Phase transitions in the neuropercolation model of neural populations with mixed local and non-local interactions

Biological Cybernetics

Volumn 92, Issue 6, 2005, Pages 367-379

  Kozma, Robert ^a   Puljic, Marko ^a   Balister, Paul ^a   Bollobás, Bela ^a   Freeman, Walter J ^b  

^a University of Memphis   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

DYNAMICS; GRAPH THEORY; MATHEMATICAL MODELS; NEUROLOGY; PARAMETER ESTIMATION; PERCOLATION (COMPUTER STORAGE); PHASE TRANSITIONS; RANDOM PROCESSES;

NEURAL POPULATIONS; NEURONS; NEUROPERCOLATION; NON-LOCAL INTERACTIONS;

NEURAL NETWORKS;

ALGORITHM; ANIMAL; ARTICLE; BIOLOGICAL MODEL; BRAIN; GROWTH, DEVELOPMENT AND AGING; HUMAN; NERVE CELL; NEUROPIL; PHYSIOLOGY;

ALGORITHMS; ANIMALS; BRAIN; HUMANS; MODELS, NEUROLOGICAL; NEURONS; NEUROPIL;

EID: 20644468605     PISSN: 03401200     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00422-005-0565-z     Document Type: Article

References (69)

1. Aihara K, Takabe T, Toyoda M (1990) Chaotic neural networks. Phys Lett A 144(6-7):333-340
2. Aizeman M, Lebowitz JL (1988) Metastability effects in bootstrap percolation. J Phys A 21:3801-3813
3. Albert R, Barabási AL (2002) Statistical mechanics of complex networks. Rev Modern Phys 74:47
4. Arhem P, Blomberg C, Liljenstrom H (2000) Disorder versus order in brain function. In: Progr neural processing, Vol. 12, ISBN 981-02-4008-2, World Scientific, Singapore
5. Bak P (1996) How nature works - the science of self-organized criticality. Springer, Berlin Heidelberg New York
6. Bak P, Tang C, Wiesenfeld K (1987) Phys Rev Lett 59:381
7. Balister PN, Bollobás B, Stacey AM (1993) Upper bounds for the critical probability of oriented percolation in two dimensions. In: Proc Royal Soc Lond Ser A 440(1908):201-220
8. Balister P, Bollobás B, Kozma R (2004) Mean field models of probabilistic cellular automata. Random Struct Algorithms (on press)
9. Balister P, Bollobás B, Johnson R, Walters M (2003) Random majority percolation, (submitted)
10. Barabási L, Bonabeau E (2003) Scale-free networks. Sci Am 288:60-69
11. Barrie JM, Freeman WJ, Lenhart M (1996) Modulation by discriminative training of spatial patterns of gamma EEG amplitude and phase in neocortex of rabbits. J Neurophysiol 76:520-539
12. Berlekamp ER, Conway JH, Guy RK (1982) Winning ways for your mathematical plays, vol 1: games in general. Academic, New York
13. Binder K (1981) Finite scale scaling analysis of Ising model block distribution function. Z Phys B 43:119-140
14. Bollobás B (1985) Random Graphs. Academic, London
15. Bollobás B, Riordan O (2003) Results on scale-free random graphs. Handbook of graphs and networks, 1-34. Wiley-VCH, Weinheim
16. Bressler SL, Kelso JAS (2001) Cortical coordination dynamics and cognition. Trends Cogn Sci 5:26-36
17. Bressler SL (2002) Understanding cognition through large-scale cortical networks. Curr Directions Psychol Sci 11:58-61
18. Bressler SL (2003) Cortical coordination dynamics and the disorganization syndrome in schizophrenia. Neuropsychopharmacology 28:S35-S39
19. Cerf R, Cirillo EN (1999) Finite size scaling in three-dimensional boot-strap percolation. Ann Probab 27(4): 1837-1850
20. Cipra BA (1987) An introduction to the ising model. Am Math Monthly 94:937-959
21. Crutchfield JP (1994) The calculi of emergence: computation, dynamics, and induction. Physica D 75:11-54
