An efficient scheme for nonlinear shock wave model in a fractal domain under Caputo fractional operator.

This paper introduces a refined approach for obtaining the analytical solution of the nonlinear shock wave model incorporating fractal derivatives. The Fractal Yang Variational Iteration Strategy (FYVIS) is utilized to obtain the approximate solution of a fractal model in the form of a series under Caputo fractional operator. The suggested method is the composition of the fractal Yang transform and the variational iteration approach. By using the two-scale fractal theory, we transform the fractal model into its traditional problem and then apply the yang transform to generate a recurrence relation. The variational iteration approach is now suitable to handle this recurrence relation without imposing any hypotheses or restrictions on variables. The derived results by the proposed scheme are shown in terms of series solution. Numerical calculations verify the accuracy and consistency of the suggested approach, demonstrating its excellent performance. The dynamic behavior of fractal components is explored by evaluating absolute errors and presenting two-dimensional diagrams across the fractal domain. This investigation underscores that the suggested technique offers an efficient and user-friendly solution for solving the nonlinear shock wave model involving fractal derivatives.

Applicability of Oculomics for Individual Risk Prediction: Repeatability and Robustness of Retinal Fractal Dimension Using DART and AutoMorph.

Purpose: To investigate whether fractal dimension (FD)-based oculomics could be used for individual risk prediction by evaluating repeatability and robustness. Methods: We used two datasets: "Caledonia," healthy adults imaged multiple times in quick succession for research (26 subjects, 39 eyes, 377 color fundus images), and GRAPE, glaucoma patients with baseline and follow-up visits (106 subjects, 196 eyes, 392 images). Mean follow-up time was 18.3 months in GRAPE; thus it provides a pessimistic lower bound because vasculature could change. FD was computed with DART and AutoMorph. Image quality was assessed with QuickQual, but no images were initially excluded. Pearson, Spearman, and intraclass correlation (ICC) were used for population-level repeatability. For individual-level repeatability, we introduce measurement noise parameter λ, which is within-eye standard deviation (SD) of FD measurements in units of between-eyes SD. Results: In Caledonia, ICC was 0.8153 for DART and 0.5779 for AutoMorph, Pearson/Spearman correlation (first and last image) 0.7857/0.7824 for DART, and 0.3933/0.6253 for AutoMorph. In GRAPE, Pearson/Spearman correlation (first and next visit) was 0.7479/0.7474 for DART, and 0.7109/0.7208 for AutoMorph (all P < 0.0001). Median λ in Caledonia without exclusions was 3.55% for DART and 12.65% for AutoMorph and improved to up to 1.67% and 6.64% with quality-based exclusions, respectively. Quality exclusions primarily mitigated large outliers. Worst quality in an eye correlated strongly with λ (Pearson 0.5350-0.7550, depending on dataset and method, all P < 0.0001). Conclusions: Repeatability was sufficient for individual-level predictions in heterogeneous populations. DART performed better on all metrics and might be able to detect small, longitudinal changes, highlighting the potential of robust methods.

Fractal fractional model for tuberculosis: existence and numerical solutions.

This paper deals with the mathematical analysis of Tuberculosis by using fractal fractional operator. Mycobacterium TB is the bacteria that causes tuberculosis. This airborne illness mostly impacts the lungs but may extend to other body organs. When the infected individual coughs, sneezes or speaks, the bacterium gets released into the air and travels from one person to another. Five classes have been formulated to study the dynamics of this disease: susceptible class, infected of DS, infected of MDR, isolated class, and recovered class. To study the suggested fractal fractional model's wellposedness associated with existence results, and boundedness of solutions. Further, the invariant region of the considered model, positive solutions, equilibrium point, and reproduction number. One would typically employ a fractional calculus approach to obtain numerical solutions for the fractional order Tuberculosis model using the Adams-Bashforth-Moulton method. The fractional order derivatives in the model can be approximated using appropriate numerical schemes designed for fractional order differential equations.

Derivation of correlation dimension from spatial autocorrelation functions.

