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 δh 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 δh in the considered ensemble of neurons is δh ≈ 1.89, close to theoretical predictions for critical networks. Finally, we show that the firing rate of a neuron decreases exponentially with δh.
Membrane potential fluctuations from in vitro recorded rat CA1 pyramidal neurons exhibit intermittent dynamics independent of spiking activity. An externally applied stimulus serves as the control parameter, driving the system in and out of its critical state. These findings suggest that individual neurons may be operating at a critical state. The information processing capacity of networks of critical units remains to be investigated.
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.
This work presents a new analysis method for two-symbol symbolic time series based on the time-to-space mapping achieved through a device of current carrying circular rings. An algorithm based on the ...theory of prime numbers is proposed for the approximate estimation of the stratified magnetic field produced by the aforementioned device. The main property of the specific algorithm is that it quantizes the stratified magnetic field. If a two-symbol symbolic time series is used to determine the flow directions of the rings’ currents, a time-to-space mapping of the dynamics of the system producing the time series is observed. A unique “fingerprint” of the symbolic dynamics is shaped by the spatial allocation of the values of the six-valued symmetric quantized magnetic field produced by the device. This allows for the quantitative evaluation of the original system’s dynamics by analyzing the resultant quantized magnetic field values space allocation, in a spectrum ranging from the lack of dynamics (randomness) to the presence of dynamics at all scales (criticality). Two examples of application–corresponding to the extremes of the dynamics spectrum, specifically, for symbolic time series resulting from (a) a random numbers generator and (b) the spin alternation of 2D-Ising in its critical state, verify the reliable time-to-space mapping of the involved symbolic dynamics. Moreover, an application to the symbolic sequence produced by the DNA of the GAPDH (Glyceraldehyde-3-Phosphate Dehydrogenase) human gene is presented as a real-world, intermediate dynamics case. The proposed symbolic time series analysis method presents the advantage that can take into account information related to both symbols, which is particularly useful in analyzing two-symbol time series of relatively short length where the probabilities of occurrence of the two symbols are not equal. By inferring the universality class of an artificial-neural-network-based hybrid spin model through the value of the critical exponent δ, it is shown that for such time series, the proposed method provides a unique way to expose the real dynamics of the underlying complex system, in contrast to the analysis of waiting times in the time domain that leads to an ambiguous quantitative result.
•Application of the method of critical fluctuations to cardiologist-annotated ECGs.•Analysis of ECG beyond the conventional (heartbeat and low-frequency variations.•Focus on high frequency ECG ...fluctuations reveals any deviations from criticality.•100% verification of the ECGs annotated as “Myocardial infarction”.•Disagreement with medical annotation (∼10%) for ECGs annotated as “Healthy controls”.
The Electrocardiogram (ECG) is a standard diagnostic tool for heart's health condition, while the “gold standard” in ECG interpretation is still by observation by the cardiologist. In this article we show that the analysis of the high frequency ECG amplitude fluctuations, which are ignored during the conventional interpretation of the ECG by the cardiologist, regarded as measurement noise, can reveal any deviations from the ideal critical behavior as well as the degree of stability of the heart in stochastic stimulus. By applying the time series analysis method termed “method of critical fluctuations” (MCF) to cardiologist-annotated human ECGs – Physikalisch-Technische Bundesanstalt (PTB) Diagnostic ECG database – we show that it is possible to discriminated between ECGs from healthy and myocardial infarction subjects, as well as to quantify the degree to which they approach the “ideal” critical state or how far from criticality they are, respectively. MCF analysis 100% verifies the characterization of the ECGs belonging to the “Myocardial infarction” class by absence of critical fluctuations. Interestingly, a disagreement with the medical classification of the order of ∼10% was found for the ECGs belonging to the “Healthy controls” set. For the specific ECGs we also find no critical fluctuations, which is a strong deviation from the rest ∼90% of the ECGs belonging to the same class and present critical fluctuations. Moreover, based on a proposed reference ECG, the autocorrelation function can also be used to reveal any differentiation of the studied ECGs from the ideal critical state.
