Lempel-Ziv Complexity Research Articles

Biomechanical assistance for basketball training movements based on cross-domain EEG physical fitness classification

Cross-domain EEG signals offer valuable insights into the cortical neuron activity patterns and the functional dynamics of the central nervous system (CNS). Within the framework of biomechanics, EEG has emerged as a critical tool to investigate the interplay between neural control and physical performance. This study explores EEG complexity parameters in specific brain regions of 24 elite athletes under three distinct states: Rest, unloaded exercise, and loaded exercise. By integrating biomechanical and electrophysiological analyses, the study uncovers functional adaptations in the parietal and occipital regions, key centers for somatosensory and visual processing, respectively, in high-performance athletes. The findings reveal no significant gender differences in EEG complexity under these conditions, but highlight the effects of long-term specialized training in enhancing CNS adaptability. This adaptation is reflected in a reduced reliance on visual input, a trait distinguishing elite athletes from non-athletes. Despite the small sample size, correlations between three nonlinear EEG parameters—maximum Lyapunov exponent, approximate entropy, and Lempel-Ziv complexity—and CNS fatigue were observed. These parameters provide a robust framework for monitoring CNS fatigue and assessing the effects of exercise on neural function. This study bridges biomechanics and neural analysis, offering a novel perspective on CNS functionality under varying exercise states. The results contribute a theoretical foundation for the development of biomechanical guidance systems tailored for basketball training, with implications for optimizing athletic performance and promoting CNS health.

A pilot human study using ketamine to treat disorders of consciousness.

Post-comatose disorders of consciousness (DoC) represent persistent neurological conditions with limited therapeutic options and a poor prognosis. Recent works advocate for exploring the effects of psychedelics to enhance brain complexity in DoC and ameliorate their consciousness. We investigated sub-anesthetic concentration of the atypical psychedelic ketamine for treating post-comatose prolonged DoC through a double-blind, placebo-controlled, cross-over trial involving three adult patients. Incremental concentrations of intravenous ketamine and saline were administered, alongside continuous electroencephalogram (EEG) recording and assessments of conscious behaviors and spastic paresis. Brain complexity, measured by Lempel-Ziv complexity (LZC) and explainable consciousness indicator (ECI), revealed increased LZC during ketamine infusion but no change in ECI. Patients exhibited reduced spastic paresis and increased arousal as time spent with eyes open but no positive change in diagnosis. No adverse effects were noted. This study contributes to understanding the relationship between consciousness and brain complexity and suggests a potential therapeutic role for ketamine in DoC.

Multimodal neurophenomenology of advanced concentration absorption meditation: An intensively sampled case study of Jhana.

Using a combination of fMRI, EEG, and phenomenology ratings, we examined the neurophenomenology of advanced concentrative absorption meditation, namely jhanas (ACAM-J), in a practitioner with over 23,000 h of meditation practice. Our study shows that ACAM-J states induce reliable changes in conscious experience and that these experiences are related to neural activity. Using resting-state fMRI functional connectivity, we found that ACAM-J is associated with decreased within-network modularity, increased global functional connectivity (GFC), and desegregation of the default mode and visual networks. Compared to control tasks, the ACAM-J were also related to widespread decreases in broadband EEG oscillatory power and increases in Lempel-Ziv complexity (LZ, a measure of brain entropy). Some fMRI findings varied by the control task used, while EEG results remained consistent, emphasizing both shared and unique neural features of ACAM-J. These differences in fMRI and EEG-measured neurophysiological properties correlated with specific changes in phenomenology - and especially with ACAM-J-induced states of bliss - enriching our understanding of these advanced meditative states. Our results show that advanced meditation practices markedly dysregulate high-level brain systems via practices of enhanced attention to sensations, corroborating recent neurocognitive theories of meditation as the deconstruction of the brain's cortical hierarchy. Overall, our results suggest that ACAM-J is associated with the modulation of large-scale brain networks in both fMRI and EEG, with potential implications for understanding the mechanisms of deep concentration practices and their effects on subjective experience.

