Robustness of coupled networks with multiple support from functional components at different scales.

Robustness is an essential component of modern network science. Here, we investigate the robustness of coupled networks where the functionality of a node depends not only on its connectivity, here measured by the size of its connected component in its own network, but also the support provided by at least M links from another network. We here develop a theoretical framework and investigate analytically and numerically the cascading failure process when the system is under attack, deriving expressions for the proportion of functional nodes in the stable state, and the critical threshold when the system collapses. Significantly, our results show an abrupt phase transition and we derive the minimum inner and inter-connectivity density necessary for the system to remain active. We also observe that the system necessitates an increased density of links inside and across networks to prevent collapse, especially when conditions on the coupling between the networks are more stringent. Finally, we discuss the importance of our results in real-world settings and their potential use to aid decision-makers design more resilient infrastructure systems.

Percolation Theories for Quantum Networks.

Quantum networks have experienced rapid advancements in both theoretical and experimental domains over the last decade, making it increasingly important to understand their large-scale features from the viewpoint of statistical physics. This review paper discusses a fundamental question: how can entanglement be effectively and indirectly (e.g., through intermediate nodes) distributed between distant nodes in an imperfect quantum network, where the connections are only partially entangled and subject to quantum noise? We survey recent studies addressing this issue by drawing exact or approximate mappings to percolation theory, a branch of statistical physics centered on network connectivity. Notably, we show that the classical percolation frameworks do not uniquely define the network's indirect connectivity. This realization leads to the emergence of an alternative theory called "concurrence percolation", which uncovers a previously unrecognized quantum advantage that emerges at large scales, suggesting that quantum networks are more resilient than initially assumed within classical percolation contexts, offering refreshing insights into future quantum network design.

Exploring QSAR models for activity-cliff prediction.

INTRODUCTION AND METHODOLOGY: Pairs of similar compounds that only differ by a small structural modification but exhibit a large difference in their binding affinity for a given target are known as activity cliffs (ACs). It has been hypothesised that QSAR models struggle to predict ACs and that ACs thus form a major source of prediction error. However, the AC-prediction power of modern QSAR methods and its quantitative relationship to general QSAR-prediction performance is still underexplored. We systematically construct nine distinct QSAR models by combining three molecular representation methods (extended-connectivity fingerprints, physicochemical-descriptor vectors and graph isomorphism networks) with three regression techniques (random forests, k-nearest neighbours and multilayer perceptrons); we then use each resulting model to classify pairs of similar compounds as ACs or non-ACs and to predict the activities of individual molecules in three case studies: dopamine receptor D2, factor Xa, and SARS-CoV-2 main protease. RESULTS AND CONCLUSIONS: Our results provide strong support for the hypothesis that indeed QSAR models frequently fail to predict ACs. We observe low AC-sensitivity amongst the evaluated models when the activities of both compounds are unknown, but a substantial increase in AC-sensitivity when the actual activity of one of the compounds is given. Graph isomorphism features are found to be competitive with or superior to classical molecular representations for AC-classification and can thus be employed as baseline AC-prediction models or simple compound-optimisation tools. For general QSAR-prediction, however, extended-connectivity fingerprints still consistently deliver the best performance amongs the tested input representations. A potential future pathway to improve QSAR-modelling performance might be the development of techniques to increase AC-sensitivity.

Unifying information propagation models on networks and influence maximization.

Information propagation on networks is a central theme in social, behavioral, and economic sciences, with important theoretical and practical implications, such as the influence maximization problem for viral marketing. Here we consider a model that unifies the classical independent cascade models and the linear threshold models, and generalize them by considering continuous variables and allowing feedback in the dynamics. We then formulate its influence maximization as a mixed integer nonlinear programming problem and adopt derivative-free methods. Furthermore, we show that the problem can be exactly solved in the special case of linear dynamics, where the selection criterion is closely related to the Katz centrality, and propose a customized direct search method with local convergence. We then demonstrate the close to optimal performance of the customized direct search numerically on both synthetic and real networks.

