Related papers: Critical phenomena in the dynamical visibility gra…

In dynamical percolation, the status of every bond is refreshed according to an independent Poisson clock. For graphs which do not percolate at criticality, the dynamical sensitivity of this property was analyzed extensively in the last…

It is possible to investigate emergence in many real systems using time-ordered data. However, classical time series analysis is usually conditioned by data accuracy and quantity. A modern method is to map time series onto graphs and study…

The dynamics of a complex system is usually recorded in the form of time series, which can be studied through its visibility graph from a complex network perspective. We investigate the visibility graphs extracted from fractional Brownian…

We study the collective behaviour of an ensemble of coupled motile elements whose interactions depend on time and are alternatively attractive or repulsive. The evolution of interactions is driven by individual internal variables with…

Random graphs have played an instrumental role in modelling real-world networks arising from the internet topology, social networks, or even protein-interaction networks within cells. Percolation, on the other hand, has been the fundamental…

We describe the critical window for percolation in the universality class of sparse growing random graphs. In our models, vertices arrive sequentially and connect independently to each earlier vertex $v$ with probability proportional to a…

We analyze critical time series of the order parameter generated with active to inactive phase transitions of spreading dynamics running on the top of heterogeneous networks. Different activation mechanisms that govern the dynamics near the…

In complex systems, external parameters often determine the phase in which the system operates, i.e., its macroscopic behavior. For nearly a century, statistical physics has extensively studied systems' transitions across phases,…

A variant of self-similar approximation theory is suggested, permitting an easy and accurate summation of divergent series consisting of only a few terms. The method is based on a power-law algebraic transformation, whose powers play the…

We analyze critical phenomena on networks generated as the union of hidden variables models (networks with any desired degree sequence) with arbitrary graphs. The resulting networks are general small-worlds similar to those a` la Watts and…

We study intersection properties of two or more independent tree-like random graphs. Our setting encompasses critical, possibly long range, Bernoulli percolation clusters, incipient infinite clusters, as well as critical branching random…

The control of complex systems is an ongoing challenge of complexity research. Recent advances using concepts of structural control deduce a wide range of control related properties from the network representation of complex systems. Here,…

This study investigates how visibility graphs constructed from Monte Carlo Markov Chain time series of spin models capture the critical behavior of the system. More precisely, we show that this approach identifies continuous phase…

We have numerically studied the trapping problem in a two-dimensional lattice where particles are continuously generated. We have introduced interaction between particles and directionality of their movement. This model presents a critical…

Recent research on temporal networks has highlighted the limitations of a static network perspective for our understanding of complex systems with dynamic topologies. In particular, recent works have shown that i) the specific order in…

We analyse, using Inhomogenous Mode-Coupling Theory, the critical scaling behaviour of the dynamical susceptibility at a distance epsilon from continuous second-order glass transitions. We find that the dynamical correlation length xi…

In this work we present a simple and fast computational method, the visibility algorithm, that converts a time series into a graph. The constructed graph inherits several properties of the series in its structure. Thereby, periodic series…

This note outlines a method for clustering time series based on a statistical model in which volatility shifts at unobserved change-points. The model accommodates some classical stylized features of returns and its relation to GARCH is…

The characterization of the "most connected" nodes in static or slowly evolving complex networks has helped in understanding and predicting the behavior of social, biological, and technological networked systems, including their robustness…

We study the susceptibility, i.e., the mean cluster size, in random graphs with given vertex degrees. We show, under weak assumptions, that the susceptibility converges to the expected cluster size in the corresponding branching process. In…