Advanced Computational Methods for Knowledge Engineering
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Limit behaviour of the minimal solution of a BSDE with singular terminal condition in the non Markovian setting
Published in Probability, Uncertainty and Quantitative Risk
We use the functional Itô calculus to prove that the solution of a BSDE with singular terminal condition verifies at the terminal time: liminft→TY(t)=ξ=Y(T)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\odds...
An Eco-routing algorithm for HEVs under traffic conditions
An extension of the bi-level optimization for the energy management of hybrid electric vehicles (HEVs) proposed in Le Rhun et al. (2019a) to the eco-routing problem is presented. Using the knowledge of traffic conditions over the entire road network, we search both the optimal path and state of charge trajectory. This problem results in finding the...
Stable recovery of deep linear networks under sparsity constraints
We study a deep linear network expressed under the form of a matrix factorization problem. It takes as input a matrix $X$ obtained by multiplying $K$ matrices (called factors and corresponding to the action of a layer). Each factor is obtained by applying a fixed linear operator to a vector of parameters satisfying a sparsity constraint. In machine...
From the reachable space of the heat equation to Hilbert spaces of holomorphic functions
This work considers systems described by the heat equation on the interval [0, π] with L^2 boundary controls and it studies the reachable space at some instant τ > 0. The main results assert that this space is generally sandwiched between two Hilbert spaces of holomorphic functions defined on a square in the complex plane and which has [0, π] as on...
A decision support tool for the urgent surgeries assignment problem
International audience
On Singularities of Flat Affine Systems With $n$ States and $n-1$ Controls
We study the set of intrinsic singularities of flat affine systems with $n-1$ controls and $n$ states using the notion of Lie-B\"acklund atlas, previously introduced by the authors. For this purpose, we prove two easily computable sufficient conditions to construct flat outputs as a set of independent first integrals of distributions of vector fiel...
A robust asymptotic observer for systems that converge to unobservable states. A batch reactor case study
In this paper we propose an observer for a dynam-ical system for which the states on the frontier of its domain are not observable, and all trajectories converge to the frontier. The proposed case study, a bioreactor in batch operating conditions with a single microbial reaction and gas production, is standard and largely encountered in practical s...
Forecasting the local progression of the Covid-19 epidemic from medical emergency calls: the example of the Paris area
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We portray the evolution of the Covid-19 epidemic during the crisis of March-April 2020 in the Paris area, by analyzing the medical emergency calls received by the EMS of the four central departments of this area (Centre 15 of SAMU 75, 92, 93 and 94). Our study reveals strong dissimilarities between these departments. We provide an algorithm, based...
Capacity Constrained Entropic Optimal Transport, Sinkhorn Saturated Domain Out-Summation and Vanishing Temperature
We propose a new method to reduce the computational cost of the Entropic Optimal Transport in the vanishing temperature (ε) limit. As in [Schmitzer, 2016], the method relies on a Sinkhorn continuation "ε-scaling" approach; but instead of truncating out the small values of the Kernel, we rely on the exact "out-summation" of saturated domains for a m...