Gromov centrality: A multiscale measure of network centrality using triangle inequality excess.

Centrality measures quantify the importance of a node in a network based on different geometric or diffusive properties, and focus on different scales. Here, we adopt a geometrical viewpoint to define a multiscale centrality in networks. Given a metric distance between the nodes, we measure the centrality of a node by its tendency to be close to geodesics between nodes in its neighborhood, via the concept of triangle inequality excess. Depending on the size of the neighborhood, the resulting Gromov centrality defines the importance of a node at different scales in the graph, and it recovers as limits well-known concepts such as the clustering coefficient and closeness centrality. We argue that Gromov centrality is affected by the geometric and boundary constraints of the network, and illustrate how it can help distinguish different types of nodes in random geometric graphs and empirical transportation networks.

Consensus from group interactions: An adaptive voter model on hypergraphs.

We study the effect of group interactions on the emergence of consensus in a spin system. Agents with discrete opinions {0,1} form groups. They can change their opinion based on their group's influence (voter dynamics), but groups can also split and merge (adaptation). In a hypergraph, these groups are represented by hyperedges of different sizes. The heterogeneity of group sizes is controlled by a parameter ß. To study the impact of ß on reaching consensus, we provide extensive computer simulations and compare them with an analytic approach for the dynamics of the average magnetization. We find that group interactions amplify small initial opinion biases, accelerate the formation of consensus, and lead to a drift of the average magnetization. The conservation of the initial magnetization, known for basic voter models, is no longer obtained.

Flow stability for dynamic community detection.

Many systems exhibit complex temporal dynamics due to the presence of different processes taking place simultaneously. An important task in these systems is to extract a simplified view of their time-dependent network of interactions. Community detection in temporal networks usually relies on aggregation over time windows or consider sequences of different stationary epochs. For dynamics-based methods, attempts to generalize static-network methodologies also face the fundamental difficulty that a stationary state of the dynamics does not always exist. Here, we derive a method based on a dynamical process evolving on the temporal network. Our method allows dynamics that do not reach a steady state and uncovers two sets of communities for a given time interval that accounts for the ordering of edges in forward and backward time. We show that our method provides a natural way to disentangle the different dynamical scales present in a system with synthetic and real-world examples.

Brexit and bots: characterizing the behaviour of automated accounts on Twitter during the UK election.

Online Social Networks (OSNs) offer new means for political communications that have quickly begun to play crucial roles in political campaigns, due to their pervasiveness and communication speed. However, the OSN environment is quite slippery and hides potential risks: many studies presented evidence about the presence of d/misinformation campaigns and malicious activities by genuine or automated users, putting at severe risk the efficiency of online and offline political campaigns. This phenomenon is particularly evident during crucial political events, as political elections. In the present paper, we provide a comprehensive description of the networks of interactions among users and bots during the UK elections of 2019. In particular, we focus on the polarised discussion about Brexit on Twitter, analysing a data set made of more than 10 millions tweets posted for over a month. We found that the presence of automated accounts infected the debate particularly in the days before the UK national elections, in which we find a steep increase of bots in the discussion; in the days after the election day, their incidence returned to values similar to the ones observed few weeks before the elections. On the other hand, we found that the number of suspended users (i.e. accounts that were removed by the platform for some violation of the Twitter policy) remained constant until the election day, after which it reached significantly higher values. Remarkably, after the TV debate between Boris Johnson and Jeremy Corbyn, we observed the injection of a large number of novel bots whose behaviour is markedly different from that of pre-existing ones. Finally, we explored the bots' political orientation, finding that their activity is spread across the whole political spectrum, although in different proportions, and we studied the different usage of hashtags and URLs by automated accounts and suspended users, targeting the formation of common narratives in different sides of the debate.

Metastable oscillatory modes emerge from synchronization in the brain spacetime connectome.

