Inverse problems in dynamic cognitive modeling

Chaos

Volumn 19, Issue 1, 2009, Pages

  Beim Graben, Peter ^a   Potthast, Roland ^a  

^a UNIVERSITY OF READING   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHM; ANIMAL; ARTIFICIAL NEURAL NETWORK; BIOLOGICAL MODEL; COGNITION; FRACTAL ANALYSIS; HUMAN; MEMORY; NERVE CELL; NERVE CELL NETWORK; NEUROSCIENCE; NONLINEAR SYSTEM; PHYSIOLOGY; PROCEDURES; THEORETICAL MODEL;

ALGORITHMS; ANIMALS; COGNITION; FRACTALS; HUMANS; MEMORY; MODELS, BIOLOGICAL; MODELS, THEORETICAL; NERVE NET; NEURAL NETWORKS (COMPUTER); NEURONS; NEUROSCIENCES; NONLINEAR DYNAMICS;

EID: 63849262991     PISSN: 10541500     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.3097067     Document Type: Article

References (156)

1. J. A. S. Kelso, Dynamic Patterns: The Self-Organization of Brain and Behavior (MIT Press, Cambridge, MA, 1995).
2. T. van Gelder, Behav. Brain Sci. 21, 615 (1998). 0140-525X
3. R. D. Beer, Trends Cogn. Sci. 4, 91 (2000). 1364-6613
4. P. beim Graben, Mind and Matter 2, 29 (2004).
5. Parallel Distributed Processing: Explorations in the Microstructure of Cognition, edited by, D. E. Rumelhart, J. L. McClelland, and the PDP Research Group (MIT Press, Cambridge, MA, 1986), Vol. 1.
6. J. Hertz, A. Krogh, and R. G. Palmer, Introduction to the Theory of Neural Computation (Perseus Books, Cambridge, MA, 1991).
7. D. Marr and T. Poggio, Massachusetts Institute of Technology Technical Report No. AIM-357, 2003.
8. Z. W. Pylyshyn, Computation and Cognition: Toward a Foundation for Cognitive Science (MIT Press, Cambridge, MA, 1986).
9. C. P. Dolan and P. Smolensky, Connect. Sci. 1, 53 (1989). 0954-0091
10. P. Smolensky, Artif. Intell. 46, 159 (1990). 0004-3702
11. P. Smolensky and G. Legendre, The Harmonic Mind: From Neural Computation to Optimality-Theoretic Grammar,(MIT Press, Cambridge, MA, 2006), Vol. 1.
12. P. Smolensky, Cogn. Sci. 30, 779 (2006). 0364-0213
13. P. beim Graben, S. Gerth, and S. Vasishth, Cognit. Neurodynamics 2, 229 (2008). 1871-4080
14. P. beim Graben, D. Pinotsis, D. Saddy, and R. Potthast, Cognit. Neurodynamics 2, 79 (2008). 1871-4080
15. M. J. Spivey and R. Dale, Psychol. Learn. Motiv. 45, 87 (2004). 0079-7421
16. B. L. van der Waerden, Algebra (Springer, New York, 2003), Vol. 2.
17. R. Haag, Local Quantum Physics: Fields, Particles, Algebras (Springer, Berlin, 1992).
18. S. -I. Amari, Biol. Cybern. 0340-1200 10.1007/BF00337259 27, 77 (1977).
19. Lectures in Supercomputational Neuroscience: Dynamics in Complex Brain Networks, edited by, P. beim Graben, C. Zhou, M. Thiel, and, J. Kurths, (Springer, Berlin, 2008), pp. 3-48.
