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Robust transient dynamics and brain functions.

Rabinovich MI, Varona P - Front Comput Neurosci (2011)

Bottom Line: In the last few decades several concepts of dynamical systems theory (DST) have guided psychologists, cognitive scientists, and neuroscientists to rethink about sensory motor behavior and embodied cognition.Specifically, we discuss a hierarchy of coarse-grain models of mental dynamics in the form of kinetic equations of modes.The analysis of the conditions for robustness, i.e., the structural stability of transient (sequential) dynamics, give us the possibility to explain phenomena like the finite capacity of our sequential working memory - a vital cognitive function -, and to find specific dynamical signatures - different kinds of instabilities - of several brain functions and mental diseases.

View Article: PubMed Central - PubMed

Affiliation: BioCircuits Institute, University of California San Diego La Jolla, CA, USA.

ABSTRACT
In the last few decades several concepts of dynamical systems theory (DST) have guided psychologists, cognitive scientists, and neuroscientists to rethink about sensory motor behavior and embodied cognition. A critical step in the progress of DST application to the brain (supported by modern methods of brain imaging and multi-electrode recording techniques) has been the transfer of its initial success in motor behavior to mental function, i.e., perception, emotion, and cognition. Open questions from research in genetics, ecology, brain sciences, etc., have changed DST itself and lead to the discovery of a new dynamical phenomenon, i.e., reproducible and robust transients that are at the same time sensitive to informational signals. The goal of this review is to describe a new mathematical framework - heteroclinic sequential dynamics - to understand self-organized activity in the brain that can explain certain aspects of robust itinerant behavior. Specifically, we discuss a hierarchy of coarse-grain models of mental dynamics in the form of kinetic equations of modes. These modes compete for resources at three levels: (i) within the same modality, (ii) among different modalities from the same family (like perception), and (iii) among modalities from different families (like emotion and cognition). The analysis of the conditions for robustness, i.e., the structural stability of transient (sequential) dynamics, give us the possibility to explain phenomena like the finite capacity of our sequential working memory - a vital cognitive function -, and to find specific dynamical signatures - different kinds of instabilities - of several brain functions and mental diseases.

No MeSH data available.


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Representative examples of dynamical images of brain functions. (1) Rhythmic oscillations (adapted from Gloveli et al., 2005; Walling and Hicks, 2006). (2) Reproducible sequences of taste-specific switching patterns in the gustatory cortex (adapted from (Jones et al., 2007) and heteroclinic channel of saddle cycles (adapted from Rabinovich et al., 2008a). (3) Integration of different modalities – Heteroclinic Binding (Rabinovich et al., 2010a) for mutual modulation of coupled sequential dynamics. (4) Bistability and hysteresis (Jones and Hardy, 1990; Rabinovich et al., 2010b). (5) Low-frequency oscillations and modulational instability in a network with non-symmetric inhibition (WLC; Rabinovich et al., 2010b). (6) Intermittency of sequences (Rabinovich et al., 2010b).
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Figure 2: Representative examples of dynamical images of brain functions. (1) Rhythmic oscillations (adapted from Gloveli et al., 2005; Walling and Hicks, 2006). (2) Reproducible sequences of taste-specific switching patterns in the gustatory cortex (adapted from (Jones et al., 2007) and heteroclinic channel of saddle cycles (adapted from Rabinovich et al., 2008a). (3) Integration of different modalities – Heteroclinic Binding (Rabinovich et al., 2010a) for mutual modulation of coupled sequential dynamics. (4) Bistability and hysteresis (Jones and Hardy, 1990; Rabinovich et al., 2010b). (5) Low-frequency oscillations and modulational instability in a network with non-symmetric inhibition (WLC; Rabinovich et al., 2010b). (6) Intermittency of sequences (Rabinovich et al., 2010b).

Mentions: Traditional efforts in modeling dynamical phenomena in the brain are predominantly based on the premise that dynamical systems tend to converge to stable fixed points or dynamical states (limit cycles or strange attractors – see Figures 1 and 2, row 1). Active neuronal networks in some specific conditions (with symmetric reciprocal interactions) give rise to a convergent mental activity involving multiple attractors (Hopfield, 1982; Cohen and Grossberg, 1983). There may be some cognitive activities, such as associative memory (Wills et al., 2005), which fits the attractor-oriented description. However, computing with attractors generally limits the use of complex dynamical networks. Once the attractor (or its vicinity) is reached, the “dynamical” nature of the brain becomes irrelevant. Furthermore, this scheme overlooks the informational qualities of the (transient) path from the initial condition to the attractor, an important phase where the brain could exploit its remarkable repertoire of behaviors. In this short review, we discuss an alternative/complementary paradigm, i.e., brain information processing based on robust transient dynamics which is observed in experiments as a sequential switching from one metastable state to another. Following the general perspective of liquid state (Maass et al., 2002) and echo-state models (Jaeger, 2003), we illustrate this paradigm with several examples that just point out the tip of an iceberg.


Robust transient dynamics and brain functions.

