I will give an introductory course on point processes that are used to model nueornal activity in the brain. I will especially focus on Hawkes processes even if I will recall some basic notions on Poisson processes as well. I will review the various methods to simulate such networks when the size is huge and comparable to animal brains or brain areas. A new algorithm especially involves...
I will give an introductory course on point processes that are used to model nueornal activity in the brain. I will especially focus on Hawkes processes even if I will recall some basic notions on Poisson processes as well. I will review the various methods to simulate such networks when the size is huge and comparable to animal brains or brain areas. A new algorithm especially involves...
Some statistical mechanics models on trees may sometimes reduce to the study of some "simple" tree recursion; this is for instance the case for the Ising model and FK-percolation model. It turns out that when the recursion is concave, we can compare this tree recursion to the one verified by (possibly non-linear) resistive networks.
I will present some recent work with Irene Ayuso Ventura...
We study the Ising model on a Galton-Watson tree with a random external field, which can be interpreted as randomly introducing "interfering vertices" with a fixed spin. This model is motivated by the study of the Ising model on tree-like random graphs, which can serve as a framework for understanding cooperative behaviour in social networks. In joint work with Quentin Berger (Sorbonne Nord),...
Series-Sinai have shown in the nineties that the ferromagnetic n.n. Ising model defined on the Cayley graph of a co-compact group of isometries of the hyperbolic plane $\mathbb{H}_2$ exhibits uncountably many, mutually singular Gibbs states at very low temperature ---one for every bi-infinite geodesic of $\mathbb{H}_2$.
They also conjectured the extremality of their states but the problem...
Dans cet exposé, je présenterai quelques résultats récents sur le comportement à long terme des processus de Hawkes inhibés, à la fois en temps continu et en temps discret. En particulier, nous soulignerons le rôle complexe de l'inhibition dans la stabilité des processus de Hawkes.
The FKPP equation is a common model in population dynamics, describing how a population spreads and grows over time and space, resulting in wave-like patterns.
Recent studies by Birzu, Hallatschek and Korolev on the noisy FKPP equation with Allee effects (or cooperation) suggest the existence of three classes of fluctuating wavefronts: pulled, semipushed and fully pushed fronts.
In this...
Some models of discrete-time epidemics can be studied in the larger setting of first-passage percolation in multitype directed configuration models, where edges have an integer length representing transmission delays. Through directed breadth-first explorations and coupling with multitype branching processes on countable state spaces, we study the distribution of geodesics between several...
In this joint project with Arno Siri-Jégousse, we introduce a novel research program connecting the fields of mathematical population genetics and self-similar (SS) Markov processes in infinite dimensions. Specifically, we propose a shift in focus from the prevalent paradigm based on the branching property as a tool to analyze the structure of population models, to one based on the...
