Neurochemical networks, nonlinear systems and functional neuroimaging |
Ad J. Dekker, January 2002
Contents:
General
introduction.
Chapter 1: Neurochemical networks as a description of
brain processes.
Chapter 2: Functional neuroimaging beyond anatomical
localization: a system theoretical perspective.
Chapter 3:
Gauging the number of variables in a description of brain processes: levels of
abstraction.
Chapter 4: Psychological interpretation of system
behavior.
Chapter 5: Successive formation of energy basins as a
model for transfer effects in learning.
General
introduction.
This series of five chapters forms an updated version of a report for the Delft University of Technology (Dekker 1998). The aim of this work is to provide a description of brain functioning with as few assumptions as possible.
Chapter 1 describes a synthesis between neural networks and biochemical networks. The resulting neurochemical networks are more general than reaction-diffusion systems. The description makes no assumptions as to the anatomy and allows biochemical contacts (‘biochemical synapes’), plasticity through altered reaction kinetics and higher-order contacts between locations.
Chapter 2 discusses the measuring of neurochemical variables through functional neuroimaging. The assumption of functional localization – that is made either implicitly or explicitly in neuroimaging studies - can be self-fulfilling. Since functions can be dynamically allocated to brain structures it is necessary to use phase-space localization (and include time-derivatives of the variables). With low temporal resolution only the more static aspects of the neurochemical network can be detected. However, these include qualitatively interesting measures of gradient dynamics such as the extrema of an energy landscape and the uphill part along a trajectory in such a landscape.
Chapter 3 deals with the question how detailed a description should be, i.e. how many variables should be measured. It introduces a definition of admissible levels of abstraction on the basis of graph theory and discusses ways to assess dynamical independence between variables and division into subsystems for nonlinear systems.
In Chapter 4 system-theoretical terms are given a psychological interpretation. This amounts to describing the psychology of an arbitrary system. Approaching an attractor is interpreted as recognition. Whereas this has been described for neural networks and point attractors, the present discussion is more general and includes higher-dimensional attractors, regions of attraction and transient attractors. A distinction is made between Hamiltonian and gradient dynamics. The clustering of observed states can be used to map out regions of attraction (gradient dynamics). In the original report (Dekker 1998) measures are given for cluster development. It is postulated that Hamiltonian dynamics are not used for the attribution of meaning to input and can be considered automatic processing. Finally, the discussion results in an alternative explanation for the timing of event-related potentials.
Chapter 5 gives a simple geometrical description of regions of attraction. Different measures for change in such a region predict different transfer effects in concept formation.
Reference.
Dekker A. J. (1998): Neurochemical
networks, nonlinear systems and functional neuroimaging. Faculty report
Technical informatics and mathematics, Delft University of Technology.
Practical information.
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Reference to this work: Dekker A. J. (2002): Neurochemical networks, nonlinear systems and functional neuroimaging. Http://www.home.zonnet.nl/dekker.aj/index.htm.
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Acknowledgements.
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