20. P. C. Bressloff and J. D. Cowan, Physica D 0167-2789 10.1016/S0167- 2789(02)00677-2 173, 226 (2002).
21. S. Coombes, G. Lord, and M. Owen, Physica D 0167-2789 10.1016/S0167-2789(03)00002-2 178, 219 (2003).
22. G. B. Ermentrout and J. B. McLeod, Proc.-R. Soc. Edinburgh, Sect. A: Math 123A, 461 (1993).
23. J. S. Griffith, Bull. Math. Biophys. 25, 111 (1963). 0007-4985
24. A. Hutt and F. M. Atay, Physica D 0167-2789 10.1016/j.physd.2005.03.002 203, 30 (2005).
25. V. K. Jirsa and H. Haken, Phys. Rev. Lett. 0031-9007 10.1103/PhysRevLett. 77.960 77, 960 (1996).
26. P. L. Nunez, Behav. Brain Sci. 0140-525X 10.1017/S0140525X00003253 23, 371 (2000).
27. K. A. Richardson, S. J. Schiff, and B. J. Gluckman, Phys. Rev. Lett. 0031-9007 10.1103/PhysRevLett.94.028103 94, 028103 (2005).
28. P. A. Robinson, C. J. Rennie, and J. J. Wright, Phys. Rev. E 1063-651X 10.1103/PhysRevE.56.826 56, 826 (1997).
29. N. Venkov, S. Coombes, and P. Matthews, Physica D 0167-2789 10.1016/j.physd.2007.04.011 232, 1 (2007).
30. H. R. Wilson and J. D. Cowan, Kybernetik 0023-5946 10.1007/BF00288786 13, 55 (1973).
31. J. J. Wright, C. J. Rennie, G. J. Lees, P. A. Robinson, P. D. Bourke, C. L. Chapman, E. Gordon, and D. L. Rowe, Neuropsychopharmacology 28, S80 (2003). 0893-133X
32. W. Erlhagen and G. Schöner, Psychol. Rev. 109, 545 (2002). 0033-295X
33. G. Schöner and E. Thelen, Psychol. Rev. 113, 273 (2006). 0033-295X
34. E. Thelen, G. Schöner, C. Scheier, and L. B. Smith, Behav. Brain Sci. 0140-525X 10.1017/S0140525X01003910 24, 1 (2001).
35. A. Newell and H. A. Simon, Commun. ACM 0001-0782 10.1145/360018.360022 19, 113 (1976).
36. J. Fodor and Z. W. Pylyshyn, Cognition 0010-0277 10.1016/0010-0277(88) 90031-5 28, 3 (1988).
37. J. E. Hopcroft and J. D. Ullman, Introduction to Automata Theory, Languages, and Computation (Addison-Wesley, Menlo Park, California, 1979).
38. J. R. Anderson, Cognitive Psychology and its Implications (W. H. Freeman, New York, NY, 1995).
39. R. L. Lewis, Encyclopedia of Cognitive Science (Macmi llan, London, 2003).
40. A. K. Joshi and Y. Schabes, in Handbook of Formal Languages and Automata, edited by, A. Salomma, and, G. Rosenberg, (Springer, Berlin, 1997), Vol. 3, pp. 69-124.
41. E. P. Stabler, in Logical Aspects of Comutational Linguistics, edited by, C. Retoŕ, (Springer, New York, 1997), pp. 68-95.
42. J. Michaelis and C. Wartena, in Constraints and Resources in Natural Language Syntax and Semantics, edited by, G. Bouma, G. -J. Kruijff, E. Hinrichs, and, R. T. Oehrle, (CSLI, Stanford, CA, 1999), pp. 263-279.
43. E. P. Stabler, Cogn. Sci. 28, 699 (2004). 0364-0213
44. J. Michaelis, in Logical Aspects of Computational Linguistics, edited by, M. Moortgat, (Springer, Berlin, 2001), pp. 179-198.
45. H. T. Siegelmann, Theor. Comput. Sci. 168, 461 (1996). 0304-3975
46. C. Moore, Phys. Rev. Lett. 0031-9007 10.1103/PhysRevLett.64.2354 64, 2354 (1990).
47. C. Moore, Nonlinearity 4, 199 (1991). 0951-7715
48. R. Badii and A. Politi, Complexity: Hierarchical Structures and Scaling in Physics (Cambridge University Press, Cambridge, 1997).