Abnormal nonlinear features of EEG microstate sequence in obsessive–compulsive disorder

BackgroundAt present, only a few studies have explored electroencephalography (EEG) microstates of patients with obsessive–compulsive disorder (OCD) and the results are inconsistent. Additionally, the nonlinear features of EEG microstate sequences contain rich information about the brain, yet how the nonlinear features of EEG microstate sequences abnormally change in patients with OCD is still unknown.MethodsResting-state EEG data were collected from 48 OCD patients and macheted 48 healthy controls (HC). Subsequently, EEG microstate analysis was used to extract the microstate temporal parameters (duration, occurrence, coverage) and nonlinear features of EEG microstate sequences (sample entropy, Lempel–Ziv complexity, Hurst index). Finally, the temporal parameters and nonlinear features of EEG microstate sequences were sent to three kinds of machine learning models to classify OCD patients.ResultsBoth groups obtained four typical EEG microstate topographies. The duration of microstates A, B, and C in OCD patients decreased significantly, while the occurrence of microstate D increased significantly compared to HC. Sample entropy and Lempel–Ziv complexity of microstate sequences in OCD patients increased significantly, while Hurst index decreased significantly compared to HC. The classification accuracy using the nonlinear features of microstate sequences reached up to 85%, significantly higher than that based on microstate temporal parameter models.ConclusionThis study provides supplementary findings on EEG microstates in OCD patients with a larger sample size. We found that the nonlinear features of EEG microstate sequences in OCD patients can serve as potential electrophysiological biomarkers for distinguishing OCD patients.

Extended dispersion entropy-based Lempel–Ziv complexity: a novel metric for rolling bearing fault diagnosis

Extended dispersion entropy-based Lempel–Ziv complexity: a novel metric for rolling bearing fault diagnosis

Accurate depth of anesthesia monitoring based on EEG signal complexity and frequency features

Accurate monitoring of the depth of anesthesia (DoA) is essential for ensuring patient safety and effective anesthesia management. Existing methods, such as the Bispectral Index (BIS), are limited in real-time accuracy and robustness. Current methods have problems in generalizability across diverse patient datasets and are sensitive to artifacts, making it difficult to provide reliable DoA assessments in real time. This study proposes a novel method for DoA monitoring using EEG signals, focusing on accuracy, robustness, and real-time application. EEG signals were pre-processed using wavelet denoising and discrete wavelet transform (DWT). Features such as Permutation Lempel–Ziv Complexity (PLZC) and Power Spectral Density (PSD) were extracted. A random forest regression model was employed to estimate anesthetic states, and an unsupervised learning method using the Hurst exponent algorithm and hierarchical clustering was introduced to detect transitions between anesthesia states. The method was tested on two independent datasets (UniSQ and VitalDB), achieving an average Pearson correlation coefficient of 0.86 and 0.82, respectively. For the combined dataset, the model demonstrated an R-squared value of 0.70, a RMSE of 6.31, a MAE of 8.38, and a Pearson correlation of 0.84, showcasing its robustness and generalizability. This approach offers a more accurate and reliable real-time DoA monitoring tool that could significantly improve patient safety and anesthesia management, especially in diverse clinical environments.

From the brain’s encoding of input dynamics to its behavior: neural dynamics shape bias in decision making

The human brain is tightly connected to the individual’s environment and its input dynamics. How the dynamics of periodic environmental stimuli influence neural activity and subsequent behavior via neural entrainment or alignment is not fully clear yet, though. This study explores how periodic environmental stimuli influence neural activity and behavior. EEG data was collected during a Go-NoGo task with a periodic intertrial interval (ITI) of 1.3 s (0.769 Hz). Results showed that the task’s temporal structure increased power spectrum activity at 0.769 Hz, which showed high intersubject variability. Higher task-periodicity effects were linked to stronger phase-based intertrial coherence (ITC) and reduced neural complexity, as measured by lower Lempel-Ziv Complexity (LZC). Additionally, higher periodicity in the power spectrum correlated with faster reaction times and stronger response bias. We conclude that the encoding of the inputs’ dynamics into the brains power spectrum shapes subsequent behavior, e.g., RT and response bias, through reducing neural complexity.

