Characterization and classification of kinesthetic motor imagery levels.

OBJECTIVE: Kinesthetic Motor Imagery (KMI) represents a robust brain paradigm intended for electroencephalography (EEG)-based commands in brain-computer interfaces (BCIs). However, ensuring high accuracy in multi-command execution remains challenging, with data from C3 and C4 electrodes reaching up to 92% accuracy. This paper aims to characterize and classify EEG-based KMI of multilevel muscle contraction without relying on primary motor cortex signals. Approach. A new method based on Hurst exponents is introduced to characterize EEG signals of multilevel KMI of muscle contraction from electrodes placed on the premotor, dorsolateral prefrontal, and inferior parietal cortices. EEG signals were recorded during a hand-grip task at four levels of muscle contraction (0, 10, 40, and 70% of the maximal isometric voluntary contraction). The task was executed under two conditions: first, physically, to train subjects in achieving muscle contraction at each level, followed by mental imagery under the KMI paradigm for each contraction level. EMG signals were recorded in both conditions to correlate muscle contraction execution, whether correct or null accurately. Independent component analysis (ICA) maps EEG signals from the sensor to the source space for preprocessing. For characterization, three algorithms based on Hurst exponents were used: the original (HO), using partitions (HRS), and applying semivariogram (HV). Finally, seven classifiers were used: Bayes network (BN), naive Bayes (NB), support vector machine (SVM), random forest (RF), random tree (RT), multilayer perceptron (MP), and k-nearest neighbours (kNN). Main results. A combination of the three Hurst characterization algorithms produced the highest average accuracy of 96.42% from kNN, followed by MP (92.85%), SVM (92.85%), NB (91.07%), RF (91.07%), BN (91.07%), and RT (80.35%). of 96.42% for kNN. Significance. Results show the feasibility of KMI multilevel muscle contraction detection and, thus, the viability of non-binary EEG-based BCI applications without using signals from the motor cortex.

Spatiotemporal patterns, sustainability, and primary drivers of NDVI-derived vegetation dynamics (2003-2022) in Nepal.

Understanding the vegetation dynamics and their drivers in Nepal has significant scientific reference value for implementing sustainable ecological policies. This study provides a comprehensive analysis of the spatio-temporal variations in vegetation cover in Nepal from 2003 to 2022 using MODIS NDVI data and explores the effects of climatic factors and anthropogenic activities on vegetation. Mann-Kendall test was used to assess the significant trend in NDVI and was integrated with the Hurst exponent to predict future trends. The driving factors of NDVI dynamics were analyzed using Pearson's correlation, partial derivative, and residual analysis methods. The results indicate that over the last 20 years, Nepal has experienced an increasing trend in NDVI at 0.0013 year-1, with 80% of the surface area (vegetation cover) showing an increasing vegetation trend (~ 28% with a significant increase in vegetation). Temperature influenced vegetation dynamics in the higher elevation areas, while precipitation and human interventions influenced the lower elevation areas. The Hurst exponent analysis predicts an improvement in the vegetation cover (greening) for a larger area compared to vegetation degradation (browning). A significantly increased area of NDVI residuals indicates a positive anthropogenic influence on vegetation cover. Anthropogenic activities have a higher relative contribution to NDVI variation followed by temperature and then precipitation. The results of residual trend and Hurst analysis in different regions of Nepal help identify degraded areas, both in the present and future. This information can assist relevant authorities in implementing appropriate policies for a sustainable ecological environment.

Aperiodic and Hurst EEG exponents across early human brain development: A systematic review.

In electroencephalographic (EEG) data, power-frequency slope exponents (1/f_ß) can provide non-invasive markers of in vivo neural activity excitation-inhibition (E:I) balance. E:I balance may be altered in neurodevelopmental conditions; hence, understanding how 1/fß evolves across infancy/childhood has implications for developing early assessments/interventions. This systematic review (PROSPERO-ID: CRD42023363294) explored the early maturation (0-26 yrs) of resting-state EEG 1/f measures (aperiodic [AE], power law [PLE] and Hurst [HE] exponents), including studies containing ≥1 1/f measures and ≥10 typically developing participants. Five databases (including Embase and Scopus) were searched during March 2023. Forty-two studies were identified (Nparticipants=3478). Risk of bias was assessed using the Quality Assessment with Diverse Studies tool. Narrative synthesis of HE data suggests non-stationary EEG activity occurs throughout development. Age-related trends were complex, with rapid decreases in AEs during infancy and heterogenous changes thereafter. Regionally, AE maxima shifted developmentally, potentially reflecting spatial trends in maturing brain connectivity. This work highlights the importance of further characterising the development of 1/f measures to better understand how E:I balance shapes brain and cognitive development.

