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

Cessac, Bruno

doi:10.1007/s00285-010-0358-4

Cited by 42 publications

(87 citation statements)

References 44 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…It was first introduced by Cottrell (1992), studied by Fricker et al (1994) and then instantiated and studied in Asmussen and Turova (1998), Cottrell and Turova (2000) and Turova (1996Turova ( , 2000. Time-discrete versions of such systems were studied by Cessac (2008Cessac ( , 2010 with a particular focus on stationary spike distributions. In order to apply this modeling to the kind of networks of interest here, we need to define in each case the reset and the interactions random variables.…”

Section: Proposition 21mentioning

confidence: 99%

A Markovian event-based framework for stochastic spiking neural networks

Touboul

Faugeras²

2011

J Comput Neurosci

View full text Add to dashboard Cite

In spiking neural networks, the information is conveyed by the spike times, that depend on the intrinsic dynamics of each neuron, the input they receive and on the connections between neurons. In this article we study the Markovian nature of the sequence of spike times in stochastic neural networks, and in particular the ability to deduce from a spike train the next spike time, and therefore produce a description of the network activity only based on the spike times regardless of the membrane potential process. To study this question in a rigorous manner, we introduce and study an event-based description of networks of noisy integrate-and-fire neurons, i.e. that is based on the computation of the spike times. We show that the firing times of the neurons in the networks constitute a Markov chain, whose transition probability is related to the probability distribution of the interspike interval of the neurons in the network. In the cases where the Markovian model can be developed, the transition probability is explicitly derived in such classical cases of neural networks as the linear integrate-and-fire neuron models with excitatory and inhibitory interactions, for different types of synapses, possibly featuring noisy synaptic integration, transmission delays and absolute and relative refractory period. This covers most of the cases that have been investigated in the event-based description of spiking deterministic neural networks.

show abstract

Section: Proposition 21mentioning

confidence: 99%

A Markovian event-based framework for stochastic spiking neural networks

Touboul

Faugeras²

2011

J Comput Neurosci

View full text Add to dashboard Cite

show abstract

“…Some authors proposed to introduce stochasticity by adding noise terms to the potential242530313334353637, yielding the leaky stochastic integrate-and-fire (LSIF) models.…”

mentioning

confidence: 99%

Phase transitions and self-organized criticality in networks of stochastic spiking neurons

Brochini

Costa

Abadi

et al. 2016

Sci Rep

102

139

View full text Add to dashboard Cite

Phase transitions and critical behavior are crucial issues both in theoretical and experimental neuroscience. We report analytic and computational results about phase transitions and self-organized criticality (SOC) in networks with general stochastic neurons. The stochastic neuron has a firing probability given by a smooth monotonic function Φ(V) of the membrane potential V, rather than a sharp firing threshold. We find that such networks can operate in several dynamic regimes (phases) depending on the average synaptic weight and the shape of the firing function Φ. In particular, we encounter both continuous and discontinuous phase transitions to absorbing states. At the continuous transition critical boundary, neuronal avalanches occur whose distributions of size and duration are given by power laws, as observed in biological neural networks. We also propose and test a new mechanism to produce SOC: the use of dynamic neuronal gains – a form of short-term plasticity probably located at the axon initial segment (AIS) – instead of depressing synapses at the dendrites (as previously studied in the literature). The new self-organization mechanism produces a slightly supercritical state, that we called SOSC, in accord to some intuitions of Alan Turing.

show abstract

“…From a theoretical point of view, Cessac (2011) suggested the same kind of dependence from the past. In the framework of leaky integrate and fire models, he considers a system with a finite number of membrane potential processes.…”

Section: Introductionmentioning

confidence: 99%

“…It is a system with a huge (about 10 11 ) number of interacting components, the neurons. This system evolves in time, and its time evolution is not described by a Markov process (Cessac 2011). In particular, the times between successive spikes of a single neuron are not exponentially distributed (see, for instance, Brillinger 1988).…”

Section: Introductionmentioning

confidence: 99%

Infinite Systems of Interacting Chains with Memory of Variable Length—A Stochastic Model for Biological Neural Nets

2013

View full text Add to dashboard Cite

We consider a new class of non Markovian processes with a countable number of interacting components. At each time unit, each component can take two values, indicating if it has a spike or not at this precise moment. The system evolves as follows. For each component, the probability of having a spike at the next time unit depends on the entire time evolution of the system after the last spike time of the component. This class of systems extends in a non trivial way both the interacting particle systems, which are Markovian, and the stochastic chains with memory of variable length which have finite state space. These features make it suitable to describe the time evolution of biological neural systems. We construct a stationary version of the process by using a probabilistic tool which is a Kalikow-type decomposition either in random environment or in space-time. This construction implies uniqueness of the stationary process. Finally we consider the case where the interactions between components are given by a critical directed Erdös-Rényi-type random graph with a large but finite number of components. In this framework we obtain an explicit upper-bound for the correlation between successive inter-spike intervals which is compatible with previous empirical findings.

show abstract

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

Cited by 42 publications

References 44 publications

A Markovian event-based framework for stochastic spiking neural networks

A Markovian event-based framework for stochastic spiking neural networks

Phase transitions and self-organized criticality in networks of stochastic spiking neurons

Infinite Systems of Interacting Chains with Memory of Variable Length—A Stochastic Model for Biological Neural Nets

Contact Info

Product

Resources

About