Rabinovich MI, Varona P - Front Comput Neurosci (2011)

Representative examples of dynamical images of brain functions. (1) Rhythmic oscillations (adapted from Gloveli et al., 2005; Walling and Hicks, 2006). (2) Reproducible sequences of taste-specific switching patterns in the gustatory cortex (adapted from (Jones et al., 2007) and heteroclinic channel of saddle cycles (adapted from Rabinovich et al., 2008a). (3) Integration of different modalities – Heteroclinic Binding (Rabinovich et al., 2010a) for mutual modulation of coupled sequential dynamics. (4) Bistability and hysteresis (Jones and Hardy, 1990; Rabinovich et al., 2010b). (5) Low-frequency oscillations and modulational instability in a network with non-symmetric inhibition (WLC; Rabinovich et al., 2010b). (6) Intermittency of sequences (Rabinovich et al., 2010b).
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3116137&req=5

Figure 2: Representative examples of dynamical images of brain functions. (1) Rhythmic oscillations (adapted from Gloveli et al., 2005; Walling and Hicks, 2006). (2) Reproducible sequences of taste-specific switching patterns in the gustatory cortex (adapted from (Jones et al., 2007) and heteroclinic channel of saddle cycles (adapted from Rabinovich et al., 2008a). (3) Integration of different modalities – Heteroclinic Binding (Rabinovich et al., 2010a) for mutual modulation of coupled sequential dynamics. (4) Bistability and hysteresis (Jones and Hardy, 1990; Rabinovich et al., 2010b). (5) Low-frequency oscillations and modulational instability in a network with non-symmetric inhibition (WLC; Rabinovich et al., 2010b). (6) Intermittency of sequences (Rabinovich et al., 2010b).
Mentions: Traditional efforts in modeling dynamical phenomena in the brain are predominantly based on the premise that dynamical systems tend to converge to stable fixed points or dynamical states (limit cycles or strange attractors – see Figures 1 and 2, row 1). Active neuronal networks in some specific conditions (with symmetric reciprocal interactions) give rise to a convergent mental activity involving multiple attractors (Hopfield, 1982; Cohen and Grossberg, 1983). There may be some cognitive activities, such as associative memory (Wills et al., 2005), which fits the attractor-oriented description. However, computing with attractors generally limits the use of complex dynamical networks. Once the attractor (or its vicinity) is reached, the “dynamical” nature of the brain becomes irrelevant. Furthermore, this scheme overlooks the informational qualities of the (transient) path from the initial condition to the attractor, an important phase where the brain could exploit its remarkable repertoire of behaviors. In this short review, we discuss an alternative/complementary paradigm, i.e., brain information processing based on robust transient dynamics which is observed in experiments as a sequential switching from one metastable state to another. Following the general perspective of liquid state (Maass et al., 2002) and echo-state models (Jaeger, 2003), we illustrate this paradigm with several examples that just point out the tip of an iceberg.

Bottom Line: In the last few decades several concepts of dynamical systems theory (DST) have guided psychologists, cognitive scientists, and neuroscientists to rethink about sensory motor behavior and embodied cognition.Specifically, we discuss a hierarchy of coarse-grain models of mental dynamics in the form of kinetic equations of modes.The analysis of the conditions for robustness, i.e., the structural stability of transient (sequential) dynamics, give us the possibility to explain phenomena like the finite capacity of our sequential working memory - a vital cognitive function -, and to find specific dynamical signatures - different kinds of instabilities - of several brain functions and mental diseases.

View Article: PubMed Central - PubMed

Affiliation: BioCircuits Institute, University of California San Diego La Jolla, CA, USA.

ABSTRACT
In the last few decades several concepts of dynamical systems theory (DST) have guided psychologists, cognitive scientists, and neuroscientists to rethink about sensory motor behavior and embodied cognition. A critical step in the progress of DST application to the brain (supported by modern methods of brain imaging and multi-electrode recording techniques) has been the transfer of its initial success in motor behavior to mental function, i.e., perception, emotion, and cognition. Open questions from research in genetics, ecology, brain sciences, etc., have changed DST itself and lead to the discovery of a new dynamical phenomenon, i.e., reproducible and robust transients that are at the same time sensitive to informational signals. The goal of this review is to describe a new mathematical framework - heteroclinic sequential dynamics - to understand self-organized activity in the brain that can explain certain aspects of robust itinerant behavior. Specifically, we discuss a hierarchy of coarse-grain models of mental dynamics in the form of kinetic equations of modes. These modes compete for resources at three levels: (i) within the same modality, (ii) among different modalities from the same family (like perception), and (iii) among modalities from different families (like emotion and cognition). The analysis of the conditions for robustness, i.e., the structural stability of transient (sequential) dynamics, give us the possibility to explain phenomena like the finite capacity of our sequential working memory - a vital cognitive function -, and to find specific dynamical signatures - different kinds of instabilities - of several brain functions and mental diseases.

No MeSH data available.


Related in: MedlinePlus