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## Different levels of Ih determine distinct temporal integration in bursting and regular-spiking neurons in rat subiculum

Fonte: Blackwell Science Inc
Publicador: Blackwell Science Inc

Tipo: Artigo de Revista Científica

EN

Relevância na Pesquisa

46.77%

Pyramidal neurons in the subiculum typically display either bursting or regular-spiking behaviour. Although this classification into two neuronal classes is well described, it is unknown how these two classes of neurons contribute to the integration of input to the subiculum. Here, we report that bursting neurons posses a hyperpolarization-activated cation current (Ih) that is two-fold larger (conductance, 5.3 ± 0.5 nS) than in regular-spiking neurons (2.2 ± 0.6 nS), whereas Ih exhibits similar voltage-dependent and kinetic properties in both classes of neurons. Bursting and regular-spiking neurons display similar morphology. The difference in Ih between the two classes of neurons is not responsible for the distinct firing patterns, as neither pharmacological blockade of Ih nor enhancement of Ih using a dynamic clamp affects the qualitative firing patterns. Instead, the difference in Ih between bursting and regular-spiking neurons determines the temporal integration of evoked synaptic input from the CA1 area. In response to stimulation at 50 Hz, bursting neurons, with a large Ih, show ∼50% less temporal summation than regular-spiking neurons. The amount of temporal summation in both neuronal classes is equal after pharmacological blockade of Ih. A computer simulation model of a subicular neuron with the properties of either a bursting or a regular-spiking neuron confirmed the pivotal role of Ih in temporal integration of synaptic input. These data suggest that in the subicular network...

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## Neural Dynamics as Sampling: A Model for Stochastic Computation in Recurrent Networks of Spiking Neurons

Fonte: Public Library of Science
Publicador: Public Library of Science

Tipo: Artigo de Revista Científica

EN

Relevância na Pesquisa

46.69%

The organization of computations in networks of spiking neurons in the brain is still largely unknown, in particular in view of the inherently stochastic features of their firing activity and the experimentally observed trial-to-trial variability of neural systems in the brain. In principle there exists a powerful computational framework for stochastic computations, probabilistic inference by sampling, which can explain a large number of macroscopic experimental data in neuroscience and cognitive science. But it has turned out to be surprisingly difficult to create a link between these abstract models for stochastic computations and more detailed models of the dynamics of networks of spiking neurons. Here we create such a link and show that under some conditions the stochastic firing activity of networks of spiking neurons can be interpreted as probabilistic inference via Markov chain Monte Carlo (MCMC) sampling. Since common methods for MCMC sampling in distributed systems, such as Gibbs sampling, are inconsistent with the dynamics of spiking neurons, we introduce a different approach based on non-reversible Markov chains that is able to reflect inherent temporal processes of spiking neuronal activity through a suitable choice of random variables. We propose a neural network model and show by a rigorous theoretical analysis that its neural activity implements MCMC sampling of a given distribution...

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## Efficient Transmission of Subthreshold Signals in Complex Networks of Spiking Neurons

Fonte: Public Library of Science (PLOS)
Publicador: Public Library of Science (PLOS)

Tipo: Artigo de Revista Científica

ENG

Relevância na Pesquisa

56.39%

#Neurons#Neural networks#Synapses#Memory#Depression#Scale-free networks#Signal processing#Signaling networks

We investigate the efficient transmission and processing of weak, subthreshold signals in a realistic neural medium in the presence of different levels of the underlying noise. Assuming Hebbian weights for maximal synaptic conductances???that naturally balances the network with excitatory and inhibitory synapses???and considering short-term synaptic plasticity affecting such conductances, we found different dynamic phases in the system. This includes a memory phase where population of neurons remain synchronized, an oscillatory phase where transitions between different synchronized populations of neurons appears and an asynchronous or noisy phase. When a weak stimulus input is applied to each neuron, increasing the level of noise in the medium we found an efficient transmission of such stimuli around the transition and critical points separating different phases for well-defined different levels of stochasticity in the system. We proved that this intriguing phenomenon is quite robust, as it occurs in different situations including several types of synaptic plasticity, different type and number of stored patterns and diverse network topologies, namely, diluted networks and complex topologies such as scale-free and small-world networks. We conclude that the robustness of the phenomenon in different realistic scenarios...

