Effectiveness of probabilistic contact tracing in epidemic containment: The role of superspreaders and transmission path reconstruction.

The recent COVID-19 pandemic underscores the significance of early stage nonpharmacological intervention strategies. The widespread use of masks and the systematic implementation of contact tracing strategies provide a potentially equally effective and socially less impactful alternative to more conventional approaches, such as large-scale mobility restrictions. However, manual contact tracing faces strong limitations in accessing the network of contacts, and the scalability of currently implemented protocols for smartphone-based digital contact tracing becomes impractical during the rapid expansion phases of the outbreaks, due to the surge in exposure notifications and associated tests.

Statistical mechanics of inference in epidemic spreading.

We investigate the information-theoretical limits of inference tasks in epidemic spreading on graphs in the thermodynamic limit. The typical inference tasks consist in computing observables of the posterior distribution of the epidemic model given observations taken from a ground-truth (sometimes called planted) random trajectory. We can identify two main sources of quenched disorder: the graph ensemble and the planted trajectory.

Matrix Product Belief Propagation for reweighted stochastic dynamics over graphs.

Stochastic processes on graphs can describe a great variety of phenomena ranging from neural activity to epidemic spreading. While many existing methods can accurately describe typical realizations of such processes, computing properties of extremely rare events is a hard task, particularly so in the case of recurrent models, in which variables may return to a previously visited state. Here, we build on the matrix product cavity method, extending it fundamentally in two directions: First, we show how it can be applied to Markov processes biased by arbitrary reweighting factors that concentrate most of the probability mass on rare events.

Inference in conditioned dynamics through causality restoration.

Estimating observables from conditioned dynamics is typically computationally hard. While obtaining independent samples efficiently from unconditioned dynamics is usually feasible, most of them do not satisfy the imposed conditions and must be discarded. On the other hand, conditioning breaks the causal properties of the dynamics, which ultimately renders the sampling of the conditioned dynamics non-trivial and inefficient.

Closest-vector problem and the zero-temperature p-spin landscape for lossy compression.

We consider a high-dimensional random constrained optimization problem in which a set of binary variables is subjected to a linear system of equations. The cost function is a simple linear cost, measuring the Hamming distance with respect to a reference configuration. Despite its apparent simplicity, this problem exhibits a rich phenomenology.