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Higher-order interactions play a key role for the operation and function of a complex system. However, how to identify them is still an open problem. Here, we propose a method to fully reconstruct the structural connectivity of a system of coupled dynamical units, identifying both pairwise and higher-order interactions from the system time evolution. Our method works for any dynamics, and allows the reconstruction of both hypergraphs and simplicial complexes, either undirected or directed, unweighted or weighted. With two concrete applications, we show how the method can help understanding the complexity of bacterial systems, or the microscopic mechanisms of interaction underlying coupled chaotic oscillators. Higher-order interactions are broadly present in biological and social networks, however patterns of such interaction are challenging to recover from observed data. The authors propose a method to infer the high-order structural connectivity of a complex system from its time evolution.

Recent studies have shown that novel collective behaviors emerge in complex systems due to the presence of higher-order interactions. However, how the collective behavior of a system is influenced by the microscopic organization of its higher-order interactions is not fully understood. In this work, we introduce a way to quantify the overlap among the hyperedges of a higher-order network, and we show that real-world systems exhibit different levels of intra-order hyperedge overlap. We then study two types of dynamical processes on higher-order networks, namely complex contagion and synchronization, finding that intra-order hyperedge overlap plays a universal role in determining the collective behavior in a variety of systems. Our results demonstrate that the presence of higher-order interactions alone does not guarantee abrupt transitions. Rather, explosivity and bistability require a microscopic organization of the structure with a low value of intra-order hyperedge overlap. Group interactions can lead to explosive onsets of collective behaviors in biological and sociotechnological systems. Here, the authors show that it is the overlap between these kind of higher-order interactions that drives whether emergence of synchrony and epidemics shows up smoothly or abruptly.

Non-reciprocal interactions play a crucial role in many social and biological complex systems. While directionality has been thoroughly accounted for in networks with pairwise interactions, its effects in systems with higher-order interactions have not yet been explored as deserved. Here, we introduce the concept of M -directed hypergraphs, a general class of directed higher-order structures, which allows to investigate dynamical systems coupled through directed group interactions. As an application we study the synchronization of nonlinear oscillators on 1-directed hypergraphs, finding that directed higher-order interactions can destroy synchronization, but also stabilize otherwise unstable synchronized states. There is increasing evidence that many higher-order interactions in complex systems are directed. Here, the authors provide a tensorial formalism for directed hypergraphs and investigate their synchronization properties generalizing the Master Stability Function approach.

A fundamental question is whether groups of nodes of a complex network can possibly display long-term cluster-synchronized behavior. While this question has been addressed for the restricted classes of unweighted and labeled graphs, it remains an open problem for the more general class of weighted networks. The emergence of coordinated motion of nodes in natural and technological networks is directly related to the network structure through the concept of an equitable partition, which determines which nodes can show long-term synchronized behavior and which nodes cannot. We provide a method to detect the presence of nearly equitable partitions in weighted networks, based on minimal information about the network structure. With this approach we are able to discover the presence of dynamical communities in both synthetic and real technological, biological, and social networks, to a statistically significant level. We show that our approach based on dynamical communities is better at predicting the emergence of synchronized behavior than existing methods to detect community structure.

The robustness of two widespread multifractal analysis methods, one based on detrended fluctuation analysis and one on wavelet leaders, is discussed in the context of time-series containing non-uniform structures with only isolated singularities. Signals generated by simulated and experimentally-realized chaos generators, together with synthetic data addressing particular aspects, are taken into consideration. The results reveal essential limitations affecting the ability of both methods to correctly infer the non-multifractal nature of signals devoid of a cascade-like hierarchy of singularities. Namely, signals harboring only isolated singularities are found to artefactually give rise to broad multifractal spectra, resembling those expected in the presence of a well-developed underlying multifractal structure. Hence, there is a real risk of incorrectly inferring multifractality due to isolated singularities. The careful consideration of local scaling properties and the distribution of Hölder exponent obtained, for example, through wavelet analysis, is indispensable for rigorously assessing the presence or absence of multifractality.

