Criticality in the relaxation phase of a spontaneously contracting atria isolated from a frog's heart

Statistical and Criticality Analysis of the Lower Ionosphere Prior to the 30 October 2020 Samos (Greece) Earthquake (M6.9), Based on VLF Electromagnetic Propagation Data as Recorded by a New VLF/LF Receiver Installed in Athens (Greece)

In this work we present the statistical and criticality analysis of the very low frequency (VLF) sub-ionospheric propagation data recorded by a VLF/LF radio receiver which has recently been established at the University of West Attica in Athens (Greece). We investigate a very recent, strong (M6.9), and shallow earthquake (EQ) that occurred on 30 October 2020, very close to the northern coast of the island of Samos (Greece). We focus on the reception data from two VLF transmitters, located in Turkey and Israel, on the basis that the EQ’s epicenter was located within or very close to the 5th Fresnel zone, respectively, of the corresponding sub-ionospheric propagation path. Firstly, we employed in our study the conventional analyses known as the nighttime fluctuation method (NFM) and the terminator time method (TTM), aiming to reveal any statistical anomalies prior to the EQ’s occurrence. These analyses revealed statistical anomalies in the studied sub-ionospheric propagation paths within ~2 weeks and a few days before the EQ’s occurrence. Secondly, we performed criticality analysis using two well-established complex systems’ time series analysis methods—the natural time (NT) analysis method, and the method of critical fluctuations (MCF). The NT analysis method was applied to the VLF propagation quantities of the NFM, revealing criticality indications over a period of ~2 weeks prior to the Samos EQ, whereas MCF was applied to the raw receiver amplitude data, uncovering the time excerpts of the analyzed time series that present criticality which were closest before the Samos EQ. Interestingly, power-law indications were also found shortly after the EQ’s occurrence. However, it is shown that these do not correspond to criticality related to EQ preparation processes. Finally, it is noted that no other complex space-sourced or geophysical phenomenon that could disturb the lower ionosphere did occur during the studied time period or close after, corroborating the view that our results prior to the Samos EQ are likely related to this mainshock.

Criticality in epidemic spread: An application in the case of COVID19 infected population

Recently, it has been successfully shown that the temporal evolution of the fraction of COVID-19 infected people possesses the same dynamics as the ones demonstrated by a self-organizing diffusion model over a lattice, in the frame of universality. In this brief, the relevant emerging dynamics are further investigated. Evidence that this nonlinear model demonstrates critical dynamics is scrutinized within the frame of the physics of critical phenomena. Additionally, the concept of criticality over the infected population fraction in epidemics (or a pandemic) is introduced and its importance is discussed, highlighting the emergence of the critical slowdown phenomenon. A simple method is proposed for estimating how far away a population is from this "singular" state, by utilizing the theory of critical phenomena. Finally, a dynamic approach applying the self-organized diffusion model is proposed, resulting in more accurate simulations, which can verify the effectiveness of restrictive measures. All the above are supported by real epidemic data case studies.

Diffusion Entropy vs. Multiscale and Rényi Entropy to Detect Progression of Autonomic Neuropathy

We review 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. The non-stationary condition is characterized by two regimes of the IPL index: (a) perennial non-stationarity, with 1 < μ < 2 and (b) slow evolution toward the stationary regime, with 2 < μ < 3. Human heartbeats and brain dynamics belong to the latter regime, with healthy physiological processes tending to be closer to the border with the perennial non-stationary regime with μ = 2. The complexity of cognitive tasks is associated with the mental effort required to address a difficult task, which leads to an increase of μ with increasing task difficulty. On this basis we explore the conjecture that disease evolution leads the IPL index μ moving from the healthy condition μ = 2 toward the border with Gaussian statistics with μ = 3, as the disease progresses. Examining heart rate time series of patients affected by diabetes-induced autonomic neuropathy of varying severity, we find that the progression of cardiac autonomic neuropathy (CAN) indeed shifts μ from the border with perennial variability, μ = 2, to the border with Gaussian statistics, μ = 3 and provides a novel, sensitive index for assessing disease progression. We find that at the Gaussian border, the dynamical complexity of crucial events is replaced by Gaussian fluctuation with long-time memory.