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## Adaptive Reduction of Large Spiking Neurons

Fonte: Universidade Rice
Publicador: Universidade Rice

Tipo: Thesis; Text
Formato: application/pdf

Relevância na Pesquisa

66.58%

This thesis develops adaptive reduction approaches for various models of large spiking neurons. Most neurons are like dendritic trees with many branches, and they communicate by nonlinear spiking behaviors. However, with the exception of Kellems' Strong-Weak model, most existing reduction approaches compromise the active ionic mechanisms that cause the spiking dynamics. The Strong-Weak model can predict the spikes caused by suprathreshold input traveling from the dendritic branches to the spike initiation zone (SIZ), but it is not able to reproduce the back propagation from SIZ to the dendritic branches after spikes. This thesis develops a new model called QAact, the mechanisms to incorporate QAact into the hybrid model to capture the back propagation behavior, and different model reduction techniques for each part of the new hybrid model where they are most advantageous. Computational tests of QAact and the new hybrid model as well as corresponding model reduction techniques on FitzHugh-Nagumo system, active nonuniform cable, and branched cell LGMD, demonstrate a significant reduction of dimension, computational complexity and running time.

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## Macroscopic description for networks of spiking neurons

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 22/06/2015

Relevância na Pesquisa

56.69%

#Quantitative Biology - Neurons and Cognition#Condensed Matter - Disordered Systems and Neural Networks#Nonlinear Sciences - Adaptation and Self-Organizing Systems#Nonlinear Sciences - Chaotic Dynamics

A major goal of neuroscience, statistical physics and nonlinear dynamics is
to understand how brain function arises from the collective dynamics of
networks of spiking neurons. This challenge has been chiefly addressed through
large-scale numerical simulations. Alternatively, researchers have formulated
mean-field theories to gain insight into macroscopic states of large neuronal
networks in terms of the collective firing activity of the neurons, or the
firing rate. However, these theories have not succeeded in establishing an
exact correspondence between the firing rate of the network and the underlying
microscopic state of the spiking neurons. This has largely constrained the
range of applicability of such macroscopic descriptions, particularly when
trying to describe neuronal synchronization. Here we provide the derivation of
a set of exact macroscopic equations for a network of spiking neurons. Our
results reveal that the spike generation mechanism of individual neurons
introduces an effective coupling between two biophysically relevant macroscopic
quantities, the firing rate and the mean membrane potential, which together
govern the evolution of the neuronal network. The resulting equations exactly
describe all possible macroscopic dynamical states of the network...

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## Efficient transmission of subthreshold signals in complex networks of spiking neurons

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Relevância na Pesquisa

56.39%

#Physics - Biological Physics#Condensed Matter - Disordered Systems and Neural Networks#Quantitative Biology - Neurons and Cognition

We investigate the efficient transmission and processing of weak,
subthreshold signals in a realistic neural medium in the presence of different
levels of the underlying noise. Assuming Hebbian weights for maximal synaptic
conductances -- that naturally balances the network with excitatory and
inhibitory synapses -- and considering short-term synaptic plasticity affecting
such conductances, we found different dynamic phases in the system. This
includes a memory phase where population of neurons remain synchronized, an
oscillatory phase where transitions between different synchronized populations
of neurons appears and an asynchronous or noisy phase. When a weak stimulus
input is applied to each neuron, increasing the level of noise in the medium we
found an efficient transmission of such stimuli around the transition and
critical points separating different phases for well-defined different levels
of stochasticity in the system. We proved that this intriguing phenomenon is
quite robust, as it occurs in different situations including several types of
synaptic plasticity, different type and number of stored patterns and diverse
network topologies, namely, diluted networks and complex topologies such as
scale-free and small-world networks. We conclude that the robustness of the
phenomenon in different realistic scenarios...

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## Optimal Design of Minimum-Power Stimuli for Spiking Neurons

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 16/11/2010

Relevância na Pesquisa

56.67%

#Mathematics - Dynamical Systems#Mathematics - Optimization and Control#Quantitative Biology - Neurons and Cognition

In this article, we study optimal control problems of spiking neurons whose
dynamics are described by a phase model. We design minimum-power current
stimuli (controls) that lead to targeted spiking times of neurons, where the
cases with unbounded and bounded control amplitude are considered. We show that
theoretically the spiking period of a neuron, modeled by phase dynamics, can be
arbitrarily altered by a smooth control. However, if the control amplitude is
bounded, the range of possible spiking times is constrained and determined by
the bound, and feasible spiking times are optimally achieved by piecewise
continuous controls. We present analytic expressions of these minimum-power
stimuli for spiking neurons and illustrate the optimal solutions with numerical
simulations.; Comment: 8 pages, 10 figures

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## Response of electrically coupled spiking neurons: a cellular automaton approach

