title: Detection of timescales in evolving complex systems.
abstract: Most complex systems are intrinsically dynamic in nature. The evolution of a dynamic complex system is typically represented as a sequence of snapshots, where each snapshot describes the configuration of the system at a particular instant of time. This is often done by using constant intervals but a better approach would be to define dynamic intervals that match the evolution of the system's configuration. To this end, we propose a method that aims at detecting evolutionary changes in the configuration of a complex system, and generates intervals accordingly. We show that evolutionary timescales can be identified by looking for peaks in the similarity between the sets of events on consecutive time intervals of data. Tests on simple toy models reveal that the technique is able to detect evolutionary timescales of time-varying data both when the evolution is smooth as well as when it changes sharply. This is further corroborated by analyses of several real datasets. Our method is scalable to extremely large datasets and is computationally efficient. This allows a quick, parameter-free detection of multiple timescales in the evolution of a complex system.
authors.affiliation: Department of Computer Science, Aalto University School of Science, P.O. Box 15400, FI-00076, Finland.
authors.forename: Richard K
authors.initials: RK
authors.lastname: Darst
authors.affiliation: Carolina Center for Interdisciplinary Applied Mathematics, Department of Mathematics, University of North Carolina, Chapel Hill, NC 27599-3250, USA.
authors.forename: Clara
authors.initials: C
authors.lastname: Granell
authors.affiliation: Departament d'Enginyeria Informàtica i Matemàtiques, Universitat Rovira i Virgili, 43007 Tarragona, Spain.
authors.forename: Alex
authors.initials: A
authors.lastname: Arenas
authors.affiliation: Departament d'Enginyeria Informàtica i Matemàtiques, Universitat Rovira i Virgili, 43007 Tarragona, Spain.
authors.forename: Sergio
authors.initials: S
authors.lastname: Gómez
authors.affiliation: Department of Computer Science, Aalto University School of Science, P.O. Box 15400, FI-00076, Finland.
authors.forename: Jari
authors.initials: J
authors.lastname: Saramäki
authors.affiliation: Department of Computer Science, Aalto University School of Science, P.O. Box 15400, FI-00076, Finland.|Center for Complex Networks and Systems Research, School of Informatics and Computing, Indiana University, Bloomington, USA.
authors.forename: Santo
authors.initials: S
authors.lastname: Fortunato