Diego Garlaschelli

Valerio Gemmetto, Diego Garlaschelli

The characterization of various properties of real-world systems requires the knowledge of the underlying network of connections among the system's components. Unfortunately, in many situations the complete topology of this network is empirically inaccessible, and one has to resort to probabilistic techniques to infer it from limited information. While network reconstruction methods have reached some degree of maturity in the case of single-layer networks (where nodes can be connected only by one type of links), the problem is practically unexplored in the case of multiplex networks, where several interdependent layers, each with a different type of links, coexist. Even the most advanced network reconstruction techniques, if applied to each layer separately, fail in replicating the observed inter-layer dependencies making up the whole coupled multiplex. Here we develop a methodology to reconstruct a class of correlated multiplexes which includes the World Trade Multiplex as a specific example we study in detail. Our method starts from any reconstruction model that successfully reproduces some desired marginal properties, including node strengths and/or node degrees, of each layer separately. It then introduces the minimal dependency structure required to replicate an additional set of higher-order properties that quantify the portion of each node's degree and each node's strength that is shared and/or reciprocated across pairs of layers. These properties are found to provide empirically robust measures of inter-layer coupling. Our method allows joint multi-layer connection probabilities to be reliably reconstructed from marginal ones, effectively bridging the gap between single-layer properties and truly multiplex information.

Edoardo Maggioni, Diego Garlaschelli, Rossana Mastrandrea et al.

Fostering coordinated pro-environmental behaviors at scale is a key challenge for climate mitigation. Individual actions only generate meaningful impact when they diffuse widely and become socially coordinated, yet monitoring such processes remains difficult with traditional survey-based tools alone. In this study, we examine whether large-scale online climate discourse is associated with differences in offline pro-environmental behavior across European regions. We combine geolocated Twitter data from the Climate Change Twitter Dataset (2017-2019) with survey-based measures from the 2019 Special Eurobarometer, focusing on the regional density of climate-related tweets and the average number of self-reported pro-environmental actions. We find a strong positive association between tweet density and pro-environmental behavior that remains robust to socio-economic controls, alternative spatial aggregations, and a wide range of robustness checks. To move beyond aggregate volume, we further decompose online discourse using Natural Language Processing tools that capture distinct social dimensions. While knowledge exchange shows no clear relationship with offline behavior, the prevalence of activism- and social support-related expressions is negatively associated with pro-environmental actions. Overall, our results suggest that online climate discourse can serve as an informative, attention-related signal of regional differences in pro-environmental behavior, but that different forms of online engagement relate to offline action in markedly different ways. More broadly, the study highlights the potential of integrating large-scale digital traces with survey data to investigate collective behavior in socio-environmental systems, while remaining explicitly observational in scope.

Riccardo Milocco, Fabian Jansen, Diego Garlaschelli

Lying at the interface between Network Science and Machine Learning, node embedding algorithms take a graph as input and encode its structure onto output vectors that represent nodes in an abstract geometric space, enabling various vector-based downstream tasks such as network modelling, data compression, link prediction, and community detection. Two apparently unrelated limitations affect these algorithms. On one hand, it is not clear what the basic operation defining vector spaces, i.e. the vector sum, corresponds to in terms of the original nodes in the network. On the other hand, while the same input network can be represented at multiple levels of resolution by coarse-graining the constituent nodes into arbitrary block-nodes, the relationship between node embeddings obtained at different hierarchical levels is not understood. Here, building on recent results in network renormalization theory, we address these two limitations at once and define a multiscale node embedding method that, upon arbitrary coarse-grainings, ensures statistical consistency of the embedding vector of a block-node with the sum of the embedding vectors of its constituent nodes. We illustrate the power of this approach on two economic networks that can be naturally represented at multiple resolution levels: namely, the international trade between (sets of) countries and the input-output flows among (sets of) industries in the Netherlands. We confirm the statistical consistency between networks retrieved from coarse-grained node vectors and networks retrieved from sums of fine-grained node vectors, a result that cannot be achieved by alternative methods. Several key network properties, including a large number of triangles, are successfully replicated already from embeddings of very low dimensionality, allowing for the generation of faithful replicas of the original networks at arbitrary resolution levels.

Maria Mircea, Diego Garlaschelli, Stefan Semrau

One of the main goals of developmental biology is to reveal the gene regulatory networks (GRNs) underlying the robust differentiation of multipotent progenitors into precisely specified cell types. Most existing methods to infer GRNs from experimental data have limited predictive power as the inferred GRNs merely reflect gene expression similarity or correlation. Here, we demonstrate, how physics-informed neural networks (PINNs) can be used to infer the parameters of predictive, dynamical GRNs that provide mechanistic understanding of biological processes. Specifically we study GRNs that exhibit bifurcation behavior and can therefore model cell differentiation. We show that PINNs outperform regular feed-forward neural networks on the parameter inference task and analyze two relevant experimental scenarios: 1. a system with cell communication for which gene expression trajectories are available and 2. snapshot measurements of a cell population in which cell communication is absent. Our analysis will inform the design of future experiments to be analyzed with PINNs and provides a starting point to explore this powerful class of neural network models further.