49. E. Mizraji, Bull. Math. Biol. 0092-8240 10.1016/S0092-8240(89)80067-9 51, 195 (1989).
50. E. Mizraji, Fuzzy Sets Syst. 50, 179 (1992). 0165-0114
51. H. T. Siegelmann and E. D. Sontag, J. Comput. Syst. Sci. 50, 132 (1995). 0022-0000
52. W. Tabor, Technical Report No. TR98-1694, 1998.
53. W. Tabor, Expert Sys. 17, 41 (2000). 0266-4720
54. W. Tabor, University of Connecticut Report, 2002.
55. J. B. Pollack, Mach. Learn. 7, 227 (1991). 0885-6125
56. C. Moore, Theor. Comput. Sci. 0304-3975 10.1016/S0304-3975(97)00028-5 201, 99 (1998).
57. C. Moore and J. P. Crutchfield, Theor. Comput. Sci. 0304-3975 10.1016/S0304-3975(98)00191-1 237, 275 (2000).
58. P. beim Graben, B. Jurish, D. Saddy, and S. Frisch, Int. J. Bifurcation Chaos Appl. Sci. Eng. 14, 599 (2004). 0218-1274
59. P. beim Graben, in Advances in Cognitive Neurodynamics, Proceedings of the International Conference on Cognitive Neurodynamics, ICCN 2007, edited by, R. Wang, F. Gu, and, E. Shen, (Springer, Berlin, 2008), pp. 469-473.
60. P. Cvitanović, G. H. Gunaratne, and I. Procaccia, Phys. Rev. A 1050-2947 10.1103/PhysRevA.38.1503 38, 1503 (1988).
61. M. B. Kennel and M. Buhl, Phys. Rev. Lett. 0031-9007 10.1103/PhysRevLett. 91.084102 91, 084102 (2003).
62. A. Maye and M. Werning, Neurocomputing 58-60, 941 (2004). 0925-2312
63. M. Werning, Synthese 146, 203 (2005). 0039-7857
64. A. Maye and M. Werning, Chaos Complexity Lett. 2, 315 (2007).
65. M. Werning and A. Maye, Chaos Complexity Lett. 2, 435 (2007).
66. A. R. Edmonds, Angular Momentum in Quantum Mechanics (Princeton University Press, New Jersey, 1957).
67. D. Gernert, BioSystems 54, 165 (2000). 0303-2647
68. H. Atmanspacher and T. Filk, BioSystems 85, 84 (2006). 0303-2647
69. P. beim Graben, Mind and Matter 4, 169 (2006).
70. H. Haken, Synergetics: An Introduction (Springer, Berlin, 1983).
71. V. S. Afraimovich, V. P. Zhigulin, and M. I. Rabinovich, Chaos 1054-1500 10.1063/1.1819625 14, 1123 (2004).
72. M. I. Rabinovich, R. Huerta, P. Varona, and V. S. Afraimovich, PLOS Comput. Biol. 4, e1000072 (2008). 1553-734X
73. M. Rabinovich, A. Volkovskii, P. Lecanda, R. Huerta, H. D. I. Abarbanel, and G. Laurent, Phys. Rev. Lett. 0031-9007 10.1103/PhysRevLett.87.068102 87, 068102 (2001).
74. R. Huerta and M. Rabinovich, Phys. Rev. Lett. 0031-9007 10.1103/PhysRevLett.93.238104 93, 238104 (2004).
75. P. Smolensky, Behav. Brain Sci. 11, 1 (1988). 0140-525X
76. R. Dale and M. J. Spivey, J. Exp. Theor. Artif. Intell. 0952-813X 10.1080/09528130500283766 17, 317 (2005).
77. P. beim Graben and H. Atmanspacher, Found. Phys. 0015-9018 10.1007/s10701-005-9013-0 36, 291 (2006).
78. M. J. Spivey and S. E. Anderson, J. Exp. Theor. Artif. Intell. 20, 239 (2008). 0952-813X
79. P. Smolensky, in Meaning in Mind: Fodor and His Critics, edited by, B. Loewer, and, G. Rey, (Blackwell, Oxford, 1991), pp. 201-227.
