# Yves D'Angelo - Université Nice Sophia-Antipolis - Keywords: Biomathematics, Modeling and Numerical Simulations, Experiments in Biology, Data Processing

We wish to address both by analytic/numerical means, and parallel & interacting lab-scale experimental realizations, the problem of the multi-scale modelling and analysis of expanding dynamical networks under external constraints, in a quite general context: biology & medecine, economics, thermodynamics, physics, power supply, social networks...

To this end, the coupling of a mathematical modelling approach with detailed experimental investigations (e.g. the here considered case of the filamentous fungus Podospora anserina, but other real-life models are welcome) can allow for a real-world archetypal versatile benchmark model, whose settings are quite easy to vary experimentally. Changing the type of the constraints applied to the network will assess the relevance & robustness of the mathematical modelling & analysis, provide some insight on the expected emergence of an "optimal" resilient design and also guide the comprehension of the (here biological) on-going process. Thanks to a positive continuous back-and-forth interaction, we wish to build a very general numerical framework, able to bridge the gap between the different scales of complex expanding networks, that may also be met in other contexts, like e.g. in tumour growth, disease spread & vaccination, network growth in mammals organs, plants, bacteria, neural networks (with high resolution imaging) and also ecology. Linked to a homogenization process, the articulation of macro-scale and micro-scale modelling, through intermediate (meso) scales, will be all the more crucial. Analytic statistical approaches & intensive computer simulations will all have to be integrated in a common framework.