A rich repertoire of oscillatory signals is detected from human brains with electro- and magnetoencephalography (EEG/MEG). However, the principles underwriting coherent oscillations and their link with neural activity remain under debate. Here, we revisit the mechanistic hypothesis that transient brain rhythms are a signature of metastable synchronization, occurring at reduced collective frequencies due to delays between brain areas. We consider a system of damped oscillators in the presence of background noise - approximating the short-lived gamma-frequency oscillations generated within neuronal circuits - coupled according to the diffusion weighted tractography between brain areas. Varying the global coupling strength and conduction speed, we identify a critical regime where spatially and spectrally resolved metastable oscillatory modes (MOMs) emerge at sub-gamma frequencies, approximating the MEG power spectra from 89 healthy individuals at rest. Further, we demonstrate that the frequency, duration, and scale of MOMs - as well as the frequency-specific envelope functional connectivity - can be controlled by global parameters, while the connectome structure remains unchanged. Grounded in the physics of delay-coupled oscillators, these numerical analyses demonstrate how interactions between locally generated fast oscillations in the connectome spacetime structure can lead to the emergence of collective brain rhythms organized in space and time.

Dynamics of majority rule on hypergraphs.

A broad range of dynamical systems involve multibody interactions, or group interactions, which may not be encoded in traditional graphical structures. In this work, we focus on a canonical example from opinion dynamics, namely the majority rule, and we investigate the possibility to represent and analyze the system by means of hypergraphs. We explore the formation of consensus, and we restrict our attention to interaction groups of size 3 in order to simplify our analysis from a combinatorial perspective. We propose different types of hypergraph models, incorporating modular structure or mean-field heterogeneity, and we recast the dynamics in terms of Fokker-Planck equations, which allows us to predict the transient dynamics toward consensus. Numerical simulations show a very good agreement between the stochastic dynamics and theoretical predictions for large population sizes.

Consensus dynamics on temporal hypergraphs.

We investigate consensus dynamics on temporal hypergraphs that encode network systems with time-dependent, multiway interactions. We compare these consensus processes with dynamics evolving on projections that remove the temporal and/or the multiway interactions of the higher-order network representation. For linear average consensus dynamics, we find that the convergence of a randomly switching time-varying system with multiway interactions is slower than the convergence of the corresponding system with pairwise interactions, which in turn exhibits a slower convergence rate than a consensus dynamics on the corresponding static network. We then consider a nonlinear consensus dynamics model in the temporal setting. Here we find that in addition to an effect on the convergence speed, the final consensus value of the temporal system can differ strongly from the consensus on the aggregated, static hypergraph. In particular, we observe a first-mover advantage in the consensus formation process: If there is a local majority opinion in the hyperedges that are active early on, then the majority in these first-mover groups has a higher influence on the final consensus value-a behavior that is not observable in this form in projections of the temporal hypergraph.

Multibody interactions and nonlinear consensus dynamics on networked systems.

Multibody interactions can reveal higher-order dynamical effects that are not captured by traditional two-body network models. In this work, we derive and analyze models for consensus dynamics on hypergraphs, where nodes interact in groups rather than in pairs. Our work reveals that multibody dynamical effects that go beyond rescaled pairwise interactions can appear only if the interaction function is nonlinear, regardless of the underlying multibody structure. As a practical application, we introduce a specific nonlinear function to model three-body consensus, which incorporates reinforcing group effects such as peer pressure. Unlike consensus processes on networks, we find that the resulting dynamics can cause shifts away from the average system state. The nature of these shifts depends on a complex interplay between the distribution of the initial states, the underlying structure, and the form of the interaction function. By considering modular hypergraphs, we discover state-dependent, asymmetric dynamics between polarized clusters where multibody interactions make one cluster dominate the other.

Community detection in networks without observing edges.

We develop a Bayesian hierarchical model to identify communities of time series. Fitting the model provides an end-to-end community detection algorithm that does not extract information as a sequence of point estimates but propagates uncertainties from the raw data to the community labels. Our approach naturally supports multiscale community detection and the selection of an optimal scale using model comparison. We study the properties of the algorithm using synthetic data and apply it to daily returns of constituents of the S&P100 index and climate data from U.S. cities.

