arXiv subjects

S. Boccaletti

Publications and source records attributed to S. Boccaletti.

At least 19 recordsLinked to original sources

arXiv2026

Parenclitic hypergraphs and their application in personalized cancer therapy

Understanding the differences between individual instances of the same complex system remains a central challenge, particularly in biological contexts. Parenclitic networks constitute a suitable means to detect deviations in correlations with respect to reference populations. Here, we introduce parenclitic hypergraphs, a general framework for identifying anomalies in higher-order correlations across arbitrary interaction orders. After validating the method on synthetic datasets and benchmark ones, we apply it to patient-derived cancer organoids, capturing temporal changes in gene expression between healthy and cancerous tissues as the disease progresses. Our approach not only reproduces known oncogenic signatures, but also reveals a previously unrecognized candidate therapeutic target. Since organoids are generated from individual patients, our method provides, for the first time, a viable protocol for personalized cancer therapy based on higher-order correlation patterns. These findings offer a novel, systems-level strategy for precision oncology grounded in complex systems theory.

q-bio.QM↗

arXiv2025

Cluster-Mediated Synchronization Dynamics in Globally Coupled Oscillators with Inertia

Globally coupled oscillator systems with inertia exhibit complex synchronization patterns, among which the emergence of a couple of secondary synchronized clusters (SCs) in addition to the primary cluster (PC) is especially distinctive. Although previous studies have predominantly focused on the collective properties of the PC, the dynamics of individual clusters and their inter-cluster interactions remain largely unexplored. Here, we demonstrate that multiple clusters emerge and coexist, forming a hierarchical pattern known as the Devil's Staircase. We identify three key findings by investigating individual cluster dynamics and inter-cluster interactions. First, the PC persistently suppresses the formation of SCs during its growth and even after it has fully formed, revealing the significant impact of inter-cluster interactions on cluster formation. Second, once established, SCs induce higher-order clusters exhibiting frequency resonance via inter-cluster interactions, resulting in the Devil's Staircase pattern. Third, sufficiently large SCs can destabilize and fragment the PC, highlighting the bidirectional nature of cluster interactions. We develop a coarse-grained Kuramoto model that treats each cluster as a macroscopic oscillator to capture these inter-cluster dynamics and the resulting phenomena. Our work marks a significant step beyond system-wide averages in the study of inertial oscillator systems, offering new insights into the rich dynamics of cluster formation and synchronization in real-world applications such as power grid networks.

nlin.AO↗

arXiv2023

Endowing networks with desired symmetries and modular behavior

Symmetries in a network regulate its organization into functional clustered states. Given a generic ensemble of nodes and a desirable cluster (or group of clusters), we exploit the direct connection between the elements of the eigenvector centrality and the graph symmetries to generate a network equipped with the desired cluster(s), with such a synthetical structure being furthermore perfectly reflected in the modular organization of the network's functioning. Our results solve a relevant problem of reverse engineering, and are of generic application in all cases where a desired parallel functioning needs to be blueprinted.

nlin.AO↗

arXiv2022

A compartmental model for cyber-epidemics

In our more and more interconnected world, a specific risk is that of a cyber-epidemic (or cyber-pandemic), produced either accidentally or intentionally, where a cyber virus propagates from device to device up to undermining the global Internet system with devastating consequences in terms of economic costs and societal harms related to the shutdown of essential services. We introduce a compartmental model for studying the spreading of a malware and of the awareness of its incidence through different waves which are evolving on top of the same graph structure (the global network of connected devices). This is realized by considering vectorial compartments made of two components, the first being descriptive of the state of the device with respect to the new malware's propagation, and the second accounting for the awareness of the device's user about the presence of the cyber threat. By introducing suitable transition rates between such compartments, one can then follow the evolution of a cyber-epidemic from the moment at which a new virus is seeded in the network, up to when a given user realizes that his/her device has suffered a damage and consequently starts a wave of awareness which eventually ends up with the development of a proper antivirus software. We then compare the overall damage that a malware is able to produce in Erdős-Rényi and scale-free network architectures for both the case in which the virus is causing a fixed damage on each device and the case where, instead, the virus is engineered to mutate while replicating from device to device. Our result constitute actually the attempt to build a specific compartmental model whose variables and parameters are entirely customized for describing cyber-epidemics.

cs.CR↗

arXiv2021

Contrarians synchronize beyond the limit of pairwise interactions

We give evidence that a population of pure contrarians globally coupled D-dimensional Kuramoto oscillators reaches a collective synchronous state when the interplay between the units goes beyond the limit of pairwise interactions. Namely, we will show that the presence of higher order interactions may induce the appearance of a coherent state even when the oscillators are coupled negatively to the mean field. An exact solution for the description of the microscopic dynamics for forward and backward transitions is provided, which entails imperfect symmetry breaking of the population into a frequency-locked state featuring two clusters of different instantaneous phases. Our results contribute to a better understanding of the powerful potential of group interactions entailing multi-dimensional choices and novel dynamical states in many circumstances, such as in social systems.

