Article argues that the Dunbar number arises as a consequence of a natural phase transition in the dynamic self-organization among N individuals within a social system. The authors provide a theoretical basis for the value of the Dunbar number and establish a theory-based bridge spanning the gap between sociology and psychology.

Article explores experimental walking synchronization and complexity restoration. The main goal is to establish a physiological foundation of these important results based on the recent advances on the dynamics of the brain, interpreted as a system at criticality.

This article reviews the literature to argue the importance of the occurrence of crucial events in the dynamics of physiological processes. Crucial events are interpreted as short time intervals of turbulence, and the time distance between two consecutive crucial events is a waiting time distribution density with an inverse power law (IPL) index µ, with µ < 3 generating non-stationary behavior.

This article is a review discussing the origin, development, and application of the renormalization group (RG) method in a variety of fields from the physical, social and life sciences, in singular perturbation theory, and reveal the need to connect the RG and the fractional calculus (FC). The authors also present recommendations for future research based on this new way of thinking.

This article studies two forms of anomalous diffusions and discusses the joint use of these prescriptions, with a phenomenological method and a theoretical projection method, leading to two apparently different diffusion equations. The authors prove that the two diffusion equations are equivalent and design a time series that corresponds to the anomalous diffusion equation proposed.

This article studies the emission of photons from germinating seeds using an experimental technique designed to detect light of extremely small intensity. It analyzes the dark count signal without germinating seeds as well as the photon emission during the germination process.

This article discusses the decision-making model (DMM), a paradigmatic instance of criticality, which deals with bounded rationality issues in a similar way as quantum probability (QP), generating choices that cannot be accounted by classical probability (CP). This work may contribute to considering criticality as another possible fundamental pillar in order to improve the understanding of cognition and of quantum mechanics.

This article is the fourth paper of the Special Issue Memory and Criticality. It bridges the the theoretical debate on the role of memory and criticality discussed in the three earlier manuscripts, with a review of key concepts in biology and focus on cell-to-cell communication in organismal development. The authors suggest that in conjunction with morphogenetic gradients, there exist gradients of information transfer creating cybernetic loops of stability and disorder, setting the stage for adaptive capability. Criticality, therefore, appears to be an important factor in the transmission, transfer and coding of information for complex adaptive system development.

This article is the third essay advocating the use the (non-integer) fractional calculus (FC) to capture the dynamics of complex networks in the twilight of the Newtonian era. Herein, the focus is on drawing a distinction between networks described by monfractal time series extensively discussed in the prequels and how they differ in function from multifractal time series, using physiological phenomena as exemplars.