Impact of prolonged chronic social isolation stress on behavior and multifractal complexity of metabolic rate in Octodon degus.

Social interaction can improve animal performance through the prevention of stress-related events, the provision of security, and the enhancement of reproductive output and survival. We investigated the effects of prolonged chronic social isolation stress on behavioral, cognitive, and physiological performance in the social, long-lived rodent Octodon degus. Degu pups were separated into two social stress treatments: control (CTRL) and chronically isolated (CI) individuals from post-natal and post-weaning until adulthood. We quantified anxiety-like behavior and cognitive performance with a battery of behavioral tests. Additionally, we measured their basal metabolic rate (BMR) and analyzed the multifractal properties of the oxygen consumption time series using Multifractal Detrended Fluctuation Analysis, a well-known method for assessing the fractal characteristics of biological signals. Our results showed that CI induced a significant increase in anxiety-like behaviors and led to a reduction in social and working memory in male degus. In addition, CI-treated degus reduced the multifractal complexity of BMR compared to CTRL, which implies a decrease in the ability to respond to environmental stressors and, as a result, an unhealthy state. In contrast, we did not observe significant effects of social stress on BMR. Multivariate analyses showed a clear separation of behavior and physiological variables into two clusters, corresponding to CI and CTRL degus. This study provides novel insights into the effects of prolonged chronic social isolation stress on behavior, cognitive performance, and metabolic complexity in this rodent animal model. To the best of our knowledge, it is the first study to integrate cognitive-behavioral performance and multifractal dynamics of a physiological signal in response to prolonged social isolation. These findings highlight the importance of social interactions for the well-being and overall performance of social animals.

Multifractal detrended fluctuation analysis of insole pressure sensor data to diagnose vestibular system disorders.

The vestibular system (VS) is a sensory system that has a vital function in human life by serving to maintain balance. In this study, multifractal detrended fluctuation analysis (MFDFA) is applied to insole pressure sensor data collected from subjects in order to extract features to identify diseases related to VS dysfunction. We use the multifractal spectrum width as the feature to distinguish between healthy and diseased people. It is observed that multifractal behavior is more dominant and thus the spectrum is wider for healthy subjects, where we explain the reason as the long-range correlations of the small and large fluctuations of the time series for this group. We directly process the instantaneous pressure values to extract features in contrast to studies in the literature where gait analysis is based on investigation of gait dynamics (stride time, stance time, etc.) requiring long walking time. Thus, as the main innovation of this work, we detrend the data to give meaningful information even for a relatively short walk. Extracted feature set was input to fundamental classification algorithms where the Support-Vector-Machine (SVM) performed best with an average accuracy of 98.2% for the binary classification as healthy or suffering. This study is a substantial part of a big project where we finally aim to identify the specific VS disease that causes balance disorder and also determine the stage of the disease, if any. Within this scope, the achieved performance gives high motivation to work more deeply on the issue.

Entropy-Based Multifractal Testing of Heart Rate Variability during Cognitive-Autonomic Interplay.

Entropy-based and fractal-based metrics derived from heart rate variability (HRV) have enriched the way cardiovascular dynamics can be described in terms of complexity. The most commonly used multifractal testing, a method using q moments to explore a range of fractal scaling in small-sized and large-sized fluctuations, is based on detrended fluctuation analysis, which examines the power-law relationship of standard deviation with the timescale in the measured signal. A more direct testing of a multifractal structure exists based on the Shannon entropy of bin (signal subparts) proportion. This work aims to reanalyze HRV during cognitive tasks to obtain new markers of HRV complexity provided by entropy-based multifractal spectra using the method proposed by Chhabra and Jensen in 1989. Inter-beat interval durations (RR) time series were obtained in 28 students comparatively in baseline (viewing a video) and during three cognitive tasks: Stroop color and word task, stop-signal, and go/no-go. The new HRV estimators were extracted from the f/α singularity spectrum of the RR magnitude increment series, established from q-weighted stable (log-log linear) power laws, namely: (i) the whole spectrum width (MF) calculated as αmax - αmin; the specific width representing large-sized fluctuations (MFlarge) calculated as α0 - αq+; and small-sized fluctuations (MFsmall) calculated as αq- - α0. As the main results, cardiovascular dynamics during Stroop had a specific MF signature while MFlarge was rather specific to go/no-go. The way these new HRV markers could represent different aspects of a complete picture of the cognitive-autonomic interplay is discussed, based on previously used entropy- and fractal-based markers, and the introduction of distribution entropy (DistEn), as a marker recently associated specifically with complexity in the cardiovascular control.

