Entropy, Volume 23, Issue 2 (February 2021) – 132 articles

Petroleum agriculture, characterized by mechanization and chemistry, is developing rapidly in China. However, petroleum agriculture has not only brought food safety problems, but also caused great obstacles to the sustainable development of society. In view of the disadvantages of oil agriculture, we provide an upgrading plan for energy systems in agriculture. This work can help reduce carbon emissions and improve food security. We introduce the most advanced technologies in Chinese agricultural development and the technical scope includes new agricultural energy power generation, agricultural energy use and the safe operation of agricultural energy systems. We describe the detailed data of agricultural bioenvironmental and energy engineering to clarify the level of agricultural energy efficiency in China. The overall conclusion of this paper is that the deep integration of agriculture and energy internet has become the development trend of agricultural energy systems. Full article

A rolling bearing early fault diagnosis method is proposed in this paper, which is derived from a refined composite multi-scale approximate entropy (RCMAE) and improved coyote optimization algorithm based probabilistic neural network (ICOA-PNN) algorithm. Rolling bearing early fault diagnosis is a time-sensitive task, which is significant to ensure the reliability and safety of mechanical fault system. At the same time, the early fault features are masked by strong background noise, which also brings difficulties to fault diagnosis. So, we firstly utilize the composite ensemble intrinsic time-scale decomposition with adaptive noise method (CEITDAN) to decompose the signal at different scales, and then the refined composite multi-scale approximate entropy of the first signal component is calculated to analyze the complexity of describing the vibration signal. Afterwards, in order to obtain higher recognition accuracy, the improved coyote optimization algorithm based probabilistic neural network classifiers is employed for pattern recognition. Finally, the feasibility and effectiveness of this method are verified by rolling bearing early fault diagnosis experiment. Full article

Fractional-order chaos has complex dynamic behavior characteristics, so its application in secure communication has attracted much attention. Compared with the design of fractional-order chaos-based cipher, there are fewer researches on security analysis. This paper conducts a comprehensive security analysis of a color image encryption algorithm using a fractional-order hyperchaotic system (CIEA-FOHS). Experimental simulation based on excellent numerical statistical results supported that CIEA-FOHS is cryptographically secure. Yet, from the perspective of cryptanalysis, this paper found that CIEA-FOHS can be broken by a chosen-plaintext attack method owing to its some inherent security defects. Firstly, the diffusion part can be eliminated by choosing some special images with all the same pixel values. Secondly, the permutation-only part can be deciphered by some chosen plain images and the corresponding cipher images. Finally, using the equivalent diffusion and permutation keys obtained in the previous two steps, the original plain image can be recovered from a target cipher image. Theoretical analysis and experimental simulations show that the attack method is both effective and efficient. To enhance the security, some suggestions for improvement are given. The reported results would help the designers of chaotic cryptography pay more attention to the gap of complex chaotic system and secure cryptosystem. Full article

The accurate classification of microbes is critical in today’s context for monitoring the ecological balance of a habitat. Hence, in this research work, a novel method to automate the process of identifying microorganisms has been implemented. To extract the bodies of microorganisms accurately, a generalized segmentation mechanism which consists of a combination of convolution filter (Kirsch) and a variance-based pixel clustering algorithm (Otsu) is proposed. With exhaustive corroboration, a set of twenty-five features were identified to map the characteristics and morphology for all kinds of microbes. Multiple techniques for feature selection were tested and it was found that mutual information (MI)-based models gave the best performance. Exhaustive hyperparameter tuning of multilayer layer perceptron (MLP), k-nearest neighbors (KNN), quadratic discriminant analysis (QDA), logistic regression (LR), and support vector machine (SVM) was done. It was found that SVM radial required further improvisation to attain a maximum possible level of accuracy. Comparative analysis between SVM and improvised SVM (ISVM) through a 10-fold cross validation method ultimately showed that ISVM resulted in a 2% higher performance in terms of accuracy (98.2%), precision (98.2%), recall (98.1%), and F1 score (98.1%). Full article

