Publications (9)
Nonlinear partial differential equations in neuroscience: from modelling to mathematical theory
José A Carrillo, Pierre Roux
Many systems of partial differential equations have been proposed as simplified representations of complex collective behaviours in large networks of neurons. In this survey, we br…
Global-in-time classical solutions and qualitative properties for the NNLIF neuron model with synaptic delay
MarÃa J. Cáceres, Pierre Roux, Delphine Salort +1
The Nonlinear Noisy Leaky Integrate and Fire (NNLIF) model is widely used to describe the dynamics of neural networks after a diffusive approximation of the mean-field limit of a s…
Noise-driven bifurcations in a nonlinear Fokker-Planck system describing stochastic neural fields
José A. Carrillo, Pierre Roux, Susanne Solem
The existence and characterisation of noise-driven bifurcations from the spatially homogeneous stationary states of a nonlinear, non-local Fokker--Planck type partial differential…
The Llama 3 Herd of Models
Aaron Grattafiori, Abhimanyu Dubey, Abhinav Jauhri +556
Modern artificial intelligence (AI) systems are powered by foundation models. This paper presents a new set of foundation models, called Llama 3. It is a herd of language models th…
A hyperbolic-elliptic-parabolic PDE model describing chemotactic E. coli colonies
Danielle Hilhorst, Pierre Roux
We study a modified version of an initial-boundary value problem describing the formation of colony patterns of bacteria \textit{Escherichia Coli}. The original system of three par…
Well-posedness and stability of a stochastic neural field in the form of a partial differential equation
José Antonio Carrillo, Pierre Roux, Susanne Solem
A system of partial differential equations representing stochastic neural fields was recently proposed with the aim of modelling the activity of noisy grid cells when a mammal trav…