6,117 research outputs found
Stochastic neural field theory and the system-size expansion
We analyze a master equation formulation of stochastic neurodynamics for a network of synaptically coupled homogeneous neuronal populations each consisting of N identical neurons. The state of the network is specified by the fraction of active or spiking neurons in each population, and transition rates are chosen so that in the thermodynamic or deterministic limit (N → ∞) we recover standard activity–based or voltage–based rate models. We derive the lowest order corrections to these rate equations for large but finite N using two different approximation schemes, one based on the Van Kampen system-size expansion and the other based on path integral methods. Both methods yield the same series expansion of the moment equations, which at O(1/N ) can be truncated to form a closed system of equations for the first and second order moments. Taking a continuum limit of the moment equations whilst keeping the system size N fixed generates a system of integrodifferential equations for the mean and covariance of the corresponding stochastic neural field model. We also show how the path integral approach can be used to study large deviation or rare event statistics underlying escape from the basin of attraction of a stable fixed point of the mean–field dynamics; such an analysis is not possible using the system-size expansion since the latter cannot accurately\ud
determine exponentially small transitions
Path mutual information for a class of biochemical reaction networks
Living cells encode and transmit information in the temporal dynamics of
biochemical components. Gaining a detailed understanding of the input-output
relationship in biological systems therefore requires quantitative measures
that capture the interdependence between complete time trajectories of
biochemical components. Mutual information provides such a measure but its
calculation in the context of stochastic reaction networks is associated with
mathematical challenges. Here we show how to estimate the mutual information
between complete paths of two molecular species that interact with each other
through biochemical reactions. We demonstrate our approach using three simple
case studies.Comment: 6 pages, 2 figure
Life-Space Foam: a Medium for Motivational and Cognitive Dynamics
General stochastic dynamics, developed in a framework of Feynman path
integrals, have been applied to Lewinian field--theoretic psychodynamics,
resulting in the development of a new concept of life--space foam (LSF) as a
natural medium for motivational and cognitive psychodynamics. According to LSF
formalisms, the classic Lewinian life space can be macroscopically represented
as a smooth manifold with steady force-fields and behavioral paths, while at
the microscopic level it is more realistically represented as a collection of
wildly fluctuating force-fields, (loco)motion paths and local geometries (and
topologies with holes). A set of least-action principles is used to model the
smoothness of global, macro-level LSF paths, fields and geometry. To model the
corresponding local, micro-level LSF structures, an adaptive path integral is
used, defining a multi-phase and multi-path (multi-field and multi-geometry)
transition process from intention to goal-driven action. Application examples
of this new approach include (but are not limited to) information processing,
motivational fatigue, learning, memory and decision-making.Comment: 25 pages, 2 figures, elsar
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