BACKGROUND: Spatial complexity is always associated with spatial autocorrelation. Spatial autocorrelation coefficients including Moran's index proved to be an eigenvalue of the spatial correlation matrixes. An eigenvalue represents a kind of characteristic length for quantitative analysis. However, if a spatial correlation process is based on self-organized evolution, complex structure, and the distributions without characteristic scale, the eigenvalue will be ineffective. In this case, a scaling exponent such as fractal dimension can be used to compensate for the shortcoming of characteristic length parameters such as Moran's index. METHOD: This paper is devoted to finding an intrinsic relationship between Moran's index and fractal dimension by means of spatial correlation modeling. Using relative step function as spatial contiguity function, we can convert spatial autocorrelation coefficients into spatial autocorrelation functions. RESULT: By decomposition of spatial autocorrelation functions, we can derive the relation between spatial correlation dimension and spatial autocorrelation functions. As results, a series of useful mathematical models are constructed, including the functional relation between Moran's index and fractal parameters. Correlation dimension proved to be a scaling exponent in the spatial correlation equation based on Moran's index. As for empirical analysis, the scaling exponent of spatial autocorrelation of Chinese cities is Dc = 1.3623±0.0358, which is equal to the spatial correlation dimension of the same urban system, D2. The goodness of fit is about R2 = 0.9965. This fractal parameter value suggests weak spatial autocorrelation of Chinese cities. CONCLUSION: A conclusion can be drawn that we can utilize spatial correlation dimension to make deep spatial autocorrelation analysis, and employ spatial autocorrelation functions to make complex spatial autocorrelation analysis. This study reveals the inherent association of fractal patterns with spatial autocorrelation processes. The work may inspire new ideas for spatial modeling and exploration of complex systems such as cities.

Multifractal fluctuations in zebrafish (Danio rerio) polarization time series.

In this work, we study the polarization time series obtained from experimental observation of a group of zebrafish (Danio rerio) confined in a circular tank. The complex dynamics of the individual trajectory evolution lead to the appearance of multiple characteristic scales. Employing the Multifractal Detrended Fluctuation Analysis (MF-DFA), we found distinct behaviors according to the parameters used. The polarization time series are multifractal at low fish densities and their average scales with ρ - 1 / 4 . On the other hand, they tend to be monofractal, and their average scales with ρ - 1 / 2 for high fish densities. These two regimes overlap at critical density ρ c , suggesting the existence of a phase transition separating them. We also observed that for low densities, the polarization velocity shows a non-Gaussian behavior with heavy tails associated with long-range correlation and becomes Gaussian for high densities, presenting an uncorrelated regime.

Predict the prevalence and incidence of Parkinson's disease using fractal interpolation-LSTM model.

The investigation of the prediction of disease population is a noticeable exploration topic in the field of sciences. As a type of neurological disease, the incidence and prevalence of Parkinson's disease are still difficult to accurately study. In this paper, a method is proposed to forecast the number of incident cases (NumIn), incidence rate (InRa), the number of prevalent cases (NumPr), and prevalence rate (PrRa) of Parkinson's disease in ten countries selected. Using past data on the incidence rate, the number of prevalent cases, and the prevalence rate from 1990 to 2019, three types of fractal interpolations with different fractal dimensions are constructed for reconstructing the past data, where the vertical scaling factors are determined by the method proposed in this article. Then, the Long Short-Term Memory (LSTM) model is employed to forecast the values of NumIn, InRa, NumPr, and PrRa with Parkinson's disease in 2020. Meanwhile, the autoregressive integrated moving average model is used to predict the values compared with the LSTM model. The evaluation metrics employed for error calculation include the root mean square error and the coefficient of determination (R2). According to the proposed optimal criteria, the best predicted results are the average of three types of prediction values based on the LSTM model by analyzing and comparing eight predicted results.

Multifractal analysis of maize and soybean DNA.

This paper investigates the complexity of DNA sequences in maize and soybean using the multifractal detrended fluctuation analysis (MF-DFA) method, chaos game representation (CGR), and the complexity-entropy plane approach. The study aims to understand the patterns and structures of these DNA sequences, which can provide insights into their genetic makeup and improve crop yield and quality. The results show that maize and soybean DNA sequences exhibit fractal properties, indicating a complex and self-organizing structure. We observe the persistence trend between sequences of base pairs, which indicates long-range correlations between base pairs. We also identified the stochastic nature of the DNA sequences of both species.