80. J. Fodor and B. P. McLaughlin, Cognition 35, 183 (1990). 0010-0277
81. D. J. Chalmers, in Proceedings of the 12th Annual Conference on Cognitive Science Society, 1990 (unpublished), pp. 340-347.
82. J. Fodor, Cognition 62, 109 (1997). 0010-0277
83. A. Prince and P. Smolensky, Science 275, 1604 (1997). 0036-8075
84. R. B. Stein, K. V. Leung, D. Mangeron, and M. N. Oǧuztöreli, Kybernetik 15, 1 (1974). 0023-5946
85. H. R. Wilson and J. D. Cowan, Biophys. J. 0006-3495 10.1016/S0006- 3495(72)86068-5 12, 1 (1972).
86. A. Arenas, A. Díaz-Guilera, J. Kurths, Y. Moreno, and C. Zhou, Phys. Rep. 0370-1573 10.1016/j.physrep.2008.09.002 469, 93 (2008).
87. Lectures in Supercomputational Neuroscience: Dynamics in Complex Brain Networks, edited by, P. beim Graben, C. Zhou, M. Thiel, and, J. Kurths, (Springer, Berlin, 2008), pp. 195-223.
88. P. beim Graben and J. Kurths, Neurocomputing 71, 999 (2008). 0925-2312
89. Neurocomputing: Foundations of Research, edited by, J. A. Anderson, and, E. Rosenfeld, (MIT Press, Cambridge, MA, 1988), Vol. 1.
90. Neurocomputing: Directions for Research, edited by, J. A. Anderson, A. Pellionisz, and, E. Rosenfeld, (MIT Press, Cambridge, MA, 1990), Vol. 2.
91. P. S. Churchland and T. J. Sejnowski, The Computational Brain (MIT Press, Cambridge, MA, 1994).
92. The Handbook of Brain Theory and Neural Networks, edited by, M. A. Arbib, (MIT Press, Cambridge, MA, 1998).
93. C. -H. Chen and V. Honavar, IEEE Trans. Neural Netw. 1045-9227 10.1109/72.788663 10, 1239 (1999).
94. W. Tabor, IEEE Trans. Neural Netw. 14, 444 (2003). 1045-9227
95. J. L. Elman, in Mind as Motion: Explorations in the Dynamics of Cognition, edited by, R. F. Port, and, T. van Gelder, (MIT Press, Cambridge, MA, 1995), pp. 19 5- 223.
96. W. Tabor, C. Juliano, and M. K. Tanenhaus, Lang. Cognit. Processes 12, 211 (1997). 0169-0965
97. W. Tabor and M. K. Tanenhaus, Cogn. Sci. 23, 491 (1999). 0364-0213
98. S. Lawrence, C. L. Giles, and S. Fong, IEEE Trans. Knowl. Data Eng. 1041-4347 10.1109/69.842255 12, 126 (2000).
99. I. Farkas and M. W. Crocker, Neurocomputing 71, 1172 (2008). 0925-2312
100. A. H. Kawamoto, J. Mem. Lang. 32, 474 (1993). 0749-596X
101. J. J. Hopfield, Proc. Natl. Acad. Sci. U.S.A. 0027-8424 10.1073/pnas.79.8.2554 79, 2554 (1982).
102. P. Smolensky, in Parallel Distributed Processing: Explorations in the Microstructure of Cognition, edited by, D. E. Rumelhart, J. L. McClelland, and the PDP Research Group (MIT Press, Cambridge, MA, 1986), Vol. 1, pp. 194-281.
103. H. Haken, Synergetic Computers and Cognition: A Top-Down Approach to Neural Nets (Springer, Berlin, 1991).
104. H. Haken, Principles of Brain Functioning (Springer, Berlin, 1996).
105. T. Vosse and G. Kempen, Cognition 75, 105 (2000). 0010-0277
106. C. Balkenius and P. Gärdenfors, in Principles of Knowledge Representation and Reasoning, edited by, J. A. Allan, R. Fikes, and, E. Sandewall, (Morgan Kaufmann, San Mateo, CA, 1991), pp. 32-39.
