71 citations · 90 across the 7 of their papers we have counts for
7 papers
Pattern Formation in a Spiking Neural-Field of Renewal Neurons
Gregory Dumont, Carmen Oana Tarniceriu
Elucidating the neurophysiological mechanisms underlying neural pattern formation remains an outstanding challenge in Computational Neuroscience. In this paper, we address the issu…
Adjoint Method for Macroscopic Phase-Resetting Curves of Generic Spiking Neural Networks
Gregory Dumont, Alberto Pérez-Cervera, Boris Gutkin
Brain rhythms emerge as a result of synchronization among interconnected spiking neurons. Key properties of such rhythms can be gleaned from the phase-resetting curve (PRC). Inferr…
Macroscopic phase resetting-curves determine oscillatory coherence and signal transfer in inter-coupled neural circuits
Gregory Dumont, Boris Gutkin
Macroscopic oscillations of different brain regions show multiple phase relationships that are persistent across time and have been implicated routing information. Various cellular…
The mean-field equation of a leaky integrate-and-fire neural network: measure solutions and steady states
Grégory Dumont, Pierre Gabriel
Neural network dynamics emerge from the interaction of spiking cells. One way to formulate the problem is through a theoretical framework inspired by ideas coming from statistical…
A theoretical connection between the noisy leaky integrate-and-fire and escape rate models: the non-autonomous case
Grégory Dumont, Jacques Henry, Carmen Oana Tarniceriu
One of the most important challenges in mathematical neuroscience is to properly illustrate the stochastic nature of neurons. Among different approaches, the noisy leaky integrate-…
Theoretical connections between mathematical neuronal models corresponding to different expressions of noise
Grégory Dumont, Jacques Henry, Carmen Oana Tarniceriu
Identifying the right tools to express the stochastic aspects of neural activity has proven to be one of the biggest challenges in computational neuroscience. Even if there is no d…
Noisy threshold in neuronal models: connections with the noisy leaky integrate-and-fire model
Grégory Dumont, Jacques Henry, Carmen Oana Tarniceriu
Providing an analytical treatment to the stochastic feature of neurons' dynamics is one of the current biggest challenges in mathematical biology. The noisy leaky integrate-and-fir…