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- Michael A. Buice, Jack D. Cowan
- Physical review. E, Statistical, nonlinear, andâ€¦
- 2007

A well-defined stochastic theory for neural activity, which permits the calculation of arbitrary statistical moments and equations governing them, is a potentially valuable tool for theoreticalâ€¦ (More)

- Michael A. Buice, Jack D. Cowan, Carson C. Chow
- Neural Computation
- 2010

Population rate or activity equations are the foundation of a common approach to modeling for neural networks. These equations provide mean field dynamics for the firing rate or activity of neuronsâ€¦ (More)

- KiJung Yoon, Michael A. Buice, Caswell Barry, Robin M. A. Hayman, Neil Burgess, Ila R. Fiete
- Nature Neuroscience
- 2013

We examined simultaneously recorded spikes from multiple rat grid cells, to explain mechanisms underlying their activity. Among grid cells with similar spatial periods, the population activity wasâ€¦ (More)

- Michael A. Buice, Jack D. Cowan
- Progress in biophysics and molecular biology
- 2009

We analyze neocortical dynamics using field theoretic methods for non-equilibrium statistical processes. Assuming the dynamics is Markovian, we introduce a model that describes both neuralâ€¦ (More)

- Michael A. Buice, Carson C. Chow
- PLoS Computational Biology
- 2013

We investigate the dynamics of a deterministic finite-sized network of synaptically coupled spiking neurons and present a formalism for computing the network statistics in a perturbative expansion.â€¦ (More)

- Michael A. Buice, Carson C. Chow
- Physical review. E, Statistical, nonlinear, andâ€¦
- 2007

The incoherent state of the Kuramoto model of coupled oscillators exhibits marginal modes in mean field theory. We demonstrate that corrections due to finite size effects render these modes stable inâ€¦ (More)

- Eric J. Hildebrand, Michael A. Buice, Carson C. Chow
- Physical review letters
- 2007

We present an approach for the description of fluctuations that are due to finite system size induced correlations in the Kuramoto model of coupled oscillators. We construct a hierarchy for theâ€¦ (More)

- Michael A. Buice, C. Channing Chow
- Journal of statistical mechanics
- 2013

Mean field theories have been a stalwart for studying the dynamics of networks of coupled neurons. They are convenient because they are relatively simple and possible to analyze. However, classicalâ€¦ (More)

- Michael A. Buice, Carson C. Chow
- Front. Comput. Neurosci.
- 2013

Much progress has been made in uncovering the computational capabilities of spiking neural networks. However, spiking neurons will always be more expensive to simulate compared to rate neuronsâ€¦ (More)

- C. Channing Chow, Michael A. Buice
- Journal of mathematical neuroscience
- 2015

Stochastic differential equations (SDEs) have multiple applications in mathematical neuroscience and are notoriously difficult. Here, we give a self-contained pedagogical review of perturbative fieldâ€¦ (More)