2002) 196
102. Moret M.A., Bisch P.M., Mundim K.C., and Pascutti P.G. New stochastic strategy to analyze helix folding. Biophys. J. 82 (2002) 1123
103. Braga R.R., Mundim K.C., and Fuks D. Modeling of boron adsorption on the (110) tungsten surface. Surf. Rev. Lett. 10 (2003) 213
104. Ding Z.N., Ellis D.E., Sigmund E., Halperin W.P., and Shriver D.F. Alkali-ion kryptand interactions and their effects on electrolyte conductivity. Phys. Chem. Chem. Phys. 5 (2003) 2072
105. Mundim K.C., Dorfman S., and Fuks D. Decohesion of Sigma(3)(111) grain boundary tungsten with boron interstitial. Surf. Rev. Lett. 10 (2003) 227
106. Inoue J.I., and Tabushi K. A generalization of the deterministic annealing EM algorithm by means of non-extensive statistical mechanics. Internat. J. Modern Phys. B 17 (2003) 5525
107. Kim J.G., Fukunishi Y., Kidera A., and Nakamura H. Stochastic formulation of sampling dynamics in generalized ensemble methods. Phys. Rev. E 69 (2004) 021101
108. Kim J.G., Fukunishi Y., Kidera A., and Nakamura H. Generalized simulated tempering realized on expanded ensembles of non-Boltzmann weights. J. Chem. Phys. 121 (2004) 5590
109. Dall' Igna Jr. A., Silva R.S., Mundim K.C., and Dardenne L.E. Performance and parameterization of the algorithm Simplified Generalized Simulated Annealing. Genetics Molecular Biol. 27 (2004) 616
110. Fukuda I., and Nakamura H. Molecular dynamics sampling scheme realizing multiple distributions. Phys. Rev. E 71 (2005) 046708
111. Correia E.R., Nascimento V.B., Castilho C.M.C., Esperidiao A.S.C., Soares E.A., and Carvalho V.E. The generalized simulated annealing algorithm in the low energy diffraction search problem. J. Phys.: Condens. Mater. 17 (2005) 1-16
112. Habeck M., Rieping W., and Nilges M. A replica-exchange Monte Carlo scheme for Bayesian data analysis. Phys. Rev. Lett. 94 (2005) 018105
113. Moret M.A., Bisch P.M., Nogueira Jr. E., and Pascutti P.G. Stochastic strategy to analyze protein folding. Physica A 353 (2005) 353
114. Gangal R., and Sharma P. Human pol II promoter prediction: Time series descriptors and machine learning. Nucleic Acids Res. 33 (2005) 1332
115. Liu H.B., and Jordan K.D. On the convergence of parallel tempering Monte Carlo simulations of LJ(38). J. Phys. Chem. A 109 (2005) 5203
116. Xu Q., Bao S.Q., Zhang R., Hu R.J., and Sbert M. Adaptive sampling for Monte Carlo global illumination using Tsallis entropy. Computational Intelligence and Security, Part 2. Proceedings Lecture Notes in Artificial Intelligence vol. 3802 (2005), Springer-Verlag, Berlin 989-994
117. Mundim K.C. An analytical procedure to evaluate electronic integrals for molecular quantum mechanical calculations. Physica A 350 (2005) 338
118. de Andrade M.D., Mundim K.C., and Malbouisson L.A.C. GSA algorithm applied to electronic structure: Hartree-Fock-GSA method. Internat. J. Quantum Chem. 103 (2005) 493-499
119. de Andrade M.D., Malbouisson L.A.C., and Mundim K.C. Generalized simulated annealing algorithm applied to electronic structure II. The unrestricted Hartree-Fock-GSA method. Internat. J. Quantum Chem. 106 (2006) 2700-2705
120. Esteves C.S., de Oliveira H.C.B., Ribeiro L., Gargano R., and Mundim K.C. Modeling diatomic potential energy curves through the generalized exponential function. Chem. Phys. Lett. 427 (2006) 10-13
121. De Andrade M.D., Nascimento M., Mundim K., and Malbouisson L. GSA algorithm applied to electronic structure II: UHF-GSA method. Internat. J. Quantum Chem. 106 (2006) 2700-2705