Postural control in gymnasts: anisotropic fractal scaling reveals proprioceptive reintegration in vestibular perturbation.

Dexterous postural control subtly complements movement variability with sensory correlations at many scales. The expressive poise of gymnasts exemplifies this lyrical punctuation of release with constraint, from coarse grain to fine scales. Dexterous postural control upon a 2D support surface might collapse the variation of center of pressure (CoP) to a relatively 1D orientation-a direction often oriented towards the focal point of a visual task. Sensory corrections in dexterous postural control might manifest in temporal correlations, specifically as fractional Brownian motions whose differences are more and less correlated with fractional Gaussian noises (fGns) with progressively larger and smaller Hurst exponent H. Traditional empirical work examines this arrangement of lower-dimensional compression of CoP along two orthogonal axes, anteroposterior (AP) and mediolateral (ML). Eyes-open and face-forward orientations cultivate greater variability along AP than ML axes, and the orthogonal distribution of spatial variability has so far gone hand in hand with an orthogonal distribution of H, for example, larger in AP and lower in ML. However, perturbing the orientation of task focus might destabilize the postural synergy away from its 1D distribution and homogenize the temporal correlations across the 2D support surface, resulting in narrower angles between the directions of the largest and smallest H. We used oriented fractal scaling component analysis (OFSCA) to investigate whether sensory corrections in postural control might thus become suborthogonal. OFSCA models raw 2D CoP trajectory by decomposing it in all directions along the 2D support surface and fits the directions with the largest and smallest H. We studied a sample of gymnasts in eyes-open and face-forward quiet posture, and results from OFSCA confirm that such posture exhibits the classic orthogonal distribution of temporal correlations. Head-turning resulted in a simultaneous decrease in this angle Δθ, which promptly reversed once gymnasts reoriented their heads forward. However, when vision was absent, there was only a discernible negative trend in Δθ, indicating a shift in the angle's direction but not a statistically significant one. Thus, the narrowing of Δθ may signify an adaptive strategy in postural control. The swift recovery of Δθ upon returning to a forward-facing posture suggests that the temporary reduction is specific to head-turning and does not impose a lasting burden on postural control. Turning the head reduced the angle between these two orientations, facilitating the release of postural degrees of freedom towards a more uniform spread of the CoP across both dimensions of the support surface. The innovative aspect of this work is that it shows how fractality might serve as a control parameter of adaptive mechanisms of dexterous postural control.

Spatial variability and directional shifts in postural control in Parkinson's disease.

Individuals with Parkinson's disease exhibit tremors, rigidity, and bradykinesia, disrupting normal movement variability and resulting in postural instability. This comprehensive study aimed to investigate the link between the temporal structure of postural sway variability and Parkinsonism by analyzing multiple datasets from young and older adults, including individuals with Parkinson's disease, across various task conditions. We used the Oriented Fractal Scaling Component Analysis (OFSCA), which identifies minimal and maximal long-range correlations within the center of pressure time series, allowing for detecting directional changes in postural sway variability. The objective was to uncover the primary directions along which individuals exerted control during the posture. The results, as anticipated, revealed that healthy adults predominantly exerted control along two orthogonal directions, closely aligned with the anteroposterior (AP) and mediolateral (ML) axes. In stark contrast, older adults and individuals with Parkinson's disease exhibited control along suborthogonal directions that notably diverged from the AP and ML axes. While older adults and those with Parkinson's disease demonstrated a similar reduction in the angle between these two control directions compared to healthy older adults, their reliance on this suborthogonal angle concerning endogenous fractal correlations exhibited significant differences from the healthy aging cohort. Importantly, individuals with Parkinson's disease did not manifest the sensitivity to destabilizing task settings observed in their healthy counterparts, affirming the distinction between Parkinson's disease and healthy aging.

