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Many real-life decision making problems can be modeled as mathematical optimization problems. Often, the data of these problems is not known with precision, because of measurement errors, variability or the time duration of the processes under study, or simple lack of access to reliable data. For

Today's information society crucially relies on cryptographic protocols, which are distributed programs that leverage cryptographic primitives to achieve various security goals such as confidentiality or integrity. Any attack in these protocols can have dramatic consequences, amplified by their ubiq

This project studies the production of the human voice and the oscillatory regimes resulting from the laryngeal and vocal tract articulation (involved in, e.g., modal or falsetto voice registers). It relies on physical modeling and nonlinear systems theory to elaborate simulations, observers-control

The GOSPEL project aims to grow the definition of Gospel, a specification language for OCaml; to develop an ecosystem of tools that understand Gospel, including documentation tools, testing tools, and program verification tools; and to carry out a number of case studies so as to validate the desi

Being a language of nature, differential equations are ubiquitous in science and technology. Thus, solving them is a fundamental computational task, with renewed challenges due to the widespread availability of HPC hardware. For applications, this task typically boils down to the numerical approxima

The recent advent of applied category theory (ACT) and large-scale projects to formalize mathematics using proof assistants such as Coq, Isabelle/HOL, or Lean have opened up promising research avenues at the crossroads of several theoretical disciplines. We propose to combine these paradigms in a fi

Computer systems are ubiquitous and identifying their possible defects is crucial already at the earliest stages of their development, when many aspects, including the environments or the execution platforms, have not been fixed. Verification must then be performed on underspecified models and, some

Classical methods of automatic control are insufficient to deal with dynamics on large networks because they scale poorly with size. This project aims at overcoming this issue by studying scalable continuous methods. In such methods, the (discrete) network and the dynamics therein (an ODE system) a

The project TASKABILE is positioned at the interface between three different areas: inverse problems, optimisation and learning. It aims to make the framework of bilevel optimisation a paradigm for the reliable and task-dependent estimation of adaptive feature-dependent models for imaging and visio

The objective of this project is to study the robust output regulation problem of finite-dimensional nonlinear systems by means of infinite-dimensional internal model controllers. The output regulation problem arises in a large number of problems such as tracking, disturbance rejection and optimal s

Given a system of differential equations, the aim of differential elimination is to compute implied relations that only involve a set of variables of special interest. It generalizes the classical Gaussian elimination to nonlinear differential equations. Techniques based on differential elimination

The P=NP problem is generally considered as one of the major problems in fundamental computer science. The difficulty of obtaining progress on this problem encouraged the researchers to focus on its variants. One of them emerges in arithmetic complexity: can we prove that some explicit polynomials c

From energy networks to space systems, complex autonomous systems have become pervasive in our society. In this context, the design of increasingly sophisticated methodologies for controlling these systems is of utmost relevance, given that they regularly operate in uncertain and dynamic circumstanc

Two celebrated results in the theory of automata and formal languages are the existence of polynomial-time algorithms for detecting equality of compressed strings and Angluin's procedure for learning deterministic automata with membership and equivalence queries. By now, these two classical result

In this project, we aim to develop and apply a new formalism to write and study pattern correspondences between sets of combinatorial object (permutations; words; trees; Dyck, Motzkin and other lattice paths), the first steps of this formalism is already visible in our recently published works.

Numerous problems in signal/image processing, statistics, and machine learning rely on the resolution of optimization problems with sparse or low-rank priors. These problems are very challenging to solve due to their combinatorial nature and can be considered as open to a large extent. Within this

DySCo will build on Seiller's theory of Interaction Graphs to revisit the foundations for computer science using the mathematics of dynamical systems. Indeed, Seiller’s work shows how graphings – a generalisation of dynamical systems – provide an expressive and powerful mathematical model of compute

Graphs are a fundamental modeling tool in science. They have been used for modeling phenomena in fields ranging from statistical physics to communication networks, distributed algorithms, logistics, biology, medicine, and social networks. Despite great successes in these areas, many real-world pheno