physics.soc-ph↗

arXiv2021

Predicting transitions in cooperation levels from network connectivity

Networks determine our social circles and the way we cooperate with others. We know that topological features like hubs and degree assortativity affect cooperation, and we know that cooperation is favoured if the benefit of the altruistic act divided by the cost exceeds the average number of neighbours. However, a simple rule that would predict cooperation transitions on an arbitrary network has not yet been presented. Here we show that the unique sequence of degrees in a network can be used to predict at which game parameters major shifts in the level of cooperation can be expected, including phase transitions from absorbing to mixed strategy phases. We use the evolutionary prisoner's dilemma game on random and scale-free networks to demonstrate the prediction, as well as its limitations and possible pitfalls. We observe good agreements between the predictions and the results obtained with concurrent and Monte Carlo methods for the update of the strategies, thus providing a simple and fast way to estimate the outcome of evolutionary social dilemmas on arbitrary networks without the need of actually playing the game.

physics.soc-ph↗

arXiv2021

Contagion in simplicial complexes

The propagation of information in social, biological and technological systems represents a crucial component in their dynamic behavior. When limited to pairwise interactions, a rather firm grip is available on the relevant parameters and critical transitions of these spreading processes, most notably the pandemic transition, which indicates the conditions for the spread to cover a large fraction of the network. The challenge is that, in many relevant applications, the spread is driven by higher order relationships, in which several components undergo a group interaction. To address this, we analyze the spreading dynamics in a simplicial complex environment, designed to capture the coexistence of interactions of different orders. We find that, while pairwise interactions play a key role in the initial stages of the spread, once it gains coverage, higher order simplices take over and drive the contagion dynamics. The result is a distinctive spreading phase diagram, exhibiting a discontinuous pandemic transition, and hence offering a qualitative departure from the traditional network spreading dynamics.

physics.soc-ph↗

arXiv2021

Evolutionary games on simplicial complexes

Elucidating the mechanisms that lead to cooperation is still one of the main scientific challenges of current times, as many common cooperative scenarios remain elusive and at odds with Darwin's natural selection theory. Here, we study evolutionary games on populations that are structured beyond pairwise interactions. Specifically, we introduce a general evolutionary approach that allows studying situations in which indirect interactions via a neighbor other than the direct pairwise connection (or via a group of neighbors), impact the strategy of the focal player. To this end, we consider simplicial graphs that encode two- and three-body interactions, which enables to study competition between all possible pairs of social dilemmas and to scrutinize the role of three-body interactions in all the observed phenomenology. We simultaneously investigate how social dilemma with different Nash equilibria compete in simplicial structures and how such a competition is modulated by the unbalance of 2- and 1-simplices, which in its turn reflects the relative prevalence of pairwise or group interactions among the players. We report a number of results that: (i) support that higher-order games allow for non-dominant strategists to emerge and coexist with dominant ones, a scenario that can't be explained by any pairwise schemes, no matter the network of contacts; (ii) characterize a novel transition from dominant defection to dominant cooperation as a function of the simplicial structure of the population; and (iii) demonstrate that 2-simplex interactions are a source of strategy diversity, i.e. increasing the relative prevalence of group interactions always promotes diverse strategic identities of individuals. Our study constitutes a step forward in the quest for understanding the roots of cooperation and the mechanisms that sustain it in real-world and social environments.

physics.soc-ph↗

arXiv2020

Controlling symmetries and clustered dynamics of complex networks

Symmetries are an essential feature of complex networks as they regulate how the graph collective dynamics organizes into clustered states. We here show how to control network symmetries, and how to enforce patterned states of synchronization with nodes clustered in a desired way. Our approach consists of perturbing the original network connectivity, either by adding new edges or by adding/removing links together with modifying their weights. By solving suitable optimization problems, we furthermore guarantee that changes made on the existing topology are minimal. The conditions for the stability of the enforced pattern are derived for the general case, and the performance of the method is illustrated with paradigmatic examples. Our results are relevant to all the practical situations in which coordination of the networked systems into diverse groups may be desirable, such as for teams of robots, unmanned autonomous vehicles, power grids and central pattern generators.

physics.soc-ph↗

arXiv2020

D-dimensional oscillators in simplicial structures: odd and even dimensions display different synchronization scenarios

