Since October 2023, I have been a postdoctoral researcher at CMAP (École Polytechnique), in the PEIPS team. My research is partially supported by an INSERM/INCa project in collaboration with Saint-Louis Hospital, as well as by the ERC SINGER obtained by Sylvie Méléard. The postdoctoral project focuses on understanding cancer cell invasion through two main aspects: a theoretical part based on the multiscale analysis of a birth-and-death process, and an applied part centered on the analysis of clinical data.
I obtained a joint PhD between the University of Paris-Est Créteil (LAMA) and the University of Sfax, Tunisia, under the supervision of Arnaud Le Ny and Mondher Damak. I defended my thesis in December 2023. My research focused on stochastic differential equations and Hawkes processes applied to long-range neural networks.
Stochastic analysis and large-scale limits: pseudo-periodic solutions, stochastic differential equations with jumps, long-time behavior of long-range interactions, population dynamics limits
Biology and clinical data analysis: dynamic Bayesian networks
Publications
[1]"Measure pseudo almost periodic solution for a class of nonlinear delayed stochastic evolution equations driven by Brownian motion."
Nadia Belmabrouk, Mondher Damak, Mohsen Miraoui. Filomat, 2021.
[2]"Dirichlet eigenvalue problems of irreversible Langevin diffusion."
Nadia Belmabrouk, Mondher Damak, Najib Yaakoubi. Statistics & Probability Letters, 2022.
[3]"Stochastic Nicholson’s blowflies model with delays."
Nadia Belmabrouk, Mondher Damak, Mohsen Miraoui. International Journal of Biomathematics, 2023.
Work in Progress
[4]"Asymptotics of multivariate Hawkes processes with long-range interactions".
Nadia Belmabrouk, Arnaud Le Ny.
[5]"Dynamics of tumour cell invasion in a quasi-critical regime".
Vincent Bansaye, Nadia Belmabrouk, Xavier Erny, Simon Girel.
[6]"A Dynamic Bayesian Network for Hematologic Mutations and Treatment Response".
Nadia Belmabrouk, Ana Fernández Baranda, Nabih Maslah, Sylvie Méléard.
Talks
17/06/2025: Research School of the MMB Chair, Aussois – "Dynamics of Tumour Cell Invasion
in a Quasi-Critical Regime"
10/04/2025: MERGE Team Seminar (CMAP École Polytechnique) – "Dynamics of Tumour Cell Invasion
in a Quasi-Critical Regime"
25-28/04/2024: Tunisian Mathematical Society Conference, Monastir – "Asymptotics of multivariate Hawkes processes with long-range interactions"
17/11/2023: SAMM Seminar, University Paris 1 – "Asymptotics of multivariate Hawkes processes with long-range interactions"
14/03/2023: Doctoral Seminar – "Asymptotics of multivariate Hawkes processes with long-range interactions"
02/11/2019: Tunisian Mathematical Society Conference – "Stochastic Nicholson’s blowflies model with delays"
04-06/08/2023: Stochastic Models in Life Science, Eurandom – "Neural Multivariate Hawkes Process with Long-Range Interactions"
21-25/06/2022: ALEA Days, CIRM, Luminy – "Hawkes processes on a long-range network"
05/06/2022: Hawkes Process Days, Institut Henri Poincaré – "Asymptotics of multivariate Hawkes processes with long-range interactions"
28/06-01/07/2021: International Conference on Mathematical Neuroscience – "Asymptotics of multivariate Hawkes processes with long-range interactions" (online)
Depuis octobre 2023, je suis post-doctorante au CMAP (École Polytechnique), au sein de l’équipe PEIPS. Mes recherches sont financées en partie par un projet INSERM/INCa, réalisé en collaboration avec l’hôpital Saint-Louis, ainsi que par l'ERC SINGER de Sylvie Méléard. Le projet de post-doctorat porte sur la compréhension de l’invasion des cellules cancéreuses, à travers deux volets : un théorique, basé sur l’analyse multi-échelle d’un processus de naissance et mort, et un autre pratique, centré sur l’analyse de données cliniques.
J’ai effectué une thèse en cotutelle (soutenue en décembre 2023) entre l’Université Paris-Est Créteil (LAMA) et l’Université de Sfax en Tunisie, sous la direction d’Arnaud Le Ny et Mondher Damak. Elle portait sur l’étude des équations différentielles stochastiques et des processus de Hawkes appliqués aux réseaux neuronaux à longue portée.
Thèmes de recherche
Systèmes de particules en interaction : Processus de Hawkes, processus de naissances-morts, modèles d’invasion, équations de Langevin
Analyse stochastique et limites à grande échelle : solutions pseudo-périodiques, équations différentielles stochastiques avec sauts, comportement en temps long des interactions à longue portée, limites de la dynamique des populations
Biologie et analyse de données cliniques : Réseaux bayésiens dynamiques
Publications
[1]"Measure pseudo almost periodic solution for a class of nonlinear delayed stochastic evolution equations driven by Brownian motion."
Nadia Belmabrouk, Mondher Damak, Mohsen Miraoui. Filomat, 2021.
[2]"Dirichlet eigenvalue problems of irreversible Langevin diffusion."
Nadia Belmabrouk, Mondher Damak, Najib Yaakoubi. Statistics & Probability Letters, 2022.
[3]"Stochastic Nicholson’s blowflies model with delays."
Nadia Belmabrouk, Mondher Damak, Mohsen Miraoui. International Journal of Biomathematics, 2023.
Travaux en cours
[4]"Asymptotics of multivariate Hawkes processes with long-range interactions".
Nadia Belmabrouk, Arnaud Le Ny.
[5]"Dynamics of tumour cell invasion in a quasi-critical regime".
Vincent Bansaye, Nadia Belmabrouk, Xavier Erny, Simon Girel.
[6]"A Dynamic Bayesian Network for Hematologic Mutations and Treatment Response".
Nadia Belmabrouk, Ana Fernández Baranda, Nabih Maslah, Sylvie Méléard.
Présentations
17/06/2025 : École de recherche de la Chaire MMB, Aussois – "Dynamics of Tumour Cell Invasion
in a Quasi-Critical Regime"
10/04/2025 : Séminaire de l’équipe MERGE (CMAP École Polytechnique) – "Dynamics of Tumour Cell Invasion
in a Quasi-Critical Regime"
25-28/04/2024 : Colloque de la Société Mathématique de Tunisie, Monastir – "Asymptotics of multivariate Hawkes processes with long-range interactions"
17/11/2023 : Séminaire SAMM, Université Paris 1 – "Asymptotics of multivariate Hawkes processes with long-range interactions"
14/03/2023 : Séminaire des doctorants – "Asymptotics of multivariate Hawkes processes with long-range interactions"
02/11/2019 : Colloque de la Société Mathématique de Tunisie – "Stochastic Nicholson’s blowflies model with delays"
04-06/08/2023 : Stochastic Models in Life Science, Eurandom – "Neural Multivariate Hawkes Process with Long-Range Interactions"
21-25/06/2022 : Journées ALEA, CIRM, Luminy – "Processus de Hawkes sur un réseau à longues portées"
05/06/2022 : Journées Processus de Hawkes, Institut Henri Poincaré – "Asymptotics of multivariate Hawkes processes with long-range interactions"
28/06-01/07/2021 : International Conference on Mathematical Neuroscience – "Multivariate Hawkes Process with Long-Range Dependencies" (en ligne)