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The EEG data indicate stochastic nonlinearity

Published online by Cambridge University Press:  04 February 2010

Walter S. Pritchard
Walter S. Pritchard
Affiliation:
Psychophysiology Laboratory, Bowman Gray Technical Center 611-12, R. J. Reynolds Tobacco Company, Winston-Salem, NC 27102. wally@rjrt.com
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Abstract

Wright & Liley contrast their theory that the global dynamics of the EEG are linear with that of Freeman, who hypothesizes an EEG governed by (nonlinear) deterministic-chaotic dynamics. A “call for further discussion” on the part of the authors is made as to how either theory fits with experimental findings indicating that EEG dynamics are non-linear but stochastic.

Type
Open Peer Commentary
Information
Behavioral and Brain Sciences , Volume 19 , Issue 2 , June 1996 , pp. 308
Copyright
Copyright © Cambridge University Press 1996

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References

Abarbanel, H. D. I., Brown, R., Sidorowich, J. J. & Tsimring, L. S. (1993) The analysis of observed chaotic data in physical systems. Review of Modem Physics 65: 1331–92. [LI]CrossRefGoogle Scholar
Abeles, M. (1982) Local cortical circuits. In: Studies in brain Junction 6. Springer-Verlag. [RM]Google Scholar
Abeles, M., Prut, Y., Bergman, H. & Vaadia, E. (1994) Synchronization in neuronal transmission and its importance for information processing. In: Temporal coding in the brain, ed. Buzsaki, G., Llinas, R., Singer, W., Berthoz, A. & Cristen, . Springer-Verlag. [ZJK]Google Scholar
Aertsen, A. & Amdt, M. (1993) Response synchronization in the visual cortex. Current Opinion in Neurobiology 3:586–94. [HP]CrossRefGoogle ScholarPubMed
Agladze, N. N., Zhadin, M. N. & lgnatjev, D. A. (1995) Electrical activity of the rabbit isolated cerebral cortex after application of acetylcholine. Journal of Higher Nervous Activity 45:782–89 (in Russian). [MNZ]Google ScholarPubMed
Ahadin, M. N., Bakharev, B. V & Muravjova, L. I. (1977) Electrophysiological correlates of habituation and conditioning. Journal of Higher Nervous Activity 27:1173–79 (in Russian). [MNZ]Google Scholar
Alkon, D., Sanchez-Andres, J.-V, Ito, E. & Oka, K. (1992) Long-term transformation of an inhibitory into an excitatory GABAergic synaptic response. Proceedings of the National Academy of Sciences 89(24):11862–66. [HRE]CrossRefGoogle ScholarPubMed
Amari, S. (1972) Learning patterns and pattern sequences by self-organising nets of threshold elements. IEEE Transactions on Computers 21:1197–1206. [aJJW]CrossRefGoogle Scholar
Amit, D. J. (1990) Modelling brain function: The world of attractor neural networks. Cambridge University Press. [aJJW]Google Scholar
Amit, D. J. (1995) The Hebbian paradigm reintegrated. Behavioral and Brain Sciences 18:681. [DJA]CrossRefGoogle Scholar
Amit, D. J. & Brunel, N. (1995) Global spontaneous activity and local structured (learned) delay activity in cortex. Submitted. [DJA, rJJW]Google Scholar
Amit, D. J. & Tsodyks, M. V. (1990) Attractor neural networks with biological probe records. Network 1:381–405. [aJJW]CrossRefGoogle Scholar
Amit, D. J. & Tsodyks, M. V. (1991) Quantitative study of attractor neural networks retrieving at low spike rates: 2. Low rate retrieval in symmetric networks. Network 2:275–94. [ajJW]CrossRefGoogle Scholar
Aradi, I., Barna, G., Érdi, P. & Gröbler, T. (1995) Chaos and learning in the olfactory bulb. International Journal of Intelligent Systems 10:89–117. [PÉ]CrossRefGoogle Scholar
Babloyantz, A. & Lourenco, C. (1994) Computation with chaos: A paradign for cortical activity. Proceedings of the National Academy of Sciences USA 91:9027–31. [IT]CrossRefGoogle Scholar
Becker, C. J. & Freeman, W. J. (1968) Prepyriform electrical activity after loss of peripheral or central input or both. Physiology & Behavior 3:597–99. [WJF]CrossRefGoogle Scholar
Bennett, C. H. 91995) Quantum information and computation. Physics Today 48:24–30. [LI]CrossRefGoogle Scholar
Bower, J. M. & Beeman, D. (1995) The book of Genesis: Exploring realistic neural models with GEneral NEural SImulation System. TELOS/Springer-Verlag. [JJW]CrossRefGoogle Scholar
Braitenberg, V. (1978) Cell assemblies in the cerebral cortex. In: Theoretical approaches to complex systems [Lecture notes in Biomathematics, vol. 21], ed. Hcim, R. & Palm, C.. Springer-Verlag. [HP]CrossRefGoogle Scholar
Braitenberg, V. & Schuz, A. (1991) Anatomy of the cortex: Statistics and geometry. Springer-Verlag. [aJJW]CrossRefGoogle Scholar
Bressler, S. L., Coppola, R. & Nakamura, R. (1993) Episodic multiregional cortical coherence at multiple frequencies during visual task performance. Nature 366:153–56. [HRE, rJJW]CrossRefGoogle ScholarPubMed
Bressler, S. L. & Freeman, W. J. (1980) Frequency analysis of olfactory system EEC in cat, rabbit and rat. EEC and Clinical Neurophysiology 50:19–24. [WJF]CrossRefGoogle Scholar
Bullock, T. H. & McClune, M. C. (1989) Lateral coherence of the electrocorticogram: A new measure of brain synchrony. Electroencephalography and Clinical Neurophysiology 73:479–98. [THB]CrossRefGoogle ScholarPubMed