Towards Multifractality through an Ernst-Type Potential in Complex Systems Dynamics.

Some possible correspondences between the Scale Relativity Theory and the Space-Time Theory can be established. Since both the multifractal Schrödinger equation from the Scale Relativity Theory and the General Relativity equations for a gravitational field with axial symmetry accept the same SL(2R)-type invariance, an Ernst-type potential (from General Relativity) and also a multi-fractal tensor (from Scale Relativity) are highlighted in the description of complex systems dynamics. In this way, a non-differentiable description of complex systems dynamics can become functional, even in the case of standard theories (General Relativity and Quantum Mechanics).

Theoretical and Experimental Aspects of Sodium Diclofenac Salt Release from Chitosan-Based Hydrogels and Possible Applications.

Two formulations based on diclofenac sodium salt encapsulated into a chitosan hydrogel were designed and prepared, and their drug release was investigated by combining in vitro results with mathematical modeling. To understand how the pattern of drug encapsulation impacted its release, the formulations were supramolecularly and morphologically characterized by scanning electron microscopy and polarized light microscopy, respectively. The mechanism of diclofenac release was assessed by using a mathematical model based on the multifractal theory of motion. Various drug-delivery mechanisms, such as Fickian- and non-Fickian-type diffusion, were shown to be fundamental mechanisms. More precisely, in a case of multifractal one-dimensional drug diffusion in a controlled-release polymer-drug system (i.e., in the form of a plane with a certain thickness), a solution that allowed the model's validation through the obtained experimental data was established. The present research reveals possible new perspectives, for example in the prevention of intrauterine adhesions occurring through endometrial inflammation and other pathologies with an inflammatory mechanism background, such as periodontal diseases, and also therapeutic potential beyond the anti-inflammatory action of diclofenac as an anticancer agent, with a role in cell cycle regulation and apoptosis, using this type of drug-delivery system.

What Is Mature and What Is Still Emerging in the Cryptocurrency Market?

In relation to the traditional financial markets, the cryptocurrency market is a recent invention and the trading dynamics of all its components are readily recorded and stored. This fact opens up a unique opportunity to follow the multidimensional trajectory of its development since inception up to the present time. Several main characteristics commonly recognized as financial stylized facts of mature markets were quantitatively studied here. In particular, it is shown that the return distributions, volatility clustering effects, and even temporal multifractal correlations for a few highest-capitalization cryptocurrencies largely follow those of the well-established financial markets. The smaller cryptocurrencies are somewhat deficient in this regard, however. They are also not as highly cross-correlated among themselves and with other financial markets as the large cryptocurrencies. Quite generally, the volume V impact on price changes R appears to be much stronger on the cryptocurrency market than in the mature stock markets, and scales as R(V)∼Vα with α≳1.

The Cracking Behavior of Two Dental Composite Materials Validated through Multifractal Analyzes.

The aim of this in vitro study was to analyze, both experimentally and theoretically, the mechanical behavior of two types of composite materials used in restoring dental integrity. The samples of each composite resin, namely Filtek Supreme XT (3M ESPE, St. Paul, MN, USA) and Filtek Z250 (3M ESPE, St. Paul, MN, USA), were experimentally analyzed by determining their compressive strength and fracture behavior. The fractured fragments of the samples were subjected to surface evaluation by scanning electron microscopy. The compressive stress-compressive strain dependencies revealed stronger cracking of the Filtek Supreme XT composite than Filtek Z250 prior to fracture. Theoretically, the evaluation was made by means of holographic implementations of such types of composite materials. A Hooke-type equation in a differential form is presented, which links the proposed theoretical model with the experimentally obtained data.

Skewed multifractal scaling of stock markets during the COVID-19 pandemic.

