Alain Barrat

Lorenzo Dall'Amico, Alain Barrat, Ciro Cattuto

Temporal graphs are commonly used to represent time-resolved relations between entities in many natural and artificial systems. Many techniques were devised to investigate the evolution of temporal graphs by comparing their state at different time points. However, quantifying the similarity between temporal graphs as a whole is an open problem. Here, we use embeddings based on time-respecting random walks to introduce a new notion of distance between temporal graphs. This distance is well-defined for pairs of temporal graphs with different numbers of nodes and different time spans. We study the case of a matched pair of graphs, when a known relation exists between their nodes, and the case of unmatched graphs, when such a relation is unavailable and the graphs may be of different sizes. We use empirical and synthetic temporal network data to show that the distance we introduce discriminates graphs with different topological and temporal properties. We provide an efficient implementation of the distance computation suitable for large-scale temporal graphs.

Carmela Troncoso, Mathias Payer, Jean-Pierre Hubaux et al.

This document describes and analyzes a system for secure and privacy-preserving proximity tracing at large scale. This system, referred to as DP3T, provides a technological foundation to help slow the spread of SARS-CoV-2 by simplifying and accelerating the process of notifying people who might have been exposed to the virus so that they can take appropriate measures to break its transmission chain. The system aims to minimise privacy and security risks for individuals and communities and guarantee the highest level of data protection. The goal of our proximity tracing system is to determine who has been in close physical proximity to a COVID-19 positive person and thus exposed to the virus, without revealing the contact's identity or where the contact occurred. To achieve this goal, users run a smartphone app that continually broadcasts an ephemeral, pseudo-random ID representing the user's phone and also records the pseudo-random IDs observed from smartphones in close proximity. When a patient is diagnosed with COVID-19, she can upload pseudo-random IDs previously broadcast from her phone to a central server. Prior to the upload, all data remains exclusively on the user's phone. Other users' apps can use data from the server to locally estimate whether the device's owner was exposed to the virus through close-range physical proximity to a COVID-19 positive person who has uploaded their data. In case the app detects a high risk, it will inform the user.

Koya Sato, Mizuki Oka, Alain Barrat et al.

Low-dimensional vector representations of network nodes have proven successful to feed graph data to machine learning algorithms and to improve performance across diverse tasks. Most of the embedding techniques, however, have been developed with the goal of achieving dense, low-dimensional encoding of network structure and patterns. Here, we present a node embedding technique aimed at providing low-dimensional feature vectors that are informative of dynamical processes occurring over temporal networks -- rather than of the network structure itself -- with the goal of enabling prediction tasks related to the evolution and outcome of these processes. We achieve this by using a modified supra-adjacency representation of temporal networks and building on standard embedding techniques for static graphs based on random-walks. We show that the resulting embedding vectors are useful for prediction tasks related to paradigmatic dynamical processes, namely epidemic spreading over empirical temporal networks. In particular, we illustrate the performance of our approach for the prediction of nodes' epidemic states in a single instance of a spreading process. We show how framing this task as a supervised multi-label classification task on the embedding vectors allows us to estimate the temporal evolution of the entire system from a partial sampling of nodes at random times, with potential impact for nowcasting infectious disease dynamics.