Psychophysiological correlations form the basis for different medical and scientific disciplines, but the nature of this relation has not yet been fully understood. One conceptual option is to understand the mental as “emerging” from neural processes in the specific sense that psychology and physiology provide two different descriptions of the same system. Stating these descriptions in terms of coarser- and finer-grained system states (macro- and microstates), the two descriptions may be equally adequate if the coarse-graining preserves the possibility to obtain a dynamical rule for the system. To test the empirical viability of our approach, we describe an algorithm to obtain a specific form of such a coarse-graining from data, and illustrate its operation using a simulated dynamical system. We then apply the method to an electroencephalographic recording, where we are able to identify macrostates from the physiological data that correspond to mental states of the subject.
REFERENCES
1.
Adler
, R. L.
, “Symbolic dynamics and Markov partitions
,” Bull., New Ser., Am. Math. Soc.
35
, 1
(1998
).2.
Allefeld
, C.
and Bialonski
, S.
, “Detecting synchronization clusters in multivariate time series via coarse-graining of Markov chains
,” Phys. Rev. E
76
, 066207
(2007
).3.
The American Electroencephalographic Society
, “Guidelines for standard electrode position nomenclature
,” J. Clin. Neurophysiol.
8
, 200
(1991
).4.
Ashby
, W. R.
, “Principles of the self-organizing system
,” in Principles of Self-Organization: Transactions of the University of Illinois Symposium
, edited by H.
von Foerster
and G. W.
Zopf
, Jr. (Pergamon
, Oxford
, 1962
), pp. 255
–278
.5.
Atmanspacher
, H.
and beim Graben
, P.
, “Contextual emergence of mental states from neurodynamics
,” Chaos Complexity Lett.
2
, 151
(2007
).6.
Beckermann
, A.
, Flohr
, H.
, and Kim
, J.
, Emergence or Reduction?
(de Gruyter
, New York
, 1992
).7.
Bishop
, R. C.
and Atmanspacher
, H.
, “Contextual emergence in the description of properties
,” Found. Phys.
36
, 1753
, 2006
.8.
Bollt
, E. M.
and Skufca
, J. D.
, “Markov partitions
,” in Encyclopedia of Nonlinear Science
, edited by A.
Scott
(Routledge
, New York
, 2005
).9.
10.
Chalmers
, D. J.
, “What is a neural correlate of consciousness?
,” in Neural Correlates of Consciousness: Empirical and Conceptual Questions
, edited by T.
Metzinger
(MIT
, Cambridge
, 2000
).11.
Chan
, K.-S.
and Tong
, H.
, Chaos: A Statistical Perspective
(Springer
, Berlin
, 2001
).12.
Darley
, V.
, “Emergent phenomena and complexity
,” in Artificial Life IV
, edited by R. A.
Brooks
and P.
Maes
(MIT Press
, Cambridge
, 1994
), pp. 411
–416
.13.
Deuflhard
, P.
and Weber
, M.
, “Robust Perron cluster analysis in conformation dynamics
,” Linear Algebr. Appl.
398
, 161
(2005
).14.
Feller
, W.
, An Introduction to Probability Theory and Its Applications
, 3rd ed. (Wiley
, New York
, 1968
), Vol. I
.15.
Froyland
, G.
, “Statistically optimal almost-invariant sets
,” Physica D
200
, 205
(2005
).16.
Feudel
, U.
, “Complex dynamics in multistable systems
,” Int. J. Bifurcation Chaos Appl. Sci. Eng.
18
, 1607
(2008
).17.
18.
Gaveau
, B.
and Schulman
, L. S.
, “Dynamical distance: Coarse grains, pattern recognition, and network analysis
,” Bull. Sci. Math.
129
, 631
(2005
).19.
Kantz
, H.
and Schreiber
, T.
, Nonlinear Time Series Analysis
(Cambridge University Press
, Cambridge
, 1997
).20.
Kim
, J.
, Supervenience and Mind
(Cambridge University Press
, Cambridge
, 1993
).21.
Lehmann
, D.
, “Multichannel topography of human alpha EEG fields
,” Electroencephalogr. Clin. Neurophysiol.
31
, 439
(1971
).22.
Lehmann
, D.
, “Principles of spatial analysis
,” in Methods of Analysis of Brain Electrical and Magnetic Signals
, edited by A. S.
Gevins
and A.
Rémond
(Elsevier
, New York
, 1987
), pp. 309
–354
23.
Lehmann
D.
, Ozaki
, H.
, and Pal
, I.
, “EEG alpha map series: Brain microstates by space-oriented adaptive segmentation
,” Electroencephalogr. Clin. Neurophysiol.
67
, 271
(1987
).24.
25.
Maturana
, H. R.
and Varela
, F. J.
, Autopoiesis and Cognition: The Realization of the Living
(Reidel
, Dordrecht
, 1980
).26.
Niedermeyer
, E.
, “Abnormal EEG patterns: Epileptic and paroxysmal
,” in Electroencephalography: Basic Principles, Clinical Applications and Related Fields
, 3rd ed. (Williams & Wilkins
, New York
, 1993
), pp. 217
–240
.27.
O’Connor
, T.
and Wong
, H. Y.
, “Emergent properties
,” in The Stanford Encyclopedia of Philosophy
, edited by E. N.
Zalta
(Winter 2006
), http://plato.stanford.edu/archives/win2006/entries/properties-emergent/.28.
Paluš
, M.
, “Nonlinearity in normal human EEG: Cycles, temporal asymmetry, nonstationarity and randomness, not chaos
,” Biol. Cybern.
75
, 389
(1996
).29.
Robinson
, C.
, Dynamical Systems. Stability, Symbolic Dynamics, and Chaos
(CRC
, Boca Raton
, 1995
).30.
Seth
, A. K.
, “Measuring emergence via nonlinear Granger causality
,” in Artificial Life XI: Proceedings of the Eleventh International Conference on the Simulation and Synthesis of Living Systems
, edited by S.
Bullock
et al. (MIT
, Cambridge
, 2008
), pp. 545
–553
.31.
Shalizi
, C. R.
and Moore
, C.
, “What is a macrostate? Subjective observations and objective dynamics
,” preprint 2008
, arXiv:cond-mat/0303625.32.
Stephan
, A.
, “Emergentism, irreducibility, and downward causation
,” Grazer Philosophische Studien
65
, 77
(2002
).33.
Takens
, F.
, “Detecting strange attractors in turbulence
,” in Dynamical Systems and Turbulence
, edited by D. A.
Rand
and L. S.
Young
(Springer
, Berlin
, 1981
), pp. 366
–381
.34.
Theiler
, J.
and Rapp
, E.
, “Re-examination of the evidence for low-dimensional, nonlinear structure in the human electroencephalogram
,” Electroencephalogr. Clin. Neurophysiol.
98
, 213
(1996
).35.
36.
Wackermann
, J.
, “Segmentation of EEG map series in -dimensional state space
,” Brain Topogr.
6
, 246
(1994
).© 2009 American Institute of Physics.
2009
American Institute of Physics
You do not currently have access to this content.