In this work we propose a model for open Markov chains that can be interpreted as a system of non-interacting particles evolving according to the rules of a Markov chain. The number of particles in the system is not constant, because we allow the particles to arrive or leave the state space according to prescribed protocols. We describe this system by looking at the population of particles on every state by establishing the rules of time-evolution of the distribution of particles. We show that it is possible to describe the distribution of particles over the state space through the corresponding moment generating function. This description is given through the dynamics ruling the behavior of such a moment generating function and we prove that the system is able to attain the stationarity under some conditions. We also show that it is possible to describe the dynamics of the two first cumulants of the distribution of particles, which in some way is a simpler technique to obtain useful information of the open Markov chain for practical purposes. Finally we also study the behavior of the time-dependent correlation functions of the number of particles present in the system. We give some simple examples of open chains that either, can be fully described through the moment generating function or partially described through the exact solution of the cumulant dynamics. Full article

In this paper, we explore the advantages of a fractional calculus based watermarking system for detecting Gaussian watermarks. To reach this goal, we selected a typical watermarking scheme and replaced the detection equation set by another set of equations derived from fractional calculus principles; then, we carried out a statistical assessment of the performance of both schemes by analyzing the Receiver Operating Characteristic (ROC) curve and the False Positive Percentage (FPP) when they are used to detect Gaussian watermarks. The results show that the ROC of a fractional equation based scheme has 48.3% more Area Under the Curve (AUC) and a False Positives Percentage median of 0.2% whilst the selected typical watermarking scheme has 3%. In addition, the experimental results suggest that the target applications of fractional schemes for detecting Gaussian watermarks are as a semi-fragile image watermarking systems robust to Gaussian noise. Full article

We present here a somewhat personalized account of the emergence of econophysics as an attractive research topic in physical, as well as social, sciences. After a rather detailed storytelling about our endeavors from Kolkata, we give a brief description of the main research achievements in a simple and non-technical language. We also briefly present, in technical language, a piece of our recent research result. We conclude our paper with a brief perspective. Full article

This paper deals with the specific construction of binary low-density parity-check (LDPC) codes. We derive lower bounds on the error exponents for these codes transmitted over the memoryless binary symmetric channel (BSC) for both the well-known maximum-likelihood (ML) and proposed low-complexity decoding algorithms. We prove the existence of such LDPC codes that the probability of erroneous decoding decreases exponentially with the growth of the code length while keeping coding rates below the corresponding channel capacity. We also show that an obtained error exponent lower bound under ML decoding almost coincide with the error exponents of good linear codes. Full article

We consider the interaction of a qubit system with a two-mode field in the presence of multi-photon transition and phase damping effect. We use the master equation to obtain the density operator when the qubit is initially prepared in its excited state and the field is in a finite-dimensional pair coherent state. The properties of the considered system, such as the population inversion, amount of the mixedness, parameter estimation, and squeezing, are explored for one- and two-photon transitions. The effects of photon addition to the field and phase damping on the evaluation of these quantumness measures are also investigated. Full article

This is a dialogue between Huw Price and Travis Norsen, loosely inspired by a letter that Price received from J. S. Bell in 1988. The main topic of discussion is Bell’s views about retrocausal approaches to quantum theory and their relevance to contemporary issues. Full article

Generally, industrial gas turbines (IGT) face transient behavior during start-up, load change, shutdown and variations in ambient conditions. These transient conditions shift engine thermal equilibrium from one steady state to another steady state. In turn, various aero-thermal and mechanical stresses are developed that are adverse for engine’s reliability, availability, and overall health. The transient behavior needs to be accurately predicted since it is highly related to low cycle fatigue and early failures, especially in the hot regions of the gas turbine. In the present paper, several critical aspects related to transient behavior and its modeling are reviewed and studied from the point of view of identifying potential research gaps within the context of fault detection and diagnostics (FDD) under dynamic conditions. Among the considered topics are, (i) general transient regimes and pertinent model formulation techniques, (ii) control mechanism for part-load operation, (iii) developing a database of variable geometry inlet guide vanes (VIGVs) and variable bleed valves (VBVs) schedules along with selection framework, and (iv) data compilation of shaft’s polar moment of inertia for different types of engine’s configurations. This comprehensive literature document, considering all the aspects of transient behavior and its associated modeling techniques will serve as an anchor point for the future researchers, gas turbine operators and design engineers for effective prognostics, FDD and predictive condition monitoring for variable geometry IGT. Full article