Bullock, T. H., McClune, M. C, Achimowicz, J. Z., Iragui-Madoz, V. J., Duckrow, R. B. & Spencer, S. S. (1995) EEC coherence has structure in the millimeter domain: Subdural and hippocampal recordings from epileptic patients. Electroencephalography and Clinical Neurophysiology 95:161–77. [THB]CrossRefGoogle Scholar
Bullock, T. H., McClune, M. C, Achimowicz, J. Z., Iragui-Madoz, V. J., Duckrow, R. B. & Spencer, S. S. (in press) Temporal fluctuations in coherence of brain waves. Proceedings of the National Academy of Sciences [THB]Google Scholar
Burkitt, G. (1994) Steady-state visually evoked potentials and travelling waves. PhD dissertation, Swinburne University of Technology, Melbourne, Australia. [aJJW]Google Scholar
Burns, B. D. (1958) Mammalian cerebral cortex. Williams and Wilkins. [WJF, rJJW]Google Scholar
Buzsaki, B. & Chrobak, J. J. (1995) Temporal structure in spatially organized neuronal emsembles: A role for intemeuronal networks. Current Opinion in Neurobiology 5:504–20. [EK]CrossRefGoogle Scholar
Caianiello, E. R., De Luca, A. & Ricciardi, L. M. (1967) Reverberations and control of neural networks. Kybernetik 4:10–18. [aJJW]CrossRefGoogle ScholarPubMed
Calvin, W. H. & Ojemann, G. A. (1994) Conversations with Neil's brain: The neural nature of thought and language. Addison Wesley. [HRE]Google Scholar
Case, R. (1992) The role of the frontal lobes in the regulation of cognitive development. Brain and Cognition 20:51–73. [AO]CrossRefGoogle ScholarPubMed
Chang, H. J. & Freeman, W. J. (in press) Parameter optimization in models of the olfactory system. Neural Networks. [WJF]Google Scholar
Churchland, P. S. (1986) Neurophilosophy–Toward a unified science of the mindbrain. MIT Press. [aJJW]Google Scholar
Churchland, P. S. & Sejnowski, T. J. (1994) The computational brain. MIT Press. [HRE]Google Scholar
Crick, F. (1994) The astonishing hypothesis: The scientific search for the soul. Scribners. [HRE]Google Scholar
Dehaene, S., Changeux, J. P. & Nadal, J. P. (1987) Neural networks that learn temporal sequences by selection. Proceedings of the National Academy of Science 84:2727–31. [aJJW]CrossRefGoogle ScholarPubMed
Dennett, D. C. (1991) Consciousness explained. Little, Brown. [HRE]Google Scholar
DeWitt, B. S. (1957) Dynamical theory in curved spaces: 1. A review of the classical and quantum action principles. Review of Modem Physics 29:377–97. [LI]CrossRefGoogle Scholar
Donchin, E. (1981) Suprise! … Surprise? Psychophysiology 18:493–513. [MM]CrossRefGoogle Scholar
Eckhom, R. (1994) Oscillatory and non-oscillatory synchronization in the visual cortex of cat and monkey. In: Oscillatory event-related brain dynamics ed. Pantev, C., Elbert, T. & Lutkenhoner, B.. NATO ASI Series A: life Sciences, vol. 271. Plenum. [ZJK]Google Scholar
Eckhom, R., Bauer, B., Jordan, W., Brosch, M., Kruse, W., Munk, M. & Reitboeck, H. J. (1988) Coherent oscillation: A mechanism of feature linking in visual cortex? Biological Cybernetics 60:121–30. [aJJW, HP]Google Scholar
Eeckman, F. H. & Freeman, W. J. (1991) Asymmetric sigmoid nonlinearity in the rat olfactory system. Brain Research 557:13–21. [aJJW]CrossRefGoogle ScholarPubMed
Elbert, T., Ray, W. J., Kowalik, Z. J., Skinner, J. E., Graf, K. E. & Birbaumer, N. (1994) Chaos and physiology: Deterministic chaos in excitable cell assemblies. Physiological Reviews 74:1–47. [ZJK, HP]CrossRefGoogle ScholarPubMed
Elbert, T. & Rockstroh, B. (1987) Threshold regulation: A key to the understanding of the combined dynamics of EEC and event-related potentials. Journal of Psychophysiology 4:317–33. [HP]Google Scholar
Érdi, P. (1983) Hierarchical approach to the brain. International Journal of Neuroscience 20:193–216. [PÉ]CrossRefGoogle ScholarPubMed
Érdi, P., Gröbler, T. & Toth, J. (1992) On the classification of some classification problems. International Symposium on Information Physics, Kyushu Institute of Technology, Iizuka, Fukuoka, Japan. [PÉ]Google Scholar
Farley, B. G. (1965) A neuronal network model and the “slow potentials” in electrophysiology. In: Computers in biomedical research, ed. Stacy, R. W. & Waxman, B. D.. Academic Press. [MNZ]Google Scholar
Farmer, J. D. (1982) Information dimension and the probabilistic structure of chaos. Zeitschrifi für Naturforschung 37a:1304–25. [HP]CrossRefGoogle Scholar
Freeman, W. J. (1964) A linear distributed feedback model for prepyriform cortex. Experimental Neurology 10:525–47. [aJJW]CrossRefGoogle ScholarPubMed
Freeman, W. J. (1972) Measurement of open-loop responses to electrical stimulation in olfactory bulb of cat. Journal of Neurophysiology 35:745–61. [aJJW]CrossRefGoogle ScholarPubMed
Freeman, W. J. (1975) Mass action in the nervous system. Academic Press. [aJJW, HRE, WJF, PLN]Google Scholar
Freeman, W. J. (1979) Nonlinear gain mediation of cortical stimulus response relations. Biological Cybernetics 33:237–47. [aJJW, WJF, HL]CrossRefGoogle ScholarPubMed