From biology to social science, the functioning of a wide range of systems is the result of elementary interactions which involve more than two constituents, so that their description has unavoidably to go beyond simple pairwise-relationships. Simplicial complexes are therefore the mathematical objects providing a faithful representation of such systems. We here present a complete theory of synchronization of $D$-dimensional oscillators obeying an extended Kuramoto model, and interacting by means of 1- and 2- simplices. Not only our theory fully describes and unveils the intimate reasons and mechanisms for what was observed so far with pairwise interactions, but it also offers predictions for a series of rich and novel behaviors in simplicial structures, which include: a) a discontinuous de-synchronization transition at positive values of the coupling strength for all dimensions, b) an extra discontinuous transition at zero coupling for all odd dimensions, and c) the occurrence of partially synchronized states at $D=2$ (and all odd $D$) even for negative values of the coupling strength, a feature which is inherently prohibited with pairwise-interactions. Furthermore, our theory untangles several aspects of the emergent behavior: the system can never fully synchronize from disorder, and is characterized by an extreme multi-stability, in that the asymptotic stationary synchronized states depend always on the initial conditions. All our theoretical predictions are fully corroborated by extensive numerical simulations. Our results elucidate the dramatic and novel effects that higher-order interactions may induce in the collective dynamics of ensembles of coupled $D$-dimensional oscillators, and can therefore be of value and interest for the understanding of many phenomena observed in nature, like for instance the swarming and/or flocking processes unfolding in three or more dimensions.

nlin.AO↗

arXiv2020

Growing scale-free simplices

The past two decades have seen significant successes in our understanding of complex networked systems, from the mapping of real-world social, biological and technological networks to the establishment of generative models recovering their observed macroscopic patterns. These advances, however, are restricted to pairwise interactions, captured by dyadic links, and provide limited insight into higher-order structure, in which a group of several components represents the basic interaction unit. Such multi-component interactions can only be grasped through simplicial complexes, which have recently found applications in social and biological contexts, as well as in engineering and brain science. What, then, are the generative models recovering the patterns observed in real-world simplicial complexes? Here we introduce, study, and characterize a model to grow simplicial complexes of order two, i.e. nodes, links and triangles, that yields a highly flexible range of empirically relevant simplicial network ensembles. Specifically, through a combination of preferential and/or non preferential attachment mechanisms, the model constructs networks with a scale-free degree distribution and an either bounded or scale-free generalized degree distribution - the latter accounting for the number of triads surrounding each link. Allowing to analytically control the scaling exponents we arrive at a highly general scheme by which to construct ensembles of synthetic complexes displaying desired statistical properties.

physics.soc-ph↗

arXiv2020

Diverse strategic identities induce dynamical states in evolutionary games

Evolutionary games provide the theoretical backbone for many aspects of our social life: from cooperation to crime, from climate inaction to imperfect vaccination and epidemic spreading, from antibiotics overuse to biodiversity preservation. An important, and so far overlooked, aspect of reality is the diverse strategic identities of individuals. While applying the same strategy to all interaction partners may be an acceptable assumption for simpler forms of life, this fails to account} for the behavior of more complex living beings. For instance, we humans act differently around different people. Here we show that allowing individuals to adopt different strategies with different partners yields a very rich evolutionary dynamics, including time-dependent coexistence of cooperation and defection, system-wide shifts in the dominant strategy, and maturation in individual choices. Our results are robust to variations in network type and size, and strategy updating rules. Accounting for diverse strategic identities thus has far-reaching implications in the mathematical modeling of social games.

physics.soc-ph↗

arXiv2020

The Master Stability Function for Synchronization in Simplicial Complexes

All interesting and fascinating collective properties of a complex system arise from the intricate way in which its components interact. Various systems in physics, biology, social sciences and engineering have been successfully modelled as networks of coupled dynamical systems, where the graph links describe pairwise interactions. This is, however, too strong a limitation, as recent studies have revealed that higher-order many-body interactions are present in social groups, ecosystems and in the human brain, and they actually affect the emergent dynamics of all these systems. Here, we introduce a general framework that allows to study coupled dynamical systems accounting for the precise microscopic structure of their interactions at any possible order. We consider the most general ensemble of identical dynamical systems, organized on the nodes of a simplicial complex, and interacting through synchronization-non-invasive coupling function. The simplicial complex can be of any dimension, meaning that it can account, at the same time, for pairwise interactions, three-body interactions and so on. In such a broad context, we show that complete synchronization exists as an invariant solution, and we give the necessary condition for it to be observed as a stable state in terms of a Master Stability Function. This generalizes the existing results valid for pairwise interactions (i.e. graphs) to the case of complex systems with the most general possible architecture. Moreover, we show how the approach can be simplified for specific, yet frequently occurring, instances, and we verify all our theoretical predictions in synthetic and real-world systems. Given the completely general character of the method proposed, our results contribute to the theory of dynamical systems with many-body interactions and can find applications in an extremely wide range of practical cases.