This article proposes a new paradigm of asymmetric multifractality in financial time series, where the scaling feature varies over two adjacent intervals. The proposed approach first locates a change-point and then performs a multifractal detrended fluctuation analysis (MF-DFA) on each interval. The study investigates the impact of the COVID-19 pandemic on asymmetric multifractal scaling by analyzing financial indices of the G3+1 nations, including the world's four largest economies, from January 2018 to November 2021. The results show common periods of local scaling with increasing multifractality after a change-point at the beginning of 2020 for the US, Japanese, and Eurozone markets. The study also identifies a significant transition in the Chinese market from a turbulent multifractal state to a stable monofractal state. Overall, this new approach provides valuable insights into the characteristics of financial time series and their response to extreme events.

Fatigue Life Modelling of Steel Suspension Coil Springs Based on Wavelet Vibration Features Using Neuro-Fuzzy Methods.

This study proposed wavelet-based approaches to characterise random vibration road excitations for durability prediction of coil springs. Conventional strain-life approaches require long computational time, while the accuracy of the vibration fatigue methods is unsatisfactory. It is therefore a necessity to establish an accurate fatigue life prediction model based on vibrational features. Wavelet-based methods were applied to determine the low-frequency energy and multifractality of road excitations. Strain-life models were applied for fatigue life evaluation from strain histories. ANFIS modelling was subsequently adopted to associate the vibration features with the fatigue life of coil springs. Results showed that the proposed wavelet-based methods were effective to determine the signal energy and multifractality of vibration signals. The established vibration-based models showed good fatigue life conservativity with a data survivability of more than 90%. The highest Pearson coefficient of 0.955 associated with the lowest RMSE of 0.660 was obtained by the Morrow-based model. It is suggested that the low-frequency energy and multifractality of the vibration signals can be used as fatigue-related features in life predictions of coil springs under random loading. Finally, the proposed model is an acceptable fatigue life prediction method based on vibration features, and it can reduce the dependency on strain data measurement.

Theoretical and Experimental Designs on Several Mechanical Properties of Cu-Al-Zn Shape Memory Alloys Used in the Processing Industry.

By assimilating shape memory alloys with mathematical multifractal-type objects, a theoretical model based on Scale Relativity Theory in the form of The Multifractal Theory of Motion, in order to explain the mechanical behavior of such material, is proposed. The model is validated by analyzing the mechanical behavior of Cu-Al-Zn shape memory alloy with various chemical compositions. More precisely, the multifractal tunnel effect can "mime" the mechanical hysteresis of such a material, a situation in which a direct correspondence for several mechanical properties of Cu-Al-Zn is highlighted (the chemical composition can be correlated with the shapes of the curves controlled through the multifractality degree, while the areas delimited by the same curves can be correlated with the multifractal specific potential, as a measure of the mechanical memory degree).

The impact of COVID-19 pandemic on the dynamic correlations between gold and U.S. equities: evidence from multifractal cross-correlation analysis.

This study exploits multifractal cross-correlation analysis (MFCCA) to investigate the impact of the COVID-19 pandemic on the cross-correlations between gold and U.S. equity markets using 1-min high-frequency data from January 1, 2019, to December 29, 2020. The MFCCA method shows that the pandemic caused an increase of multifractality in cross-correlations between the two markets. Specifically, the cross-correlations of small fluctuations became more persistent while those of large fluctuations became less persistent, explaining the source of multifractality. The findings of this study carry significant implications for investors, academicians, and policymakers. For example, the increase of multifractality of cross-correlation means that the non-linear relationship between gold and U.S. equity returns prevails more during economic downturns. Therefore, academicians may resort to non-linear techniques to evaluate the relationship between gold and U.S. equity markets during the health pandemic. Moreover, investors can know the value of hedging benefits over different investment time horizons during the pandemic. Finally, policymakers can better assess the economic downturns (i.e., those caused by health pandemics) over the dynamics of cross-correlation between gold and equity markets to make sound financial policies.

On the inner dynamics between Fossil fuels and the carbon market: a combination of seasonal-trend decomposition and multifractal cross-correlation analysis.