Freeman, W. J. (1987a) Techniques used in the search for die physiological basis of the EEC. In: Handbook of electroencephalography and clinical neurophysiology, vol. 3A, ed. Gevins, A. S. & Remond, A.. Elsevier. [aJJW]Google Scholar
Freeman, W. J. (1987b) Simulation of chaotic EEC patterns with dynamic model of the olfactory system. Biological Cybernetics 56:139–50. [aJJW]CrossRefGoogle Scholar
Freeman, W. J. (1988) Strange attractors diat govern mammalian brain dynamics shown by trajectories of electroencephalographic (EEG) potential. IEEE Transactions on Circuits and Systems 35:781–83. [aJJW]CrossRefGoogle Scholar
Freeman, W. J. (1991) Predictions on neoeortical dynamics derived from studies in paleoeortex. In: Induced rhythms of the brain, ed. Basar, E. & Bullock, T. H.. Birkhaeuser Boston Inc. [aJJW, ZJK]Google Scholar
Freeman, W. J. (1992) Tutorial in neurobiology: From single neurons to brain chaos. International Journal of Bifurcation and Chaos 2:451–82. [WJF]CrossRefGoogle Scholar
Freeman, W. J. (1994) Neural mechanisms underlying destabilization of cortex by sensory input. Physica D 75:151–64. [IT]CrossRefGoogle Scholar
Freeman, W. J. (1995a) Societies of brains: A study in the neuroscience of love and hate. Erlbaum. [HRE, WJF, IT]Google Scholar
Freeman, W. J. (1995b) Foreword. In: Chaos theory in psychology and the life sciences, ed. Robertson, R. & Combs, A.. Erlbaum. [rJJW, MM]Google Scholar
Freeman, W. J. (1995c) Chaos in the brain: Possible roles in biological intelligence. International Journal of Intelligent Systems 10:71–88. [IT]CrossRefGoogle Scholar
Freeman, W. J. & Barrie, J. M. (1994) Chaotic oscillations and the genesis of meaning in cerebral cortex. In: Temporal coding in the brain, ed. Buzsaki, C., Llinás, R., Singer, W., Berthoz, A. & Christen, Y.. Springer-Verlag. [WJF]Google Scholar
Freeman, W. J., Barrie, J. M., Lenhart, M. & Tang, R. X. (1995) Spatial phase gradients in neoeortical EECs give modal diameter of “binding” domains in perception. Society for Neuroscience Abstracts 21:1649. [WJF]Google Scholar
Freeman, W. J. & Jakubith, S. (1993) Bifurcation analysis of continuous time dynamics of oscillatory neural networks. In: Brain theory, ed. Aertson, A.. Springer-Verlag. [aJJW, ZJK]Google Scholar
Freeman, W. J. & Skarda, C. A. (1985)' Spatial EEG patterns, nonlinear dynamics and perception: The neo-Sherringtonian view. Brain Research Reviews 10:147–75. [aJJW]CrossRefGoogle Scholar
Friedrich, R., Fuchs, A. & Hakan, H. (1991) Spatio-temporal EEG patterns. In: Rhythms in physiological systems, ed. Hakan, H. & Koepshen, H. P.. Springer-Verlag. [PLN]Google Scholar
Fuchs, A., Kelso, J. A. S. & Hakan, H. (1992) Phase transitions in the human brain spatial mode dynamics. International Journal of Bifurcation and Chaos 2:917–39. [PLN]CrossRefGoogle Scholar
Gevins, A. S., Schaffer, R. E., Doyle, J. C., Cuttilo, B. A., Tannehill, R. S. & Bressler, S. L. (1983) Shadows of thought: Shifting lateralisation of human brain electrical patterns during a brief visuomotor task. Science 220:97–99. [aJJW]CrossRefGoogle ScholarPubMed
Glass, L., Kaplan, D. T. & Lewis, J. E. (1993) Tests for deterministic dynamics in real and model neural networks. In: Nonlinear dynamical analysis of the EEG, ed. Jansen, B. H. & Brandt, M. E.. World Scientific. [WSP]Google Scholar
Graham, R. (1978) Path-integral methods on nonequilibrium thermodynamics and statistics. In: Stochastic processes in nonequilibrium systems, ed. Garrido, L., Seglar, P. & Shepherd, P. J.. Springer-Verlag. [LI]Google Scholar
Grassberger, P. & Procaccia, I. (1983) Measuring die strangeness of strange attractors. Physica D 9:189–208. [MM, WSP]CrossRefGoogle Scholar
Gray, C. M., Koenig, P., Engel, K. A. & Singer, W. (1989) Oscillatory responses in cat visual cortex exhibit intereolumnar synchronisation which reflects global stimulus properties. Nature 338:334–37. [aJJW, HP]CrossRefGoogle ScholarPubMed
Gregson, R. A. M. (1992) Cognitive load as a determinant of the dimensionality of the electroencephalogram: A replication study. Biological Psychology 35:165–78. [MM]CrossRefGoogle Scholar
Grey, G. M., Koning, P., Engle, A. K. & Singer, W. (1989) Oscillatory responses in cat visual cortex exhibit inter-columnar synchronization which reflects global stimulus properties. Nature 338:334–37. [PLN]CrossRefGoogle Scholar
Griniasty, M., Tsodyks, M. V. & Amit, D. J. (1993) Conversion of temporal correlations between stimuli to spatial correlations between attractors. Neural Computation 5:1–17. [aJJW]CrossRefGoogle Scholar
Haken, H. (1977) Synergistics: An introduction. Springer-Verlag. [PÈ]Google Scholar
Hopfield, J. J. (1982) Neural networks and physical systems with emergent collective computational abilities. Proceedings of National Academy of Sciences 79:2554–58. [aJJW]CrossRefGoogle ScholarPubMed
Hopfield, J. J. (1984) Neurones with graded response have collective computational properties like those of two state neurones. Proceedings of National Academy of Science 81:3088–92. [aJJW]CrossRefGoogle Scholar