122. Agostini F.P., Soares-Pinto D.D.O., Moret M.A., Osthoff C., and Pascutti P.G. Generalized simulated annealing applied to protein folding studies. J. Comp. Chem. 27 (2006) 1142-1155
123. Wang C.J., and Wang X.F. Nonextensive thermostatistical investigation of free electronic gas in metal. Acta Phys. Sinica 55 (2006) 2138-2143
124. Gao Y.Q., and Yang L. On the enhanced sampling over energy barriers in molecular dynamics simulation. J. Chem. Phys. 125 (2006) 114103
125. Moret M.A., Pascutti P.G., Bisch P.M., Mundim M.S.P., and Mundim K.C. Classical and quantum conformational analysis using Generalized Genetic Algorithm. Physica A 363 (2006) 260-268
126. Hannig J., Chong E.K.P., and Kulkarni S.R. Relative frequencies of generalized simulated annealing. Math. Oper. Res. 31 (2006) 199-216
127. Escobedo F.A., and Martinez-Veracoechea F.J. Optimized expanded ensembles for simulations involving molecular insertions and deletions. I. Closed systems. J. Chem. Phys. 127 (2007) 174103
128. Kamberaj H., and van der Vaart A. Multiple scaling replica exchange for the conformational sampling of biomolecules in explicit water. J. Chem. Phys. 127 (2007) 234102
129. Rick S.W. Replica exchange with dynamical scaling. J. Chem. Phys. 126 (2007) 054102
130. Yang L.J., Grubb M.P., and Gao Y.Q. Application of the accelerated molecular dynamics simulations to the folding of a small protein. J. Chem. Phys. 126 (2007) 125102
131. Morishita T., and Mikami M. Enhanced sampling via strong coupling to a heat bath: Relationship between Tsallis and multicanonical algorithms. J. Chem. Phys. 127 (2007) 034104
132. Deng J.J., Chen H.S., Chang C.L., and Yang Z.X. A superior random number generator for visiting distributions in GSA. Internat. J. Comput. Math. 81 (2004) 103
133. Deng J.J., Chang C.L., and Yang Z.X. An exact random number generator for visiting distribution in GSA. I. J. Simulation 6 (2005) 54-61
134. Schanze T. An exact D-dimensional Tsallis random number generator for generalized simulated annealing. Comput. Phys. Commun. 175 (2006) 708-712
135. Thistleton W., Marsh J.A., Nelson K., and Tsallis C. Generalized Box-Muller method for generating q-Gaussian random deviates. IEEE Trans. Inform. Theory 53 (2007) 4805-4810
136. Cannas S.A., Stariolo D., and Tamarit F.A. Learning dynamics of simple perceptrons with non-extensive cost functions. Netw. Comput. Neural Sci. 7 (1996) 141
137. Anastasiadis A.D., and Magoulas G.D. Nonextensive statistical mechanics for hybrid learning of neural networks. Physica A 344 (2004) 372
138. Anastasiadis A.D., and Magoulas G.D. Evolving stochastic learning algorithm based on Tsallis entropic index. Eur. Phys. J. B 50 (2006) 277-283
139. Magoulas G.D., and Anastasiadis A. Approaches to adaptive stochastic search based on the nonextensive q-distribution. Internat. J. Bifurcation Chaos 16 (2006) 2081-2091
140. Niven R.K. q-exponential structure of arbitrary-order reaction kinetics. Chem. Eng. Sci. 61 (2006) 3785-3790
141. Fukuda I., and Nakamura H. Construction of an extended invariant for an arbitrary ordinary differential equation with its development in a numerical integration algorithm. Phys. Rev. E 73 (2006) 026703
142. Nguyen P.H., Mittag E., Torda A.E., and Stock G. Improved Wang-Landau sampling through the use smoothed potential-energy surfaces. J. Chem. Phys. 124 (2006) 154107
143. Frank T.D., Daffertshofer A., Beek P.J., and Haken H. Impacts of noise on a field theoretical model of the human brain. Physica D 127 (1999) 233