In this work, first, it is confirmed that a recently introduced symbolic time-series-analysis method based on the prime-numbers-based algorithm (PNA), referred to as the “PNA-based symbolic ...time-series analysis method” (PNA-STSM), can accurately determine the exponent of the distribution of waiting times in the symbolic dynamics of two symbols produced by the 3D Ising model in its critical state. After this numerical verification of the reliability of PNA-STSM, three examples of how PNA-STSM can be applied to the category of systems that obey the dynamics of the on–off intermittency are presented. Usually, such time series, with on–off intermittency, present bimodal amplitude distributions (i.e., with two lobes). As has recently been found, the phenomenon of on–off intermittency is associated with the spontaneous symmetry breaking (SSB) of the second-order phase transition. Thus, the revelation that a system is close to SSB supports a deeper understanding of its dynamics in terms of criticality, which is quite useful in applications such as the analysis of pre-earthquake fracture-induced electromagnetic emission (also known as fracture-induced electromagnetic radiation) (FEME/FEMR) signals. Beyond the case of on–off intermittency, PNA-STSM can provide credible results for the dynamics of any two-symbol symbolic dynamics, even in cases in which there is an imbalance in the probability of the appearance of the two respective symbols since the two symbols are not considered separately but, instead, simultaneously, considering the information from both branches of the symbolic dynamics.
Several evidence has been reported corroborating the view that the MHz band fracture-induced electromagnetic emissions (FEME), also known as fracture-induced electromagnetic radiation (FEMR), which ...are detected prior to shallow main earthquakes (EQs) of moment magnitude Mw>5.5 with epicenters on land or near coastline, can be studied in analogy to a Z(2) spin system undergoing a second-order phase transition. Specifically, by analyzing MHz FEME/FEMR time series recorded prior to several earthquakes in the past >20 years, information has been extracted about the organization to critical state, the critical state itself, as well as for the step-by-step development of the spontaneous symmetry breaking (SSB) phenomenon. Using the “method of critical fluctuations” (MCF) and a recently proposed method for the wavelet-based detection of scaling behavior in noisy experimental data, we identified for the first time a different way of breaking the symmetry embedded in the MHz FEME/FEMR time series recorded by the hELlenic Seismo-ElectroMagnetics Network (ELSEM-Net) prior to the devastating (Mw=7.8 and Mw=7.5) EQs that occurred in south-east Turkey on 06/02/2023. Particularly, after the achievement of the critical state, indications were found that, although the underlying system started to break the symmetry according to the second-order phase transition mechanism (through SSB), SSB was not completed. Instead, the system seems to have changed symmetry and presented indications that the break of symmetry was finally achieved according to the first-order phase transition mechanism. Specifically, after the incomplete SSB, it was found to present tricritical behavior, followed by indications of triple degeneration of the order parameter fixed-point. This change of behavior observed in the MHz FEME/FEMR is a puzzling phenomenon for several reasons, which are discussed in detail, whereas suggestions are expressed as a first attempt for the possible explanation of the new findings.
This paper reports an attempt to use ultra-low-frequency (ULF) magnetic field data from a space weather monitoring magnetometer array in the study of earthquake (EQ) precursors in Greece. The data ...from four magnetometer stations of the Hell
c
eo
agnetic
rray (
) have been analyzed in the search for possible precursors to a strong EQ that occurred south of Lesvos Island on 12 June 2017, with magnitude Mw = 6.3 and focal depth = 12 km. The analysis includes conventional statistical methods, as well as criticality analysis, using two independent methods, the natural time (NT) method and the method of critical fluctuations (MCF). In terms of conventional statistical methods, it is found that the most convincing ULF precursor was observed in the data of ULF (20-30 mHz) depression (depression of the horizontal component of the magnetic field), which is indicative of lower ionospheric perturbation just 1 day before the EQ. Additionally, there are indications of a precursor in the direct ULF emission from the lithosphere 4 days to 1 day before the EQ. Further study in terms of NT analysis identifies criticality characteristics from 8 to 2 days before the EQ both for lithospheric ULF emission and ULF depression, while MCF reveals indications of criticality in all recorded magnetic field components, extending from 10 to 3 days before the EQ. Beyond the recordings of the geomagnetic stations of ENIGMA, the recordings of the fracto-electromagnetic emission stations of the H
lenic
eismo-
lectro
agnetics
work (
) in Greece have been analyzed. The MHz recordings at the station that is located on Lesvos Island presented criticality characteristics (by means of both NT analysis and MCF) 11 days before the EQ, while a few days later (7-6 days before the EQ), the kHz recordings of the same station presented tricritical behavior. It is noted that the magnetosphere was quiet for a period of two weeks before the EQ and including its occurrence.