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 29/11/2005

Relevância na Pesquisa

56.39%

#Quantitative Biology - Neurons and Cognition#Condensed Matter - Disordered Systems and Neural Networks#Nonlinear Sciences - Cellular Automata and Lattice Gases#Physics - Biological Physics

Experimental data suggest that some classes of spiking neurons in the first
layers of sensory systems are electrically coupled via gap junctions or
ephaptic interactions. When the electrical coupling is removed, the response
function (firing rate {\it vs.} stimulus intensity) of the uncoupled neurons
typically shows a decrease in dynamic range and sensitivity. In order to assess
the effect of electrical coupling in the sensory periphery, we calculate the
response to a Poisson stimulus of a chain of excitable neurons modeled by
$n$-state Greenberg-Hastings cellular automata in two approximation levels. The
single-site mean field approximation is shown to give poor results, failing to
predict the absorbing state of the lattice, while the results for the pair
approximation are in good agreement with computer simulations in the whole
stimulus range. In particular, the dynamic range is substantially enlarged due
to the propagation of excitable waves, which suggests a functional role for
lateral electrical coupling. For probabilistic spike propagation the Hill
exponent of the response function is $\alpha=1$, while for deterministic spike
propagation we obtain $\alpha=1/2$, which is close to the experimental values
of the psychophysical Stevens exponents for odor and light intensities. Our
calculations are in qualitative agreement with experimental response functions
of ganglion cells in the mammalian retina.; Comment: 11 pages...

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## Fluctuations and information filtering in coupled populations of spiking neurons with adaptation

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Relevância na Pesquisa

56.54%

Finite-sized populations of spiking elements are fundamental to brain
function, but also used in many areas of physics. Here we present a theory of
the dynamics of finite-sized populations of spiking units, based on a
quasi-renewal description of neurons with adaptation. We derive an integral
equation with colored noise that governs the stochastic dynamics of the
population activity in response to time-dependent stimulation and calculate the
spectral density in the asynchronous state. We show that systems of coupled
populations with adaptation can generate a frequency band in which sensory
information is preferentially encoded. The theory is applicable to fully as
well as randomly connected networks, and to leaky integrate-and-fire as well as
to generalized spiking neurons with adaptation on multiple time scales.

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## On the Dynamical Complexity of Small-World Networks of Spiking Neurons

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Relevância na Pesquisa

56.32%

A computer model is described which is used to assess the dynamical
complexity of a class of networks of spiking neurons with small-world
properties. Networks are constructed by forming an initially segregated set of
highly intra-connected clusters and then applying a probabilistic rewiring
method reminiscent of the Watts-Strogatz procedure to make inter-cluster
connections. Causal density, which counts the number of independent significant
interactions among a system's components, is used to assess dynamical
complexity. This measure was chosen because it employs lagged observations, and
is therefore more sensitive to temporally smeared evidence of segregation and
integration than its alternatives. The results broadly support the hypothesis
that small-world topology promotes dynamical complexity, but reveal a narrow
parameter range within which this occurs for the network topology under
investigation, and suggest an inverse correlation with phase synchrony inside
this range.; Comment: Accepted for Physical Review E

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## Bayesian Inference with Spiking Neurons

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 19/06/2014

Relevância na Pesquisa

56.32%

Humans and other animals behave as if we perform fast Bayesian inference
underlying decisions and movement control given uncertain sense data. Here we
show that a biophysically realistic model of the subthreshold membrane
potential of a single neuron can exactly compute the numerator in Bayes rule
for inferring the Poisson parameter of a sensory spike train. A simple network
of spiking neurons can construct and represent the Bayesian posterior density
of a parameter of an external cause that affects the Poisson parameter,
accurately and in real time.

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## A theoretical basis for efficient computations with noisy spiking neurons

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 18/12/2014

Relevância na Pesquisa

56.6%

#Computer Science - Neural and Evolutionary Computing#Quantitative Biology - Neurons and Cognition#68Q10

Network of neurons in the brain apply - unlike processors in our current
generation of computer hardware - an event-based processing strategy, where
short pulses (spikes) are emitted sparsely by neurons to signal the occurrence
of an event at a particular point in time. Such spike-based computations
promise to be substantially more power-efficient than traditional clocked
processing schemes. However it turned out to be surprisingly difficult to
design networks of spiking neurons that are able to carry out demanding
computations. We present here a new theoretical framework for organizing
computations of networks of spiking neurons. In particular, we show that a
suitable design enables them to solve hard constraint satisfaction problems
from the domains of planning - optimization and verification - logical
inference. The underlying design principles employ noise as a computational
resource. Nevertheless the timing of spikes (rather than just spike rates)
plays an essential role in the resulting computations. Furthermore, one can
demonstrate for the Traveling Salesman Problem a surprising computational
advantage of networks of spiking neurons compared with traditional artificial
neural networks and Gibbs sampling. The identification of such advantage has
been a well-known open problem.; Comment: main paper: 21 pages...