107. P. Gärdenfors, Foundations of Computation, edited by, J. v. Eijck, and, A. Visser, (MIT-Press, Cambridge, MA, 1994), pp. 49-77.
108. R. Blutner, Synthese 141 (2004). 0039-7857
109. E. Mizraji and J. Lin, Int. J. Bifurcation Chaos Appl. Sci. Eng. 11, 155 (2001). 0218-1274
110. M. H. Christiansen and N. Chater, Cogn. Sci. 23, 417 (1999). 0364-0213
111. S. -I. Amari, Kybernetik 14, 201 (1974). 0023-5946
112. R. Albert and A. -L. Barabási, Rev. Mod. Phys. 0034-6861 10.1103/RevModPhys.74.47 74, 47 (2002).
113. L. Zemanová, C. Zhou, and J. Kurths, Physica D 0167-2789 10.1016/j.physd.2006.09.008 224, 202 (2006).
114. C. Zhou, L. Zemanová, G. Zamora, C. C. Hilgetag, and J. Kurths, Phys. Rev. Lett. 0031-9007 10.1103/PhysRevLett.97.238103 97, 238103 (2006).
115. M. Kaiser and C. C. Hilgetag, Neurocomputing 58-60, 297 (2004). 0925-2312
116. O. Sporns, D. R. Chialvo, M. Kaiser, and C. C. Hilgetag, Trends Cogn. Sci. 1364-6613 10.1016/j.tics.2004.07.008 8, 418 (2004).
117. W. Maass, T. Natschläger, and H. Markram, Neural Comput. 0899-7667 10.1162/089976602760407955 14, 2531 (2002).
118. V. K. Jirsa and H. Haken, Physica D 0167-2789 10.1016/S0167-2789(96) 00166-2 99, 503 (1997).
119. V. K. Jirsa, A. Fuchs, and J. A. S. Kelso, Neural Comput. 0899-7667 10.1162/089976698300016954 10, 2019 (1998).
120. P. C. Bressloff, J. D. Cowan, M. Golubitsky, P. J. Thomas, and M. C. Wiener, Philos. Trans. R. Soc. London, Ser. B 0962-8436 10.1098/rstb.2000.0769 356, 299 (2001).
121. P. C. Bressloff, J. D. Cowan, M. Golubitsky, P. J. Thomas, and M. C. Wiener, Neural Comput. 0899-7667 10.1162/089976602317250861 14, 473 (2002).
