We propose to lay the theoretical foundations and design efficient computational methods for analyzing, quantifying and exploring relations and variability in structured data sets, such as collections of geometric shapes, point clouds, and large networks or graphs, among others. Unlike existing methods that are tied and often limited to the underlying data representation, our goal is to design a unified framework in which variability can be processed in a way that is largely agnostic to the underlying data type. In particular, we propose to depart from the standard representations of objects as collections of primitives, such as points or triangles, and instead to treat them as functional spaces that can be easily manipulated and analyzed. Since real-valued functions can be defined on a wide variety of data representations and as they enjoy a rich algebraic structure, such an approach can provide a completely novel unified framework for representing and processing different types of data. Key to our study will be the exploration of relations and variability between objects, which can be expressed as operators acting on functions and thus treated and analyzed as objects in their own right using the vast number of tools from functional analysis in theory and numerical linear algebra in practice. Such a unified computational framework of variability will enable entirely novel applications including accurate shape matching, efficiently tracking and highlighting most relevant changes in evolving systems, such as dynamic graphs, and analysis of shape collections. Thus, it will permit not only to compare or cluster objects, but also to reveal where and how they are different and what makes instances unique, which can be especially useful in medical imaging applications. Ultimately, we expect our study to create to a new rigorous, unified paradigm for computational variability, providing a common language and sets of tools applicable across diverse underlying domains.

What do black holes and particular exotic materials, where strong correlations preclude any description based on weakly-coupled quasiparticles, have in common? Their low energy dynamics are expected to fall within the regime of effective field theories, such as hydrodynamics, where the dynamics are governed by the flow of conserved densities based on the symmetries of the system. However it is often hard to know what the boundaries of this regime are. This is even more true when a system is “quasi”-hydrodynamic meaning one of the conserved quantities, such as the number of particles, decays due to the presence of a “breaking parameter”. Gauge/gravity dualities are relationships from string theory that connect classical black holes to particular quantum theories that have the unusual property of rapidly becoming (quasi)hydrodynamic when perturbed. I seek to use gauge/gravity dualities to answer the following questions: When is quasihydrodynamics a good description of nature (in particular for large values of the breaking parameter)? For what ranges of parameters is it applicable? The first question can be explored by considering models of interdisciplinary relevance and searching for commonalities through which we can categorise them. To answer the second we can make use of the special properties of gauge/gravity theories - the existence of relationships between distinct models (dualities) to compute new results from old. The Marie Curie fellowship will allow me to strengthen my position as the intermediary between condensed matter and string theory, with this project as the initial bridging point. I will use the fellowship to increase my output in high impact journals (e.g. Physical Review Letters), apply for longer term grants and gain knowledge in a new area of physics (condensed matter) through the guidance and experience of my project supervisor Dr.~Blaise Goutéraux. He is the ideal host for this proposal, having extensive experience in these areas.

The possibility of architecturing composite materials to obtain new mechanical properties has lead to the field of metamaterials, which opened numerous research directions and routes for real life applications. In the context of acoustics, designing a microstructure allows us to control the propagation of waves in various ways. A compelling way to do so is to pick a pattern and repeat it periodically. The obtained structure, called a ``phononic crystals'' has the ability to stop certain frequencies and directions. This can be utilize to guide waves to targeted location or along specific paths. In the last decade, a powerful new tool has been added to the design of phononic crystals: that of topological waves. Originating from the physics of conductors and insulators, this allows one to guide waves across fabrication defects without losing energy from partial reflection. The objective of this research proposal is to design new types of waveguides based on a combination of topology and disorder. One of the limitations of acoustic topological insulators is that the analogy with the physics of metal is only approximate. Hence, the robustness to the presence of defect is also. Here, the idea is to conceive structures with topological properties not despite the presence of disorder, but induced by it. This will lead to exceptionally robust wave guiding, since a defect in an otherwise disordered medium is essentially invisible. We will explore two directions, based on analogies with two solid state physics phenomena. The first is the Topological Anderson insulator, where waves propagate at the interface between two phononic crystals with disorder added. The second one is the anti-localization effect in honeycomb lattices such that adding disorder increases the wave transmission. The first part of the project is the theoretical modelling and design of acoustical metamaterials displaying these effects, and the second part will consist in their experimental implementation.