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## Simulation of networks of spiking neurons: A review of tools and strategies

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Relevância na Pesquisa

56.49%

We review different aspects of the simulation of spiking neural networks. We
start by reviewing the different types of simulation strategies and algorithms
that are currently implemented. We next review the precision of those
simulation strategies, in particular in cases where plasticity depends on the
exact timing of the spikes. We overview different simulators and simulation
environments presently available (restricted to those freely available, open
source and documented). For each simulation tool, its advantages and pitfalls
are reviewed, with an aim to allow the reader to identify which simulator is
appropriate for a given task. Finally, we provide a series of benchmark
simulations of different types of networks of spiking neurons, including
Hodgkin-Huxley type, integrate-and-fire models, interacting with current-based
or conductance-based synapses, using clock-driven or event-driven integration
strategies. The same set of models are implemented on the different simulators,
and the codes are made available. The ultimate goal of this review is to
provide a resource to facilitate identifying the appropriate integration
strategy and simulation tool to use for a given modeling problem related to
spiking neural networks.; Comment: 49 pages...

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## A discrete time neural network model with spiking neurons. Rigorous results on the spontaneous dynamics

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 01/06/2007

Relevância na Pesquisa

56.32%

#Mathematics - Dynamical Systems#Nonlinear Sciences - Chaotic Dynamics#Quantitative Biology - Neurons and Cognition

We derive rigorous results describing the asymptotic dynamics of a discrete
time model of spiking neurons introduced in \cite{BMS}. Using symbolic dynamic
techniques we show how the dynamics of membrane potential has a one to one
correspondence with sequences of spikes patterns (``raster plots''). Moreover,
though the dynamics is generically periodic, it has a weak form of initial
conditions sensitivity due to the presence of a sharp threshold in the model
definition. As a consequence, the model exhibits a dynamical regime
indistinguishable from chaos in numerical experiments.; Comment: 56 pages, 1 Figure, to appear in Journal of Mathematical Biology

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## Thermodynamic Order Parameters and Statistical-Mechanical Measures for Characterization of the Burst and Spike Synchronizations of Bursting Neurons

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Relevância na Pesquisa

46.65%

#Quantitative Biology - Neurons and Cognition#Nonlinear Sciences - Chaotic Dynamics#Physics - Biological Physics

We are interested in characterization of population synchronization of
bursting neurons which exhibit both the slow bursting and the fast spiking
timescales, in contrast to spiking neurons. Population synchronization may be
well visualized in the raster plot of neural spikes which can be obtained in
experiments. The instantaneous population firing rate (IPFR) $R(t)$, which may
be directly obtained from the raster plot of spikes, is often used as a
realistic collective quantity describing population behaviors in both the
computational and the experimental neuroscience. For the case of spiking
neurons, realistic thermodynamic order parameter and statistical-mechanical
spiking measure, based on $R(t)$, were introduced in our recent work to make
practical characterization of spike synchronization. Here, we separate the slow
bursting and the fast spiking timescales via frequency filtering, and extend
the thermodynamic order parameter and the statistical-mechanical measure to the
case of bursting neurons. Consequently, it is shown in explicit examples that
both the order parameters and the statistical-mechanical measures may be
effectively used to characterize the burst and spike synchronizations of
bursting neurons.; Comment: arXiv admin note: text overlap with arXiv:1403.1255

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## Mean-Field Analysis of Orientation Selectivity in Inhibition-Dominated Networks of Spiking Neurons

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Relevância na Pesquisa

56.32%

Mechanisms underlying the emergence of orientation selectivity in the primary
visual cortex are highly debated. Here we study the contribution of
inhibition-dominated random recurrent networks to orientation selectivity, and
more generally to sensory processing. By simulating and analyzing large-scale
networks of spiking neurons, we investigate tuning amplification and contrast
invariance of orientation selectivity in these networks. In particular, we show
how selective attenuation of the common mode and amplification of the
modulation component take place in these networks. Selective attenuation of the
baseline, which is governed by the exceptional eigenvalue of the connectivity
matrix, removes the unspecific, redundant signal component and ensures the
invariance of selectivity across different contrasts. Selective amplification
of modulation, which is governed by the operating regime of the network and
depends on the strength of coupling, amplifies the informative signal component
and thus increases the signal-to-noise ratio. Here, we perform a mean-field
analysis which accounts for this process.; Comment: 19 figures