144. Cidade G.A.G., Anteneodo C., Roberty N.C., and Silva Neto A.J. A generalized approach for atomic force microscopy image restoration with Bregman distances as Tikhonov regularization terms. Inverse Problems Eng. 8 (2000) 457
145. Pak Y., Enyedy I.J., Varady J., Kung J.W., Lorenzo P.S., Blumberg P.M., and Wang S.M. Structural basis of binding of high-affinity ligands to protein kinase C: Prediction of the binding modes through a new molecular dynamics method and evaluation by site-directed mutagenesis. J. Medicinal Chemistry 44 (2001) 1690
146. Esquef I., Albuquerque M., and Albuquerque M. Nonextensive entropic image thresholding. Proc. XV Brazilian Symposium on Computer Graphics and Image Processing, 7-10 October 2002, Fortaleza (2002), IEEE 402
147. R. Smolikova, M.P. Wachowiak, G.D. Tourassi, A. Elmaghraby, J.M. Zurada, Characterization of ultrasonic backscatter based on generalized entropy, in: IEEE CNF, 24th Annual Conference and the Annual Fall Meeting of the Biomedical Engineering Society, Proceedings of the Second Joint Conference, vol. 2, 23-26 October 2002, pp. 953-954, doi:10.1109/IEMBS.2002.1106222
148. Anino M.M., Torres M.E., and Schlotthauer G. Slight parameter changes detection in biological models: A multiresolution approach. Physica A 324 (2003) 645
149. Torres M.E., Anino M.M., and Schlotthauer G. Automatic detection of slight parameter changes associated to complex biomedical signals using multiuresolution q-entropy. Med. Eng. Phys. 25 (2003) 859
150. M. Shen, Q. Zhang, P.J. Beadle, Nonextensive entropy analysis of non-stationary ERP signals, in: IEEE International Conference on Neural Networks and Signal Processing, Nanjing, China, 14-17 December 2003, pp. 806-809
151. Tukmakov A.L. Application of the function of the number of states of a dynamic system to investigation of electroencephalographic reaction to photostimulation. Zhurnal Vysshei Nervnoi Deyatelnosti imeni i P Pavlova 53 (2003) 523
152. Rufiner H.L., Torres M.E., Gamero L., and Milone D.H. Introducing complexity measures in nonlinear physiological signals: Application to robust speech recognition. Physica A 332 (2004) 496
153. de Albuquerque M.P., Esquef I.A., Mello A.R.G., and de Albuquerque M.P. Image thresholding using Tsallis entropy. Pattern Recognit. Lett. 25 (2004) 1059
154. Martin S., Morison G., Nailon W., and Durrani T. Fast and accurate image registration using Tsallis entropy and simultaneous perturbation stochastic approximation. Electron. Lett. 40 10 (2004) 20040375
155. Shitong W., and Chung F.L. Note on the equivalence relationship between Renyi-entropy based and Tsallis-entropy based image thresholding. Pattern Recognit. Lett. 26 (2005) 2309-2312
156. Wachowiak M.P., Smolikova R., Tourassi G.D., and Elmaghraby A.S. Estimation of generalized entropies with sample spacing. Pattern. Anal. Appl. 8 (2005) 95-101
157. Karmeshu, and Sharma S. q-exponential product-form solution of packet distribution in queueing networks: Maximization of Tsallis entropy. IEEE Comm. Lett. 10 (2006) 585-587
158. Sahoo P.K., and Arora G. Image thresholding using two-dimensional Tsallis-Havrda-Charvat entropy. Pattern Recognit. Lett. 27 (2006) 520-528
159. S. Liao, W. Fan, A.C.S. Chung, D.Y. Yeung, Facial expression recognition using advanced local binary patterns, Tsallis entropies and global appearance features, in: 2006 IEEE International Conference on Image Processing, 8-11 October 2006, p. 665, doi:10.1109/ICIP.2006.312418
160. Ben Hamza A. Nonextensive information-theoretic measure for image edge detection. J. Electron. Imaging 15 (2006) 013011