This study examines the inner dynamics of multifractality between the carbon market (EU ETS) and four major fossil fuel energy markets: Brent Crude Oil (BRN), Richards Bay Coal (RBC), UK Natural Gas (NGH2), and FTSE350 electricity index (FTSE350) from January 04, 2016, to March 04, 2022. First, we decompose the daily price changes by applying seasonal and trend decomposition using loess (STL). Then, we examine the inner dynamics of multifractality and cross-correlation by employing multifractal detrended fluctuation analysis (MFDFA) and multifractal detrended cross-correlation analysis (MFDCCA) using the remaining components of the return series. Our findings reveal that all series and the cross-correlations of carbon and fossil fuels markets have multifractal characteristics. We find crude oil to be the most efficient market (lowest multifractal), while coal is the least efficient (highest multifractal). Only coal shows persistent, whereas the other markets exhibit antipersistent behavior. Interestingly, the coal and EU ETS pair demonstrates a higher degree of multifractal patterns. In contrast, the pair of natural gas and EU ETS exhibits the lowest multifractal characteristics among the energy markets. Only the crude oil market shows persistent cross-correlations in the multifractality. These findings have important academic and managerial implications for investors and policymakers.

Multifractal Analysis of MODIS Aqua and Terra Satellite Time Series of Normalized Difference Vegetation Index and Enhanced Vegetation Index of Sites Affected by Wildfires.

The MODIS Aqua and Terra Normalized Difference Vegetation Index (NDVI) and Enhanced Vegetation Index (EVI) time series acquired during nearly two decades (2000 to 2020) covering the area burned by the Camp Fire (California) in 2018 is investigated in this study by using the multifractal detrended fluctuation analysis in relation to the recovery process of vegetation after fire. In 2008, the same area was partially burned by two wildfires, the BTU Lightning Complex Fire and the Humboldt Fire. Our results indicate that all vegetation index time series are featured by six- and twelve-month modulating periodicities, with a larger spectral content at longer periods for two-fire-affected sites. Furthermore, two fires cause an increase of the persistence of the NDVI and EVI time series and an increase of the complexity, suggesting that the recovery process of vegetation dynamics of fire-affected sites is characterized by positive feedback mechanisms, driving the growth-generating phenomena, which become even more effective in those sites affected by two fires.

Market Efficiency and Cross-Correlations of Chinese New Energy Market with Other Assets: Evidence from Multifractality Analysis.

Despite the upgrading of the attention and investment of new energy in Chinese public, its market efficiency and associations with other assets are relatively rarely explored. This paper, firstly, explores the multifractal feature and market efficiency of Chinese new energy market (NEI) by the multifractal detrended fluctuation analysis. Secondly, the multifractal cross-correlation analysis is performed to discuss the multifractality of cross-correlations between NEI and crude oil, external new energy indices (Global (SPGCE), United States (ECO) and Europe (ERIX)) and safe-haven asset (GOLD) respectively. The results show that Chinese new energy market has obvious multifractality with low market efficiency, which is mainly sourced from long-range correlation. It has the strongest linkages with external new energy markets and most insignificant association with gold. The heterogeneous sources contribute to their multifractal cross-correlations. It provides useful enlightenment for decision-makers to implement energy policy and reform, and for investors to make investment decisions.

Characterizing stroke-induced changes in the variability of lower limb kinematics using multifractal detrended fluctuation analysis.

Movement variability reflects the adaptation of the neuromuscular control system to internal or external perturbations, but its relationship to stroke-induced injury is still unclear. In this study, the multifractal detrended fluctuation analysis was used to explore the stroke-induced changes in movement variability by analyzing the joint angles in a treadmill-walking task. Eight healthy subjects and ten patients after stroke participated in the experiment, performing a treadmill-walking task at a comfortable speed. The kinematics data of the lower limbs were collected by the motion-capture system, and two indicators, the degree of multifractality (α) and degree of correlation [h(2)], were used to investigate the mechanisms underlying neuromuscular control. The results showed that the knee and ankle joint angles were multifractal and persistent at various scales, and there was a significant difference in the degree of multifractality and the degree of correlation at the knee and ankle joint angles among the three groups, with the values being ranked in the following order: healthy subjects < non-paretic limb < paretic limb. These observations highlighted increased movement variability and multifractal strength in patients after stroke due to neuromotor defects. This study provided evidence that multifractal detrended analysis of the angles of the knee and ankle joints is useful to investigate the changes in movement variability and multifractal after stroke. Further research is needed to verify and promote the clinical applications.

Fractal Structure of Brain Electrical Activity of Patients With Mental Disorders.

