# Prochain Exposé

mardi 10 avril, 10h30 en salle Minquiers

Arnaud Martin

Belief functions applied to crowdsourcing

The goal of information fusion is to combine information coming from several sources. In this context that is important to model the data and the sources in order to take decision in the most sure and precise way. The main approaches of information fusion will be presented, we will focus on the theory of belief functions. We will consider a problem of classification where the sources give information on an observation to its belonging to a class. We will give some illustration on crowdsourcing problems.

# Exposés des semaines suivantes

Mercredi 2 mai, 11h en salle Minquiers

Sylvie Putot and Eric Goubault

Inner and Outer Approximating Flowpipes for Delay Dierential Equations

Delay differential equations are fundamental for modeling networked control systems where the underlying network induces delay for retrieving values from sensors or delivering orders to actuators. They are notoriously difficult to integrate as these are actually functional equations, the initial state being a function. We propose a scheme to compute inner and outer approximated flowpipes for such equations with uncertain initial states and parameters. Inner-approximated flowpipes are guaranteed to contain only reachable states, while outer-approximated flowpipes enclose all reachable states. We also introduce a notion of robust inner-approximation, which we believe opens promising perspectives for verication, beyond property falsication. The efficiency of our approach relies on the combination of Taylor models in time, with an abstraction or parameterization in space based on ane forms, or zonotopes. It also relies on an extension of the mean-value theorem, which allows us to deduce inner-approximated flowpipes, from flowpipes outerapproximating the solution of the DDE and its Jacobian with respect to constant but uncertain parameters and initial conditions. We present some experimental results obtained with our C++ implementation.

Jeudi 17 mai, 14h en salle Métivier

Certified Polynomial Optimization for System Verification

Semidefinite programming (SDP) is relevant to a wide range of mathematical fields, including combinatorial optimization, control theory, matrix completion. In 2001, Lasserre introduced a hierarchy of SDP relaxations for approximating polynomial infima. My talk emphasizes new applications of this SDP hierarchy in system verification, with a flavor of either computer science or mathematics, investigated during my research. In real algebraic geometry, I describe how to use these hierarchies to approximate as close as desired exact projections of semialgebraic sets. In nonlinear optimization, SDP hierarchies allow to compute Pareto curves (associated with multi-criteria problems) as well as solutions of transcendental problems. These hierarchies can also be easily interleaved with computer assisted proofs. An appealing motivation was to solve efficiently thousands of nonlinear inequalities occurring in the formal proof of Kepler Conjecture by Hales. Finally, SDP can provide precise information to analyze roundoff errors, motivated by automatic tuning of reconfigurable hardware (e.g. FPGA) to algorithm specifications. I will eventually focus on explaining how these hierarchies allow to characterize sets of interest in control and dynamical systems, in particular reachable sets and invariant measures.