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We present a Bayesian approach for the Contamination Source Detection problem in Water Distribution Networks. Given an observation of contaminants in one or more nodes in the network, we try to give probable explanation for it assuming that contamination is a rare event. We introduce extra variables to characterize the place and pattern of the first contamination event. Then we write down the posterior distribution for these extra variables given the observation obtained by the sensors. Our method relies on Belief Propagation for the evaluation of the marginals of this posterior distribution and the determination of the most likely origin. The method is implemented on a simplified binary forward-in-time dynamics. Simulations on data coming from the realistic simulation software EPANET on two networks show that the simplified model is nevertheless flexible enough to capture crucial information about contaminant sources.
We study the inference of the origin and the pattern of contamination in water distribution networks. We assume a simplified model for the dyanmics of the contamination spread inside a water distribution network, and assume that at some random locati
Learned neural solvers have successfully been used to solve combinatorial optimization and decision problems. More general counting variants of these problems, however, are still largely solved with hand-crafted solvers. To bridge this gap, we introd
The community detection problem requires to cluster the nodes of a network into a small number of well-connected communities. There has been substantial recent progress in characterizing the fundamental statistical limits of community detection under
Belief propagation is a widely used message passing method for the solution of probabilistic models on networks such as epidemic models, spin models, and Bayesian graphical models, but it suffers from the serious shortcoming that it works poorly in t
This paper proposes a belief propagation (BP)-based algorithm for sequential detection and estimation of multipath components (MPCs) parameters based on radio signals. Under dynamic channel conditions with moving transmitter and/or receiver, the numb