Resting-State Electroencephalogram Complexity Is Associated With Oral Ketamine Treatment Response: A Bayesian Analysis of Lempel-Ziv Complexity and Multiscale Entropy.

Subanesthetic doses of ketamine are a promising novel treatment for suicidality; however, the evidence for predictive biomarkers is sparse. Recently, measures of complexity, including Lempel-Ziv complexity (LZC) and multiscale entropy (MSE), have been implicated in ketamine's therapeutic action. We evaluated electroencephalogram (EEG)-derived LZC and MSE differences between responders and nonresponders to oral ketamine treatment. A total of 31 participants received six single, weekly (titrated) doses of oral racemic ketamine (0.5-3mg/kg) and underwent EEG scans at baseline (Week 0), post-treatment (Week 6), and follow-up (Week 10). Resting-state (eyes closed and open) recordings were processed in EEGLAB, and complexity metrics were extracted using the Neurokit2 package. Participants were designated responders or nonresponders by clinical response (Beck Suicide Scale [BSS] score reduction of ≥50% from baseline to the respective timepoint or score ≤6) and then compared in terms of complexity across resting-state conditions and time. Employing a Bayesian mixed effects model, we found strong evidence that LZC was higher in the eyes-open compared to eyes-closed condition, as were MSE scales 1-3. At a global level, responders displayed elevated eyes-open baseline complexity compared to nonresponders, with these values decreasing from baseline to post-treatment (Week 6) in responders only. Exploratory analyses revealed that the elevated baseline eyes-open LZC in responders was spatially localized to the left frontal lobe (F1, AF3, FC1, and F3). EEG-complexity metrics may be sensitive biomarkers for evaluating and predicting oral ketamine treatment response, with the left prefrontal cortex bein a possible treatment response region.

EEG microstate in people with different degrees of fear of heights during virtual high-altitude exposure

Previous neuroimaging studies based on electroencephalography (EEG) microstate analysis have identified abnormal neural electric activity in patients with psychiatric diseases. However, the microstate information in individuals with different degrees of fear of heights (FoH) remains unknown so far. The aim of the study was therefore to explore the changes of EEG microstate characteristics in different FoH individuals when exposed to high-altitude stimulated by virtual reality (VR). First, acrophobia questionnaire (AQ) before the experiment and 32-channel EEG signals under the virtual high-altitude exposure were collected from 69 subjects. Second, each subject was divided into one of three levels of FoH including no-FoH, mild or moderate FoH (m-FoH) and severe FoH (s-FoH) groups according to their AQ scores. Third, using microstate analysis, we transformed EEG data into sequences of characteristic topographic maps and computed EEG microstate features including microstate basic parameters, microstate sequences complexity and microstate energy. Finally, the extracted features as inputs were sent to train and test an support vector machine (SVM) for classifying different FoH groups. The results demonstrated that five types of microstates (labeled as A, B, C, D and F) were identified across all subjects, of which microstates A-D resembled the four typical microstate classes and microstate F was a non-canonical microstate. Significantly decreased occurrence, coverage and duration of microstate F and transition probabilities from other microstates to microstate F in m-FoH and s-FoH groups were observed compared to no-FoH group. It was also demonstrated that both m-FoH and s-FoH groups showed a notable reduction in sample entropy and Lempel-Ziv complexity. Moreover, energies of microstate D for m-FoH group and microstate B for s-FoH group in right parietal, parietooccipital and occipital regions exhibited prominent decreases as comparison to people without FoH. But, no significant differences were found between m-FoH and s-FoH groups. Additionally, the results indicated that AQ-anxiety scores were negatively correlated with microstate basic metrics as well as microstate energy. For classification, the performance of SVM reached a relatively high accuracy of 89 % for distinguishing no-FoH from m-FoH. In summary, the findings highlight the alterations of EEG microstates in people with fear of heights induced by virtual high-altitude, reflecting potentially underlying abnormalities in the allocation of neural assemblies. Therefore, the combination of EEG microstate analysis and VR may be a potential valuable approach for the diagnosis of fear of heights.

