Related papers: Hidden geometry and dynamics of complex networks: …

Dimensionality is a critical factor in determining the properties of solids and is an apparent built-in character of the crystal structure. However, it can be an emergent and tunable property in geometrically frustrated spin systems. Here,…

Geometric graph models of systems as diverse as proteins, robots, and mechanical structures from DNA assemblies to architected materials point towards a unified way to represent and control them in space and time. While much work has been…

Topological data analysis can reveal higher-order structure beyond pairwise connections between vertices in complex networks. We present a new method based on discrete Morse theory to study topological properties of unweighted and…

Geometric frustration offers a pathway to soft matter self-assembly with controllable finite sizes. While the understanding of frustration in soft matter assembly derives almost exclusively from continuum elastic descriptions, a current…

Complex textured surfaces occur in nature and industry, from fingerprints to lithography-based micropatterns. Wrinkling by confinement to an incompatible substrate is an attractive way of generating reconfigurable patterned topographies,…

We review the recent fast progress in statistical physics of evolving networks. Interest has focused mainly on the structural properties of random complex networks in communications, biology, social sciences and economics. A number of giant…

Empirical complex systems can be characterized not only by pairwise interactions, but also by higher-order (group) interactions influencing collective phenomena, from metabolic reactions to epidemics. Nevertheless, higher-order networks'…

Most of the complex social, technological and biological networks have a significant community structure. Therefore the community structure of complex networks has to be considered as a universal property, together with the much explored…

A systematic study of both classical and quantum geometric frustrated Ising models with a competing ordering mechanism is reported in this paper. The ordering comes in the classical case from a coupling of 2D layers and in the quantum model…

Meso-scale structures (communities) are used to understand the macro-scale properties of complex networks, such as their functionality and formation mechanisms. Micro-scale structures are known to exist in most complex networks (e.g., large…

Hypergraphs have emerged as a powerful modeling framework to represent systems with multiway interactions, that is systems where interactions may involve an arbitrary number of agents. Here we explore the properties of real-world…

Although higher-order interactions are known to affect the typical state of dynamical processes giving rise to new collective behavior, how they drive the emergence of rare events and fluctuations is still an open problem. We investigate…

Machine-learning techniques have proved successful in identifying ordered phases of matter. However, it remains an open question how far they can contribute to the understanding of phases without broken symmetry, such as spin liquids. Here…

Although jammed packings of soft spheres exist in potential energy landscapes with a vast number of minima, when subjected to cyclic shear they may revisit the same configurations repeatedly. Simple hysteretic spin models, in which particle…

Hierarchies permeate the structure of real networks, whose nodes can be ranked according to different features. However, networks are far from tree-like structures and the detection of hierarchical ordering remains a challenge, hindered by…

Simplicial complexes are generalized network structures able to encode interactions occurring between more than two nodes. Simplicial complexes describe a large variety of complex interacting systems ranging from brain networks, to social…

The geometric arrangement of interacting (magnetic) dipoles is a question of fundamental importance in physics, chemistry and engineering. Motivated by recent progress concerning the self-assembly of magnetic structures, the equilibrium…

We study extremely diluted spin models of neural networks in which the connectivity evolves in time, although adiabatically slowly compared to the neurons, according to stochastic equations which on average aim to reduce frustration. The…

The geometric renormalization technique for complex networks has successfully revealed the multiscale self-similarity of real network topologies and can be applied to generate replicas at different length scales. In this letter, we extend…

Multiplex networks are collections of networks with identical nodes but distinct layers of edges. They are genuine representations for a large variety of real systems whose elements interact in multiple fashions or flavors. However,…