Related papers: Fundamental interactions in self-organized critica…
Higher-order interactions that nonlinearly couple more than two nodes are important in many networked systems, and their effects on collective dynamics are increasingly being studied. Here we provide an overview of this rapidly growing…
Recent studies uncovered important core/periphery network structures characterizing complex sets of cooperative and competitive interactions between network nodes, be they proteins, cells, species or humans. Better characterization of the…
Cooperative behaviors are deeply embedded in structured biological and social systems. Networks are often employed to portray pairwise interactions among individuals, where network nodes represent individuals and links indicate who…
Morphogenesis emerges from dynamic feedback among geometry, mechanics, and chemistry; however, disentangling these contributions in living systems remains challenging. Here, we focus on the interplay between geometry and mechanics by…
Many real-world complex systems are characterized by non-pairwise -- higher-order -- interactions among system's units, and can be effectively modeled as hypergraphs. Directed hypergraphs distinguish between source and target sets within…
In this work, we propose a comprehensive theoretical framework combining percolation theory with nonlinear dynamics in order to study hypergraphs with a time-varying giant component. We consider in particular hypergraphs with higher-order…
Directed cycles form the fundamental motifs in natural, social and artificial networks, yet their distinct computational roles remain under-explored, particularly in the context of higher-order structure and function. In this work, we…
We develop a novel method based in the sparse random graph to account the interplay between geometric frustration and disorder in cluster magnetism. Our theory allows to introduce the cluster network connectivity as a controllable…
The most fundamental social interactions among humans occur face to face. Their features have been extensively studied in recent years, owing to the availability of high-resolution data on individuals' proximity. Mathematical models based…
Neuronal networks can present activity described by power-law distributed avalanches presumed to be a signature of a critical state. Here we study a random-neighbor network of excitable cellular automata coupled by dynamical synapses. The…
We explore the consequences of introducing higher-order interactions in a geometric complex network of Morris-Lecar neurons. We focus on the regime where travelling synchronization waves are observed out of a first-neighbours based…
There has recently been an explosion of interest in how "higher-order" structures emerge in complex systems. This "emergent" organization has been found in a variety of natural and artificial systems, although at present the field lacks a…
Percolation theory dictates an intuitive picture depicting correlated regions in complex systems as densely connected clusters. While this picture might be adequate at small scales and apart from criticality, we show that highly correlated…
Higher-order connectivity in complex systems described by simplexes of different orders provides a geometry for simplex-based dynamical variables and interactions. Simplicial complexes that constitute a functional geometry of the human…
The synaptic connectivity of cortical networks features an overrepresentation of certain wiring motifs compared to simple random-network models. This structure is shaped, in part, by synaptic plasticity that promotes or suppresses…
Spatial self-organization emerges in distributed systems exhibiting local interactions when nonlinearities and the appropriate propagation of signals are at work. These kinds of phenomena can be modeled with different frameworks, typically…
Higher-order interactions underlie complex phenomena in systems such as biological and artificial neural networks, but their study is challenging due to the scarcity of tractable models. By leveraging a generalisation of the maximum entropy…
The co-evolution of structure and dynamics, known as adaptivity, is a fundamental property in various systems and drives diverse emergent behaviors. However, the adaptivity in previous works is primarily stemmed from pairwise situations,…
Entrainment of randomly coupled oscillator networks by periodic external forcing applied to a subset of elements is numerically and analytically investigated. For a large class of interaction functions, we find that the entrainment window…
Self-organizations of ordered patterns in far-from-equilibrium many-body systems host fundamental importance in many disciplines. Meanwhile, complex systems often feature hierarchical structures with distinct scales for different layers,…