Hopfield, J. J. & Tank, D. W. (1986) Computing with neural circuits: A model. Science 233:625–33. [aJJW]CrossRefGoogle ScholarPubMed
Houk, J. (1974) Feedback control of muscle: A synthesis of the peripheral mechanisms. In: Medical physiology, 13th ed., ed. Mountcastle, V. B.. Mosby. [WJF]Google Scholar
Ikeda, K., Otsuka, K. & Matsumoto, K. (1989) Maxwell-Bloch turbulence. Progress of Theoretical Physics [Suppl.] 99:295–313. [IT]CrossRefGoogle Scholar
Ingber, L. (1981) Towards a unified brain theory. Journal of Social and Biological Structures 4:211–24. [LI]CrossRefGoogle Scholar
Ingber, L. (1982) Statistical mechanics of neocortical interactions: 1. Basic formulation. Physica D 5:83–107. [LI]CrossRefGoogle Scholar
Ingber, L. (1983) Statistical mechanics of neocortical interactions: Dynamics of synaptic modification. Physical Review A 28:395–416. [LI, PLN]CrossRefGoogle Scholar
Ingber, L. (1984a) Path-integral Riemannian contributions to nuclear Schrödinger equation. Physical Review D 29:1171–74. [LI]Google Scholar
Ingber, L. (1984b) Statistical mechanics of neocortical interactions: Derivation of shortterm-memory capacity. Physical Review A 29:3346–58. [LI]CrossRefGoogle Scholar
Ingber, L. (1984c) Statistical mechanics of nonlinear nonequilibrium financial markets. Mathematical Modelling 5:343–61. [LI]CrossRefGoogle Scholar
Ingber, L. (1985) Statistical mechanics of neocortical interactions: Stability and duration of the 7 ± 2 rule of short-term-memory capacity. Physical Review A 31:1183–86. [LI]CrossRefGoogle Scholar
Ingber, L. (1989) Very fast simulated re-annealing. Mathematical and Computer Modelling 12:967–73. [LI]CrossRefGoogle Scholar
Ingber, L. (1990) Statistical mechanical aids to calculating term structure models. Physical Review A 42:7057–64. [LI]CrossRefGoogle ScholarPubMed
Ingber, L. (1991) Statistical mechanics of neoeortical interactions: A scaling paradigm applied to electroencephalography. Physical Review A 44:4017–60. [LI]CrossRefGoogle ScholarPubMed
Ingber, L. (1992) Generic mesoscopic neural networks based on statistical mechanics of neocortical interactions. Physical Review A 45:2183–R2186. [LI]CrossRefGoogle ScholarPubMed
Ingber, L. (1993) Adaptive simulated annealing (ASA) [ftp.alumni.caltech.edu:/pub/ingber/ASA-shar, ASA-shar.Z, ASA.tar.Z, ASA.tar.gz, ASA.zip]. Lester Ingber Research. [LI]Google Scholar
Ingber, L. (1994) Statistical mechanics of neocortical interactions: Path-integral evolution of short-term memory. Physical Review E 49:4652–64. [LI]CrossRefGoogle ScholarPubMed
Ingber, L. (1995a) Statistical mechanics of multiple scales of neocortical interactions. In: Neocortical dynamics and human EEG rhythms, ed. Nunez, P. L.. Oxford University Press. [LI, PLN]Google Scholar
Ingber, L. (1995b) Statistical mechanics of neocortical interactions (SMN1). SMNI Lecture Plates. Lester Ingber Research. [LI]Google Scholar
Ingber, L. (1996a) Adaptive simulated annealing of canonical momenta indicators of financial market. Submitted. [LI]CrossRefGoogle Scholar
Ingber, L. (1996b) Trading markets with canonical momenta and adaptive simulated annealing. Submitted. [LI]Google Scholar
Ingber, L. (in press a) Statistical mechanics of neocortical interactions: Constraints on 40 Hz models of short-term memory. Physical Review E [LI]Google Scholar
Ingber, L. (in press b) Statistical mechanics of nonlinear nonequilibrium financial markets: Applications to optimized trading. Mathematical and Computer Modelling. [LI]Google Scholar
Ingber, L. (in press c) Statistical mechanics of neocortical interactions: Statistical mechanics of neoeortical interactions: Multiple scales of EEG. Electroencephalography and Clinical Neurophysiology. [LI]Google Scholar
Ingber, L. & Nunez, P. L. (1990) Multiple scales of statistical physics of neocortex: Application to electroencephalogaphy. Mathematical and Computer Modelling 13:83–95. [aJJW, LI]CrossRefGoogle Scholar
Ingber, L. & Nunez, P. L. (1995) Statistical mechanics of neocortical interactions: High resolution pathintegral calculation of short-term memory. Physical Review E 51:5074–83. [LI, PLN]CrossRefGoogle ScholarPubMed
Ingber, L., Srinivasan, R. & Nunez, P. L. (in press) Path-integral evolution of chaos embedded in noise: Duffing neocortical analog. Mathematical and Computer Modelling. [LI]Google Scholar
Joliot, M., Ribary, U. & Llinás, R. (1994) Human oscillatory brain activity near 40 Hz coexists with cognitive temporal binding. Proceedings of the National Academy of Sciences USA 91:11748–51. [EK]CrossRefGoogle ScholarPubMed
Kaneko, K. (1990a) Globally coupled chaos violates the law of large numbers. Physical Review Letters 65:1391–94. [aJJW, ZJK, IT]CrossRefGoogle ScholarPubMed
Kaneko, K. (1990b) Clustering, coding, switching, hierarchical ordering, and control in a network of chaotic elements. Physica D 41:137–72. [IT]CrossRefGoogle Scholar
Kaneko, K. (1992) Mean field fluctuation in network of chaotic elements. Physica D 55:368–84. [aJJW, IT]CrossRefGoogle Scholar
Kaplan, D. & Glass, L. (1992) Direct test for determinism in a time series. Physical Review Letters 68:427–30. [ZJK, WSP]CrossRefGoogle Scholar
