631 research outputs found
Macroscopic equations governing noisy spiking neuronal populations
At functional scales, cortical behavior results from the complex interplay of
a large number of excitable cells operating in noisy environments. Such systems
resist to mathematical analysis, and computational neurosciences have largely
relied on heuristic partial (and partially justified) macroscopic models, which
successfully reproduced a number of relevant phenomena. The relationship
between these macroscopic models and the spiking noisy dynamics of the
underlying cells has since then been a great endeavor. Based on recent
mean-field reductions for such spiking neurons, we present here {a principled
reduction of large biologically plausible neuronal networks to firing-rate
models, providing a rigorous} relationship between the macroscopic activity of
populations of spiking neurons and popular macroscopic models, under a few
assumptions (mainly linearity of the synapses). {The reduced model we derive
consists of simple, low-dimensional ordinary differential equations with}
parameters and {nonlinearities derived from} the underlying properties of the
cells, and in particular the noise level. {These simple reduced models are
shown to reproduce accurately the dynamics of large networks in numerical
simulations}. Appropriate parameters and functions are made available {online}
for different models of neurons: McKean, Fitzhugh-Nagumo and Hodgkin-Huxley
models
Scaling of a large-scale simulation of synchronous slow-wave and asynchronous awake-like activity of a cortical model with long-range interconnections
Cortical synapse organization supports a range of dynamic states on multiple
spatial and temporal scales, from synchronous slow wave activity (SWA),
characteristic of deep sleep or anesthesia, to fluctuating, asynchronous
activity during wakefulness (AW). Such dynamic diversity poses a challenge for
producing efficient large-scale simulations that embody realistic metaphors of
short- and long-range synaptic connectivity. In fact, during SWA and AW
different spatial extents of the cortical tissue are active in a given timespan
and at different firing rates, which implies a wide variety of loads of local
computation and communication. A balanced evaluation of simulation performance
and robustness should therefore include tests of a variety of cortical dynamic
states. Here, we demonstrate performance scaling of our proprietary Distributed
and Plastic Spiking Neural Networks (DPSNN) simulation engine in both SWA and
AW for bidimensional grids of neural populations, which reflects the modular
organization of the cortex. We explored networks up to 192x192 modules, each
composed of 1250 integrate-and-fire neurons with spike-frequency adaptation,
and exponentially decaying inter-modular synaptic connectivity with varying
spatial decay constant. For the largest networks the total number of synapses
was over 70 billion. The execution platform included up to 64 dual-socket
nodes, each socket mounting 8 Intel Xeon Haswell processor cores @ 2.40GHz
clock rates. Network initialization time, memory usage, and execution time
showed good scaling performances from 1 to 1024 processes, implemented using
the standard Message Passing Interface (MPI) protocol. We achieved simulation
speeds of between 2.3x10^9 and 4.1x10^9 synaptic events per second for both
cortical states in the explored range of inter-modular interconnections.Comment: 22 pages, 9 figures, 4 table
Optimality Model of Unsupervised Spike-Timing Dependent Plasticity: Synaptic Memory and Weight Distribution
We studied the hypothesis that synaptic dynamics is controlled by three basic principles: (1) synapses adapt their weights so that neurons can effectively transmit information, (2) homeostatic processes stabilize the mean firing rate of the postsynaptic neuron, and (3) weak synapses adapt more slowly than strong ones, while maintenance of strong synapses is costly. Our results show that a synaptic update rule derived from these principles shares features, with spike-timing-dependent plasticity, is sensitive to correlations in the input and is useful for synaptic memory. Moreover, input selectivity (sharply tuned receptive fields) of postsynaptic neurons develops only if stimuli with strong features are presented. Sharply tuned neurons can coexist with unselective ones, and the distribution of synaptic weights can be unimodal or bimodal. The formulation of synaptic dynamics through an optimality criterion provides a simple graphical argument for the stability of synapses, necessary for synaptic memory
A Model of Stimulus-Specific Neural Assemblies in the Insect Antennal Lobe
It has been proposed that synchronized neural assemblies in the antennal lobe of insects encode the identity of olfactory stimuli. In response to an odor, some projection neurons exhibit synchronous firing, phase-locked to the oscillations of the field potential, whereas others do not. Experimental data indicate that neural synchronization and field oscillations are induced by fast GABAA-type inhibition, but it remains unclear how desynchronization occurs. We hypothesize that slow inhibition plays a key role in desynchronizing projection neurons. Because synaptic noise is believed to be the dominant factor that limits neuronal reliability, we consider a computational model of the antennal lobe in which a population of oscillatory neurons interact through unreliable GABAA and GABAB inhibitory synapses. From theoretical analysis and extensive computer simulations, we show that transmission failures at slow GABAB synapses make the neural response unpredictable. Depending on the balance between GABAA and GABAB inputs, particular neurons may either synchronize or desynchronize. These findings suggest a wiring scheme that triggers stimulus-specific synchronized assemblies. Inhibitory connections are set by Hebbian learning and selectively activated by stimulus patterns to form a spiking associative memory whose storage capacity is comparable to that of classical binary-coded models. We conclude that fast inhibition acts in concert with slow inhibition to reformat the glomerular input into odor-specific synchronized neural assemblies
The Effect of Nonstationarity on Models Inferred from Neural Data
Neurons subject to a common non-stationary input may exhibit a correlated
firing behavior. Correlations in the statistics of neural spike trains also
arise as the effect of interaction between neurons. Here we show that these two
situations can be distinguished, with machine learning techniques, provided the
data are rich enough. In order to do this, we study the problem of inferring a
kinetic Ising model, stationary or nonstationary, from the available data. We
apply the inference procedure to two data sets: one from salamander retinal
ganglion cells and the other from a realistic computational cortical network
model. We show that many aspects of the concerted activity of the salamander
retinal neurons can be traced simply to the external input. A model of
non-interacting neurons subject to a non-stationary external field outperforms
a model with stationary input with couplings between neurons, even accounting
for the differences in the number of model parameters. When couplings are added
to the non-stationary model, for the retinal data, little is gained: the
inferred couplings are generally not significant. Likewise, the distribution of
the sizes of sets of neurons that spike simultaneously and the frequency of
spike patterns as function of their rank (Zipf plots) are well-explained by an
independent-neuron model with time-dependent external input, and adding
connections to such a model does not offer significant improvement. For the
cortical model data, robust couplings, well correlated with the real
connections, can be inferred using the non-stationary model. Adding connections
to this model slightly improves the agreement with the data for the probability
of synchronous spikes but hardly affects the Zipf plot.Comment: version in press in J Stat Mec
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