Automated recognition of mental cognitive workload through nonlinear EEG analysis

Nowadays, with the remarkable advancements in detection instruments and artificial intelligence, there has been extensive utilization of human mental state monitoring in various domains. Few studies have explored how nonlinear analysis methods can detect cognitive workload despite the complex nature of EEG signals and advancements in signal processing techniques. In addition, the fuzziness of human mental conditions makes the need to use fuzzy engineering tools tangible in this field. Therefore, this investigation aimed to develop a decision support algorithm to improve previous efforts for the classification of task EEG and resting through machine learning algorithms. Various nonlinear features were calculated from all 19 EEG channels: Hurst exponent, Lempel–Ziv complexity, detrended fluctuation analysis, Higuchi fractal dimension, Katz fractal dimension, permutation entropy, singular value decomposition entropy, Petrosian fractal dimension, sample entropy, and Lyapunov exponent. During the classification step, a newly developed EPC-FC (Expert per Class Fuzzy Classifier) is introduced, utilizing an ensemble framework with specialized sub-classifiers for identifying a particular condition. By training sub-classifiers with the negative correlation learning (NCL) approach, the EPC-FC is designed to be exceptionally adaptable. Additionally, the separation of sub-classifiers within each class provides versatility and clarity to the system’s design. The proposed approach based on fuzzy systems and nonlinear analyses was applied to EEG data for mental workload recognition, which provides an excellent accuracy of 98.50% and an F1-score of 98.56% which is much higher than previous findings in this field. Also, the obtained results indicate that utilizing the proposed EPC-FC classifier maintains a consistently high accuracy exceeding 90% across various levels of SNRs. The obtained results proved the high potential of nonlinear analysis to detect cognitive states of the brain, which is consistent with the nonlinear and fuzzy nature of EEG data. Other nonlinear approaches should be considered for future studies to improve the current results.

Research on aquatic biological signal recognition based on mode decomposition and deep learning

Abstract As an important research content in the field of marine biology and ecology, aquatic biological signal (ABS) recognition is of great significance for understanding marine ecosystems, protecting biodiversity, and monitoring environmental changes. To improve the recognition accuracy of ABS, this paper proposes a new ABS recognition method based on mode decomposition and deep learning. First, real ABS data were obtained from the public website, and some data were selected for the simulation experiment. Secondly, the signal is decomposed using improved variational mode decomposition by human evolutionary optimization algorithm (HEOA-VMD), and the decomposed intrinsic mode function (IMF) set is classified into low complexity and high complexity IMF using improved Lempel-Ziv complexity (ILZC) and reverse permutation entropy (RPE). Then, mutual information (MI) is used to select double eigenvectors from low and high complexity IMF, respectively, and recognition is performed based on the double eigenvectors using weighted-convolutional neural network (CNN)-bidirectional gate recurrent unit (BIGRU)-Attention model. Finally, the proposed ABS recognition method is applied to both chaotic and real signals, and additional proof of universality is performed using real signals. The result of the study shows that the accuracy of the proposed method for the recognition of chaotic and real signals is as high as 97.3% and 98.0%. In conclusion, the research on ABS recognition in this paper is successful and has a broad application prospect.

Dispersion network-transition entropy: A metric for characterizing the complexity of nonlinear signals.

