(Maths-IA) Identifying a piecewise affine signal from its nonlinear observation - application to DNA replication analysis

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 thestate-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.