161. Cvejic N., Canagarajah C.N., and Bull D.R. Image fusion metric based on mutual information and Tsallis entropy. Electron. Lett. 42 11 (2006)
162. Shioya H., and Gohara K. Generalized phase retrieval algorithm based on information measures. Optics Comm. 266 (2006) 88
163. Rokach L. Decomposition methodology for classification tasks: A meta decomposer framework. Pattern Anal. Appl. 9 (2006) 257
164. W. Guo, S. Cui, Fast convergence with q-expectation in EM-based blind iterative detection, in: IEEE CNF, Fortieth Asilomar Conference on Signals, Systems and Computers, ACSSC '06, October-November 2006, p. 458, doi:10.1109/ACSSC.2006.354789
165. Y. Li, X. Fan, G. Li, Image segmentation based on Tsallis-entropy and Renyi-entropy and their comparison, in: 2006 IEEE International Conference on Industrial Informatics, INDIN'06 Article 4053516, 2007, p. 943
166. Nakib A., Oulhadj H., and Siarry P. Image histogram thresholding based on multiobjective optimization. Signal Process. 87 (2007) 2516
167. Sneddon R. The Tsallis entropy of natural information. Physica A 386 (2007) 101
168. Li Y.L., Yu S.L., and Zheng G. Separation method for overlapping voltammetric peaks based on the fractional-order differential. Chinese J. Anal. Chem. 35 (2007) 747
169. Ziviani A., Gomes A.T.A., Monsores M.L., and Rodrigues P.S.S. Network anomaly detection using nonextensive entropy. IEEE Commun. Lett. 11 (2007) 1034
170. Jiang T., Xiang W., Richardson P.C., Guo J., and Zhu G. PAPR reduction of OFDM signals using partial transmit sequences with low computational complexity. IEEE Trans. Broadcast. 53 (2007) 719
171. Wang S., Chung F.L., and Xiong F. A novel image thresholding method based on Parzen window estimate. Pattern Recognit. 41 (2008) 117
172. P. Zhao, P. Van Eetvelt, C. Goh, N. Hudson, S. Wimalaratna, E.C. Ifeachor, EEG markers of Alzheimer's disease using Tsallis entropy, Communicated at the 3rd International Conference on Computational Intelligence in Medicine and Healthcare, CIMED2007, July 25-27, Plymouth, UK, 2007
173. D. Kouvatsos, S.A. Assi, On the analysis of queues with long range dependent traffic: An extended maximum entropy approach, in: IEEE CNF, 3rd EuroNGI Conference on Next Generation Internet Networks, 21-23 May 2007, p. 226, doi:10.1109/NGI.2007.371220
174. P.A. Ritto, Non extensive statistic of Tsallis in the heartbeat of healthy humans, preprint (2007), arxiv:0705.3817 [physics.data-an]
175. Poza J., Hornero R., Escudero J., Fernandez A., and Sanchez C.I. Regional analysis of spontaneous MEG rhythms in patients with Alzheimer's desease using spectral entropies. Ann. Biomed. Eng. 36 (2008) 141
176. Livadiotis G. Approach to the block entropy modeling and optimization. Physica A 387 (2008) 2471
177. Gamero L.G., Plastino A., and Torres M.E. Wavelet analysis and nonlinear dynamics in a nonextensive setting. Physica A 246 (1997) 487
178. Capurro A., Diambra L., Lorenzo D., Macadar O., Martin M.T., Mostaccio C., Plastino A., Rofman E., Torres M.E., and Velluti J. Tsallis entropy and cortical dynamics: The analysis of EEG signals. Physica A 257 (1998) 149
179. Capurro A., Diambra L., Lorenzo D., Macadar O., Martins M.T., Mostaccio C., Plastino A., Perez J., Rofman E., Torres M.E., and Velluti J. Human dynamics: The analysis of EEG signals with Tsallis information measure. Physica A 265 (1999) 235
180. M. Tanaka, T. Watanabe, T. Mishima, Tsallis entropy in scalespaces, in: L.J. Latecki, R.A. Melter, D.M. Mount, A.Y. Wu (Eds.), SPIE Conference on Vision Geometry VIII, vol. 3811 (Proceedings of SPIE, October 1999)
