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- Nir Friedman, Shinya Ito, +5 authors Thomas C Butler
- Physical review letters
- 2012

The tasks of neural computation are remarkably diverse. To function optimally, neuronal networks have been hypothesized to operate near a nonequilibrium critical point. However, experimental evidence for critical dynamics has been inconclusive. Here, we show that the dynamics of cultured cortical networks are critical. We analyze neuronal network data… (More)

- R E Lee DeVille, Eric Vanden-Eijnden, Cyrill B Muratov
- Physical review. E, Statistical, nonlinear, and…
- 2005

We carefully examine two mechanisms--coherence resonance and self-induced stochastic resonance--by which small random perturbations of excitable systems with large time scale separation may lead to the emergence of new coherent behaviors in the form of limit cycles. We analyze what controls the degree of coherence in these two mechanisms and classify their… (More)

- R E Lee DeVille, Charles S Peskin
- Bulletin of mathematical biology
- 2008

We describe and analyze a model for a stochastic pulse-coupled neural network, in which the randomness in the model corresponds to synaptic failure and random external input. We show that the network can exhibit both synchronous and asynchronous behavior, and surprisingly, that there exists a range of parameters for which the network switches spontaneously… (More)

- R E Lee DeVille, Eric Vanden-Eijnden
- Biophysical journal
- 2008

It has been observed in numerical experiments that adding a cargo to a motor protein can regularize its gait. Here we explain these results via asymptotic analysis on a general stochastic motor protein model. This analysis permits a computation of various observables (e.g., the mean velocity) of the motor protein and shows that the presence of the cargo… (More)

- R E Lee Deville, Cyrill B Muratov, Eric Vanden-Eijnden
- The Journal of chemical physics
- 2006

A general mechanism is proposed by which small intrinsic fluctuations in a system far from equilibrium can result in nearly deterministic dynamical behaviors which are markedly distinct from those realized in the meanfield limit. The mechanism is demonstrated for the kinetic Monte Carlo version of the Schnakenberg reaction where we identified a scaling… (More)

- R E Lee Deville, Eric Vanden-Eijnden
- Bulletin of mathematical biology
- 2008

We investigate the origin of the regularity and synchrony which have been observed in numerical experiments of two realistic models of molecular motors, namely Fisher-Kolomeisky's model of myosin V for vesicle transport in cells and Duke's model of myosin II for sarcomere shortening in muscle contraction. We show that there is a generic organizing principle… (More)

A general mechanism is proposed by which small intrinsic fluctuations in a system far from equilibrium can result in nearly deterministic dynamical behaviors which are markedly distinct from those realized in the meanfield limit. The mechanism is demonstrated for the kinetic Monte-Carlo version of the Schnakenberg reaction where we identified a scaling… (More)

We consider a Brownian ratchet model where the particle on the ratchet is coupled to a cargo. We show that in a distinguished limit where the diffusion coefficient of the cargo is small, and the amplitude of thermal fluctuations is small, the system becomes completely coherent: the times at which the particle jumps across the teeth of the ratchet become… (More)

- R. E. L. DeVille, N. Riemer, Matthew West
- J. Comput. Physics
- 2011

Stochastic particle-resolved methods are a useful way to compute the time evolution of the multi-dimensional size distribution of atmospheric aerosol particles. An effective approach to improve the efficiency of such models is the use of weighted computational particles. Here we introduce particle weighting functions that are power laws in particle size to… (More)

- R E Lee Deville, Charles S Peskin
- Bulletin of mathematical biology
- 2012

We describe and analyze a model for a stochastic pulse-coupled neuronal network with many sources of randomness: random external input, potential synaptic failure, and random connectivity topologies. We show that different classes of network topologies give rise to qualitatively different types of synchrony: uniform (Erdős-Rényi) and "small-world" networks… (More)