MBI Publications

MBI Publications for Paul Bressloff (4)

  • A. Oster and P. Bressloff
    Laminar network model for the joint development of ocular dominance columns and CO blobs in V1
    (In Preparation)

    Abstract

  • A. Oster and P. Bressloff
    A laminar network model for the joint development of ocular dominance columns and CO blobs in V1
    (In Preparation)

    Abstract

  • P. Bressloff and A. Oster
    A theory for the alignment of cortical feature maps during development
    Phys Rev E Stat Nonlin Soft Matter PhysVol. 82 No. 2 Pt 1 (2010)

    Abstract

  • P. Bressloff and J. Newby
    Path integrals and large deviations in stochastic hybrid systems.
    Physical review. E, Statistical, nonlinear, and soft matter physicsVol. 89 No. 4 (2014) pp. 042701

    Abstract

    We construct a path-integral representation of solutions to a stochastic hybrid system, consisting of one or more continuous variables evolving according to a piecewise-deterministic dynamics. The differential equations for the continuous variables are coupled to a set of discrete variables that satisfy a continuous-time Markov process, which means that the differential equations are only valid between jumps in the discrete variables. Examples of stochastic hybrid systems arise in biophysical models of stochastic ion channels, motor-driven intracellular transport, gene networks, and stochastic neural networks. We use the path-integral representation to derive a large deviation action principle for a stochastic hybrid system. Minimizing the associated action functional with respect to the set of all trajectories emanating from a metastable state (assuming that such a minimization scheme exists) then determines the most probable paths of escape. Moreover, evaluating the action functional along a most probable path generates the so-called quasipotential used in the calculation of mean first passage times. We illustrate the theory by considering the optimal paths of escape from a metastable state in a bistable neural network.

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