122. P. C. Bressloff, Phys. Rev. Lett. 0031-9007 10.1103/PhysRevLett.89.088101 89, 088101 (2002).
123. P. C. Bressloff and J. D. Cowan, J. Physiol. (Paris) 97, 221 (2003). 0022-3751
124. P. C. Bressloff, Biol. Cybern. 0340-1200 10.1007/s00422-005-0002-3 93, 256 (2005).
125. A. M. Oster and P. C. Bressloff, Bull. Math. Biol. 68, 73 (2006). 0340-1200
126. R. Kress, Linear Integral Equations (Springer-Verlag, Berlin, 1989).
127. D. Colton and R. Kress, Inverse Acoustic and Electromagnetic Scattering Theory (Springer-Verlag, Berlin, 1998).
128. H. W. Engl, M. Hanke, and A. Neubauer, Regularization of Inverse Problems (Kluwer Academic, Dordrecht, 1996).
129. A. Neumaier, SIAM Rev. 0036-1445 10.1137/S0036144597321909 40, 636 (1998).
130. R. Kress, Numerical Analysis, Graduate Texts in Mathematics (Springer-Verlag, New York, 1999).
131. R. Potthast and P. beim Graben, " Existence and properties of solutions for neural field equations.," Math. Models Meth. Appl. Sci. (to be published). 0036-1445
132. R. Potthast and P. beim Graben, " Inverse problems in neural field theory.," SIAM J. Appl. Dyn. Syst. (unpublished). 0036-1445
133. H. Bersini, M. Saerens, and L. G. Sotelino, IEEE Trans. Neural Netw. 5, 945 (1994). 1045-9227
134. B. A. Pearlmutter, Neural Comput. 1, 263 (1989). 0899-7667
135. B. A. Pearlmutter, IEEE Trans. Neural Netw. 1045-9227 10.1109/72.410363 6, 1212 (1995).
136. L. G. Sotelino, M. Saerens, and H. Bersini, Neural Netw. 7, 767 (1994). 0893-6080
137. G. -Z. Sun, H. -H. Chen, and Y. -C. Le, Proceedings International Joint Conference on Neural Networks (IJCNN 91), 1991 (unpublished), Vol. 2, pp. 13-18.
138. C. Igel, W. Erlhagen, and D. Jancke, Neurocomputing 36, 225 (2001). 0925-2312
139. D. O. Hebb, The Organization of Behavior (Wiley, New York, NY, 1949).
140. M. Breakspear, J. A. Roberts, J. R. Terry, S. Rodrigues, N. Mahant, and P. A. Robinson, Cereb. Cortex 16, 1296 (2006). 1047-3211
141. Z. P. Kilpatrick, S. E. Folias, and P. C. Bressloff, SIAM J. Appl. Dyn. Syst. 1536-0040 10.1137/070699214 7, 161 (2008).
142. V. K. Jirsa and J. A. S. Kelso, Phys. Rev. E 1063-651X 10.1103/PhysRevE.62.8462 62, 8462 (2000).
143. C. J. Rennie, P. A. Robinson, and J. J. Wright, Biol. Cybern. 0340-1200 10.1007/s00422-002-0310-9 86, 457 (2002).
144. D. Lehmann, Electroencephalogr. Clin. Neurophysiol. 31, 439 (1971). 0013-4694
145. D. Lehmann, H. Ozaki, and I. Pal, Electroencephalogr. Clin. Neurophysiol. 67, 271 (1987). 0013-4694
146. R. Friedrich, A. Fuchs, and H. Haken, in Rhythms in Physiological Systems, edited by, H. Haken, and, H. P. Koepchen, (Springer, Berlin, 1991), pp. 315-338.
147. C. Allefeld and J. Kurths, Int. J. Bifurcation Chaos Appl. Sci. Eng. 0218-1274 10.1142/S0218127404009521 14, 417 (2004).
148. M. Paluš, I. Dvoák, and I. David, Physica A 185, 433 (1992). 0378-4371
149. P. beim Graben, S. Frisch, A. Fink, D. Saddy, and J. Kurths, Phys. Rev. E 1063-651X 10.1103/PhysRevE.72.051916 72, 051916 (2005).
150. V. K. Jirsa, R. Friedrich, and H. Haken, Physica D 0167-2789 10.1016/0167-2789(95)00226-X 89, 100 (1995).
151. H. Obrig and A. Villringer, J. Cereb. Blood Flow Metab. 0271-678X 10.1097/00004647-200301000-00001 23, 1 (2003).
152. K. J. Friston, P. Fletcher, O. Josephs, A. Holmes, M. D. Rugg, and R. Turner, Neuroimage 7, 30 (1998). 1053-8119
153. O. David and K. J. Friston, Neuroimage 20, 1743 (2003). 1053-8119
154. O. David, S. J. Kiebel, L. Harrison, J. Mattout, J. Kilner, and K. J. Friston, Neuroimage 30, 1255 (2006). 1053-8119
155. A. Galka, O. Yamashita, T. Ozaki, R. Biscay, and P. Valdeś-Sosa, Neuroimage 23, 435 (2004). 1053-8119
156. A. Galka, T. Ozaki, H. Muhle, U. Stephani, and M. Siniatchkin, Cognit. Neurodynamics 2, 101 (2008). 1871-4080