181. Sun Y., Chan K.L., Krishnan S.M., and Dutt D.N. Tsallis' multiscale entropy for the analysis of nonlinear dynamical behavior of ECG signals. In: Singh M., et al. (Ed). Medical Diagnostic Techniques and Procedures (1999), Narosa Publishing House, London 49
182. Martin M.T., Plastino A.R., and Plastino A. Tsallis-like information measures and the analysis of complex signals. Physica A 275 (2000) 262
183. Torres M.E., and Gamero L.G. Relative complexity changes in time series using information measures. Physica A 286 (2000) 457
184. N.V. Thakor, J. Paul, S. Tong, Y. Zhu, A. Bezerianos, Entropy of brain rhythms: Normal versus injury EEG, in: Proceedings of 11th IEEE Signal Processing Workshop, 2001, pp. 261-264
185. L. Cimponeriu, S. Tong, A. Bezerianos, N.V. Thakor, Synchronization and information processing across the cerebral cortexfollowing cardiac arrest injury, in: Proceedings of 24th IEEE/EMBS Conference, 26-28 October 2002, San Antonio, Texas
186. Tong S., Bezerianos A., Paul J., Zhu Y., and Thakor N. Nonextensive entropy measure of EEG following brain injury from cardiac arrest. Physica A 305 (2002) 619-628
187. Rosso O.A., Martin M.T., and Plastino A. Brain electrical activity analysis using wavelet based informational tools. Physica A 313 (2002) 587
188. Rosso O.A., Martin M.T., and Plastino A. Brain electrical activity analysis using wavelet-based informational tools (II): Tsallis non-extensivity and complexity measures. Physica A 320 (2003) 497
189. Tong S., Bezerianos A., Malhotra A., Zhu Y., and Thakor N. Parameterized entropy analysis of EEG following hypoxic-ischemic brain injury. Phys. Lett. A 314 (2003) 354
190. Bezerianos A., Tong S., and Thakor N. Time-dependent entropy estimation of EEG rhythm changes following brain ischemia. Ann. Biomed. Eng. 31 (2003) 221
191. R.G. Geocadin, S. Tong, A. Bezerianos, S. Smith, T. Iwamoto, N.V. Thakor, D.F. Hanley, Approaching brain injury after cardiac arrest: From bench to bedside, in: Proceedings of Neuroengineering Workshop, Capri, 2003, p. 277
192. Thakor N., and Tong S. Advances in quantitative electroencephalogram analysis methods. Ann. Rev. Biomed. Eng. 6 (2004) 453
193. Borges E.P., Tsallis C., Miranda J.G.V., and Andrade R.F.S. Mother wavelet functions generalized through q-exponentials. J. Phys. A 37 (2004) 9125
194. Plastino A., Martin M.T., and Rosso O.A. Generalized information measures and the analysis of brain electrical signals. In: Gell-Mann M., and Tsallis C. (Eds). Nonextensive Entropy - Interdisciplinary Applications (2004), Oxford University Press, New York
195. Plastino A., and Rosso O.A. Entropy and statistical complexity in brain activity. In: Boon J.P., and Tsallis C. (Eds). Nonextensive Statistical Mechanics: New Trends, New Perspectives. Europhys. News 36 (2005) 224
196. Rosso O.A., Martin M.T., Figliola A., Keller K., and Plastino A. EEG analysis using wavelet-based information tools. J. Neurosci. Methods 153 (2006) 163
197. Zunino L., Perez D.G., Martin M.T., Plastino A., Garavaglia M., and Rosso O.A. Characterization of Gaussian self-similar stochastic processes using wavelet-based informational tools. Phys. Rev. E 75 (2007) 021115
198. Perez D.G., Zunino L., Martin M.T., Garavaglia M., Plastino A., and Rosso O.A. Model-free stochastic processes studied with q-wavelet-based informational tools. Phys. Lett. A 364 (2007) 259
199. Sun S., Zhang L., and Guo C. Medical image registration by minimizing divergence measure based on Tsallis entropy. Internat. J. Biomed. Sci. 2 (2007) 75
