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Correlation dimension of complex networks
Lucas Lacasa, Jesus Gomez-Gardeñes
We propose a new measure to characterize the dimension of complex networks based on the ergodic theory of dynamical systems. This measure is derived from the correlation sum of a t…
Phase transition in the Countdown problem
Lucas Lacasa, Bartolo Luque
Here we present a combinatorial decision problem, inspired by the celebrated quiz show called the countdown, that involves the computation of a given target number T from a set of…
Crossover phenomenon in the performance of an Internet search engine
Lucas Lacasa, Jacopo Tagliabue, Andrew Berdahl
In this work we explore the ability of the Google search engine to find results for random N-letter strings. These random strings, dense over the set of possible N-letter words, ad…
Feigenbaum graphs at the onset of chaos
Bartolo Luque, Lucas Lacasa, Alberto Robledo
We analyze the properties of the self-similar network obtained from the trajectories of unimodal maps at the transition to chaos via the horizontal visibility (HV) algorithm. We fi…
Analytical properties of horizontal visibility graphs in the Feigenbaum scenario
Bartolo Luque, Lucas Lacasa, Fernando J. Ballesteros +1
Time series are proficiently converted into graphs via the horizontal visibility (HV) algorithm, which prompts interest in its capability for capturing the nature of different clas…