This work was aimed at a comparative analysis of the degree of multifractality of electroencephalographic time series obtained from a group of healthy subjects and from patients with mental disorders. We analyzed long-term records of patients with paranoid schizophrenia and patients with depression. To evaluate the properties of multifractal scaling of various electroencephalographic time series, the method of maximum modulus of the wavelet transform and multifractal analysis of fluctuations without a trend were used. The stability of the width and position of the singularity spectrum for each of the test groups was revealed, and a relationship was established between the correlation and anticorrelation dynamics of successive values of the electroencephalographic time series and the type of mental disorders. It was shown that the main differences between the multifractal properties of brain activity in normal and pathological conditions lie in the different width of the multifractality spectrum and its location associated with the correlated or anticorrelated dynamics of the values of successive time series. It was found that the schizophrenia group is characterized by a greater degree of multifractality compared to the depression group. Thus, the degree of multifractality can be included in a set of tests for differential diagnosis and research of mental disorders.

Turing's cascade instability supports the coordination of the mind, brain, and behavior.

Turing inspired a computer metaphor of the mind and brain that has been handy and has spawned decades of empirical investigation, but he did much more and offered behavioral and cognitive sciences another metaphor-that of the cascade. The time has come to confront Turing's cascading instability, which suggests a geometrical framework driven by power laws and can be studied using multifractal formalism and multiscale probability density function analysis. Here, we review a rapidly growing body of scientific investigations revealing signatures of cascade instability and their consequences for a perceiving, acting, and thinking organism. We review work related to executive functioning (planning to act), postural control (bodily poise for turning plans into action), and effortful perception (action to gather information in a single modality and action to blend multimodal information). We also review findings on neuronal avalanches in the brain, specifically about neural participation in body-wide cascades. Turing's cascade instability blends the mind, brain, and behavior across space and time scales and provides an alternative to the dominant computer metaphor.

Fractal methods applied to the seminiferous lumen images can quantify testicular changes induced by heat stress.

Male infertility affects many couples around the world and can be related to environmental factors such as exposure to high temperatures. Even so, automated methods evaluating the seminiferous tubules to detect testicular damage are still scarce. In search of new approaches to automation in the microscopic analysis of the testis; the present study used the fractal dimension, lacunarity, multifractality and quantitative morphometry to quantify changes in microphotographs of the seminiferous lumen in testicles reversibly damaged by heat stress (43 °C, 12 min). The parameters fractal dimension, lacunarity, multifractality (Dq and α), perimeter, feret and circularity were able to detect changes in the seminiferous lumen at 7, 15 and 30 days after the testicular damage. These methods also detected the recovery of spermatogenesis at 60 days after heat stress. Area, f(α), centroid X and Y, roundness, rectangle height and width were unable to detect changes caused by heat stress. In conclusion, computer assisted methods applied to the seminiferous lumen images can be a useful new viewpoint to analyze microscopic changes in the testicles, a fast low-cost tool to assist in the automated quantification of testicular damage.

Spatial Characteristics Analysis for Coupling Strength among Air Pollutants during a Severe Haze Period in Zhengzhou, China.

This paper investigates the multifractal characteristics of six air pollutants using the coupling detrended fluctuation analysis method. The results show that coupling correlations exist among the air pollutants and have multifractal characteristics. The sources of multifractality are identified using the chi square test. The coupling strengths between different pollutants are quantified. In addition, the coupling contribution of a series in the haze system is calculated, and SO2, as the main pollutant, plays a key role in the pollution system. Moreover, the Kriging interpolation method is used to analyze the spatial characteristic on coupling contribution of SO2. The spatial analysis of coupling strength for air pollutants will provide an effective approach for pollution control.

Comparing the asymmetric efficiency of dirty and clean energy markets pre and during COVID-19.

In the backdrop of the recent COVID-19 pandemic, the study examines the comparative asymmetric efficiency of dirty and clean energy markets pre and during the COVID-19 pandemic. For this purpose, we utilize an asymmetric multifractality detrended fluctuation analysis (A-MF-DFA). The study's findings uncover the presence of asymmetric multifractality in clean and dirty energy markets. In addition, multifractality in the energy markets is sensitive to trends, time horizon and major events. More importantly, the results suggest superior efficiency of clean-energy markets compared to conventional energies. We confirm the time-varying nature of market efficiency in the energy markets, and during the recent COVID-19 outbreak, market inefficiencies in the clean and dirty energy markets soared. In this way, the study holds meaningful insights for policymakers, energy policy practitioners, investors, and financial market participants to choose between clean (dirty) investments based on their asymmetric efficiency (inefficiency).