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## Frequency-Domain Order Parameters for the Burst And Spike Synchronization Transitions of Bursting Neurons

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Relevância na Pesquisa

46.75%

We are interested in characterization of synchronization transitions of
bursting neurons in the frequency domain. Instantaneous population firing rate
(IPFR) $R(t)$, which is directly obtained from the raster plot of neural
spikes, is often used as a realistic collective quantity describing population
activities in both the computational and the experimental neuroscience. For the
case of spiking neurons, a realistic time-domain order parameter, based on
$R(t)$, was introduced in our recent work to characterize the spike
synchronization transition. Unlike the case of spiking neurons, the IPFR $R(t)$
of bursting neurons exhibits population behaviors with both the slow bursting
and the fast spiking timescales. For our aim, we decompose the IPFR $R(t)$ into
the instantaneous population bursting rate $R_b(t)$ (describing the bursting
behavior) and the instantaneous population spike rate $R_s(t)$ (describing the
spiking behavior) via frequency filtering, and extend the realistic order
parameter to the case of bursting neurons. Thus, we develop the
frequency-domain bursting and spiking order parameters which are just the
bursting and spiking "coherence factors" $\beta_b$ and $\beta_s$ of the
bursting and spiking peaks in the power spectral densities of $R_b$ and $R_s$
(i.e....

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## Distribution of Orientation Selectivity in Recurrent Networks of Spiking Neurons with Different Random Topologies

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Relevância na Pesquisa

56.36%

Neurons in the primary visual cortex are more or less selective for the
orientation of a light bar used for stimulation. A broad distribution of
individual grades of orientation selectivity has in fact been reported in all
species. A possible reason for emergence of broad distributions is the
recurrent network within which the stimulus is being processed. Here we compute
the distribution of orientation selectivity in randomly connected model
networks that are equipped with different spatial patterns of connectivity. We
show that, for a wide variety of connectivity patterns, a linear theory based
on firing rates accurately approximates the outcome of direct numerical
simulations of networks of spiking neurons. Distance dependent connectivity in
networks with a more biologically realistic structure does not compromise our
linear analysis, as long as the linearized dynamics, and hence the uniform
asynchronous irregular activity state, remain stable. We conclude that linear
mechanisms of stimulus processing are indeed responsible for the emergence of
orientation selectivity and its distribution in recurrent networks with
functionally heterogeneous synaptic connectivity.; Comment: 12 figures

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## Generalized activity equations for spiking neural network dynamics

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Relevância na Pesquisa

46.67%

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 neurons because of the inherent disparity in time
scales - the spike duration time is much shorter than the inter-spike time,
which is much shorter than any learning time scale. In numerical analysis, this
is a classic stiff problem. Spiking neurons are also much more difficult to
study analytically. One possible approach to making spiking networks more
tractable is to augment mean field activity models with some information about
spiking correlations. For example, such a generalized activity model could
carry information about spiking rates and correlations between spikes
self-consistently. Here, we will show how this can be accomplished by
constructing a complete formal probabilistic description of the network and
then expanding around a small parameter such as the inverse of the number of
neurons in the network. The mean field theory of the system gives a rate-like
description. The first order terms in the perturbation expansion keep track of
covariances.

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## Modeling networks of spiking neurons as interacting processes with memory of variable length

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 23/02/2015

Relevância na Pesquisa

56.32%

We consider a new class of non Markovian processes with a countable number of
interacting components, both in discrete and continuous time. Each component is
represented by a point process indicating if it has a spike or not at a given
time. The system evolves as follows. For each component, the rate (in
continuous time) or the probability (in discrete time) of having a spike
depends on the entire time evolution of the system since the last spike time of
the component. In discrete time this class of systems extends in a non trivial
way both Spitzer's interacting particle systems, which are Markovian, and
Rissanen's stochastic chains with memory of variable length which have finite
state space. In continuous time they can be seen as a kind of Rissanen's
variable length memory version of the class of self-exciting point processes
which are also called "Hawkes processes", however with infinitely many
components. These features make this class a good candidate to describe the
time evolution of networks of spiking neurons. In this article we present a
critical reader's guide to recent papers dealing with this class of models,
both in discrete and in continuous time. We briefly sketch results concerning
perfect simulation and existence issues...

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