Biological ion channels are fundamental to maintaining life. In this manuscript we apply our recently developed statistical and linear response theory to investigate Na${}^{+}$ conduction through the prokaryotic Na${}^{+}$ channel NaChBac. This work is extended theoretically by the derivation of ionic conductivity and current in an electrochemical gradient, thus enabling us to compare to a range of whole-cell data sets performed on this channel. Furthermore, we also compare the magnitudes of the currents and populations at each binding site to previously published single-channel recordings and molecular dynamics simulations respectively. In doing so, we find excellent agreement between theory and data, with predicted energy barriers at each of the four binding sites of $\sim 4,2.9,3.6$, and $4kT$. Full article

The high proportion of CO₂/CH₄ in low aggregated value natural gas compositions can be used strategically and intelligently to produce more hydrocarbons through oxidative methane coupling (OCM). The main goal of this study was to optimize direct low-value natural gas conversion via CO₂-OCM on metal oxide catalysts using robust multi-objective optimization based on an entropic measure to choose the most preferred Pareto optimal point as the problem’s final solution. The responses of CH₄ conversion, C₂ selectivity, and C₂ yield are modeled using the response surface methodology. In this methodology, decision variables, e.g., the CO₂/CH₄ ratio, reactor temperature, wt.% CaO and wt.% MnO in ceria catalyst, are all employed. The Pareto optimal solution was obtained via the following combination of process parameters: CO₂/CH₄ ratio = 2.50, reactor temperature = 1179.5 K, wt.% CaO in ceria catalyst = 17.2%, wt.% MnO in ceria catalyst = 6.0%. By using the optimal weighting strategy w₁ = 0.2602, w₂ = 0.3203, w₃ = 0.4295, the simultaneous optimal values for the objective functions were: CH₄ conversion = 8.806%, C₂ selectivity = 51.468%, C₂ yield = 3.275%. Finally, an entropic measure used as a decision-making criterion was found to be useful in mapping the regions of minimal variation among the Pareto optimal responses and the results obtained, and this demonstrates that the optimization weights exert influence on the forecast variation of the obtained response. Full article

Multi-focus image fusion is the process of combining focused regions of two or more images to obtain a single all-in-focus image. It is an important research area because a fused image is of high quality and contains more details than the source images. This makes it useful for numerous applications in image enhancement, remote sensing, object recognition, medical imaging, etc. This paper presents a novel multi-focus image fusion algorithm that proposes to group the local connected pixels with similar colors and patterns, usually referred to as superpixels, and use them to separate the focused and de-focused regions of an image. We note that these superpixels are more expressive than individual pixels, and they carry more distinctive statistical properties when compared with other superpixels. The statistical properties of superpixels are analyzed to categorize the pixels as focused or de-focused and to estimate a focus map. A spatial consistency constraint is ensured on the initial focus map to obtain a refined map, which is used in the fusion rule to obtain a single all-in-focus image. Qualitative and quantitative evaluations are performed to assess the performance of the proposed method on a benchmark multi-focus image fusion dataset. The results show that our method produces better quality fused images than existing image fusion techniques. Full article

In this work, methods of description of crystal nucleation by using the statistical approach are analyzed. Findings from classical nucleation theory (CNT) for the average time of formation of the first supercritical nucleus are linked with experimental data on nucleation in glass-forming liquids stemming from repetitive cooling protocols both under isothermal and isochronal conditions. It is shown that statistical methods of lifetime analysis, frequently used in medicine, public health, and social and behavioral sciences, are applicable to crystal nucleation problems in glass-forming liquids and are very useful tools for their exploration. Identifying lifetime with the time to nucleate as a random variable in homogeneous and non-homogeneous Poisson processes, solutions for the nucleation rate under steady-state conditions are presented using the hazard rate and related parameters. This approach supplies us with a more detailed description of nucleation going beyond CNT. In particular, we show that cumulative hazard estimation enables one to derive the plotting positions for visually examining distributional model assumptions. As the crystallization of glass-forming melts can involve more than one type of nucleation processes, linear dependencies of the cumulative hazard function are used to facilitate assignment of lifetimes to each nucleation mechanism. Full article