22. Dafilis MP, Liley DTJ, Cadusch PJ (2001) Robust chaos in a model of the electro-encephalogram: Implications for brain dynamics. Chaos 11:474-478
23. Duarte AMS (1989) Simulation of acellular automaton with an oriented bootstrap rule. Physica A 157:1075-1079
24. Erdõs P, Rényi A (1960). On the evolution of random graphs. Publ Math Inst Hung Acad Sci 5:17-61
25. Freeman WJ (1975) Mass action in the nervous system. Academic, New York
26. Freeman WJ (1999) Noise-induced first-order phase transitions in chaotic brain activity. Int J Bifurcation Chaos 9(11):2215-2218
27. Freeman WJ (2003a) The wave packet: an action potential for the 21st Century. J Integrative Neurosci 2:3-30
28. Freeman WJ (2003b) Evidence from human scalp EEG of global chaotic itinerancy. Chaos 13:1067-1077
29. Freeman WJ (2003c) A neurobiological theory of meaning in perception. Part 1. Information and meaning in nonconvergent and nonlocal brain dynamics. Int J Bifurc Chaos 13:2493-2511
30. Freeman WJ, Burke BC, Holmes MD (2003a) Aperiodic phase re-setting in scalp EEG of beta-gamma oscillations by state transitions at alpha-theta rates. Hum Brain Mapp 19:248-272
31. Freeman WJ, Burke BC, Holmes MD, Vanhatalo S (2003b) Spatial spectra of scalp EEG and EMG from awake humans. Clin Neurophysiol 114:1055-1060
32. Freeman WJ (2004) Origin, structure, and role of background EEG activity. Part 1. Analytic amplitude. Clin Neurophysiol 115:2077-2088
33. Fristen KJ (2000) The labile brain. I. Neuronal transients and nonlinear coupling. Phil Trans R Soc Lond B 355:215-236
34. Gruber AJ, Solla SA, Surmeier DJ, Houk JC (2003) Modulation of striatal single units by expected reward: A spiny neuron model displaying dopamine-induced Instability. J Neurophysiol 90:1095-1114
35. Haken H (1999) What can synergetics contribute to the understanding of brain functioning? In: Uhl C (ed) Analysis of neurophysiological brain functioning. Springer, Berlin Heidelberg New York, pp 7-40
36. Gács P (1990) A Toom rule that increases the thickness of sets. J Statist Phys 59(1-2): 171-193
37. Gravener J, McDonald E (1997) Bootstrap percolation in a polluted environment. J Statist Phys 87(3-4):915-927
38. Grimmett G (1999) Percolation in fundamental principles of mathematical sciences. Springer, Berlin Heidelberg New York xiv+444 pp
39. Hopfield JJ (1982) Neural networks and physical systems with emergent collective computational abilities. Proc Nat Acad Sci USA 79:2554-2558
40. Hoppensteadt FC, Izhikevich EM (1998) Thalamo-cortical interactions modeled by weakly connected oscillators: could the brain use FM radio principles? BioSystems 48:85-94
41. Ingber L (1995) Statistical mechanics of multiple scales of neocortical interactions. In: Nunez PL (ed) Neocortical dynamics and human EEG rhythms. Oxford, New York, pp 628-681
42. Jensen HJ (1998) Self-organized criticality - emergent behavior in physical and biological systems. Cambridge University Press, Cambridge
43. Kaneko K (1990) Clustering, coding, switching, hierarchical ordering, and control in a network of chaotic elements. Physica D 41:137-172
44. Kaneko K, Tsuda I (2001) Complex systems: chaos and beyond. A constructive approach with applications in life sciences
45. Kauffman SA (1990) Requirements for evolvability in complex systems: orderly dynamics and frozen components. Physica D 42:135-152
46. Korn H, Faure P (2003) Is there chaos in the brain? II. Experimental evidence and related models. Comptes Rendus Biologies 326:787-840
