The coronavirus known as COVID-19 has spread worldwide since December 2019. Without any vaccination or medicine, the means of controlling it are limited to quarantine and social distancing. Here we study spatio-temporal propagation first wave virus in China compare other global locations. We provide a comprehensive picture spatial from Hubei provinces terms distance, population size, human mobility their scaling relations. Since strict been usually applied between cities, more insight into...

The new coronavirus known as COVID-19 is spread world-wide since December 2019. Without any vaccination or medicine, the means of controlling it are limited to quarantine and social distancing. Here we study spatio-temporal propagation first wave virus in China compare other global locations. We provide a comprehensive picture spatial from Hubei provinces terms distance, population size, human mobility their scaling relations. Since strict has been usually applied between cities, more...

Abstract K-core percolation is a fundamental dynamical process in complex networks with applications that span numerous real-world systems. Earlier studies focus primarily on random without spatial constraints and reveal intriguing mixed-order transitions. However, systems, ranging from transportation communication to brain networks, are not but spatially embedded. Here, we study k-core two-dimensional embedded show that, contrast regular percolation, the length of connections can control...

Percolation on interdependent networks generalizes the well-studied percolation model in a single network to multiple interacting systems, unveiling spontaneous cascading failures, abrupt collapses, and high vulnerability. The main novelty of has been introduction two types links, connectivity within dependency between them. interplay these interactions results novel critical phenomena phase transitions. This abstract paradigm was recently applied magnetic networks, as an experimentally...

Cascades are self-reinforcing processes underlying the systemic risk of many complex systems. Understanding universal aspects these phenomena is fundamental interest, yet typically bound to numerical observations in ad-hoc models and limited insights. Here, we develop a unifying approach that reveals two distinct universality classes cascades determined by global symmetry cascading process. We provide hyperscaling arguments predicting hybrid critical characterized combination both mean-field...

The dynamics of cascading failures in spatial interdependent networks significantly depends on the interaction range dependency couplings between layers. In particular, for an increasing couplings, different types phase transition accompanied by various cascade kinetics can be observed, including mixed-order characterized critical branching phenomena, first-order with nucleation cascades, and continuous second-order weak cascades. We also describe cascades at mutual resistive superconductors...

Epidemic spread on networks is one of the most studied dynamics in network science and has important implications real epidemic scenarios. Nonetheless, epidemics how it affected by underline structure infection channels are still not fully understood. Here we apply susceptible-infected-recovered model study analytically numerically a recently developed spatial modular imitating cities country. The assumes that inside city connect many different locations, while between less usually directly...

We study the critical features of order parameter's fluctuations near threshold mixed-order phase transitions in randomly interdependent spatial networks. Remarkably, we find that although structure parameter is not scale invariant, its are fractal up to a well-defined correlation length ξ^{'} diverges when approaching transition threshold. characterize self-similar nature these through their effective dimension d_{f}^{'}=3d/4, and exponent ν^{'}=2/d, where d system. By analyzing percolation...

Abstract The models of k -core percolation and interdependent networks (IN) have been extensively studied in their respective fields. A recent study has revealed that they share several common critical exponents. However, newly discovered exponents IN not explored percolation, the origin similarity still remains unclear. Thus, this paper, by considering on random networks, we first verify two (fractal fluctuation dimension, <?CDATA $d^{^{\prime}}_\textrm{f}$?> <mml:math...

Many interdependent, real-world infrastructures involve interconnections between different communities or cities. Here we study if and how the effects of such can be described as an external field for interdependent networks experiencing first-order percolation transitions. We find that critical exponents $\gamma$ $\delta$, related to also defined transitions but they have values than those found second-order Surprisingly, both sets even within a single model networks, depending on...

The study of interdependent networks has recently experienced a boost with the development experimentally testable materials that physically realize their novel critical behaviors, calling for systematic studies go beyond percolation paradigm. Here we kinetics and phase transitions model spatial ferromagnetic where dependency couplings between are realized by thermal interaction having tunable range. We show how phenomena diagram this realistic highly affected range dissipation latter...

We study a spatial network model with exponentially distributed link lengths on an underlying grid of points, undergoing structural crossover from random, Erdős-Rényi graph, to d-dimensional lattice at the characteristic interaction range ζ. find that, whilst far percolation threshold random part giant component scales linearly ζ, close criticality it extends in space until universal length scale ζ^{6/(6-d)}, for d<6, before crossing over one. demonstrate behavior spatiotemporal...

We study the effect of localized attacks on a multiplex network, where each layer is network communities embedded in space. assume that nodes are densely connected within community and sparsely to neighboring communities. To investigate percolation processes this realistic system we develop an analytical scheme, applying finite-element method. find, both by simulation theory, many cases there critical size damage above which it will spread entire collapse. In addition, show for constant...

Many realistic systems such as infrastructures are characterized by spatial structure and anisotropic alignment. Here we propose study a model for dealing with characteristics introducing parameter that controls the strength of anisotropy in network. This is added to an existing isotropic used describe networks under constraints, thus generalizing take into account both features. We resilience using percolation process find has negative impact on network's robustness. In addition, our...

Abstract The importance of understanding human mobility patterns has led many studies to examine their spatial-temporal scaling laws. These mainly reveal that travel can be highly non-homogeneous with power-law distributions distances and times. However, investigating quantifying the extent variability in time space when traveling same air distance not been addressed so far. Using taxi data from five large cities, we focus on several novel measures explore spatio-temporal variations routes...

Understanding the resilience of infrastructures such as transportation network has significant importance for our daily life. Recently, a homogeneous spatial model was developed studying embedded networks with characteristic link length power-grids and brain. However, although many real-world are spatially their links have characteristics pipelines, power lines or ground they not but rather heterogeneous. For example, density within cities significantly higher than between cities. Here we...

We study the transient dynamics of an A+B→0 process on a pair randomly coupled networks, where reactants are initially separated. find that, for sufficiently small fractions q cross couplings, concentration A (or B) particles decays linearly in first stage and crosses over to second linear decrease at mixing time t_{x}. By numerical analytical arguments, we show that symmetric homogeneous structures t_{x}∝(〈k〉/q)log(〈k〉/q) 〈k〉 is mean degree both networks. Being this behavior marked contrast...

The divergence of the correlation length ξ at criticality is an important phenomenon percolation in two-dimensional systems. Substantial speed-ups to calculation threshold and component distribution have been achieved by utilizing disjoint sets, but existing algorithms this sort cannot measure length. Here we utilize parallel axis theorem track as nodes are added system, allowing us sets for entire process with arbitrary precision a single sweep. This algorithm enables direct measurement...

Cascades are self-reinforcing processes underlying the systemic risk of many natural and socio-technical systems. Understanding universal aspects these phenomena is a fundamental topic, yet typically bound to numerical observations in ad-hoc models limited insights. Here, we develop unifying approach show that regime shifts by long-range cascades characterized two universality classes defined parity invariance process. We provide hyperscaling arguments predicting critical exponents with...

The paradigm of interdependent networks has recently been manifested in experimentally testable lab setup superconducting networks. This system experiences an abrupt transition due to the thermal dissipation between but its underlying mechanism remains elusive. Here we study critical behavior and transition, unveiling unique microscopic nature. characteristics result a macroscopic long-living plateau that lasts for thousands seconds increases with size system. We characterize find exponents...