Extracting meaningful information from signals has always been a challenge. Due to the influence of environmental noise, collected signals often exhibit nonlinear characteristics, rendering traditional metrics inadequate in capturing the dynamic properties and complex structures of signals. To address this challenge, this study proposes an innovative metric for quantifying signal complexity-dispersion network-transition entropy (DNTE), which integrates the concepts of complex networks and information entropy. Specifically, we assign single cumulative distribution function values to network nodes and utilize Markov chains to represent links, transforming nonlinear signals into weighted directed complex networks. Subsequently, we assess the importance of network nodes and links, and employ the mathematical expression of information entropy to calculate the DNTE value, quantifying the complexity of the original signal. Next, through extensive experiments on simulated chaotic models and real underwater acoustic signals, we confirm the outstanding performance of DNTE. The results indicate that, compared to Lempel-Ziv complexity, permutation entropy, and dispersion entropy, DNTE not only more accurately reflects changes in signal complexity but also exhibits higher computational efficiency. Importantly, DNTE demonstrates optimal performance in distinguishing different categories of chaotic models, ships, and modulation signals, showcasing its significant potential in extracting effective information from signals.

UAV propeller fault diagnosis using deep learning of non-traditional χ2-selected Taguchi method-tested Lempel–Ziv complexity and Teager–Kaiser energy features

Fault detection and isolation in unmanned aerial vehicle (UAV) propellers are critical for operational safety and efficiency. Most existing fault diagnosis techniques rely basically on traditional statistical-based methods that necessitate better approaches. This study explores the application of untraditional feature extraction methodologies, namely Permutation Entropy (PE), Lempel–Ziv Complexity (LZC), and Teager–Kaiser Energy Operator (TKEO), on the PADRE dataset, which encapsulates various rotor fault configurations. The extracted features were subjected to a Chi-Square (χ2) feature selection process to identify the most significant features for input into a Deep Neural Network. The Taguchi method was utilized to test the performance of the recorded features, correspondingly. Performance metrics, including Accuracy, F1-Score, Precision, and Recall, were employed to evaluate the model’s effectiveness before and after the feature selection. The achieved accuracy has increased by 0.9% when compared with results utilizing traditional statistical methods. Comparative analysis with prior research reveals that the proposed untraditional features surpass traditional methods in diagnosing UAV propeller faults. It resulted in improved performance metrics with Accuracy, F1-Score, Precision, and Recall reaching 99.6%, 99.5%, 99.5%, and 99.5%, respectively. The results suggest promising directions for future research in UAV maintenance and safety protocols.

Complex Function-Based Fault Detection: A New Method to Measure the Complexity of Nonlinear Time Series

In this paper, we propose a new complexity computation based on the complex function. This measure exploits the dispersion Lempel–Ziv complexity (DLZC) and the dispersion statistical complexity measure based on Jensen–Shannon divergence (DCJS) of the analytic signal and constructs the binary complex function, called complex number complexity (CNC). The statistical measure depicts the complex system from different angle and mines more potential information. Through simulation experiments, we prove that the proposed method is able to detect data fluctuations more sensitively and accurately. For an application, the CNC is applied to fault detection which has different fault diameters and rotational speeds. The results deliver that the CNC measure can well represent the complexity of faulty bearings and has significant differences in any two fault types. The technique is effective to characterize different fault.

Breathwork-induced psychedelic experiences modulate neural dynamics.

Breathwork is an understudied school of practices involving intentional respiratory modulation to induce an altered state of consciousness (ASC). We simultaneously investigate the phenomenological and neural dynamics of breathwork by combining Temporal Experience Tracing, a quantitative methodology that preserves the temporal dynamics of subjective experience, with low-density portable EEG devices. Fourteen novice participants completed a course of up to 28 breathwork sessions-of 20, 40, or 60min-in 28days, yielding a neurophenomenological dataset of 301 breathwork sessions. Using hypothesis-driven and data-driven approaches, we found that "psychedelic-like" subjective experiences were associated with increased neural Lempel-Ziv complexity during breathwork. Exploratory analyses showed that the aperiodic exponent of the power spectral density-but not oscillatory alpha power-yielded similar neurophenomenological associations. Non-linear neural features, like complexity and the aperiodic exponent, neurally map both a multidimensional data-driven composite of positive experiences, and hypothesis-driven aspects of psychedelic-like experience states such as high bliss.