47. Kozma R (1998) Intermediate-range coupling generates low-dimensional attractors deeply in the chaotic region of one-dimensional lattices. Phys Lett A 244(1-3):85-91
48. Kozma R, Freeman WJ (2001) Chaotic resonance - methods and applications for robust classification of noisy and variable patterns. Int J Bifurcation Chaos 11:1607-1629
49. Kozma R, Balister P, Bollobás B, Freeman WJ (2001) Dynamical percolation models of phase transitions in the cortex In: Proceedings NOLTA 01 nonlinear theory and applications symposium, Miyagi, Japan, vol. 1, pp 55-59
50. Kozma R, Balister P, Bollobás B, Chen H, Freeman WJ (2003) Analysis of scaling laws in a local random cellular automata model (submitted)
51. Kozma R, Puljic M, Balister P, Bollobás B, Freeman WJ (2004) Neuropercolation: a random cellular automata approach to spatio-temporal neurodynamics. Lecture Notes Computer Science LNCS vol 3350, Springer, Berlin Heidelberg New York, pp 435-443
52. Linkenkaer-Hansen K, Nikouline VM, Palva JM, Iimoniemi RJ (2001) Long-range temporal correlations and scaling behavior in human brain oscillations. J Neurosci 15:1370-1377
53. Maes C, Vande Velde K (1997) Relative energies for non-Gibbsian states. Comm Math Phys 189(2):277-286
54. Makowiec D (1999) Stationary states for Toom cellular automata in simulations. Phys Rev E 55:3795
55. Marcq P, Chaté H, Manneville P (1997) Universality in Ising-like phase transitions of lattices of coupled chaotic maps. Phys Rev E 55(3):2606-2627
56. Newman MEJ (2000) Models of the small world. J Stat Phys 101:819-841
57. Ohl FW, Scheich H, Freeman WJ (2001) Change in pattern of ongoing cortical activity with auditory category learning. Nature 412:733-736
58. Ohl FW, Deliano M, Scheich H, Freeman WJ (2003) Early and late patterns of stimulus-related activity in auditory cortex of trained animals. Biol Cybern 88:374-379
59. Peters A, Palay SL, deF H (1991) Webster fine structure of the nervous system: neurons and their supporting cells. Oxford University Press, Oxford)
60. Pomeau Y (1993) Periodic behavior in cellular automata. J Stat Phys 70(5-6): 1379-1382
61. Puljic M, Kozma R, (2003) Phase transitions in a probabilistic cellular neural network model having local and remote connections. IEEE/INNS International Joint Conference Neural Network IJCNN'2003, pp 831-835
62. Puljic M, Kozma R (2005) Activation clustering in neural and social networks. Complexity (in press)
63. Schiff SJ et al (1994) Controlling chaos in the brain. Nature 370:615-620
64. Skarda CA, Freeman WJ (1987) How brains make chaos in order to make sense of the world. Behav Brain Sci 10:161-195
65. Stam CJ, Breakspear M, van Cappellen van Walsum A-M, van Dijk BW (2003) Nonlinear synchronization in EEG and whole-head recordings of healthy subjects. Hum Brain Mapp 19:63-78
66. Stauffer D, Aharony A (1994) Introduction to percolation theory. Selwood Printing Ltd, West Sussex
67. Toom AL, Vasilyev NB, Stavskaya ON, Mityushin LG, Kurdyumov GL, Prigorov SA (1990) Discrete local Markov systems in Stochastic cellular systems:ergodicity, memory, morphogenesis. In: Dobrushin RL, Kryukov VI, Toom AL (eds) Nonlinear Science: theory and applications. Manchester University Press, UK
68. Wang XF, Chen GR (2003) Complex networks: small-world, scale-free and beyond. IEEE Trans Circuits Syst 31:6-20
69. Watts DJ, Strogatz SH (1998) Collective dynamics of small-world networks. Nature 393:440-442