Kay, L., Shimoide, K. & Freeman, W. J. (1995) Comparison of EEG time series from rat olfactory system with model composed of nonlinear coupled oscillators. International Journal of Bifurcation and Chaos 5:849–58. [IT]CrossRefGoogle Scholar
Kerszberg, M., Dehaene, S. & Changeux, J. P. (1992) Stabilization of complex input-output functions in neural clusters formed by synapse selection. Neural Networks 5:403–13. [AO]CrossRefGoogle Scholar
Kishida, K. (1982) Physical Langevin model and the time-series model in systems far from equilibrium. Physical Review A 25:496–507. [LI]CrossRefGoogle Scholar
Kishida, K. (1984) Equivalent random force and time-series model in systems far from equilibrium. Jounal of Mathematical Physics 25:1308–13. [LI]CrossRefGoogle Scholar
Kleinfeld, D. (1986) Sequential state generation by model neural networks. Proceedings of National Academy of Sciences 83:9469–73. [rJJW]CrossRefGoogle ScholarPubMed
Kowalik, Z. J., Elbert, T. & Hoke, M. (1993) Mapping brain functions: The largest Lyapunov exponents derived from multi-channel magnetoencephalography. In: Nonlinear dynamic analysis of the EEG, & Jansen, B. H. & Brandt, M. E.. Singapore: World Scientific. [ZJK]Google Scholar
Krakowska, D., Waleszczyk, W., Bekisz, M. & Wrobel, A. (1995) General 20 Hz synchronization within cortico-thalamic division of the cat's visual system shifts to specific pattern during visual attention. European Journal of Neuroscience [Suppl.] 8:38. [ZJK]Google Scholar
Langouche, F., Roekaerts, D. & Tirapegui, E. (1982) Functional integration and semiclassical expansions. Reidel. [LI]CrossRefGoogle Scholar
Langton, C. G., Taylor, C., Farmer, J. D., & Rassmussen, S., Eds. (1992) Artificial life 2: Santa Fe Institute studies in the sciences of complexity [Proceedings vol. 10]. Addison-Wesley. [arJJW]Google Scholar
Liley, D. T. J. (1995) Models of electrocortical dynamics. PhD thesis, University of Auckland, New Zealand. [rJJW]Google Scholar
liley, D. T. J. & Wright, J. J. (1994) Intracortical connectivity of pyramidal and stellate cells: Estimates of synaptic densities and coupling symmetry. Network: Computation in Neural Systems 5:175–89. [arJJW]CrossRefGoogle Scholar
Liljenström, H. (1991) Modeling the dynamics of olfactory cortex using simplified network units and relistic architecture. International Journal Systems 2:1–15. [HL]Google Scholar
Liljenström, H. & Hasselmo, M. E. (1995) Cholinergic modulation of cortical oscinamics. Journal of Neurophysiology 74:288–97. [HL]CrossRefGoogle Scholar
Liljenström, H. & Wu, X. (1995) Noise-enhanced performance in a cortical associative memory model. International Systems 6:19–29. [HL]Google Scholar
Lisman, J. E. & Idiart, M. A. P. (1995) Storage of 7 ± 2 short-term memories in oscillatory subcycles. Science 267:1512–15. [LI]CrossRefGoogle Scholar
Little, W. A. & Shaw, G. L. (1975) A statistical theory of short and long term memory. Behavioural Biology 14:115–33. [aJJW]CrossRefGoogle ScholarPubMed
Llinás, R. & Ribary, U. (1993) Coherent 40-Hz oscillation characterized dream state in humans. Proceedings of the National Academy of Sciences USA 90:2078–81. [EK]CrossRefGoogle ScholarPubMed
Lopes da Silva, F. H. & Storm van Leeuwen, W. (1978) The cortical alpha rhythm in dog: The depth and surface profile of phase. In: Architectonics of the cerebral cortex, ed. Brazier, M. A. B. & Petsche, H.. Raven. [aJJW]Google Scholar
Lopes da Silva, F. H., van Rotterdam, A., Barts, P., van Heusden, E. & Burr., B. (1976) Models of neuronal populations, the basic mechanisms of rhythmicity. Progress in Brain Research 45:282–308. [MNZ]Google ScholarPubMed
Lutzenberger, W., Elbert, T., Ray, W. J. & Birbaumer, N. (1993) The scalp distribution of the fractal dimension of the EEG and its variation with mental tasks. Brain Topography 5:27–34. [MM]CrossRefGoogle Scholar
Matsumoto, K. & Tsuda, I. 91983) Noise-induced order. Journal of Statistical Physics 31:87–106. [IT]CrossRefGoogle Scholar
McCulloch, W. S. & Pitts, W. H. (1943) A logical calculus of ideas immanent in nervous activity. Bulletin of Mathematical Biophysics 5:115–33. [HRE]CrossRefGoogle Scholar
Menon, V., Freeman, W. J., Cutillo, B. A., Desmond, J. E., Ward, M. F., Bressler, S. L., Laxer, K. D., Barbaro, N. M. & Gevins, A. S. (in press) Spatio-temporal correlations in human gamma band electroeorticograms. Electroencephalography and Clincal Neurophysiology. [WJF]Google Scholar
Miller, G. A. (1956) The magical number seven, plus or minus two. Psychology Review 63:81–97. [LI]CrossRefGoogle ScholarPubMed
Miller, K. D., Keller, J. D. & Stryker, M. P. (1989) Ocular dominance column development: Analysis and simulation. Science 245:605–15. [AO]CrossRefGoogle ScholarPubMed
Miller, R. (1975) Distribution and properties of commissural and other neurons in cat sensorimotor cortex. Journal of Comparative Neurology 164:361–74. [RM]CrossRefGoogle ScholarPubMed
Miller, R. (1989) Cortico-hippocampal interplay: Self-organizing phase-locked loops for indexing memory. Psychobiology 17:115–28. [RM]CrossRefGoogle Scholar