nlin.AO↗

arXiv2017

Relay synchronization in multiplex networks

Relay (or remote) synchronization between two not directly connected oscillators in a network is an important feature allowing distant coordination. In this work, we report a systematic study of this phenomenon in multiplex networks, where inter-layer synchronization occurs between distant layers mediated by a relay layer that acts as a transmitter. We show that this transmission can be extended to higher order relay configurations, provided symmetry conditions are preserved. By first order perturbative analysis, we identify the dynamical and topological dependencies of relay synchronization in a multiplex. We find that the relay synchronization threshold is considerably reduced in a multiplex configuration, and that such synchronous state is mostly supported by the lower degree nodes of the outer layers, while hubs can be de-multiplexed without affecting overall coherence. Finally, we experimentally validated the analytical and numerical findings by means of a multiplex of three layers of electronic circuits.the analytical and numerical findings by means of a multiplex of three layers of electronic circuits.

nlin.CD↗

arXiv2017

Emergent explosive synchronization in adaptive complex networks

Adaptation plays a fundamental role in shaping the structure of a complex network and improving its functional fitting. Even when increasing the level of synchronization in a biological system is considered as the main driving force for adaptation, there is evidence of negative effects induced by excessive synchronization. This indicates that coherence alone can not be enough to explain all the structural features observed in many real-world networks. In this work, we propose an adaptive network model where the dynamical evolution of the node states towards synchronization is coupled with an evolution of the link weights based on an anti-Hebbian adaptive rule, which accounts for the presence of inhibitory effects in the system. We found that the emergent networks spontaneously develop the structural conditions to sustain explosive synchronization. Our results can enlighten the shaping mechanisms at the heart of the structural and dynamical organization of some relevant biological systems, namely brain networks, for which the emergence of explosive synchronization has been observed.

physics.soc-ph↗

arXiv2017

Multiple peaks patterns of epidemic spreading in multi-layer networks

The study of epidemic spreading on populations of networked individuals has seen recently a great deal of significant progresses. A common point of all past studies is, however, that there is only one peak of infected density in each single epidemic spreading episode. At variance, real data from different cities over the world suggest that, besides a major single peak trait of infected density, a finite probability exists for a pattern made of two (or multiple) peaks. We show that such a latter feature is fully distinctive of a multilayered network of interactions, and reveal that actually a two peaks pattern emerges from different time delays at which the epidemic spreads in between the two layers. Further, we show that essential ingredients are different degree distributions in the two layers and a weak coupling condition between the layers themselves. Moreover, an edge-based theory is developed which fully explains all numerical results. Our findings may therefore be of significance for protecting secondary disasters of epidemics, which are definitely undesired in real life.

physics.soc-ph↗

arXiv2016

Inter-layer synchronization in non-identical multi-layer networks

Inter-layer synchronization is a dynamical state occurring in multi-layer networks composed of identical nodes. The state corresponds to have all layers synchronized, with nodes in each layer which do not necessarily evolve in unison. So far, the study of such a solution has been restricted to the case in which all layers had an identical connectivity structure. When layers are not identical, the inter-layer synchronous state is no longer a stable solution of the system. Nevertheless, when layers differ in just a few links, an approximate treatment is still feasible, and allows one to gather information on whether and how the system may wander around an inter-layer synchronous configuration. We report the details of an approximate analytical treatment for a two-layer multiplex, which results in the introduction of an extra inertial term accounting for structural differences. Numerical validation of the predictions highlights the usefulness of our approach, especially for small or moderate topological differences in the intra-layer coupling. Moreover, we identify a non-trivial relationship between the betweenness centrality of the missing links and the intra-layer coupling strength. Finally, by the use of two multiplexed identical layers of electronic circuits in a chaotic regime, we study the loss of inter-layer synchronization as a function of the betweenness centrality of the removed links.

nlin.AO↗

arXiv2016

Explosive transitions in complex networks' structure and dynamics: percolation and synchronization

Percolation and synchronization are two phase transitions that have been extensively studied since already long ago. A classic result is that, in the vast majority of cases, these transitions are of the second-order type, i.e. continuous and reversible. Recently, however, explosive phenomena have been reported in com- plex networks' structure and dynamics, which rather remind first-order (discontinuous and irreversible) transitions. Explosive percolation, which was discovered in 2009, corresponds to an abrupt change in the network's structure, and explosive synchronization (which is concerned, instead, with the abrupt emergence of a collective state in the networks' dynamics) was studied as early as the first models of globally coupled phase oscillators were taken into consideration. The two phenomena have stimulated investigations and de- bates, attracting attention in many relevant fields. So far, various substantial contributions and progresses (including experimental verifications) have been made, which have provided insights on what structural and dynamical properties are needed for inducing such abrupt transformations, as well as have greatly enhanced our understanding of phase transitions in networked systems. Our intention is to offer here a monographic review on the main-stream literature, with the twofold aim of summarizing the existing results and pointing out possible directions for future research.

nlin.AO↗