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Cognitive Neurodynamics
Erschienen in: Cognitive Neurodynamics 4/2008

01.12.2008 | Review

Interpreting neurodynamics: concepts and facts

verfasst von: Harald Atmanspacher, Stefan Rotter

Erschienen in: Cognitive Neurodynamics | Ausgabe 4/2008

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Abstract

The dynamics of neuronal systems, briefly neurodynamics, has developed into an attractive and influential research branch within neuroscience. In this paper, we discuss a number of conceptual issues in neurodynamics that are important for an appropriate interpretation and evaluation of its results. We demonstrate their relevance for selected topics of theoretical and empirical work. In particular, we refer to the notions of determinacy and stochasticity in neurodynamics across levels of microscopic, mesoscopic and macroscopic descriptions. The issue of correlations between neural, mental and behavioral states is also addressed in some detail. We propose an informed discussion of conceptual foundations with respect to neurobiological results as a viable step to a fruitful future philosophy of neuroscience.
Vorheriger Artikel Population based models of cortical drug response: insights from anaesthesia
Nächster Artikel Modeling brain dynamics using computational neurogenetic approach

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Fußnoten
1
Another recommended compendium of approaches in theoretical neuroscience, with historical scope, is the two-volume opus entitled Neurocomputing (Anderson and Rosenfeld 1988; Anderson et al. 1990). It offers a substantial collection of seminal papers, each introduced with contextual background by the editors, emphasizing the evolution of ideas and mutual relations between individual articles.
 
2
The notion of a neural system includes the brain, but of course it covers more. Although many of the issues addressed in the following will refer to the brain, there are additional features that exceed brain dynamics. For this reason we do, in general, refer to neurodynamics rather than brain dynamics.
 
3
The terminology is adopted from Jammer’s discussion of Heisenberg’s usage of these terms (Jammer 1974).
 
4
In physics, for instance, the mathematical formalism required for an ontic and individual description is generally different from the formalism required for an epistemic and statistical description (Atmanspacher and Primas 2003).
 
5
However, the corresponding probability distribution can also be viewed in an individual, ontic interpretation (in terms of a distribution “as a whole”), as in kinetic theory (à la Prigogine) or in classical continuum mechanics (à la Truesdell).
 
6
From the perspective of statistical modeling, the two situations are known as fixed-effect modeling (with errors) versus random-effect modeling (with variation). Within a stochastic approach, the latter case is sometimes characterized as doubly stochastic (cf. Sect. 2.3).
 
7
In quantum systems, the situation is even more subtle since ontic states are usually not dispersion-free. This must not be confused with fluctuations or statistical spreads, amounting to variations due to supposed valuations by point functions.
 
8
For a discussion of time-reversal invariant equations of motion versus invariances of their solutions see Atmanspacher et al. (2006).
 
9
We use the terms “stochasticity” and “stochastic behavior” as synonymous with “randomness” and “random behavior”, as Halmos (1986) suggested: “ ‘Stochastic’ is a learnedly elegant way of saying ‘random’ ”. The notion of randomness seems to be favored in the Russian tradition, whereas stochasticity is more frequently used in the Anglo-American terminology.
 
10
Langevin equations are linear in x; nonlinear generalizations are due to Ito and Stratonovich. The stochastic term ξ in Eq. (1) is most often considered to be uncorrelated (white) noise.
 
11
Note that Finetti (1974), in his definition of subjective probability, proposed to utilize the distinction between randomness and stochasticity in the following way. In his terminology, randomness refers to the objects of probability theory, while stochasticity refers to what is valid in the sense of probability theory. As indicated above, we use randomness and stochasticity synonymously throughout this article.
 
12
Note that, alternatively, transition matrices (of stochastic processes) are called doubly stochastic if the transition probabilities in both rows and columns are normalized. They are called uniformly stochastic if the distribution of N states is given by p i  = 1/N.
 
13
Schulmann and Gaveau (2001) discussed this issue in terms of the question of how to choose proper coarse grainings of physical state spaces.
 
14
This is often, somewhat misleadingly, called “downward causation”, cf. Sect. 2.2. Another notion, coined by Haken, is that higher-level obervables (order parameters) “enslave” lower-level observables.
 
15
In symbolic dynamics, one tries to map a lower-level dynamics of fine-grained states to the dynamics of coarser equivalence classes of states (Lind and Marcus 1991). For this purpose one needs to find a partition whose cells are invariant under the dynamics, so that their definition is robust. For nonlinear systems, such partitions (so-called generating partitions or Markov partitions) are generally inhomogeneous and not easy to find.
 
16
As a rule, this works if the number of degrees is sufficiently large or the fluctuations are sufficiently fast. For instance, moving from a mechanical two-body problem to a three-body problem does not simplify the treatment, but the extension to a many-body problem does.
 
17
As mentioned above, Haken (1983) coined the notion of the “slaving principle” for such an adiabatic elimination of fast relaxing variables. The variables that exhibit the slow high-level dynamics are often called “order parameters”. They characterize cooperative behavior of a system as a whole which constrains the motion of its components. Analogous to the mentioned example of Bénard convection, a coherent action of a neuronal assembly constrains the activity of individual neurons.
 
18
Recent work of Zumdieck et al. (2004) demonstrates that, beyond chaotic attractors, long chaotic transients may abound in complex networks.
 
19
See Sect. 3.4 for more examples of such types of dynamics and associated equivalence classes of states.
 
20
In a pivotal paper studying correlations between cells in biochemical networks, Boogerd et al. (2005) have shown that emergent systemic properties of a biochemical network depend critically on triple correlations R(A,B,C) that cannot be reduced to pairwise correlations R(A,B), R(B,C), and R(C,A).
 
21
The distinction between effective and causal models in Stephan (2004) takes this point into account.
 
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Metadaten
Titel
Interpreting neurodynamics: concepts and facts
verfasst von
Harald Atmanspacher
Stefan Rotter
Publikationsdatum
01.12.2008
Verlag
Springer Netherlands
Erschienen in
Cognitive Neurodynamics / Ausgabe 4/2008
Print ISSN: 1871-4080
Elektronische ISSN: 1871-4099
DOI
https://doi.org/10.1007/s11571-008-9067-8

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