Renewal and Memory Properties in Complex Systems: Justifying the existence of Crucial Events in Heartbeat.
Rama Kalaga · 2025
This paper tries to address the issue of self-organization and the role of memory in heartbeat. It first reviews some of the methods used to study self-organization and memory in heartbeat and connects this to the state of extended criticality in physiological time series. Criticality is a unique organizational phase of matter where local interactions generate observable global properties. This state is characterized by a long-range order characterized by correlations in the order parameters that decay very slowly in time. It then investigates the presence of memory in such correlations and comments on the nature of physiological time series employing the two-point time correlation function technique as a method of analysis and experimentally establishing the presence of memory and crucial events in physiological time series. It then uses diffusion entropy analysis (DEA) to help experimentally verify the existence of memory in crucial events. It tries to explain how these results support the idea of a particular class of renewal events known as Crucial Events. This work shows that complex time series containing Crucial Events are characterized by the presence of memory and Self Organized Temporal Criticality, leading us to believe that Self Organized Temporal Criticality provides the most comprehensive description of a complex system like a heartbeat. Keywords: Memory, Renewal, Self Organized, Complexity