Fractals in Neuroimaging.

Several natural phenomena can be described by studying their statistical scaling patterns, hence leading to simple geometrical interpretation. In this regard, fractal geometry is a powerful tool to describe the irregular or fragmented shape of natural features, using spatial or time-domain statistical scaling laws (power-law behavior) to characterize real-world physical systems. This chapter presents some works on the usefulness of fractal features, mainly the fractal dimension and the related Hurst exponent, in the characterization and identification of pathologies and radiological features in neuroimaging, mainly, magnetic resonance imaging.

Fractal Time Series: Background, Estimation Methods, and Performances.

Over the past 40 years, from its classical application in the characterization of geometrical objects, fractal analysis has been progressively applied to study time series in several different disciplines. In neuroscience, starting from identifying the fractal properties of neuronal and brain architecture, attention has shifted to evaluating brain signals in the time domain. Classical linear methods applied to analyzing neurophysiological signals can lead to classifying irregular components as noise, with a potential loss of information. Thus, characterizing fractal properties, namely, self-similarity, scale invariance, and fractal dimension (FD), can provide relevant information on these signals in physiological and pathological conditions. Several methods have been proposed to estimate the fractal properties of these neurophysiological signals. However, the effects of signal characteristics (e.g., its stationarity) and other signal parameters, such as sampling frequency, amplitude, and noise level, have partially been tested. In this chapter, we first outline the main properties of fractals in the domain of space (fractal geometry) and time (fractal time series). Then, after providing an overview of the available methods to estimate the FD, we test them on synthetic time series (STS) with different sampling frequencies, signal amplitudes, and noise levels. Finally, we describe and discuss the performances of each method and the effect of signal parameters on the accuracy of FD estimation.

Dynamics of neuronal firing modulated by high-frequency electrical pulse stimulations at axons in rat hippocampus.

Objective. The development of electrical pulse stimulations in brain, including deep brain stimulation, is promising for treating various brain diseases. However, the mechanisms of brain stimulations are not yet fully understood. Previous studies have shown that the commonly used high-frequency stimulation (HFS) can increase the firing of neurons and modulate the pattern of neuronal firing. Because the generation of neuronal firing in brain is a nonlinear process, investigating the characteristics of nonlinear dynamics induced by HFS could be helpful to reveal more mechanisms of brain stimulations. The aim of present study is to investigate the fractal properties in the neuronal firing generated by HFS.Approach. HFS pulse sequences with a constant frequency 100 Hz were applied in the afferent fiber tracts of rat hippocampal CA1 region. Unit spikes of both the pyramidal cells and the interneurons in the downstream area of stimulations were recorded. Two fractal indexes-the Fano factor and Hurst exponent were calculated to evaluate the changes of long-range temporal correlations (LRTCs), a typical characteristic of fractal process, in spike sequences of neuronal firing.Mainresults. Neuronal firing at both baseline and during HFS exhibited LRTCs over multiple time scales. In addition, the LRTCs significantly increased during HFS, which was confirmed by simulation data of both randomly shuffled sequences and surrogate sequences.Conclusion. The purely periodic stimulation of HFS pulses, a non-fractal process without LRTCs, can increase rather than decrease the LRTCs in neuronal firing.Significance. The finding provides new nonlinear mechanisms of brain stimulation and suggests that LRTCs could be a new biomarker to evaluate the nonlinear effects of HFS.

Roughness Evolution Induced by Third-Body Wear.

Surface roughness is a key factor when it comes to friction and wear, as well as to other physical properties. These phenomena are controlled by mechanisms acting at small scales, in which the topography of apparently flat surfaces is revealed. Roughness in natural surfaces has been reported to conform to self-affine statistics in a wide variety of settings (ranging from earthquake physics to micro-electro-mechanical devices), meaning that the height profile can be described using a spectrum where the amplitude is proportional to its wavelength raised to a constant power, which is related to a statistical parameter named Hurst exponent. We analyze the roughness evolution in atomistic surfaces during molecular dynamics simulations of wear. Both pairs of initially flat and initially rough surfaces in contact are worn by a third body formed by particles trapped between them during relative sliding. During the first sliding stages, the particles trapped between the first bodies scratch the surfaces. Once the former becomes coated with atoms from the latter, the wear process slows down and becomes "adhesive like." The initial particle sizes are consistent with the minimum size to be expected for the debris, but tend to grow by material removal from the surfaces and to agglomerate. We show that, for the particular configurations under consideration, the surface roughness seems to converge to a steady state characterized by Hurst exponent close to 0.8, independently of the initial conditions. Supplementary Information: The online version contains supplementary material available at 10.1007/s11249-024-01833-9.

