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We continue the work of a series of previous studies of a mathematical model that describes the mean-field limit behavior of a homogeneous network of excitatory point spiking neurons. Contrary to other models, here noise is intrinsic to the…
Neurons and networks in the cerebral cortex must operate reliably despite multiple sources of noise. To evaluate the impact of both input and output noise, we determine the robustness of single-neuron stimulus selective responses, as well…
The activity of a neural network is defined by patterns of spiking and silence from the individual neurons. Because spikes are (relatively) sparse, patterns of activity with increasing numbers of spikes are less probable, but with more…
The continuous integration of experimental data into coherent models of the brain is an increasing challenge of modern neuroscience. Such models provide a bridge between structure and activity, and identify the mechanisms giving rise to…
Recent remarkable advances in the experimental techniques have provided a background for inferring neuronal couplings from point process data that includes a great number of neurons. Here, we propose a systematic procedure for pre- and…
Synchronized oscillations in networks of inhibitory and excitatory coupled bursting neurons are common in a variety of neural systems from central pattern generators to human brain circuits. One example of the latter is the subcortical…
Cortical activity in-vivo displays relaxational time scales much longer than the membrane time constant of the neurons or the deactivation time of ionotropic synaptic conductances. The mechanisms responsible for such slow dynamics are not…
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…
Simulation speed matters for neuroscientific research: this includes not only how quickly the simulated model time of a large-scale spiking neuronal network progresses, but also how long it takes to instantiate the network model in computer…
In the classic view of cortical rhythms, the interaction between excitatory pyramidal neurons (E) and inhibitory parvalbumin neurons (I) has been shown to be sufficient to generate gamma and beta band rhythms. However, it is now clear that…
For energy-efficient computation in specialized neuromorphic hardware, we present spiking neural coding, an instantiation of a family of artificial neural models grounded in the theory of predictive coding. This model, the first of its…
We analyze the collective dynamics of hierarchically structured networks of densely connected spiking neurons. These networks of sub-networks may represent interactions between cell assemblies or different nuclei in the brain. The dynamical…
We present a formal, mathematical foundation for modeling and reasoning about the behavior of $synchronous$, $stochastic$ $Spiking$ $Neural$ $Networks$ $(SNNs)$, which have been widely used in studies of neural computation. Our approach…
Neurophysiologists are nowadays able to record from a large number of extracellular electrodes and to extract, from the raw data, the sequences of action potentials or spikes generated by many neurons. Unfortunately these ''many neurons''…
The synergy between spiking neural networks and neuromorphic hardware holds promise for the development of energy-efficient AI applications. Inspired by this potential, we revisit the foundational aspects to study the capabilities of…
Correlations are employed in modern physics to explain microscopic and macroscopic phenomena, like the fractional quantum Hall effect and the Mott insulator state in high temperature superconductors and ultracold atoms. Simultaneously…
Stimulus from the environment that guides behavior and informs decisions is encoded in the firing rates of neural populations. Each neuron in the populations, however, does not spike independently: spike events are correlated from cell to…
In this paper, we build a model for biological neural nets where the activity of the network is described by Hawkes processes having a variable length memory. The particularity of this paper is to deal with an infinite number of components.…
The characterization of coordinated activity in neuronal populations has received renewed interest in the light of advancing experimental techniques which allow recordings from multiple units simultaneously. Across both in vitro and in vivo…
This paper predicts the ability to externally control the firing times of a cortical neuron whose behavior follows the Izhikevich neuron model. The Izhikevich neuron model provides an efficient and biologically plausible method to track a…