Pressure and Equilibrium States in Ergodic Theory

Chazottes, Jean-René; Keller, Gerhard

doi:10.1007/978-0-387-30440-3_414

Cited by 4 publications

(2 citation statements)

References 51 publications

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“…The supremum in (2) is taken over m ( inv ) , the set of time-translation invariant (stationary) probabilities on the set of rasters for N neurons. h is the entropy rate, see Ruelle (1969, 1978); Keller (1998); Chazottes and Keller (2009) for the general definition.…”

Section: Theoretical Frameworkmentioning

confidence: 99%

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Gibbs distribution analysis of temporal correlations structure in retina ganglion cells

Vasquez

Marre

Palacios

et al. 2012

Journal of Physiology-Paris

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We present a method to estimate Gibbs distributions with spatio-temporal constraints on spike trains statistics. We apply this method to spike trains recorded from ganglion cells of the salamander retina, in response to natural movies. Our analysis, restricted to a few neurons, performs more accurately than pairwise synchronization models (Ising) or the 1-time step Markov models (Marre et al. (2009)) to describe the statistics of spatio-temporal spike patterns and emphasizes the role of higher order spatio-temporal interactions.

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Section: Theoretical Frameworkmentioning

confidence: 99%

“…The computation of d KL ( μ, ν ) is numerically delicate but, in the present context, the following holds. For ν a time-translation invariant probability and μ a Gibbs measure with a potential ψ , one has, Keller (1998); Chazottes and Keller (2009):

d_{KL} (ν, μ) = P (ψ) - ν [ψ] - h (ν) .

…”

Section: Estimation Of Gibbs Distributionsmentioning

confidence: 99%

Gibbs distribution analysis of temporal correlations structure in retina ganglion cells

Vasquez

Marre

Palacios

et al. 2012

Journal of Physiology-Paris

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Spike Train Statistics from Empirical Facts to Theory: The Case of the Retina

Cessac

Palacios

2012

Modeling in Computational Biology and Biomedicine

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This chapter focuses on methods from statistical physics and probability theory allowing the analysis of spike trains in neural networks. Taking as an example the retina we present recent works attempting to understand how retina ganglion cells encode the information transmitted to the visual cortex via the optical nerve, by analyzing their spike train statistics. We compare the maximal entropy models used in the literature of retina spike train analysis to rigorous results establishing the exact form of spike train statistics in conductance-based Integrate-and-Fire neural networks. 1.1 Introduction Given a stimulus from the external world (e.g., visual scene, sound or smell) biological sensors at the periphery of the nervous system are able to transduce the physical manifestations of this stimulus (light emission, air pressure variations, chemical concentrations) into sequences of action potentials (spike trains), which propagate through the nervous system. Then, the brain is able to analyze those spike trains and infer crucial information on the nature of the stimulus. Critical-yet unsolved-questions in neuroscience are How is the physical signal encoded by the nervous system? How does the brain analyze the spike trains? What are the underlying computational coding principles? At the current stage of scientific knowledge, answering those questions is still a challenge for biology and computational neuroscience. Among sensory systems the retina provides functionality such as detection of movement, orientation, temporal and spatial prediction, response to flash omissions and contrast, that were up to recently viewed as the exclusive duty of higher brain centers [24]. The retina is an accessible part of the brain [15] and a prominent system to study the neurobiology and the underlying computational capacity of the neural coding. As a matter of fact, there is currently a wide research activity in understanding how the retina encodes visual information. However, basic questions are still open, such as: Are the ganglion cells (which send spikes from the eyes to the brain via the optical nerve), independent signal-encoders or are neural correlations important for coding a visual scene, and how to interpret them?

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A discrete time neural network model with spiking neurons: II: Dynamics with noise

Cessac

2010

J. Math. Biol.

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We provide rigorous and exact results characterizing the statistics of spike trains in a network of leaky Integrate-and-Fire neurons, where time is discrete and where neurons are submitted to noise, without restriction on the synaptic weights. We show the existence and uniqueness of an invariant measure of Gibbs type and discuss its properties. We also discuss Markovian approximations and relate them to the approaches currently used in computational neuroscience to analyse experimental spike trains statistics.

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Pressure and Equilibrium States in Ergodic Theory

Cited by 4 publications

References 51 publications

Gibbs distribution analysis of temporal correlations structure in retina ganglion cells

Gibbs distribution analysis of temporal correlations structure in retina ganglion cells

Spike Train Statistics from Empirical Facts to Theory: The Case of the Retina

A discrete time neural network model with spiking neurons: II: Dynamics with noise

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