Many properties of the structure and dynamics of complex networks derive from the characteristics of the spectrum of the associated Laplacian matrix, specifically from the set of its eigenvalues. In this paper, we show that there exist graphs for which the ratio between the length of the spectrum (that is, the difference between the largest and smallest eigenvalues of the Laplacian matrix) and its spread (the difference between the second smallest eigenvalue and the smallest one) is equal to the golden ratio. We call such graphs Golden Laplacian Graphs (GLG). In this paper, we first find all such graphs with a number of nodes n≤10. We then prove several graph-theoretic and algebraic properties that characterize these graphs. These graphs prove to be extremely robust, as they have large vertex and edge connectivity along with a large isoperimetric constant. Finally, we study the synchronization properties of GLGs, showing that they are among the top synchronizable graphs of the same size. Therefore, GLGs represent very good candidates for engineering and communication networks.

In this paper we study phase synchronization in random complex networks of coupled periodic oscillators. In particular, we show that, when amplitude dynamics is not negligible, phase synchronization may be enhanced. To illustrate this, we compare the behavior of heterogeneous units with both amplitude and phase dynamics and pure (Kuramoto) phase oscillators. We find that in small network motifs the behavior crucially depends on the topology and on the node frequency distribution. Surprisingly, the microscopic structures for which the amplitude dynamics improves synchronization are those that are statistically more abundant in random complex networks. Thus, amplitude dynamics leads to a general lowering of the synchronization threshold in arbitrary random topologies. Finally, we show that this synchronization enhancement is generic of oscillators close to Hopf bifurcations. To this aim we consider coupled FitzHugh-Nagumo units modeling neuron dynamics.

Companies working on semiconductors must currently assure the customers of not only the performance of the semiconductor device per se, but also its performance when it is implemented in a real board, therefore including the role of parasitic effects. It is therefore very important to evaluate, especially during the design phase, not only the single device, but the complete board and their mutual interactions. This consideration opens a new area of investigation in the field of electronic systems engineering. In the current literature, the problem of a software evaluation of parasitic dynamics and electromagnetic effects on printed boards is addressed from the point of view of researchers. Moreover, it is fundamental to have a complete view of the various tools that could be usefully adopted from the perspective of manufacturers. This is the main motivation of this technical note, which performs a comparative analysis of the most prominent software tools for printed circuit boards’ (PCBs) simulation. The main features, the key aspects, and the limitations of the software packages are analyzed in terms of the industrial design of power electronics devices, in order to ensure efficiency and fastness in the semiconductor market.

Imperfections are unavoidable in production processes of real devices. Despite this, and despite the fact that real devices usually operate in regimes far from ideality, they still work. This is related to the fact that imperfections give rise to hidden dynamics, which, opportunely excited, have an overall positive effect on the device. In this paper, we focus on a complex and imperfect electromechanical structure which can be considered as a paradigm for imperfect systems. The electrical and mechanical interactions within the structure generate complex patterns of vibration which may prevent the system to reach the correct working conditions. A control strategy to ensure the optimal working conditions based on the excitation of the hidden dynamics induced by imperfections is discussed, characterizing its effect with respect to the control signal properties and to the power provided to the structure.

Multi-agent models often describe populations segregated either in the physical space, i.e. subdivided in metapopulations, or in the ecology of opinions, i.e. partitioned in echo chambers. Here we show how both kinds of segregation can emerge from the interplay between homophily and social influence in a simple model of mobile agents endowed with a continuous opinion variable. In the model, physical proximity determines a progressive convergence of opinions but differing opinions result in agents moving away from each others. This feedback between mobility and social dynamics determines the onset of a stable dynamical metapopulation scenario where physically separated groups of like-minded individuals interact with each other through the exchange of agents. The further introduction of confirmation bias in social interactions, defined as the tendency of an individual to favor opinions that match his own, leads to the emergence of echo chambers where different opinions coexist also within the same group. We believe that the model may be of interest to researchers investigating the origin of segregation in the offline and online world.