Miller, R. (1993) An interpretation, based on cell assembly theory, of the psychological impairments following lesions of the the hippocampus and related structures. In:The memory system of the brain: Advanced series in neuroscience, vol. 4. Singapore: World Scientific. [RM]Google Scholar
Miller, R. (1994) What is the contribution of axonal conduction delay to temporal structure in brain dynamics? In:Oscillatory event-related brain dynamics [NATO ASI Series, vol. 271], ed. Pantev, C., Elbert, T. & Lutkenhoner, B.. Plenum. [RM]Google Scholar
Miller, R. (in press) Axonal conduction time and human cerebral laterality: A psychobiological theory. Gordon and Breach. [RM]CrossRefGoogle Scholar
Minsky, M. (1993) Book review: Allen Newell, Unified theory of cognition. Artificial Intelligence 59:343–54. [EK, rJJW]Google Scholar
Miyashita, Y. (1988) Neuronal correlate of visual associative long-term memory in the primate temporal cortex. Nature 335:817–20. [aJJW]CrossRefGoogle ScholarPubMed
Miyashita, Y. & Chang, H. S. (1988) Neural correlate of pictorial short-term memory in the primate temporal cortex. Nature 331:68–70. [aJJW]CrossRefGoogle Scholar
Molnár, M. (1994) On the origin of the P3 event-related potential component. International Journal of Psychophysiology 17:129–44. [MM]CrossRefGoogle ScholarPubMed
Molnár, M. & Skinner, J. E. (1992) Low-dimensional chaos in event-related brain potentials. International Journal of Neuroscience 66:263–76. [MM]Google ScholarPubMed
Molnár, M., Skinner, J. E., Csépe, V., Winkler, I. & Karmos, G. (1995) Correlation dimension changes accompanying the occurrence of the msimatch-negativity and the P3 event-related potential component. Electroencephalography and Clinical Neurophysiology 95:118–26. [MM]CrossRefGoogle ScholarPubMed
Mühlnickel, W., Rendtorff, N., Kowalik, Z. J., Rockstroh, B., Miltner, W. & Elbert, T. (1994) Testing the determinism of EEG and MEG. lntegrative Physiological and Behavioral Science 29:260–67. [ZJK]Google ScholarPubMed
Nadal, J. P., Toulouse, G., Changeux, J. P. & Dehaene, S. (1986) Europhysics Letters 1(10):535–42. [aJJW]CrossRefGoogle Scholar
Nebenzahl, I. (1987) Recall of associated memories. Journal of Mathematical Biology 25:511–19. [aJJW]CrossRefGoogle ScholarPubMed
Nicolis, G. & Prigogine, I. (1977) Self-organization in nonequilibrium systems. Wiley-Interscience. [PÉ, IT]Google Scholar
Nunez, P. L. (1989a) Generation of human EEG by a combination of long and short range neocortical interactions. Brain Topography 1:199–215. [aJJW]CrossRefGoogle ScholarPubMed
Nunez, P. L. (1989b) Towards a physics of neocortex. In: Advanced methods of physiological systems modelling, vol. 2., ed. Marmarelis, V. Z.. Plenum. [PLN]Google Scholar
Nunez, P. L. (1995) Neocortical dynamics and human EEG rhythms. Oxford University Press. [aJJW, WJF, LI, PLN]Google Scholar
Nunez, P. L., Ed. (1981) Electric fields of the brain: The neurophysics of EEG. Oxford University Press. [aJJW, PLN]Google Scholar
Nunez, P. L., Silberstein, R. B., Cadusch, P. J., Wijesinghe, R. S., Westdorp, A. F. & Srinivasan, R. (1994) A theoretical and experimental study of high-resolution EEG based on surface Laplacians and cortical imaging. Electrocncephalography and Clinical Neurophysiology 90:40–57. [PLN]CrossRefGoogle ScholarPubMed
Nunez, P. L. & Srinivasan, R. (1993) Implications of recording strategy for estimates of neocortical dynamics with electroencephalography. Chaos 3:257–66. [aJJW]CrossRefGoogle ScholarPubMed
Oliver, A., Johnson, M. H. & Shrager, J. (1995) The emergence of hierarchical clustered representations in a Hebbian neural network model. Submitted. [AO]CrossRefGoogle Scholar
Palus, M. (1994) Nonlinearity in normal human EEG: Cycles and randomness not chaos [Santa Fe Institute publication no. 94–10–054]. Santa Fe Institute. [WSP]Google Scholar
Parisi, G. (1986a) A memory which forgets. Journal of Physics 19:L617–L620. [aJJW]Google Scholar
Parisi, G. (1986b) Asymmetric neural networks and the process of learning. Journal of Physics 19:L675–L680. [aJJW]Google Scholar
Penrose, R. (1989) The emperor's new mind. Oxford University Press. [HRE]CrossRefGoogle Scholar
Peretto, P. & Niez, J. J. (1986) Collective properties of neuronal networks. In: Disordered systems and biological organisation, ed. Bienenstock, E., Fogelman-Soulie, F. & Weisbuch, G.. Springer-Verlag. [aJJW]Google Scholar
Pfurtscheller, G. & Cooper, R. (1975) Frequency dependence of the transmission of the EEG from cortex to scalp. Electroencephalography and Clinical Neurophysiology 38:93–96. [PLN]CrossRefGoogle Scholar
picton, T. W. & Hillyard, S. A. (1988) Endogenous event related potentials. In: EEG handbook, ed. Picton, T. W.. Elsevier. [aJJW]Google Scholar
Pijn, J. P., van Neerven, J., Noest, A.& Lopes da Silva, F. H. 91991) Chaos or noise in EEG signals; dependence on state and brain site. Electroencephalography and Clincal Neurophysiology 79:371–81. [WSP]CrossRefGoogle Scholar