Reduced Retinal Vascular Density and Skeleton Length in Amblyopia.

Purpose: This study aimed to investigate the possible relationship between retinal vascular abnormalities and amblyopia by analyzing vascular structures of fundus images. Methods: In this observational study, retinal fundus images were collected from 36 patients with unilateral amblyopia, 33 patients with bilateral amblyopia, and 36 healthy control volunteers. We developed a customized training algorithm based on U-Net to digitalize the vasculature in the fundus images to quantify vascular density (area and fractal dimension), skeleton length, and number of bifurcation points. For statistical comparisons, this study divided participants into two groups. The amblyopic eyes and the fellow eyes of patients with unilateral amblyopia formed the paired group, while bilateral amblyopic patients and healthy controls formed the independent group. Results: In the paired group, the vascular area (P = 0.007), vascular fractal dimension (P = 0.007), and vascular skeleton length (P = 0.002) of the amblyopic eyes were significantly smaller than those of the fellow eyes. In the independent group, significant decreases in the vascular fractal dimension (P = 0.006) and skeleton length (P = 0.048) were observed in bilateral amblyopia compared to control. The vascular area was also significantly correlated with best-corrected visual acuity in amblyopic eyes. Conclusions: This study demonstrated that retinal vascular density and skeleton length in amblyopic eyes were significantly smaller compared to control, indicating an association between the changes in retinal vascular features and the state of amblyopia. Translational Relevance: Our algorithm presents amblyopic retinal vascular changes that are more biologically interpretable for both clinicians and researchers.

Multi-scale fractal Fourier Ptychographic microscopy to assess the dose-dependent impact of copper pollution on living diatoms.

Accumulation of bioavailable heavy metals in aquatic environment poses a serious threat to marine communities and human health due to possible trophic transfers through the food chain of toxic, non-degradable, exogenous pollutants. Copper (Cu) is one of the most spread heavy metals in water, and can severely affect primary producers at high doses. Here we show a novel imaging test to assay the dose-dependent effects of Cu on live microalgae identifying stress conditions when they are still capable of sustaining a positive growth. The method relies on Fourier Ptychographic Microscopy (FPM), capable to image large field of view in label-free phase-contrast mode attaining submicron lateral resolution. We uniquely combine FPM with a new multi-scale analysis method based on fractal geometry. The system is able to provide ensemble measurements of thousands of diatoms in the liquid sample simultaneously, while ensuring at same time single-cell imaging and analysis for each diatom. Through new image descriptors, we demonstrate that fractal analysis is suitable for handling the complexity and informative power of such multiscale FPM modality. We successfully tested this new approach by measuring how different concentrations of Cu impact on Skeletonema pseudocostatum diatom populations isolated from the Sarno River mouth.

Retinal Fractal Dimension Is a Potential Biomarker for Systemic Health-Evidence From a Mixed-Age, Primary-Care Population.

Purpose: To investigate whether fractal dimension (FD), a retinal trait relating to vascular complexity and a potential "oculomics" biomarker for systemic disease, is applicable to a mixed-age, primary-care population. Methods: We used cross-sectional data (96 individuals; 183 eyes; ages 18-81 years) from a university-based optometry clinic in Glasgow, Scotland, to study the association between FD and systemic health. We computed FD from color fundus images using Deep Approximation of Retinal Traits (DART), an artificial intelligence-based method designed to be more robust to poor image quality. Results: Despite DART being designed to be more robust, a significant association (P < 0.001) between image quality and FD remained. Consistent with previous literature, age was associated with lower FD (P < 0.001 univariate and when adjusting for image quality). However, FD variance was higher in older patients, and some patients over 60 had FD comparable to those of patients in their 20s. Prevalent systemic conditions were significantly (P = 0.037) associated with lower FD when adjusting for image quality and age. Conclusions: Our work suggests that FD as a biomarker for systemic health extends to mixed-age, primary-care populations. FD decreases with age but might not substantially decrease in everyone. This should be further investigated using longitudinal data. Finally, image quality was associated with FD, but it is unclear whether this finding is measurement error caused by image quality or confounded by age and health. Future work should investigate this to clarify whether adjusting for image quality is appropriate. Translational Relevance: FD could potentially be used in regular screening settings, but questions around image quality remain.