Study protocol for "Psilocybin in patients with fibromyalgia: brain biomarkers of action".

Chronic pain is a leading cause of disability worldwide. Fibromyalgia is a particularly debilitating form of widespread chronic pain. Fibromyalgia remains poorly understood, and treatment options are limited or moderately effective at best. Here, we present a protocol for a mechanistic study investigating the effects of psychedelic-assisted-therapy in a fibromyalgia population. The principal focus of this trial is the central mechanism(s) of psilocybin-therapy i.e., in the brain and on associated mental schemata, primarily captured by electroencephalography (EEG) recordings of the acute psychedelic state, plus pre and post Magnetic Resonance Imaging (MRI). Twenty participants with fibromyalgia will complete 8 study visits over 8 weeks. This will include two dosing sessions where participants will receive psilocybin at least once, with doses varying up to 25mg. Our primary outcomes are 1) Lempel-Ziv complexity (LZc) recorded acutely using EEG, and the 2) the (Brief Experiential Avoidance Questionnaire (BEAQ) measured at baseline and primary endpoint. Secondary outcomes will aim to capture broad aspects of the pain experience and related features through neuroimaging, self-report measures, behavioural paradigms, and qualitative interviews. Pain Symptomatology will be measured using the Brief Pain Inventory Interference Subscale (BPI-IS), physical and mental health-related function will be measured using the 36-Item Short Form Health Survey (SF-36). Further neurobiological investigations will include functional MRI (fMRI) and diffusion tensor imaging (changes from baseline to primary endpoint), and acute changes in pre- vs post-acute spontaneous brain activity - plus event-related potential functional plasticity markers, captured via EEG. The results of this study will provide valuable insight into the brain mechanisms involved in the action of psilocybin-therapy for fibromyalgia with potential implications for the therapeutic action of psychedelic-therapy more broadly. It will also deliver essential data to inform the design of a potential subsequent RCT.

Dorsal and median raphe neuronal firing dynamics characterized by nonlinear measures.

The dorsal (DRN) and median (MRN) raphe are important nuclei involved in similar functions, including mood and sleep, but playing distinct roles. These nuclei have a different composition of neuronal types and set of neuronal connections, which among other factors, determine their neuronal dynamics. Most works characterize the neuronal dynamics using classic measures, such as using the average spiking frequency (FR), the coefficient of variation (CV), and action potential duration (APD). In the current study, to refine the characterization of neuronal firing profiles, we examined the neurons within the raphe nuclei. Through the utilization of nonlinear measures, our objective was to discern the redundancy and complementarity of these measures, particularly in comparison with classic methods. To do this, we analyzed the neuronal basal firing profile in both nuclei of urethane-anesthetized rats using the Shannon entropy (Bins Entropy) of the inter-spike intervals, permutation entropy of ordinal patterns (OP Entropy), and Permutation Lempel-Ziv Complexity (PLZC). Firstly, we found that classic (i.e., FR, CV, and APD) and nonlinear measures fail to distinguish between the dynamics of DRN and MRN neurons, except for the OP Entropy. We also found strong relationships between measures, including the CV with FR, CV with Bins entropy, and FR with PLZC, which imply redundant information. However, APD and OP Entropy have either a weak or no relationship with the rest of the measures tested, suggesting that they provide complementary information to the characterization of the neuronal firing profiles. Secondly, we studied how these measures are affected by the oscillatory properties of the firing patterns, including rhythmicity, bursting patterns, and clock-like behavior. We found that all measures are sensitive to rhythmicity, except for the OP Entropy. Overall, our work highlights OP Entropy as a powerful and useful quantity for the characterization of neuronal discharge patterns.

Unraveling the complexity of rapid eye movement microstates: insights from nonlinear EEG analysis.