Multiscale dynamical embeddings of complex networks.

Complex systems and relational data are often abstracted as dynamical processes on networks. To understand, predict, and control their behavior, a crucial step is to extract reduced descriptions of such networks. Inspired by notions from control theory, we propose a time-dependent dynamical similarity measure between nodes, which quantifies the effect a node-input has on the network. This dynamical similarity induces an embedding that can be employed for several analysis tasks. Here we focus on (i) dimensionality reduction, i.e., projecting nodes onto a low-dimensional space that captures dynamic similarity at different timescales, and (ii) how to exploit our embeddings to uncover functional modules. We exemplify our ideas through case studies focusing on directed networks without strong connectivity and signed networks. We further highlight how certain ideas from community detection can be generalized and linked to control theory, by using the here developed dynamical perspective.

Dynamical exploration of the repertoire of brain networks at rest is modulated by psilocybin.

Growing evidence from the dynamical analysis of functional neuroimaging data suggests that brain function can be understood as the exploration of a repertoire of metastable connectivity patterns ('functional brain networks'), which potentially underlie different mental processes. The present study characterizes how the brain's dynamical exploration of resting-state networks is rapidly modulated by intravenous infusion of psilocybin, a tryptamine psychedelic found in "magic mushrooms". We employed a data-driven approach to characterize recurrent functional connectivity patterns by focusing on the leading eigenvector of BOLD phase coherence at single-TR resolution. Recurrent BOLD phase-locking patterns (PL states) were assessed and statistically compared pre- and post-infusion of psilocybin in terms of their probability of occurrence and transition profiles. Results were validated using a placebo session. Recurrent BOLD PL states revealed high spatial overlap with canonical resting-state networks. Notably, a PL state forming a frontoparietal subsystem was strongly destabilized after psilocybin injection, with a concomitant increase in the probability of occurrence of another PL state characterized by global BOLD phase coherence. These findings provide evidence of network-specific neuromodulation by psilocybin and represent one of the first attempts at bridging molecular pharmacodynamics and whole-brain network dynamics.

From networks to optimal higher-order models of complex systems.

Rich data is revealing that complex dependencies between the nodes of a network may escape models based on pairwise interactions. Higher-order network models go beyond these limitations, offering new perspectives for understanding complex systems.

Structure and dynamical behavior of non-normal networks.

We analyze a collection of empirical networks in a wide spectrum of disciplines and show that strong non-normality is ubiquitous in network science. Dynamical processes evolving on non-normal networks exhibit a peculiar behavior, as initial small disturbances may undergo a transient phase and be strongly amplified in linearly stable systems. In addition, eigenvalues may become extremely sensible to noise and have a diminished physical meaning. We identify structural properties of networks that are associated with non-normality and propose simple models to generate networks with a tunable level of non-normality. We also show the potential use of a variety of metrics capturing different aspects of non-normality and propose their potential use in the context of the stability of complex ecosystems.

The struggle for existence in the world market ecosystem.

The global trade system can be viewed as a dynamic ecosystem in which exporters struggle for resources: the markets in which they export. We can think that the aim of an exporter is to gain the entirety of a market share (say, car imports from the United States). This is similar to the objective of an organism in its attempt to monopolize a given subset of resources in an ecosystem. In this paper, we adopt a multilayer network approach to describe this struggle. We use longitudinal, multiplex data on trade relations, spanning several decades. We connect two countries with a directed link if the source country's appearance in a market correlates with the target country's disappearing, where a market is defined as a country-product combination in a given decade. Each market is a layer in the network. We show that, by analyzing the countries' network roles in each layer, we are able to classify them as out-competing, transitioning or displaced. This classification is a meaningful one: when testing the future export patterns of these countries, we show that out-competing countries have distinctly stronger growth rates than the other two classes.