Traits of criticality in membrane potential fluctuations of pyramidal neurons in the CA1 region of rat hippocampus

Evidence that neural circuits are operating near criticality has been provided at various levels of brain organisation with a presumed role in maximising information processing and multiscale activity association. Criticality has been linked to excitation at both the single-cell and network levels, as action potential generation marks an obvious phase transition from a resting to an excitable state. Using in vitro intracellular recordings, we examine irregular, small amplitude membrane potential fluctuations from CA1 pyramidal neurons of Wistar male rats. We show that these fluctuations, confounded with noise, carry information relevant to the neuronal state. The underlying dynamics exhibit intermittent characteristics shown to describe the temporal fluctuations of the order parameter of a macroscopic system at its critical point even in the absence of firing. An externally applied stimulus serves as the control parameter, driving the system in and out of its critical state. Based on our experimental observations we calculate the equivalent of the isothermal critical exponent δ_h finding a value which depends on the applied stimulus. For each neuron there is a stimulus amplitude for which the critical behaviour becomes most pronounced. The corresponding mean value of δ_h in the considered ensemble of neurons is δ_h  ≈ 1.89, close to theoretical predictions for critical networks. Finally, we show that the firing rate of a neuron decreases exponentially with δ_h .

Intermittency-induced criticality in a resistor-inductor-diode circuit

The current fluctuations of a driven resistor-inductor-diode circuit are investigated here looking for signatures of critical behavior monitored by the driving frequency. The experimentally obtained time series of the voltage drop across the resistor (as directly proportional to the current flowing through the circuit) were analyzed by means of the method of critical fluctuations in analogy to thermal critical systems. Intermittent criticality was revealed for a critical frequency band signifying the transition between the normal rectifier phase in the low frequencies and a full-wave conducting, capacitorlike phase in the high frequencies. The transition possesses critical characteristics with a characteristic exponent p_{l}=1.65. A fractal analysis in terms of the rescale range (R/RSS) and detrended fluctuation analysis methods yielded results fully compatible with the critical dynamics analysis. Suggestions for the interpretation of the observed behavior in terms of p-n junction operation are discussed.

Unimodal maps and order parameter fluctuations in the critical region

Recently it has been argued that the fluctuations of the order parameter of a system undergoing a second order transition, when considered as a time series, possess characteristic nonstochastic patterns at the critical point. These patterns can be described by a unimodal intermittent map (critical map) and are clearly distinguished from colored noise. In the present work we extend the method introduced in [Y. F. Contoyiannis, F. K. Diakonos, and A. Malakis, Phys. Rev. Lett. 89, 035701 (2002)], in order to reveal universal properties in the deformation of the dynamics of the order parameter fluctuations when departing from the critical point. We show that the obtained systematic change in the order parameter fluctuation pattern can be observed in the critical region of thermal critical systems such as the mean field and the 3D Ising model. In addition, we consider the case of order parameter fluctuations near a tricritical point and we derive an associated characteristic deterministic behavior. A corresponding analysis in the Z(3) model confirms our results. Thus, the method of critical fluctuations introduced previously and generalized here, provides us with a classification scheme allowing for the characterization of temporal fluctuations in an observed time series in terms of critical phenomena.

Monitoring of a preseismic phase from its electromagnetic precursors

Fracture in disordered media is a complex problem for which a definitive physical and theoretical treatment is still lacking. We view earthquakes (EQ's) as large-scale fracture phenomena in the Earth's heterogeneous crust. Our main observational tool is the monitoring of the microfractures, which occur in the prefocal area before the final breakup, by recording their kHz-MHz electromagnetic (EM) emissions, with the MHz radiation appearing earlier than the kHz. Two fundamental questions (unanswered yet) that scientists in this field ought to address are as follows. (i) Is there a way of estimating the time to global failure? (ii) Is the evolution towards global failure irreversible after the appearance of distinguishing features in the preseismic EM time series? We attempt to put forward physically powerful arguments with regard to answering these two basic questions. Our approach will be in terms of critical phase transitions in statistical physics, drawing on recently published results. We obtain two major results. First, the initial MHz part of the preseismic emission, which has anti-persistent behavior, is triggered by microfractures in the highly disordered system that surrounds the essentially homogeneous "backbone asperities" within the prefocal area and could be described in analogy with a thermal continuous phase transition. However, the analysis reveals that the system is gradually driven out of equilibrium. Considerations of the symmetry-breaking and "intermittent dynamics of critical fluctuations" method estimate the time beyond which the process generating the preseismic EM emission could continue only as a nonequilibrium instability. Second, the abrupt emergence of strong kHz emission in the tail of the precursory radiation, showing strong persistent behavior, is thought to be due to the fracture of the high-strength "backbones". The associated phase of the EQ nucleation is a nonequilibrium process without any footprint of an equilibrium thermal phase transition. The family of asperities sustains the system. Physically, the appearance of persistent properties may indicate that the process acquires a self-regulating character and to a great degree the property of irreversibility, one of the important components of predictive capability. We address the role of the order of material heterogeneity on the transition from anti-persistent to persistent behavior.