Pritchard, W. S., Duke, D. W. & Krieble, K. K. (1995) Dimensional analysis of resting human EEG: 2. Surrogate-data testing indicates nonlinearity but now low-dimensional chaos. Psychophysiology 32:486–91. [ZJK, WSP]CrossRefGoogle Scholar
Pritchard, W. S., Krieble, K. K. & Duke, D. W. (1995b) No effect of cigarette smoking on electroencephalographic nonlinearity. Psychopharatnacology 199:349–51. [WSP]CrossRefGoogle Scholar
Rapp, P. E., Albano, A. M., Schinah, T. I. & Farwell, L. A. (1993) Filtered noise can mimic low dimensional chaotic attractors. Physical Review E 47:2289–97. [LI]CrossRefGoogle ScholarPubMed
Rapp, P. E., Bashore, T. R., Martineire, J. M., Albano, A. M., Zimmerrman, I. D. & Mees, A. I. (1989) Dynamics of brain electrical activity. Brain Topography 2:99–118. [MM]CrossRefGoogle ScholarPubMed
Ruelle, D. (1994) Physics Today 47:24–30. [aJJW]CrossRefGoogle Scholar
Ruppeiner, G. (1995) Riemannian geometry in thermodynamic fluctuation theory. Review of Modern Physics 67:605–59. [LI]CrossRefGoogle Scholar
Sakai, K. & Miyashita, Y. (1991) Neural organisation for the long-term memory of paired associates. Nature 354:152–55. [aJJW]CrossRefGoogle ScholarPubMed
Schiff, J. S., Jerger, K., Duong, D. H., Chang, T., Spano, M. L. & Ditto, W. L. (1994) Controlling chaos in the brain. Nature 370:615–20. [aJJW]CrossRefGoogle ScholarPubMed
Schuz, A. (1994) Patchiness as a means to get a message across. Trends in Neuroscience 17:365. [RMJ]CrossRefGoogle ScholarPubMed
Shepherd, G. M. (1994) Neurobiology, 3d ed.Oxford University Press. [HRE]Google Scholar
Sholl, D. A. (1953) Dendritic organization in the neurones of the visual and motor cortices of the cat. Journal of Anatomy 87:387–407. [aJJW]Google ScholarPubMed
Silberstein, R. B. (1994) Neuromodulation of neocortical dynamics. In: Neocortical dynamics and human EEG rhythms, ed. Nunez, P. L.. Oxford University Press. [aJJW]Google Scholar
Silberstein, R. B. (1995) Neuromodulation of neocortical dynamics. In: Neocortical dynamics and human EEG rhythms, ed. Nunez, P. L.. Oxford University Press. [PLN]Google Scholar
Singer, W. (1994) Putative functions of temporal correlations in neocortical processing. In: Large-scale neuronal theories of the brain, ed. Koch, C.& Davis, J. L.. MIT Press. [rJJW]Google Scholar
Skarda, C. A. & Freeman, W. J. (1987) How brains make chaos in order to make sense of the world. Behavioral and Brain Sciences 10:161–95. [MM]CrossRefGoogle Scholar
Skinner, J. E., Molnár, M. & Tomberg, C. (1994) The point correlation dimension: Performance with nonstationaiy surrogate data and noise. lntegrative Physiological and Behavior Science 29:217–34. [MM]CrossRefGoogle ScholarPubMed
Skinner, J. E., Molnár, M., Vybiral, T. & Mitra, M. (1992) Application of chaos theory to biology and medicine. lntegrative Physiological and Behavioral Science 27:39–53. [MM]CrossRefGoogle ScholarPubMed
Steriade, M., Gloor, P., Llinas, R. R., Lopes da Silva, F. H. & Mesulam, M. M. (1990) Basic mechanisms of cerebral rhythmic activities. Electroencephalography and Clinical Neurophysiology 76:481–508. [arJJW]CrossRefGoogle ScholarPubMed
Stewart, M. & Fox, S. E. (1990) Do septal neurons pace the hippocampal theta rhythm? TINS 13:163–68. [EK]Google ScholarPubMed
Stryker, M. P. (1989) Is grandmother an oscillation? Nature 338:297–98. [aJJW]CrossRefGoogle ScholarPubMed
Swadlow, H. A. (1994) Efferent neurons and suspected interneurons in motor cortex of the awake rabbit: Axonal properties, sensory receptive fields and subthreshold synaptic inputs. Journal of Neurophysiology 71:437–53. [RM]CrossRefGoogle ScholarPubMed
Thatcher, R. W., Krause, P. J. & Hrybyk, M. (1986) Cortico-cortical associations and EEG coherence: A two-compartmental model. Electroencephalography and Clinical Neurophysiology 64:123–43. [aJJW, RM]CrossRefGoogle ScholarPubMed
Theiler, J., Eubank, S., Longtin, A., Galdrikian, B. & Farmer, J. D. (1992) Testing for nonlinearity in time series: The method of surrogate data. Physica D 58:77–94. [WSP]CrossRefGoogle Scholar
Tovee, M. J. & Rolls, E. T. (1992) Oscillatory activity is not evident in the primate temporal visual cortex. Neuroreport 3:369–72. [aJJW]CrossRefGoogle Scholar
Truesdell, C. (1969) Rational thermodynamics. McGraw-Hill. [PÉ]Google Scholar
Tsuda, I. (1991) Chaotic neural networks and thesaurus. In: Neurocomputers and attention: I. Neurobiology, synchronization and chaos, ed. Holden, A.V. & Krukov, V. I.. Manchester University. [IT]Google Scholar
Tsuda, I. (1992) Dynamic link of memory-chaotic memory maps in non-equilibrium neural networks. Neural Networks 5:313–26. [aJJW]CrossRefGoogle Scholar
Tsuda, I. (1994) Can stochastic renewal of maps be a model for cerebral cortex? Physica D 75:165–178. [aJJW]CrossRefGoogle Scholar
Tsuda, I., Koemer, E. & Shimuzu, H. (1987) Memory dynamics in asynchronous neural networks. Progress in Theoretical Physics 78:51–71. [aJJW, IT]CrossRefGoogle Scholar
Tsuda, I. & Matsumoto, K. (1984) Noise-induced order: Complexity theoretical digression. In: Chaos and statistical methods, ed. Kuramoto, Y.. Springer-Verlag. [IT]Google Scholar
