In this article, the authors show that the widely accepted conviction that a connection can be established between the probability density entropy and the Kolmogorov-Sinai (KS) entropy is questionable.

This article discusses dynamic approach to the thermodynamics of superdiffusion.

Article discussing the fractional Brownian motion (FBM) as a nonstationary process and an alternative paradigm for DNA sequences.

Article discussing research on anomalous diffusion and ballistic peaks.

This article discusses a non-Gaussian indicator to measure the deviation from Gaussian statistics of a diffusion process generated by dichotomous fluctuations with infinite memory.

Article addressing the problem of establishing which is the proper form of quantum master equation generating a survival probability identical to that corresponding to the nonergodic sequence of "light on" and "light off" fluorescence fluctuations in blinking quantum dots.

Article discussing fluorescence intermittency in blinking quantum dots.

Article on power spectra for both interrupted and perennial aging processes.

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 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 discusses the dynamics of EEG entropy.

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.

In this article, the authors study a set of cooperatively interacting units at criticality, and prove with analytical and numerical arguments that they generate the same renewal non-Poisson intermittency as that produced by blinking quantum dots.

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.

Article on diffusion entropy and waiting time statistics of hard-x-ray solar flares.

Article discussing research on cooperation and neural systems and bridging complexity and periodicity.

Article on the renewal and memory origin of anomalous diffusion and a discussion of their joint action.

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

Article discussing a study on complexity and the fractional calculus.

Article exploring the topology of black holes.

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 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 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.