Increased regional Hurst exponent reflects response inhibition related neural complexity alterations in pediatric bipolar disorder patients during an emotional Go-Nogo task.

Fractal patterns have been shown to change in resting- and task-state blood oxygen level-dependent signals in bipolar disorder patients. However, fractal characteristics of brain blood oxygen level-dependent signals when responding to external emotional stimuli in pediatric bipolar disorder remain unclear. Blood oxygen level-dependent signals of 20 PBD-I patients and 17 age- and sex-matched healthy controls were extracted while performing an emotional Go-Nogo task. Neural responses relevant to the task and Hurst exponent of the blood oxygen level-dependent signals were assessed. Correlations between clinical indices and Hurst exponent were estimated. Significantly increased activations were found in regions covering the frontal lobe, parietal lobe, temporal lobe, insula, and subcortical nuclei in PBD-I patients compared to healthy controls in contrast of emotional versus neutral distractors. PBD-I patients exhibited higher Hurst exponent in regions that involved in action control, such as superior frontal gyrus, inferior frontal gyrus, inferior temporal gyrus, and insula, with Hurst exponent of frontal orbital gyrus correlated with onset age. The present study exhibited overactivation, increased self-similarity and decreased complexity in cortical regions during emotional Go-Nogo task in patients relative to healthy controls, which provides evidence of an altered emotional modulation of cognitive control in pediatric bipolar disorder patients. Hurst exponent may be a fractal biomarker of neural activity in pediatric bipolar disorder.

Complexity Measures for EEG Microstate Sequences: Concepts and Algorithms.

EEG microstate sequence analysis quantifies properties of ongoing brain electrical activity which is known to exhibit complex dynamics across many time scales. In this report we review recent developments in quantifying microstate sequence complexity, we classify these approaches with regard to different complexity concepts, and we evaluate excess entropy as a yet unexplored quantity in microstate research. We determined the quantities entropy rate, excess entropy, Lempel-Ziv complexity (LZC), and Hurst exponents on Potts model data, a discrete statistical mechanics model with a temperature-controlled phase transition. We then applied the same techniques to EEG microstate sequences from wakefulness and non-REM sleep stages and used first-order Markov surrogate data to determine which time scales contributed to the different complexity measures. We demonstrate that entropy rate and LZC measure the Kolmogorov complexity (randomness) of microstate sequences, whereas excess entropy and Hurst exponents describe statistical complexity which attains its maximum at intermediate levels of randomness. We confirmed the equivalence of entropy rate and LZC when the LZ-76 algorithm is used, a result previously reported for neural spike train analysis (Amigó et al., Neural Comput 16:717-736, https://doi.org/10.1162/089976604322860677 , 2004). Surrogate data analyses prove that entropy-based quantities and LZC focus on short-range temporal correlations, whereas Hurst exponents include short and long time scales. Sleep data analysis reveals that deeper sleep stages are accompanied by a decrease in Kolmogorov complexity and an increase in statistical complexity. Microstate jump sequences, where duplicate states have been removed, show higher randomness, lower statistical complexity, and no long-range correlations. Regarding the practical use of these methods, we suggest that LZC can be used as an efficient entropy rate estimator that avoids the estimation of joint entropies, whereas entropy rate estimation via joint entropies has the advantage of providing excess entropy as the second parameter of the same linear fit. We conclude that metrics of statistical complexity are a useful addition to microstate analysis and address a complexity concept that is not yet covered by existing microstate algorithms while being actively explored in other areas of brain research.

Decreased long-range temporal correlations in the resting-state functional magnetic resonance imaging blood-oxygen-level-dependent signal reflect motor sequence learning up to 2 weeks following training.