Although rapid eye movement (REM) sleep is conventionally treated as a unified state, it comprises two distinct microstates: phasic and tonic REM. Recent research emphasizes the importance of understanding the interplay between these microstates, hypothesizing their role in transient shifts between sensory detachment and external awareness. Previous studies primarily employed linear metrics to probe cognitive states, such as oscillatory power, while in this study, we adopt Lempel-Ziv Complexity (LZC), to examine the nonlinear features of electroencephalographic (EEG) data from the REM microstates and to gain complementary insights into neural dynamics during REM sleep. Our findings demonstrate a noteworthy reduction in LZC during phasic REM compared to tonic REM states, signifying diminished EEG complexity in the former. Additionally, we noted a negative correlation between decreased LZC and delta band power, along with a positive correlation with alpha band power. This study highlights the potential of nonlinear EEG metrics, particularly LZC, in elucidating the distinct features of REM microstates. Overall, this research contributes to advancing our understanding of the complex dynamics within REM sleep and opens new avenues for exploring its implications in both clinical and nonclinical contexts.

Major depressive disorder recognition by quantifying EEG signal complexity using proposed APLZC and AWPLZC

BackgroundSeeking objective quantitative indicators is important for accurately recognizing major depressive disorder (MDD). Lempel-Ziv complexity (LZC), employed to characterize neurological disorders, faces limitations in tracking dynamic changes in EEG signals due to defects in the coarse-graining process, hindering its precision for MDD objective quantitative indicators. MethodsThis work proposed Adaptive Permutation Lempel-Ziv Complexity (APLZC) and Adaptive Weighted Permutation Lempel-Ziv Complexity (AWPLZC) algorithms by refining the coarse-graining process and introducing weight factors to effectively improve the precision of LZC in characterizing EEGs and further distinguish MDD patients better. APLZC incorporated the ordinal pattern, while False Nearest Neighbor and Mutual Information algorithms were introduced to determine and adjust key parameters adaptively. Furthermore, we proposed AWPLZC by assigning different weights to each pattern based on APLZC. Thirty MDD patients and 30 healthy controls (HCs) were recruited and their 64-channel resting EEG signals were collected. The complexities of gamma oscillations were then separately computed using LZC, APLZC, and AWPLZC algorithms. Subsequently, a multi-channel adaptive K-nearest neighbor model was constructed for identifying MDD patients and HCs. ResultsLZC, APLZC, and AWPLZC algorithms achieved accuracy rates of 78.29 %, 90.32 %, and 95.13 %, respectively. Sensitivities reached 67.96 %, 85.04 %, and 98.86 %, while specificities were 88.62 %, 95.35 %, and 89.92 %, respectively. Notably, AWPLZC achieved the best performance in accuracy and sensitivity, with a specificity limitation. LimitationThe sample size is relatively small. ConclusionAPLZC and AWPLZC algorithms, particularly AWPLZC, demonstrate superior effectiveness in differentiating MDD patients from HCs compared with LZC. These findings hold significant clinical implications for MDD diagnosis.

Urban Meteorology, Pollutants, Geomorphology, Fractality, and Anomalous Diffusion

The measurements, recorded as time series (TS), of urban meteorology, including temperature (T), relative humidity (RH), wind speed (WS), and pollutants (PM10, PM2.5, and CO), in three different geographical morphologies (basin, mountain range, and coast) are analyzed through chaos theory. The parameters calculated at TS, including the Lyapunov exponent (λ > 0), the correlation dimension (DC < 5), Kolmogorov entropy (SK > 0), the Hurst exponent (0.5 < H < 1), Lempel–Ziv complexity (LZ > 0), the loss of information (<ΔI> < 0), and the fractal dimension (D), show that they are chaotic. For the different locations of data recording, CK is constructed, which is a proportion between the sum of the Kolmogorov entropies of urban meteorology and the sum of the Kolmogorov entropies of the pollutants. It is shown that, for the three morphologies studied, the numerical value of the CK quotient is compatible with the values of the exponent α of time t in the expression of anomalous diffusion applied to the diffusive behavior of atmospheric pollutants in basins, mountain ranges, and coasts. Through the Fréchet heavy tail study, it is possible to define, in each morphology, whether urban meteorology or pollutants exert the greatest influence on the diffusion processes.