Improving SSVEP-BCI Performance Through Repetitive Anodal tDCS-Based Neuromodulation: Insights From Fractal EEG and Brain Functional Connectivity.

This study embarks on a comprehensive investigation of the effectiveness of repetitive transcranial direct current stimulation (tDCS)-based neuromodulation in augmenting steady-state visual evoked potential (SSVEP) brain-computer interfaces (BCIs), alongside exploring pertinent electroencephalography (EEG) biomarkers for assessing brain states and evaluating tDCS efficacy. EEG data were garnered across three distinct task modes (eyes open, eyes closed, and SSVEP stimulation) and two neuromodulation patterns (sham-tDCS and anodal-tDCS). Brain arousal and brain functional connectivity were measured by extracting features of fractal EEG and information flow gain, respectively. Anodal-tDCS led to diminished offsets and enhanced information flow gains, indicating improvements in both brain arousal and brain information transmission capacity. Additionally, anodal-tDCS markedly enhanced SSVEP-BCIs performance as evidenced by increased amplitudes and accuracies, whereas sham-tDCS exhibited lesser efficacy. This study proffers invaluable insights into the application of neuromodulation methods for bolstering BCI performance, and concurrently authenticates two potent electrophysiological markers for multifaceted characterization of brain states.

Pore structure characterization and its influence on aqueous phase trapping damage in tight gas sandstone reservoirs.

Aqueous phase trapping (APT), which is one of the most prominent damages, seriously restricts the natural gas production in tight gas sandstone with low permeability. Pore size and microscopic pore structures are the most important factors to determine the water blocking damage. In this paper, 9 core samples from tight gas sandstone with various physical properties were employed, and the pore size distribution (PSD) of the core samples were investigated by high pressure mercury intrusion tests (HPMI). Results showed that the porosity of core samples ranges from 5.68% to 13.7%, and the permeability ranges from 0.00456 to 7.86 mD, which is a typical tight reservoir with strong heterogeneity. According to the HPMI capillary curve, the cores can be divided into two types: Type I and Type II, and the pore sizes of type I are larger than that of type II. Fractal distributions were obtained using HPMI data to further determine the pore structure characteristics of tight reservoirs. The pore structures of tight sandstones display the multifractal fractal feature: D1 corresponding to macro-pores, and D2 corresponding to fractal dimension of micro-pores. Furthermore, APT damage was determined by the permeability recovery ratios (Kr) after gas flooding tests. The correlation of Kr and PSD and fractal dimensions were jointly analyzed in tight gas sandstone. Although positive correlations between pore size parameters and the permeability recovery ratios were observed with relatively weak correlations, for those core samples with very close permeability, pore size parameters (both permeability and PSD) is inadequate in clarifying this damage. The fractal dimension can well describe the complexity and heterogeneity of flow channels in pores, which can become the determining factor to distinguish the flow capacity of tight sandstone. The D2 for samples of type I and type II exhibited a good negative relation with Kr with a correlation coefficient of 0.9878 and 0.7723, respectively. The significance of this finding is that for tight gas sandstone, fractal dimensions, especially the small pore fractal dimension (D2), can be used to predict the possible APT damage very well.

Multifractal Analysis of Choroidal SDOCT Images in the Detection of Retinitis Pigmentosa.

The aim of this paper is to investigate whether a multifractal analysis can be applied to study choroidal blood vessels and help ophthalmologists in the early diagnosis of retinitis pigmentosa (RP). In a case study, we used spectral domain optical coherence tomography (SDOCT), which is a noninvasive and highly sensitive imaging technique of the retina and choroid. The image of a choroidal branching pattern can be regarded as a multifractal. Therefore, we calculated the generalized Renyi point-centered dimensions, which are considered a measure of the inhomogeneity of data, to prove that it increases in patients with RP as compared to those in the control group.

