System manager scholarship

The Research, Innovation and Dissemination Center on Neuromathematics (RIDC NeuroMat) is offering scholarships for information technology professionals interested in being part of a breakthrough and innovative scientific project.

Opening for data and computational statistics scientist

The Research, Innovation and Dissemination Center on Neuromathematics (RIDC NeuroMat) is offering a scholarship for data and computational statistics scientists or professionals from related areas interested in being part of a breakthrough and innovative scientific project.

Opening for architecture and software developer

The Research, Innovation and Dissemination Center on Neuromathematics (RIDC NeuroMat) is offering a scholarship for information technology professionals interested in being part of a breakthrough and innovative scientific project.

A system of interacting neurons with short term synaptic facilitation

Antonio Galves, Eva Löcherbach, Christophe Pouzat, Errico Presutti

In this paper we present a simple microscopic stochastic model describing short term plasticity within a large homogeneous network of interacting neurons. Each neuron is represented by its membrane potential and by the residual calcium concentration within the cell at a given time. Neurons spike at a rate depending on their membrane potential. When spiking, the residual calcium concentration of the spiking neuron increases by one unit. Moreover, an additional amount of potential is given to all other neurons in the system. This amount depends linearly on the current residual calcium concentration within the cell of the spiking neuron. In between successive spikes, the potentials and the residual calcium concentrations of each neuron decrease at a constant rate.

A Result of Metastability for an Infinite System of Spiking Neurons

Morgan André

In 2018, Ferrari et al. wrote a paper called “Phase Transition for Infinite Systems of Spiking Neurons” in which they introduced a continuous time stochastic model of interacting neurons. This model consists in a countable number of neurons, each of them having an integer-valued membrane potential, which value determine the rate at which the neuron spikes. This model has also a parameter ūĚõĺ, corresponding to the rate of the leak times of the neurons, that is, the times at which the membrane potential of a given neuron is spontaneously reset to its resting value (which is 0 by convention). As its title says, it was proven in this previous article that this model presents a phase transition phenomenon with respect to ūĚõĺ. Here we prove that this model also exhibits a metastable behavior. By this we mean that if   ūĚõĺ  is small enough, then the re-normalized time of extinction of a finite version of this system converges toward an exponential random variable of mean 1 as the number of neurons goes to infinity.

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