Projet de thèse en Mathématiques
Sous la direction de Vincent Danos.
Thèses en préparation à Paris Sciences et Lettres , dans le cadre de Sciences Mathématiques de Paris Centre , en partenariat avec DIENS - Département d'informatique de l'École normale supérieure (laboratoire) et de Ecole normale supérieure (établissement de préparation de la thèse) depuis le 01-10-2015 .
Conception des methodes computationelles pour des modeles pleine-cellule; construire extension du "Flux Balance Analysis" pour gérer des systèmes biologiques (cellules) en croissance
Parallel Simulation of Modular Complex Systems
CURRENT WORK (SECOND YEAR): Define and construct model of resource storage in cells; analyse the impact of storage on cellular growth. Build on work started in first year, by applying max-plus (tropical) algebra theoretical results to talk about cellular ressource allocation. CURRENT WORK (FIRST YEAR): Adapt and construct computational methods for the "whole-cell" modeling paradigm; build on the method of Flux Balance Analysis in order to deal with growth systems. INITAL PhD DESCRIPTION: The study of complex systems holds the solution for some important questions: climate change, economics, the spread of epidemics, bio-engineering, energy transition, large-scale computationally structured social systems, etc. Their structure is that of heterogenous coupled processes operating across a range of time and spatial scales. Models of these systems are difficult to investigate by purely analytical means and require complicated transactions with data. They are typically large and rely on different paradigms such as differential equations, discrete event systems, Boolean networks, and often include stochastic elements. Flexibility of the model manipulation, consistency, correctness and amenability to effcient parallel execution of its simulations become critical questions. Biological cells, metabolic networks, signalling pathways, agent-based financial models and earth systems are examples of systems modelled in this way. Methods for composing systems of homogeneous types are well studied. Methods for composing heterogeneous systems less so, as are methods for automatically decomposing systems and recomposing them in a way to maximise parallelism and minimise or at least control error and drift. This project will use concepts from tropical analysis, global sensitivity analysis, and clustering techniques to optimally re-partition the problem and geometric integration, and speculative execution to efficiently compute results with maximal parallelism and provable error bounds. A software implementation will be produced, together with an operational semantics for reasoning about this class of problem.