Mind the last spike—firing rate models for mesoscopic populations of spiking neurons
T Schwalger, AV Chizhov - Current opinion in neurobiology, 2019 - Elsevier
Highlights•Generalized integrate-and-fire (GIF) models permit efficient extraction of point
neuron parameters, which reproduce the spiking behavior of multiple cell types and are …
neuron parameters, which reproduce the spiking behavior of multiple cell types and are …
Phase transitions and self-organized criticality in networks of stochastic spiking neurons
Phase transitions and critical behavior are crucial issues both in theoretical and
experimental neuroscience. We report analytic and computational results about phase …
experimental neuroscience. We report analytic and computational results about phase …
[HTML][HTML] Mean-field limit of generalized Hawkes processes
J Chevallier - Stochastic Processes and their Applications, 2017 - Elsevier
We generalize multivariate Hawkes processes mainly by including a dependence with
respect to the age of the process, ie the delay since the last point. Within this class, we …
respect to the age of the process, ie the delay since the last point. Within this class, we …
[HTML][HTML] Multi-class oscillating systems of interacting neurons
S Ditlevsen, E Löcherbach - Stochastic Processes and their Applications, 2017 - Elsevier
We consider multi-class systems of interacting nonlinear Hawkes processes modeling
several large families of neurons and study their mean field limits. As the total number of …
several large families of neurons and study their mean field limits. As the total number of …
[HTML][HTML] Mean field limits for nonlinear spatially extended Hawkes processes with exponential memory kernels
We consider spatially extended systems of interacting nonlinear Hawkes processes
modeling large systems of neurons placed in R d and study the associated mean field limits …
modeling large systems of neurons placed in R d and study the associated mean field limits …
Self-organized supercriticality and oscillations in networks of stochastic spiking neurons
Networks of stochastic spiking neurons are interesting models in the area of theoretical
neuroscience, presenting both continuous and discontinuous phase transitions. Here, we …
neuroscience, presenting both continuous and discontinuous phase transitions. Here, we …
Overview: PCA models and issues
R Fernández, PY Louis, FR Nardi - Probabilistic Cellular Automata: Theory …, 2018 - Springer
Probabilistic cellular automata (PCA) are interacting discrete stochastic dynamical systems
used as a modeling tool for a wide range of natural and societal phenomena. Their key …
used as a modeling tool for a wide range of natural and societal phenomena. Their key …
Low-dimensional firing-rate dynamics for populations of renewal-type spiking neurons
B Pietras, N Gallice, T Schwalger - Physical Review E, 2020 - APS
The macroscopic dynamics of large populations of neurons can be mathematically analyzed
using low-dimensional firing-rate or neural-mass models. However, these models fail to …
using low-dimensional firing-rate or neural-mass models. However, these models fail to …
Heterogeneous neuronal and synaptic dynamics for spike-efficient unsupervised learning: Theory and design principles
B Chakraborty, S Mukhopadhyay - arXiv preprint arXiv:2302.11618, 2023 - arxiv.org
This paper shows that the heterogeneity in neuronal and synaptic dynamics reduces the
spiking activity of a Recurrent Spiking Neural Network (RSNN) while improving prediction …
spiking activity of a Recurrent Spiking Neural Network (RSNN) while improving prediction …
Phase transition for infinite systems of spiking neurons
We prove the existence of a phase transition for a stochastic model of interacting neurons.
The spiking activity of each neuron is represented by a point process having rate 1 …
The spiking activity of each neuron is represented by a point process having rate 1 …