Recovery coupling in multilayer networks

Triadic percolation induces dynamical topological patterns in higher-order networks

Triadic interactions are higher-order interactions which occur when a set of nodes affects the interaction between two other nodes. Examples of triadic interactions are present in the brain when glia modulate the synaptic signals among neuron pairs or when interneuron axo-axonic synapses enable presynaptic inhibition and facilitation, and in ecosystems when one or more species can affect the interaction among two other species. On random graphs, triadic percolation has been recently shown to turn percolation into a fully fledged dynamical process in which the size of the giant component undergoes a route to chaos. However, in many real cases, triadic interactions are local and occur on spatially embedded networks. Here, we show that triadic interactions in spatial networks induce a very complex spatio-temporal modulation of the giant component which gives rise to triadic percolation patterns with significantly different topology. We classify the observed patterns (stripes, octopus, and small clusters) with topological data analysis and we assess their information content (entropy and complexity). Moreover, we illustrate the multistability of the dynamics of the triadic percolation patterns, and we provide a comprehensive phase diagram of the model. These results open new perspectives in percolation as they demonstrate that in presence of spatial triadic interactions, the giant component can acquire a time-varying topology. Hence, this work provides a theoretical framework that can be applied to model realistic scenarios in which the giant component is time dependent as in neuroscience.

Deep-learning reconstruction of complex dynamical networks from incomplete data

Reconstructing complex networks and predicting the dynamics are particularly challenging in real-world applications because the available information and data are incomplete. We develop a unified collaborative deep-learning framework consisting of three modules: network inference, state estimation, and dynamical learning. The complete network structure is first inferred and the states of the unobserved nodes are estimated, based on which the dynamical learning module is activated to determine the dynamical evolution rules. An alternating parameter updating strategy is deployed to improve the inference and prediction accuracy. Our framework outperforms baseline methods for synthetic and empirical networks hosting a variety of dynamical processes. A reciprocity emerges between network inference and dynamical prediction: better inference of network structure improves the accuracy of dynamical prediction, and vice versa. We demonstrate the superior performance of our framework on an influenza dataset consisting of 37 US States and a PM2.5 dataset covering 184 cities in China.

Decoupling evolution of economic activity and carbon transfer in China: A multi-level analysis from network perspective

Economic activities among multiple regions are always accompanied by carbon transfers. Analyzing coupling characteristics of economic activities and carbon transfer linkages based on the supply-demand relationships, can further reveal the networked structures of the multiregional interactions and common development trend of various industries, shedding light on carbon emission governance and high-quality development. This study advances novel coupling network models at the regional and industrial levels, and empirically analyzes the coupling characteristics in China based on the input-output data in 2012, 2015, and 2017. The findings reveal a noticeable decoupling process of economic activities and carbon transfers, but with distinct characteristics at the regional and industrial levels. The widening differences in coupling among provinces indicate increasing regional disparities. The decoupling process at the industrial level is primarily driven by the decreased connectivity in networked carbon transfers, instead of economic activities, reflecting the significant variations of industries' low-carbon development. The carbon decoupling process is notably more pronounced in supply-demand chains associated with export as the final use, compared to those linked with capital formation and final consumption. Analysis of coupling characteristics and the identification of decoupling evolution process enhance our understanding of the relationship between economic activities and carbon transfer, and may provide valuable insights for prioritizing actions and achieving efficient carbon emission reduction.

The dynamic nature of percolation on networks with triadic interactions

Percolation establishes the connectivity of complex networks and is one of the most fundamental critical phenomena for the study of complex systems. On simple networks, percolation displays a second-order phase transition; on multiplex networks, the percolation transition can become discontinuous. However, little is known about percolation in networks with higher-order interactions. Here, we show that percolation can be turned into a fully fledged dynamical process when higher-order interactions are taken into account. By introducing signed triadic interactions, in which a node can regulate the interactions between two other nodes, we define triadic percolation. We uncover that in this paradigmatic model the connectivity of the network changes in time and that the order parameter undergoes a period doubling and a route to chaos. We provide a general theory for triadic percolation which accurately predicts the full phase diagram on random graphs as confirmed by extensive numerical simulations. We find that triadic percolation on real network topologies reveals a similar phenomenology. These results radically change our understanding of percolation and may be used to study complex systems in which the functional connectivity is changing in time dynamically and in a non-trivial way, such as in neural and climate networks.

Measuring accessibility to public services and infrastructure criticality for disasters risk management

Component criticality analysis of infrastructure systems has traditionally focused on physical networks rather than infrastructure services. As an example, a key objective of transport infrastructure is to ensure mobility and resilient access to public services, including for the population, service providers, and associated supply chains. We introduce a new user-centric measure for estimating infrastructure criticality and urban accessibility to critical public services - particularly healthcare facilities without loss of generality - and the effects of disaster-induced infrastructure disruptions. Accessibility measures include individuals' choices of all services in each sector. The approach is scalable and modular while preserving detailed features necessary for local planning decisions. It relies on open data to simulate various disaster scenarios, including floods, seismic, and compound shocks. We present results for Lima, Peru, and Manila, Philippines, to illustrate how the approach identifies the most affected areas by shocks, underserved populations, and changes in accessibility and critical infrastructure components. We capture the changes in people's choices of health service providers under each scenario. For Lima, we show that the floods of 2020 caused an increase in average access times to all health services from 33 minutes to 48 minutes. We identify specific critical road segments for ensuring access under each scenario. For Manila, we locate the 22% of the population who lost complete access to all higher health services due to flooding of over 15 cm. The approach is used to identify and prioritize targeted measures to strengthen the resilience of critical public services and their supporting infrastructure systems, while putting the population at the center of decision-making.

Fragmentation of outage clusters during the recovery of power distribution grids

The understanding of recovery processes in power distribution grids is limited by the lack of realistic outage data, especially large-scale blackout datasets. By analyzing data from three electrical companies across the United States, we find that the recovery duration of an outage is connected with the downtime of its nearby outages and blackout intensity (defined as the peak number of outages during a blackout), but is independent of the number of customers affected. We present a cluster-based recovery framework to analytically characterize the dependence between outages, and interpret the dominant role blackout intensity plays in recovery. The recovery of blackouts is not random and has a universal pattern that is independent of the disruption cause, the post-disaster network structure, and the detailed repair strategy. Our study reveals that suppressing blackout intensity is a promising way to speed up restoration.

Conserved Control Path in Multilayer Networks

The determination of directed control paths in complex networks is important because control paths indicate the structure of the propagation of control signals through edges. A challenging problem is to identify them in complex networked systems characterized by different types of interactions that form multilayer networks. In this study, we describe a graph pattern called the conserved control path, which allows us to model a common control structure among different types of relations. We present a practical conserved control path detection method (CoPath), which is based on a maximum-weighted matching, to determine the paths that play the most consistent roles in controlling signal transmission in multilayer networks. As a pragmatic application, we demonstrate that the control paths detected in a multilayered pan-cancer network are statistically more consistent. Additionally, they lead to the effective identification of drug targets, thereby demonstrating their power in predicting key pathways that influence multiple cancers.