Spatial Λ-Fleming Viot processes, or SLFVs, are a family of models describing the evolution of genetic diversity for populations living in a spatial continuum. Their main characteristic is their « event-based » reproduction dynamics, which makes it possible to control local reproduction rates. Therefore, they are particularly suited to the study of populations living in unbounded regions.
In this talk, I will introduce a family of SLFV processes, called k-parent SLFVs, which were developed to model spatially expanding populations. I will present what is currently known of the growth properties of the occupied area in k-parent SLFVs. Of particular interest is the growth dynamics of the limiting process when k→ +∞, which is reminiscent of continuous first-passage percolation but has distinct growth features. I will conclude with preliminary results obtained on the genetic diversity at the front edge.
Based on a joint work with Amandine Véber (MAP5, Univ. Paris Cité) and Matt Roberts (Univ. Bath).

In a high-dimensional context, a classical approach to estimate the unknown parameter in a Gaussian linear regression consists in minimizing the penalized least-squares criterion. To get an oracle inequality on the predictive risk, the model selection theory developed by L. Birgé and P. Massart (2001) gives some penalty shapes known up to multiplicative constants. First, controlling the prediction quality is not sufficient to limit the selection of inactive variables. Thus, under a simplified model, we propose a theoretical study of the FDR criterion onto the model selection procedure. A data-dependent heuristics is then implemented to calibrate one of the penalty constants allowing to avoid selecting inactive variables while maintaining a high prediction quality. Secondly, under the general model, we propose an algorithm that extends the slope heuristics principle to calibrate the last two constants while maintaining a reasonnable control of the predictive risk.

Cette rencontre vise à réunir des spécialistes de mathématiques appliquées, de biologie et de médecine pour discuter ensemble de développements récents sur divers aspects de la croissance tumorale en lien avec son hétérogénéité : réponse aux thérapies ciblées, ADN circulant, populations de cellules tumorales en interaction, questions d’estimation et de prédiction…

L’événement s’inscrit dans le cadre du projet nancéien « Modeling ctDNA dynamics for detecting targeted therapy resistance » financé par ITMO Cancer. L’atelier sera francophone avec 10 interventions.

L’objectif est de créer des conditions propices au dialogue entre les communautés, avec un équilibre théorie/pratique et des intervenants s’adressant à un public varié.

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