Multiscale sample entropy analysis has been developed to quantify the complexity and the predictability of a time series, originally developed for physiological time series. In this study, the analysis was applied to the turbulence data. We measured time series data for the velocity fluctuation, in either the longitudinal or transverse direction, of turbulent soap film flows at various locations. The research was to assess the feasibility of using the entropy analysis to qualitatively characterize turbulence, without using any conventional energetic analysis of turbulence. The study showed that the application of the entropy analysis to the turbulence data is promising. From the analysis, we successfully captured two important features of the turbulent soap films. It is indicated that the turbulence is anisotropic from the directional disparity. In addition, we observed that the most unpredictable time scale increases with the downstream distance, which is an indication of the decaying turbulence. Full article

Network physiology has emerged as a promising paradigm for the extraction of clinically relevant information from physiological signals by moving from univariate to multivariate analysis, allowing for the inspection of interdependencies between organ systems. However, for its successful implementation, the disruptive effects of artifactual outliers, which are a common occurrence in physiological recordings, have to be studied, quantified, and addressed. Within the scope of this study, we utilize Dispersion Entropy (DisEn) to initially quantify the capacity of outlier samples to disrupt the values of univariate and multivariate features extracted with DisEn from physiological network segments consisting of synchronised, electroencephalogram, nasal respiratory, blood pressure, and electrocardiogram signals. The DisEn algorithm is selected due to its efficient computation and good performance in the detection of changes in signals for both univariate and multivariate time-series. The extracted features are then utilised for the training and testing of a logistic regression classifier in univariate and multivariate configurations in an effort to partially automate the detection of artifactual network segments. Our results indicate that outlier samples cause significant disruption in the values of extracted features with multivariate features displaying a certain level of robustness based on the number of signals formulating the network segments from which they are extracted. Furthermore, the deployed classifiers achieve noteworthy performance, where the percentage of correct network segment classification surpasses 95% in a number of experimental setups, with the effectiveness of each configuration being affected by the signal in which outliers are located. Finally, due to the increase in the number of features extracted within the framework of network physiology and the observed impact of artifactual samples in the accuracy of their values, the implementation of algorithmic steps capable of effective feature selection is highlighted as an important area for future research. Full article

Most conventional wind turbine fault diagnosis techniques only use a single type of signal as fault feature and their performance could be limited to such signal characteristics. In this paper, multiple types of signals including vibration, temperature, and stator current are used simultaneously for wind turbine misalignment diagnosis. The model is constructed by integrated methods based on Dempster–Shafer (D–S) evidence theory. First, the time domain, frequency domain, and time–frequency domain features of the collected vibration, temperature, and stator current signal are respectively taken as the inputs of the least square support vector machine (LSSVM). Then, the LSSVM outputs the posterior probabilities of the normal, parallel misalignment, angular misalignment, and integrated misalignment of the transmission systems. The posterior probabilities are used as the basic probabilities of the evidence fusion, and the fault diagnosis is completed according to the D–S synthesis and decision rules. Considering the correlation between the inputs, the vibration and current feature vectors’ dimensionalities are reduced by t-distributed stochastic neighbor embedding (t-SNE), and the improved artificial bee colony algorithm is used to optimize the parameters of the LSSVM. The results of the simulation and experimental platform demonstrate the accuracy of the proposed model and its superiority compared with other models. Full article