200. Torres M.E., Rufiner H.L., Milone D.H., and Cherniz A.S. Multiresolution information measures applied to speech recognition. Physica A 385 (2007) 319
201. Cai S.M., Jiang Z.H., Zhou T., Zhou P.L., Yang H.J., and Wang B.H. Scale invariance of human electroencephalogram signals in sleep. Phys. Rev. E 76 (2007) 061903
202. E.C. Ramberg, Methods and apparatus for designing high-dimensional combinatorial experiments, Patent record available from the World Intellectual Property Organization, WIPO, 2002
203. Y. Wang, M. Falcioni, S.J. Turner, E.C. Ramberg, Methods and apparatus for designing high-dimensional combinatorial experiments, Patent record available from the US Patent Office, 2002
204. J.T. Flick, J. Joseph, Method for diagnosing heart disease, predicting sudden death, and analyzing treatment response using multifractal analysis, Patent record available from the US Patent Office, 2003
205. Fujitsu Ltd. (FUIT), Simulation program for computing thermo-dynamic quantities in medical applications, includes calculator to calculate average thermo-dynamic quantity along acquired track based on sampling, Patent JP2003044524-A, (2003-424391)
206. R. Ugajin, Information processing method and information processing apparatus, Patent record available from the US Patent Office, 2003
207. S.V. Ulyanov, S. Panfilov, T. Hagiwara, K. Takahashi, L. Litvintseva, V.S. Ulyanov, Intelligent mechatronic control suspension system based on quantum soft computing, Patent record available from the World Intellectual Property Organization, WIPO, 2004
208. R.S. Sneddon, Method for measuring information in natural data, Patent record available from the US Patent Office, 2005
209. I. Fukuda, H. Nakamura, Simulation apparatus, Patent record available from the Japanese Patent Office, 2003
210. R.S. Sneddon, Sneddon and Assoc. Inc. (SNED-Non-standard), Data value measuring method for electro encephalography data, involves computing attribute for each data subset so that attribute is dependent on data in each subset and attribute is equal to variability of data in each data subset, Patent US2005159919-A1 (2005-540950)
211. I. Fukuda, H. Nakamura, Fujitsu Ltd (FUIT); Dokuritsu Gyosei Hojin Sangyo Gijutsu So (Doku-Non-standard), Sampling simulation device e.g. for medicine, integrates deterministic differential equations numerically for reproducing distribution obtained by combining Tsallis distributions, Patent US2006184340-A1; Patent JP2006221578-A (2006-633933)
212. I. Fukuda, H. Nakamura, Sampling simulation device by deterministic system capable of generating multiple distributions simultaneously, Patent record available from the Japanese Patent Office, 2006
213. I. Fukuda, H. Nakamura, Deterministic sampling simulation device for generating a plurality of distribution simultaneously, Patent record available from the US Patent Office, 2006
214. M. Weiger, M. Fey, T. Speck, Method for automatic shimming for nuclear magnetic resonance spectroscopy, Patent record available from the European Patent Office, 2006
215. J.T. Flick, J. Joseph, Method for diagnosing heart disease, predicting sudden death, and analyzing treatment response using multifractial analysis, Patent record available from the US Patent Office, 2006
216. Y. Wang, M. Falcioni, S.J. Turner, E.C. Ramberg, Methods and apparatus for preparing high-dimensional combinatorial experiments, Patent record available from the US Patent Office, 2006
217. M.W. Deem, M. Falcioni, Library design in combinatorial chemistry by Monte Carlo methods, Patent record available from the US Patent Office, 2006