Uttley, A. M. (1956) The probability of neural connexions. Proceedings of the Royal Society B 142:229–41. [aJJW]Google Scholar
van Kampen, N. G. (1976) Fluctuations in closed and open non-linear systems. In: Statistical physics, ed. Pál, L.& Szépfalusy, P.. North-Holland. [LI]Google Scholar
van Rotterdam, A., Lopes da Silva, F. H., van Den Ende, J., Veirgever, M. A. & Hermans, A. J. (1982) A model of the spatiotemporal characteristics of the alpha rhythm. Bulletin of Mathematical Biology 44:283–305. [rJJW, PLN, MJZ]CrossRefGoogle Scholar
Ventriglia, F. (1988) Computational simulation of cortical-like neural systems. Bulletin of Mathematical Biology 52:397–429. [PÉ]CrossRefGoogle Scholar
Ventriglia, F. (1990) Towards a kinetic theory of some global brain activities. Acta Neurologica 52:1–17. [PÉ]Google Scholar
Verleger, R. (1988) Event-related potentials and cognition: A critique of the context updating hypothesis and an alternative interpretation of the P3. Behavioral and Brain Sciences 11:343–427. [MM]CrossRefGoogle Scholar
Vinogradova, O. S., Brazhnik, E. S., Stafekhina, V. S. & Kitchigina, V. F. (1993) Acetylcholine, theta-rhythm and activity of hippocampus: 2. Septal input. Neuroscience 53:971–79. [EK]CrossRefGoogle Scholar
Vorobjov, N. A., Pavlik, V. D., Bakharev, B. V. & Zhadin, M. N. (1988) Spectra of electrical activity of the neocortex and hippocampus at stimulation of the reticular formation. Journal of Higher Nervous Activity 38:313–22 (in Russian). [MNZ]Google Scholar
Whittington, M. A., Traub, R. D. & Jeffreys, J. G. R. (1995) Synchronized oscillations in interneuronal networks driven by metabotropic glutamate receptor activation. Nature 373:612–15. [HRE]CrossRefGoogle ScholarPubMed
Wilczek, F. (1994) A call for a new physics. Science 266:1737–38. [LI]CrossRefGoogle Scholar
Wilson, M. A. & Bower, J. M. (1992) Cortical oscillations and temporal interactions in a computer simulation of periform cortex. Journal of Neurophysiology 67:981–95. [HL]CrossRefGoogle Scholar
Wilson, M. A. & Cowan, J. D. (1973) A mathematical theory of the functional dynamics of cortical and thalamic nervous tissue. Kybernetik 13:55–80. [aJJW, PLN]CrossRefGoogle ScholarPubMed
Wright, J. J. (1990) Reticular activation and the dynamics of neuronal networks. Biological Cybernetics 62:289–98. [aJJW]CrossRefGoogle ScholarPubMed
Wright, J. J., Kydd, R. R & Sergejew, A. A. (1990a) Autoregression models of EEG. Biological Cybernetics 62:201–10. [arJJW]CrossRefGoogle ScholarPubMed
Wright, J. J. & Liley, D. T. J. (1994) A millimetric-scale simulation of electrocortical wave dynamics based on anatomical estimates of cortical synaptic density. Network: Computation in Neural Systems 5:191–202. [aJJW]CrossRefGoogle Scholar
Wright, J. J. & Liley, D. T. J. (1995) Simulation of electrocortical waves. Biological Cybernetics 72:347–56. [arJJW]CrossRefGoogle ScholarPubMed
Wright, J. J. & Sergejew, A. A. (1991) Radial coherence, wave velocity and damping of electrocortical waves. Electroencejrfialography and Clinical Neurophysiology 79:403–12. [arJJW]CrossRefGoogle ScholarPubMed
Wright, J. J., Sergejew, A. A. & Liley, D. T. J. (1994) Computer simulation of electrocortical activity at millimetric scale. Electroencephalography and clinical Neurophysiology 90:365–75. [aJJW]CrossRefGoogle ScholarPubMed
Wright, J. J., Sergejew, A. A. & Stampfer, H. G. (1990b) Inverse filter computation of the neural impulse giving rise to the auditory evoked potential. Brain Topography 2:293–302. [aJJW]CrossRefGoogle Scholar
Wu, X. & Liljenström, H. (1994) Regulating the nonlinear dynamics of olfactory cortex. Network: Computation in Neural Systems 5:47–60. [HL]CrossRefGoogle Scholar
Yao, Y. & Freeman, W. J. (1990) Model of biological pattern recognition with spatially chaotic dynamics. Neural Networks 3(2):153–70. [HRE]CrossRefGoogle Scholar
Yeterian, E. H. & Pandya, D. N. (1988) Architectonic features of the primate brain: Implications for information processing and behavior. In: Information processing by the brain, ed. Markovich, H. J.. Hans Huber. [EK]Google Scholar
Zhadin, M. N. (1977) Model of conditioning and analysis of functional significance of electrophysiological correlates of learning. Journal of Higher Nervous Activity 27:949–56 (in Russian). [MNZ]Google Scholar
Zhadin, M. N. (1982) Theory of rhythmic processes in the cerebral cortex. Academic Press (in Russian). [MNZ]Google Scholar
Zhadin, M. N. (1984) Rhythmic processes in cerebral cortex. Journal of Theoretical Biology 108:565–95. [PLN, MNZ]CrossRefGoogle ScholarPubMed
Zhadin, M. N. (1991) Biophysical mechanisms of the EEG formation. In: Mathematical approaches to brain functioning diagnostics, ed. Dvorak, I.& Holden, A. V.. Manchester University Press. [MNZ]Google Scholar
Zhadin, M. N. (1994) Formation of rhythmic processes in the bioelectric activity of the cerebral cortex. Biophysics 39:133–50. [MNZ]Google ScholarPubMed
Zhang, G. & Simon, H. A. (1985) STM capacity for Chinese words and idioms: Chunking and acoustical loop hypotheses. Memory & Cognition 13:193–201. [LI]CrossRefGoogle ScholarPubMed