Clara Lage (ENS de Lyon) - Identification d'un signal affine par morceaux à partir de son observation non linéaire - application à l'analyse de la réplication de l'ADN

An important challenge in DNA replication analysis is to recover the so-called replication timing profile, that contains important information about the DNA replication dynamics. We show that using recent replication data, this problem can be expressed as a nonlinear inverse problem where the unknown timing profile is assumed to be piecewise affine. We propose a novel formalism and computational approach to harness it. In the noiseless case, we establish sufficient identifiability conditions for the timing profile, and prove that it is the solution of a non-convex optimization problem. This problem is specially challenging because of its multiple local minima. We propose the DNA-inverse optimization method that provably finds the global solution in the noiseless case and is shown to be numerically effective for noisy signals. Besides being more computationally effective than the state-of-the-art optimization methods, our approach automatically recovers the full configuration of the replication dynamics. This is crucial for DNA replication analysis, and was not possible with previous methods.