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.

Article exploring the topology of black holes.

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.

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.

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 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 establishes an approach that simultaneously detects the statistical properties of crucial events and a connection with the wave-like nature of brain dynamics.

This article addresses the question of how teams cope with environmental threats by investigating two drivers of team resilience: the team size and the density of social interactions among team members.

This article emphasizes that 1/f noise has two different origins, one compatible with Laplace determinism and one determined by unpredictable crucial events.

This article uses the self-organized temporal criticality (SOTC) model to identify the timing of crucial events as a new mechanism with which to generate criticality, thereby establishing a way for the internal dynamics of the decision making process to suppresss the sensitivity of social opinion to either zealot or independent minorities.

This article presents a novel optimization algorithm belonging to the class of swarm intelligence optimization methods.

This article proposes a social model of spontaneous self-organization generating criticality and resilience, called Self-Organized Temporal Criticality (SOTC).

This article introduces a form of Self-organized Criticality (SOC) inspired by the new generation of evolutionary game theory, which ranges from physiology to sociology.

This article discusses how the energetic loss caused by projection from higher to lower dimensions and by the Monster group’s non-abelian features is correlated with the present-day asymmetry in the thermodynamic arrow.

This article shows that the Borsuk-Ulam theorem applies also to multisensory integration: two environmental stimuli from different sensory modalities display similar features when mapped into cortical neurons.

This article introduces a novel technique of fMRI images analysis, called computational proximity method, i.e., nucleus clustering in Voronoï tessellations.

This article proposes that the brain (and other self-organised biological systems) can be characterised via the mathematical apparatus of a gauge theory.

Article on the effect of noise and detector sensitivity on a dynamical process and the inverse power law and Mittag-Leffler interevent time survival probabilities.

Paper discussing fractional calculus tying the microscopic and macroscopic scales of complex network dynamics.

Article on symmetry-induced intermittency in a stochastic reflexive model.