The calculations of the dimensionless layer monomer density profiles for a dilute solution of phantom ideal ring polymer chains and star polymers with $f=4$ arms in a $\Theta$-solvent confined in a slit geometry of two parallel walls with repulsive surfaces and for the mixed case of one repulsive and the other inert surface were performed. Furthermore, taking into account the Derjaguin approximation, the dimensionless layer monomer density profiles for phantom ideal ring polymer chains and star polymers immersed in a solution of big colloidal particles with different adsorbing or repelling properties with respect to polymers were calculated. The density-force relation for the above-mentioned cases was analyzed, and the universal amplitude ratio B was obtained. Taking into account the small sphere expansion allowed obtaining the monomer density profiles for a dilute solution of phantom ideal ring polymers immersed in a solution of small spherical particles, or nano-particles of finite size, which are much smaller than the polymer size and the other characteristic mesoscopic length of the system. We performed molecular dynamics simulations of a dilute solution of linear, ring, and star-shaped polymers with $N=300$, 300 (360), and 1201 (4 × 300 + 1-star polymer with four arms) beads accordingly. The obtained analytical and numerical results for phantom ring and star polymers are compared with the results for linear polymer chains in confined geometries. Full article

The Sigma-Pi structure investigated in this work consists of the sum of products of an increasing number of identically distributed random variables. It appears in stochastic processes with random coefficients and also in models of growth of entities such as business firms and cities. We study the Sigma-Pi structure with Bernoulli random variables and find that its probability distribution is always bounded from below by a power-law function regardless of whether the random variables are mutually independent or duplicated. In particular, we investigate the case in which the asymptotic probability distribution has always upper and lower power-law bounds with the same tail-index, which depends on the parameters of the distribution of the random variables. We illustrate the Sigma-Pi structure in the context of a simple growth model with successively born entities growing according to a stochastic proportional growth law, taking both Bernoulli, confirming the theoretical results, and half-normal random variables, for which the numerical results can be rationalized using insights from the Bernoulli case. We analyze the interdependence among entities represented by the product terms within the Sigma-Pi structure, the possible presence of memory in growth factors, and the contribution of each product term to the whole Sigma-Pi structure. We highlight the influence of the degree of interdependence among entities in the number of terms that effectively contribute to the total sum of sizes, reaching the limiting case of a single term dominating extreme values of the Sigma-Pi structure when all entities grow independently. Full article

In this paper, we perform a belief propagation (BP) decoding threshold analysis of spatially coupled (SC) turbo-like codes (TCs) (SC-TCs) on the additive white Gaussian noise (AWGN) channel. We review Monte-Carlo density evolution (MC-DE) and efficient prediction methods, which determine the BP thresholds of SC-TCs over the AWGN channel. We demonstrate that instead of performing time-consuming MC-DE computations, the BP threshold of SC-TCs over the AWGN channel can be predicted very efficiently from their binary erasure channel (BEC) thresholds. From threshold results, we conjecture that the similarity of MC-DE and predicted thresholds is related to the threshold saturation capability as well as capacity-approaching maximum a posteriori (MAP) performance of an SC-TC ensemble. Full article

Obtaining key and rich visual information under sophisticated road conditions is one of the key requirements for advanced driving assistance. In this paper, a newfangled end-to-end model is proposed for advanced driving assistance based on the fusion of infrared and visible images, termed as FusionADA. In our model, we are committed to extracting and fusing the optimal texture details and salient thermal targets from the source images. To achieve this goal, our model constitutes an adversarial framework between the generator and the discriminator. Specifically, the generator aims to generate a fused image with basic intensity information together with the optimal texture details from source images, while the discriminator aims to force the fused image to restore the salient thermal targets from the source infrared image. In addition, our FusionADA is a fully end-to-end model, solving the issues of manually designing complicated activity level measurements and fusion rules existing in traditional methods. Qualitative and quantitative experiments on publicly available datasets RoadScene and TNO demonstrate the superiority of our FusionADA over the state-of-the-art approaches. Full article