Decreased long-range temporal correlations (LRTC) in brain signals can be used to measure cognitive effort during task execution. Here, we examined how learning a motor sequence affects long-range temporal memory within resting-state functional magnetic resonance imaging signal. Using the Hurst exponent (HE), we estimated voxel-wise LRTC and assessed changes over 5 consecutive days of training, followed by a retention scan 12 days later. The experimental group learned a complex visuomotor sequence while a complementary control group performed tightly matched movements. An interaction analysis revealed that HE decreases were specific to the complex sequence and occurred in well-known motor sequence learning associated regions including left supplementary motor area, left premotor cortex, left M1, left pars opercularis, bilateral thalamus, and right striatum. Five regions exhibited moderate to strong negative correlations with overall behavioral performance improvements. Following learning, HE values returned to pretraining levels in some regions, whereas in others, they remained decreased even 2 weeks after training. Our study presents new evidence of HE's possible relevance for functional plasticity during the resting-state and suggests that a cortical subset of sequence-specific regions may continue to represent a functional signature of learning reflected in decreased long-range temporal dependence after a period of inactivity.

Scaling Exponents of Time Series Data: A Machine Learning Approach.

In this study, we present a novel approach to estimating the Hurst exponent of time series data using a variety of machine learning algorithms. The Hurst exponent is a crucial parameter in characterizing long-range dependence in time series, and traditional methods such as Rescaled Range (R/S) analysis and Detrended Fluctuation Analysis (DFA) have been widely used for its estimation. However, these methods have certain limitations, which we sought to address by modifying the R/S approach to distinguish between fractional Lévy and fractional Brownian motion, and by demonstrating the inadequacy of DFA and similar methods for data that resembles fractional Lévy motion. This inspired us to utilize machine learning techniques to improve the estimation process. In an unprecedented step, we train various machine learning models, including LightGBM, MLP, and AdaBoost, on synthetic data generated from random walks, namely fractional Brownian motion and fractional Lévy motion, where the ground truth Hurst exponent is known. This means that we can initialize and create these stochastic processes with a scaling Hurst/scaling exponent, which is then used as the ground truth for training. Furthermore, we perform the continuous estimation of the scaling exponent directly from the time series, without resorting to the calculation of the power spectrum or other sophisticated preprocessing steps, as done in past approaches. Our experiments reveal that the machine learning-based estimators outperform traditional R/S analysis and DFA methods in estimating the Hurst exponent, particularly for data akin to fractional Lévy motion. Validating our approach on real-world financial data, we observe a divergence between the estimated Hurst/scaling exponents and results reported in the literature. Nevertheless, the confirmation provided by known ground truths reinforces the superiority of our approach in terms of accuracy. This work highlights the potential of machine learning algorithms for accurately estimating the Hurst exponent, paving new paths for time series analysis. By marrying traditional finance methods with the capabilities of machine learning, our study provides a novel contribution towards the future of time series data analysis.

A pattern of cognitive resource disruptions in childhood psychopathology.

The Hurst exponent (H) isolated in fractal analyses of neuroimaging time series is implicated broadly in cognition. Within this literature, H is associated with multiple mental disorders, suggesting that H is transdimensionally associated with psychopathology. Here, we unify these results and demonstrate a pattern of decreased H with increased general psychopathology and attention-deficit/hyperactivity factor scores during a working memory task in 1,839 children. This pattern predicts current and future cognitive performance in children and some psychopathology in 703 adults. This pattern also defines psychological and functional axes associating psychopathology with an imbalance in resource allocation between fronto-parietal and sensorimotor regions, driven by reduced resource allocation to fronto-parietal regions. This suggests the hypothesis that impaired working memory function in psychopathology follows from a reduced cognitive resource pool and a reduction in resources allocated to the task at hand.

Dynamical Analyses Show That Professional Archers Exhibit Tighter, Finer and More Fluid Dynamical Control Than Neophytes.

