Complexity Matching and Requisite Variety

Abstract

Complexity matching emphasizes the condition necessary to efficiently transport information from one complex system to another and the mechanism can be traced back to the 1957 Introduction to Cybernetics by Ross Ashby. Unlike this earlier work we argue that complexity can be expressed in terms of crucial events, which are generated by the processes of spontaneous self-organization. Complex processes, ranging from biological to sociological, must satisfy the homeodynamic condition and host crucial events that have recently been shown to drive the information transport between complex systems. We adopt a phenomenological approach, based on the subordination to periodicity that makes it possible to combine homeodynamics and self-organization induced crucial events. The complexity of crucial events is defined by the waiting-time probability density function (PDF) of the intervals between consecutive crucial events, which have an inverse power law (IPL) PDF ψ(τ ) ∝ 1/(τ ) µ with 1 < µ < 3. We establish the coupling between two temporally complex systems using a phenomenological approach inspired by models of swarm cognition and prove that complexity matching, namely sharing the same IPL index µ, facilitates the transport of information, generating perfect synchronization, reminiscent of, but distinct from chaos synchronization. This advanced form of complexity matching is expected to contribute a significant progress in understanding and improving the bio-feedback therapies.Author Summary This paper is devoted to the control of complex dynamical systems, inspired to real processes of biological and sociological interest. The concept of complexity we adopt focuses on the assumption that the processes of self-organization generate intermittent fluctuations and that the time distance between two consecutive fluctuations is described by a distribution density with an inverse power law structure making the second moment of these time distances diverge. These fluctuations are called crucial events and are responsible for the ergodicity breaking that is widely revealed by the experimental observation of biological dynamics. We argue that the information transport from one to another complex system is ruled by these crucial events and we propose an efficient theoretical prescription leading to qualitative agreement with experimental results, shedding light into the processes of social learning. The theory of this paper is expected to have important medical applications, such as an improvement of the biofeedback techniques, the heart-brain communication and a significant progress on cognition and the contribution of emotions to cognition.

Entropic Approach to the Detection of Crucial Events

“…On the basis of the present results, we conclude that the frequencies of the brain wave may affect the brain physiological process with SFBM contributions that are killed by the DEA analysis resting on the adoption of the method of stripes and that the form of 1/ f noise generated by the brain in the awake condition is due to ASBM, thereby supporting the conjecture that the brain-heart correlation is a consequence of complexity matching [55], mainly resting on tuning temporal complexity rather than frequencies.…”

Complexity Matching: Restoring the Complexity of Locomotion in Older People Through Arm-in-Arm Walking

“…This attunement of complexities has been observed in a number of synchronization experiments (Stephen et al, 2008; Marmelat and Delignières, 2012; Abney et al, 2014; Delignières and Marmelat, 2014; Coey et al, 2016; Almurad et al, 2017). Mahmoodi et al (2018) emphasized the role of crucial events, which play a fundamental role in the transport of information between complex networks. Crucial events are generated by the processes of self-organization, and the series of waiting times separating successive crucial events presents 1/ f properties.…”

Complex Periodicity and Synchronization

“…PG and KM thank the US Army Research Office for supporting this work through grant W911NF1901. This manuscript has been released as a pre-print at arXiv (Mahmoodi et al, 2018 ).…”