This paper presents our study of the presence of the unstable critical point in spontaneous symmetry breaking (SSB) in the framework of Ginzburg–Landau (G-L) free energy. Through a 3D Ising spin ...lattice simulation, we found a zone of hysteresis where the unstable critical point continued to exist, despite the system having entered the broken symmetry phase. Within the hysteresis zone, the presence of the kink–antikink SSB solitons expands and, therefore, these can be observed. In scalar field theories, such as Higgs fields, the mass of this soliton inside the hysteresis zone could behave as a tachyon mass, namely as an imaginary quantity. Due to the fact that groups Ζ(2) and SU(2) belong to the same universality class, one expects that, in future experiments of ultra-relativistic nuclear collisions, in addition to the expected bosons condensations, structures of tachyon fields could appear.
In course of the preparation of a strong earthquake (EQ), the fracture of the highly heterogeneous system surrounding the fault has been suggested to follow the theory of critical phenomena and ...continuous phase transitions. Among the variety of electromagnetic phenomena which have been reported to be observed prior to a strong EQ, the ground-observed fracture-induced electromagnetic emissions (EME) in the MHz band have repeatedly been reported to present intermittency-induced criticality, while it has been suggested that reflect the specific stage of EQ preparation. Moreover, based on the analysis of pre-EQ MHz EME time series, it has been suggested that the underlying cracking procedure is organized to criticality by means of the Lévy flight mechanism. In an attempt to gain a deeper understanding to the involved EQ preparation processes and the organization to critical state, we study here the pre-EQ MHz EME presenting critical characteristics in terms of the mechanism of Lévy flight and its possible engagement with Gaussian stochastic processes. We suggest that if the analysis of the MHz EME time series according to the method of critical fluctuations indicates critical characteristics with a power law exponent, p2, value in the range 1.5,2, then a strong EQ should not be expected to follow. This is because such a result indicates a slow transition from the Lévy to the Gaussian process, cutting-off the long scales due to the Gaussian mechanism. This prevents the organization of the critical state to be completed according to the Lévy flight scenario and the spreading of the correlations all over the focal area. The above hypothesis is corroborated by a number of MHz EME time series analyses.
•Fracture-induced electromagnetic emissions in the MHz band are analyzed.•Intermittency-induced criticality has repeatedly been identified.•The results are re-evaluated in view of Lévy flight and Gaussian processes.•Power law exponent p2∈ (1.5,2) indicates that no strong EQ is expected.
It has recently been found that the evolution of the preparation of a strong earthquake (EQ), as it is monitored through fracture-induced electromagnetic emissions (EME) in the MHz band, presents ...striking similarity with the evolution of a thermal system as temperature drops, since distinct steps of the evolution of the phenomenon of spontaneous symmetry breaking (SSB) can be identified. Here, the study of fracture-induced EME in the MHz band in analogy to thermal systems is extended to the phase of local fracture structures that follow after the SSB (and the occurrence of the main EQ). By comparing fracture-induced MHz EME associated with the strongest EQs (MW=6.9) that occurred in Greece during the last twenty years with the 3D Ising model, a way to distinguish whether a possible identification of post-SSB power-laws immediately after a very strong EQ is a sign for the preparation of a new strong EQ or not is provided. In the suggested approach, the time series analysis method known as the method of critical fluctuations is used, enhanced by the autocorrelation function.
•The phase of broken symmetry, after spontaneous-symmetry-breaking (SSB), is studied.•Using 3D Ising is shown that power-laws survive at temperatures close after SSB.•Preseismic MHz electromagnetic emissions are studied in analogy to thermal systems.•Low autocorrelation values in post-SSB lower-laws imply no strong quake is expected.
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