Quantifying the dynamical features of discrete tasks is essential to understanding athletic performance for many sports that are not repetitive or cyclical. We compared three dynamical features of the (i) bow hand, (ii) drawing hand, and (iii) center of mass during a single bow-draw movement between professional and neophyte archers: dispersion (convex hull volume of their phase portraits), persistence (tendency to continue a trend as per Hurst exponents), and regularity (sample entropy). Although differences in the two groups are expected due to their differences in skill, our results demonstrate we can quantify these differences. The center of mass of professional athletes exhibits tighter movements compared to neophyte archers (6.3 < 11.2 convex hull volume), which are nevertheless less persistent (0.82 < 0.86 Hurst exponent) and less regular (0.035 > 0.025 sample entropy). In particular, the movements of the bow hand and center of mass differed more between groups in Hurst exponent analysis, and the drawing hand and center of mass were more different in sample entropy analysis. This suggests tighter neuromuscular control over the more fluid dynamics of the movement that exhibits more active corrections that are more individualized. Our work, therefore, provides proof of principle of how well-established dynamical analysis techniques can be used to quantify the nature and features of neuromuscular expertise for discrete movements in elite athletes.

Identifying Alzheimer's disease and mild cognitive impairment with atlas-based multi-modal metrics.

Introduction: Multi-modal neuroimaging metrics in combination with advanced machine learning techniques have attracted more and more attention for an effective multi-class identification of Alzheimer's disease (AD), mild cognitive impairment (MCI) and health controls (HC) recently. Methods: In this paper, a total of 180 subjects consisting of 44 AD, 66 MCI and 58 HC subjects were enrolled, and the multi-modalities of the resting-state functional magnetic resonance imaging (rs-fMRI) and the structural MRI (sMRI) for all participants were obtained. Then, four kinds of metrics including the Hurst exponent (HE) metric and bilateral hippocampus seed independently based connectivity metrics generated from fMRI data, and the gray matter volume (GMV) metric obtained from sMRI data, were calculated and extracted in each region of interest (ROI) based on a newly proposed automated anatomical Labeling (AAL3) atlas after data pre-processing. Next, these metrics were selected with a minimal redundancy maximal relevance (MRMR) method and a sequential feature collection (SFC) algorithm, and only a subset of optimal features were retained after this step. Finally, the support vector machine (SVM) based classification methods and artificial neural network (ANN) algorithm were utilized to identify the multi-class of AD, MCI and HC subjects in single modal and multi-modal metrics respectively, and a nested ten-fold cross-validation was utilized to estimate the final classification performance. Results: The results of the SVM and ANN based methods indicated the best accuracies of 80.36 and 74.40%, respectively, by utilizing all the multi-modal metrics, and the optimal accuracies for AD, MCI and HC were 79.55, 78.79 and 82.76%, respectively, in the SVM based method. In contrast, when using single modal metric, the SVM based method obtained a best accuracy of 72.62% with the HE metric, and the accuracies for AD, MCI and HC subjects were just 56.82, 80.30 and 75.86%, respectively. Moreover, the overlapping abnormal brain regions detected by multi-modal metrics were mainly located at posterior cingulate gyrus, superior frontal gyrus and cuneus. Conclusion: Taken together, the SVM based method with multi-modal metrics could provide effective diagnostic information for identifying AD, MCI and HC subjects.

Nonlinear features of gaze behavior during joint attention in children with autism spectrum disorder.

Since children with autism spectrum disorder (ASD) might exhibit a variety of aberrant response to joint attention (RJA) behaviors, there is growing interest in identifying robust, reliable and valid eye-tracking metrics for determining differences in RJA behaviors between typically developing (TD) children and those with ASD. Previous eye-tracking studies have not been deeply investigated nonlinear features of gaze time-series during RJA. As a main motivation, this study aimed to extract three nonlinear features (i.e., complexity, long-range correlation, and local instability) of gaze time-series during RJA in children with ASD, which can be measured by fractal dimension (FD), Hurst exponent (H), and largest Lyapunov exponent (LLE), respectively. To illustrate our idea, this study adopted a publicly accessible database, including eye-tracking data collected during RJA from 19 children with ASD (7.74 ± 2.73) and 30 TD children (8.02 ± 2.89), and conducted a battery of nonparametric analysis of covariance (ANCOVA), where gender was used as covariable. Findings showed that gaze time-series during RJA in autistic children may generally have greater FD but lower H than that in TD controls. This implies that children with ASD possess more complex and unpredictable gaze behaviors during RJA than TD children. Furthermore, nonlinear metrics outperformed traditional eye-tracking metrics in obtaining higher identification performance with an accuracy of 82% and an AUC value of 0.81, distinguishing the differences between successful and failed RJA trails, and predicting the severity of ASD symptoms. Findings might bring some new insights into the understanding of the impairments in RJA behaviors for children with ASD.