This proposal seeks to develop a fundamental mechanism-based understanding of the mechanics of ferromagnetic shape memory alloys under high pressures and short time scales. Extreme conditions i.e., large stresses, pressures and strain rates, cause these materials to release large coupled energy densities. This multi-functionality originates at microscopic scales, and is governed by the evolution of solid-solid phase transformations. However, the kinetics of these phase transformations are poorly understood at extreme pressures and strain rates, limiting predictive material design tools. The proposed research programme will result in unique experimental infrastructure and multi-scale data sets to fill these knowledge gaps. A high throughput laser-driven shock compression experiment will be developed with in-situ high-speed optical instrumentation and microscopy. This setup will be integrated with a home-built multi-physics platform to apply (quasi-)static magnetic fields in-situ. Using this unique experimental capability, my team will build multi-scale data sets on the multi-physical response of single crystal Ni-Mn-Ga (chosen as a model material) at high pressures (>10 GPa) and strain rates (order of 10^6/s). These data sets, in combination with uniaxial data at comparable strain rates (performed using miniature Kolsky bar experiments), will allow us to de-couple the effects of pressure on the multi-physical macroscopic response and micro-structure evolution in single crystal Ni-Mn-Ga. Analysis of these large multi-dimensional data sets will be performed using a hybrid computational code developed within a multi-scale continuum modeling framework to discover the kinetic laws that govern phase boundary kinetics under complex stress states, high pressures, and short time scales. This fundamental understanding will aid the design and synthesis of ferromagnetic devices for impact absorption, pulsed power generation and solid-state heat pumping.

The lungs are the primary organs of the respiratory system in humans and many animals, responsible for molecular exchanges between external air and internal blood through mechanical ventilation. It has an extraordinary complex architecture, with the inherent fractal structure of the bronchial and blood vessel trees, as well as the hierarchical structure of the parenchyma. Lung biomechanics has been extensively studied by physiologists, experimentally as well as theoretically, from the air flow, blood flow and tissue stress points of view, laying the ground for our current fundamental understanding of the relationship between function and mechanical behavior. However, many questions remain, notably in the intricate coupling between the multiple constituents, between the many phenomena taking place at different spatial and temporal scales in health and disease. For example, even for healthy lungs, there is no quantitative model allowing to link tissue-level and organ-level experimental material responses. These fundamental questions represent real clinical challenges, as pulmonary diseases are an important health burden. Interstitial lung diseases, for instance, affect several million people globally. Idiopathic Pulmonary Fibrosis, notably, a progressive form of interstitial lung diseases where some alveolar septa get thicker and stiffer while others get completely damaged, remains poorly understood, poorly diagnosed, and poorly treated, with a current median survival rate inferior to 5 years. It has, however, been hypothesized that a mechanical vicious cycle is in place within the parenchyma of IPF patients, where fibrosis and damage induce large stresses, which in turns favor fibrosis. The general goal of this project is twofold: (i) scientifically, to better understand pulmonary (solid) mechanics, from the alveolar scale to the organ in health and (IPF) disease; (ii) clinically, to improve diagnosis and prognosis of (IPF) patients through personalized computational modeling. More precisely, I propose to develop a many-scale model of the parenchymal biomechanics, at all relevant spatial scales from the alveolus to the organ, and at the temporal scales of the breathing cycle and fibrosis process. Different representations at successive spatial scales will be linked by a computational nonlinear homogenization strategy with a priori model reduction based on a neural network. The model will integrate the rather unique experimental data produced by Drs. Bel-Brunon and Trunfio-Sfarghiu from LaMCoS (INSA-Lyon), i.e., 30 microtomography images at alveolar scale, plus 10 inflation tests of lobules: microstructures will be extracted from the images and systematically analyzed, and model parameters will be estimated from the mechanical tests. The model will also integrate clinical-radiological data provided by Profs. Nunes and Brillet from Avicenne APHP Hospital, i.e., standard pulmonary function tests and thoracic computed tomography imaging on 10 IPF patients plus 5 normal lung controls: a pipeline to estimate observable model parameters from clinical data will be set up, and generic values will be defined for the remaining parameters. The model and estimation procedure will represent augmented diagnosis and prognosis tools for the clinicians. The project will be coordinated by Dr. Genet, who is currently an Assistant Professor in the Mechanics Department of École Polytechnique with research posting within the M?DISIM team, which belongs to both INRIA and the Solid Mechanics Laboratory of École Polytechnique/CNRS. Throughout the project he will be assisted by Drs. Chapelle and Moireau at INRIA/École Polytechnique, and maintain strong scientific collaborations with the LaMCoS at INSA-Lyon and Télécom-SudParis, as well as strong clinical collaborations with the Avicenne APHP Hospital and Hypoxia & Lung Laboratory of Paris XIII University/INSERM.