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.
Highlights
Most complex systems are intrinsically dynamic in nature
We live in a dynamic world, where most things are subject to steady change
One can decide to use a constant slice size corresponding to some characteristic temporal scale of the dynamics, or a variable slice size that follows the rate of the dynamic activity
Summary
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. Whether we consider the interactions between people, proteins, or Internet devices, there is a complex dynamics that may progress continuously with varying rates[1], or be punctuated by sudden bursts[2] For understanding such complex systems, rich empirical data with detailed time-domain information is required, together with proper statistical tools to make use of it. The choice of slice size will be determined both by the availability and granularity of data, and by the timescales that reflect evolutionary changes in the configuration of events It follows that there is a clear need for a principled way of automatically identifying suitable evolutionary timescales in data-driven investigations of evolving complex systems. A proper time-slicing method should produce meaningful evolutionary timescales www.nature.com/scientificreports/
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