Valentin Marc Schmutz

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Coarse-graining microscopic models of biological neural networks to obtain mesoscopic models of neural activities is an essential step towards multi-scale models of the brain. Here, we extend a recent theory for mesoscopic population dynamics with static s ...

How does reliable computation emerge from networks of noisy neurons? While individual neurons are intrinsically noisy, the collective dynamics of populations of neurons taken as a whole can be almost deterministic, supporting the hypothesis that, in the br ...

We propose a mean-field model of interacting point processes where each process has a memory of the time elapsed since its last event (age) and its recent past (leaky memory), generalizing Age-dependent Hawkes processes. The model is motivated by interacti ...

Bottom-up models of functionally relevant patterns of neural activity provide an explicit link between neuronal dynamics and computation. A prime example of functional activity patterns are propagating bursts of place-cell activities called hippocampal rep ...

Population equations for infinitely large networks of spiking neurons have a long tradition in theoret-ical neuroscience. In this work, we analyze a recent generalization of these equations to populations of finite size, which takes the form of a nonlinear ...

We study the asymptotic stability of a two-dimensional mean-field equation, which takes the form of a nonlocal transport equation and generalizes the time-elapsed neuron network model by the inclusion of a leaky memory variable. This additional variable ca ...

Can spiking neural networks (SNNs) approximate the dynamics of recurrent neural networks? Arguments in classical mean-field theory based on laws of large numbers provide a positive answer when each neuron in the network has many “duplicates”, i.e., other n ...

Valentin Marc Schmutz

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Mesoscopic population equations for spiking neural networks with synaptic short-term plasticity

Taming neuronal noise with large networks

Mean-field limit of age and leaky memory dependent Hawkes processes

Mesoscopic description of hippocampal replay and metastability in spiking neural networks with short-term plasticity

On a Finite-Size Neuronal Population Equation

Long Time Behavior of an Age- and Leaky Memory-Structured Neuronal Population Equation

Emergent Rate-Based Dynamics in Duplicate-Free Populations of Spiking Neurons