The Free Energy Principle (FEP) is currently one of the most promising frameworks with which to address a unified explanation of life-related phenomena. With powerful formalism that embeds a small set of assumptions, it purports to deal with complex adaptive dynamics ranging from barely unicellular organisms to complex cultural manifestations. The FEP has received increased attention in disciplines that study life, including some critique regarding its overall explanatory power and its true potential as a grand unifying theory (GUT). Recently, FEP theorists presented a contribution with the main tenets of their framework, together with possible philosophical interpretations, which lean towards so-called Markovian Monism (MM). The present paper assumes some of the abovementioned critiques, rejects the arguments advanced to invalidate the FEP’s potential to be a GUT, and overcomes criticism thereof by reviewing FEP theorists’ newly minted metaphysical commitment, namely MM. Specifically, it shows that this philosophical interpretation of the FEP argues circularly and only delivers what it initially assumes, i.e., a dual information geometry that allegedly explains epistemic access to the world based on prior dual assumptions. The origin of this circularity can be traced back to a physical description contingent on relative system-environment separation. However, the FEP itself is not committed to MM, and as a scientific theory it delivers more than what it assumes, serving as a heuristic unification principle that provides epistemic advancement for the life sciences. Full article

Fractal groups (also called self-similar groups) is the class of groups discovered by the first author in the 1980s with the purpose of solving some famous problems in mathematics, including the question of raising to von Neumann about non-elementary amenability (in the association with studies around the Banach-Tarski Paradox) and John Milnor’s question on the existence of groups of intermediate growth between polynomial and exponential. Fractal groups arise in various fields of mathematics, including the theory of random walks, holomorphic dynamics, automata theory, operator algebras, etc. They have relations to the theory of chaos, quasi-crystals, fractals, and random Schrödinger operators. One important development is the relation of fractal groups to multi-dimensional dynamics, the theory of joint spectrum of pencil of operators, and the spectral theory of Laplace operator on graphs. This paper gives a quick access to these topics, provides calculation and analysis of multi-dimensional rational maps arising via the Schur complement in some important examples, including the first group of intermediate growth and its overgroup, contains a discussion of the dichotomy “integrable-chaotic” in the considered model, and suggests a possible probabilistic approach to studying the discussed problems. Full article

Isothermal titration calorimetry is frequently employed to determine the critical micelle concentration and the micellization enthalpy of surfactants in terms of geometrical characteristics of the titration curves. Previously we have shown theoretically that even for an infinitesimal injection, the heat per titrant mol depends on the stock solution concentration. In this work, we explore experimentally the influence of the stock solution concentration on the geometrical characteristics of the titration curve and its effect in determining the critical micelle concentration and the micellization enthalpy of surfactants. The systematic study of this phenomenology involves a great number of measurements at different temperatures with several repetitions carried out using a robotic calorimeter. As surfactant hexadecyltrimethylamonium bromide was used. The magnitude and shape of the heat titration depend on the stock solution concentration. As a consequence, the inflexion-point, break-point, and step-height decrease until a limiting value. A qualitative analysis suggests that the limiting value depends only on substance. This work shows that graphical methods could not be suitable for the calculation of the critical micelle concentration and micellization enthalpy because the magnitude and shape of the titration curve depend on the stock solution concentration. Micellar properties should be calculated by the application of theoretical models as in the ligand-binding studies. Full article

The reliable transmission of multimedia information that is coded through highly compression efficient encoders is a challenging task. This article presents the iterative convergence performance of IrRegular Convolutional Codes (IRCCs) with the aid of the multidimensional Sphere Packing (SP) modulation assisted Differential Space Time Spreading Codes (IRCC-SP-DSTS) scheme for the transmission of H.264/Advanced Video Coding (AVC) compressed video coded stream. In this article, three different regular and irregular error protection schemes are presented. In the presented Regular Error Protection (REP) scheme, all of the partitions of the video sequence are regular error protected with a rate of 3/4 IRCC. In Irregular Error Protection scheme-1 (IREP-1) the H.264/AVC partitions are prioritized as A, B & C, respectively. Whereas, in Irregular Error Protection scheme-2 (IREP-2), the H.264/AVC partitions are prioritized as B, A, and C, respectively. The performance of the iterative paradigm of an inner IRCC and outer Rate-1 Precoder is analyzed by the EXtrinsic Information Transfer (EXIT) Chart and the Quality of Experience (QoE) performance of the proposed mechanism is evaluated using the Bit Error Rate (BER) metric and Peak Signal to Noise Ratio (PSNR)-based objective quality metric. More specifically, it is concluded that the proposed IREP-2 scheme exhibits a gain of 1 dB $E_b/N_0$ with reference to the IREP-1 and $E_b/N_0$ gain of 0.6 dB with reference to the REP scheme over the PSNR degradation of 1 dB. Full article