Exploring vegetation trends and restoration possibilities in Pakistan by using Hurst exponent.

Vegetation cover change and its interaction with climate are significant to study as it has impact on ecosystem stability. We used the Normalized Difference Vegetation Index (NDVI) and climatic factors (temperature and rainfall) for investigating the relationship between vegetation and climate. We also traced spatiotemporal changes in the vegetation in Pakistan from 2000 to 2020; we used the Hurst exponent to estimate future vegetation trends in Pakistan. Our results show an increase in vegetation throughout Pakistan, and the Punjab Province is showing the highest significant vegetation trend at 88.51%. Our findings reveal that the response of vegetation to climate change varies by region and is influenced by local climatic conditions. However, the relationship between rainfall and annual NDVI is stronger than the temperature in the study area-Pakistan. The Hurst exponent value is above 0.5 in all four provinces, that is, the indication of consistent vegetation trends in the future. The highest values are observed in Punjab and Khyber Pakhtunkhwa (KPK). In the Punjab Province, 88.41% of the area showed positive development, with forests in particular showing a significant positive effect on land use classes. On the other hand, the Sindh Province has the highest negative result at 2.87%, with urban areas showing the highest negative development. To sum up, the NDVI pattern and change attribute suggest vegetation restoration in Pakistan.

Multi-spatiotemporal AOD trends and association with land use changes over the Guangdong-Hong Kong-Macao Greater Bay Area during 2001-2021.

Analyzing long-term variations of aerosol optical depth (AOD) is beneficial for determining high-pollutant-risk areas and formulating mitigation policies. In this study, multi-spatiotemporal trends and periodicity of AOD, as well as the persistence over the Guangdong-Hong Kong-Macao Greater Bay Area from 2001 to 2021, were investigated by the extreme-point symmetric mode decomposition (ESMD), Theil-Sen Median trend analysis and Hurst exponent. The results elucidate that AOD exhibits fluctuant variations during the 21-year period with the year 2012 as the turning point. There is a slight upward tendency (0.009 year-1) in the pre-2012 period but a pronounced downward trend (- 0.03 year-1) in the post-2012 period, suggesting an overall declining trend in the study area. The northern cities in the area present an increasing-stable-decreasing trend of monthly average AOD, whereas other cities have an increasing-fluctuating-decreasing trend over the study period. The decreasing rate in the western parts is higher than that in the eastern parts, like Zhaoqing, Jiangmen and Foshan city. A continuous decline of AOD is dominated over the study area, whereas an anti-persistence tendency is accumulated in the northeastern parts. Additionally, elevated AOD can be observed in unused land, water bodies and construction land, while grassland, cropland and woodland have lower AOD. The decreasing rate is larger when land-use types with high AOD are converted to those with low AOD; otherwise, the decreasing rate is smaller. The results have a great significance for improving the understanding of long-term variations of AOD, as well as providing a scientific basis to formulate environmental protection and mitigation practices.

Are clean energy markets efficient? A multifractal scaling and herding behavior analysis of clean and renewable energy markets before and during the COVID19 pandemic.

The literature lacks thorough and adequate evidence of the efficiency and herding behavior of clean and renewable energy markets. Therefore, the key objective of this paper is to explore the multifractality and efficiency of six clean energy markets by applying a robust method of Multifractal detrended fluctuation analysis (MFDFA) on daily data over a lengthy period. In addition, to examine the inner dynamics of clean energy markets around the global pandemic (COVID19), the data are further divided into two sub-periods of before and during COVID19. Our sampled clean energy markets exhibit multifractal behavior with a significant impact on the efficiency and intensified presence of multifractality during the COVID19 period. Overall, TXCT and BSEGRNX were the most efficient clean energy markets, but the ranking of TXCT deteriorated significantly in the sub-periods. The presence of multifractality and herding behavior symmetry intensified during the crisis period, which gives a potential for advancing portfolio management techniques. Moreover, our study provides practical implications and new insights for various market participants for better management and understanding of risks.