We prove that, within the class of pair potential Hamiltonians, the excess entropy is a universal, temperature-independent functional of the density and pair correlation function. This result extends Henderson’s theorem, which states that the free energy is a temperature dependent functional of the density and pair correlation. The stationarity and concavity of the excess entropy functional are discussed and related to the Gibbs–Bugoliubov inequality and to the free energy. We apply the Kirkwood approximation, which is commonly used for fluids, to both fluids and solids. Approximate excess entropy functionals are developed and compared to results from thermodynamic integration. The pair functional approach gives the absolute entropy and free energy based on simulation output at a single temperature without thermodynamic integration. We argue that a functional of the type, which is strictly applicable to pair potentials, is also suitable for first principles calculation of free energies from Born–Oppenheimer molecular dynamics performed at a single temperature. This advancement has the potential to reduce the evaluation the free energy to a simple modification to any procedure that evaluates the energy and the pair correlation function. Full article

An earthquake of Mw6.4 hit the coastal zone of Albania on 26 November 2019, at 02:54:11 UTC. It was intensively felt at about 34 km away, in Tirana City, where damages and lives lost occurred. To emphasize a pre-seismic geomagnetic signature before the onset of this earthquake, the data collected on the interval 15 October–30 November 2019, at the Panagjurishte (PAG)-Bulgaria and Surlari (SUA)-Romania observatories were analyzed. Further on, for geomagnetic signal identification we used the polarization parameter (BPOL) which is time invariant in non-seismic conditions and it becomes unstable due to the strain effect related to the Mw6.4earthquake. Consequently, BPOL time series and its standard deviations are performed for the both sites using ultra low frequency (ULF)-fast Fourier transform (FFT) band-pass filtering. A statistical analysis, based on a standardized random variable equation, was applied to emphasize on the BPOL* (PAG) and ABS BPOL* (PAG) time series the anomalous signal’s singularity and, to differentiate the transient local anomalies due to the Mw6.4 earthquake, from the internal and external parts of the geomagnetic field, taken PAG observatory as reference. Finally, the ABS BPOL* (PAG-SUA) time series were obtained on the interval 1–30 November 2019, where a geomagnetic signature greater than 2.0, was detected on 23 November and the lead time was 3 days before the onset of the Mw6.4earthquake. Full article

We study a two state “jumping diffusivity” model for a Brownian process alternating between two different diffusion constants, $D_{+}>D_{-}$, with random waiting times in both states whose distribution is rather general. In the limit of long measurement times, Gaussian behavior with an effective diffusion coefficient is recovered. We show that, for equilibrium initial conditions and when the limit of the diffusion coefficient $D_{-}⟶0$ is taken, the short time behavior leads to a cusp, namely a non-analytical behavior, in the distribution of the displacements $P(x,t)$ for $x⟶0$. Visually this cusp, or tent-like shape, resembles similar behavior found in many experiments of diffusing particles in disordered environments, such as glassy systems and intracellular media. This general result depends only on the existence of finite mean values of the waiting times at the different states of the model. Gaussian statistics in the long time limit is achieved due to ergodicity and convergence of the distribution of the temporal occupation fraction in state $D_{+}$ to a $\delta$-function. The short time behavior of the same quantity converges to a uniform distribution, which leads to the non-analyticity in $P(x,t)$. We demonstrate how super-statistical framework is a zeroth order short time expansion of $P(x,t)$, in the number of transitions, that does not yield the cusp like shape. The latter, considered as the key feature of experiments in the field, is found with the first correction in perturbation theory. Full article