The butterfly effect in oral and maxillofacial surgery: Understanding and applying chaos theory and complex systems principles.

The present paper provides a historical context for chaos theory, originating in the 1960s with Edward Norton Lorenz's efforts to predict weather patterns. It introduces chaos theory, fractal geometry, nonlinear dynamics, and the butterfly effect, highlighting their exploration of complex systems. The authors aim to bridge the gap between chaos theory and oral and maxillofacial surgery (OMFS) through a literature review, exploring its applications and emphasizing the prevention of minor deviations in OMFS to avoid significant consequences. A comprehensive literature review was conducted on PubMed, Web of Science, and Google Scholar databases. The selection process adhered to the PRISMA-ScR guidelines and Leiden Manifesto principles. Articles focusing on chaos theory principles in health sciences, published in the last two decades, were included. The review encompassed 37 articles after screening 386 works. It revealed applications in outcome variation, surgical planning, simulations, decision-making, and emerging technologies. Potential applications include predicting infections, malignancies, dental fractures, and improving decision-making through disease prediction systems. Emerging technologies, despite criticisms, indicate advancements in AI integration, contributing to enhanced diagnostic accuracy and personalized treatment strategies. Chaos theory, a distinct scientific framework, holds potential to revolutionize OMFS. Its integration with advanced techniques promises personalized, less traumatic surgeries and improved patient care. The interdisciplinary synergy of chaos theory and emerging technologies presents a future in which OMFS practices become more efficient, less traumatic, and achieve a level of precision never seen before.

Emergence of fractal geometries in the evolution of a metabolic enzyme.

Fractals are patterns that are self-similar across multiple length-scales1. Macroscopic fractals are common in nature2-4; however, so far, molecular assembly into fractals is restricted to synthetic systems5-12. Here we report the discovery of a natural protein, citrate synthase from the cyanobacterium Synechococcus elongatus, which self-assembles into Sierpinski triangles. Using cryo-electron microscopy, we reveal how the fractal assembles from a hexameric building block. Although different stimuli modulate the formation of fractal complexes and these complexes can regulate the enzymatic activity of citrate synthase in vitro, the fractal may not serve a physiological function in vivo. We use ancestral sequence reconstruction to retrace how the citrate synthase fractal evolved from non-fractal precursors, and the results suggest it may have emerged as a harmless evolutionary accident. Our findings expand the space of possible protein complexes and demonstrate that intricate and regulatable assemblies can evolve in a single substitution.

Physiological and chaos effect on dynamics of neurological disorder with memory effect of fractional operator: A mathematical study.

BACKGROUND AND OBJECTIVE: To study the dynamical system, it is necessary to formulate the mathematical model to understand the dynamics of various diseases that are spread worldwide. The main objective of our work is to examine neurological disorders by early detection and treatment by taking asymptomatic. The central nervous system (CNS) is impacted by the prevalent neurological condition known as multiple sclerosis (MS), which can result in lesions that spread across time and place. It is widely acknowledged that multiple sclerosis (MS) is an unpredictable disease that can cause lifelong damage to the brain, spinal cord, and optic nerves. The use of integral operators and fractional order (FO) derivatives in mathematical models has become popular in the field of epidemiology. METHOD: The model consists of segments of healthy or barian brain cells, infected brain cells, and damaged brain cells as a result of immunological or viral effectors with novel fractal fractional operator in sight Mittag Leffler function. The stability analysis, positivity, boundedness, existence, and uniqueness are treated for a proposed model with novel fractional operators. RESULTS: Model is verified the local and global with the Lyapunov function. Chaos Control will use the regulate for linear responses approach to bring the system to stabilize according to its points of equilibrium so that solutions are bounded in the feasible domain. To ensure the existence and uniqueness of the solutions to the suggested model, it makes use of Banach's fixed point and the Leray Schauder nonlinear alternative theorem. For numerical simulation and results the steps Lagrange interpolation method at different fractional order values and the outcomes are compared with those obtained using the well-known FFM method. CONCLUSION: Overall, by offering a mathematical model that can be used to replicate and examine the behavior of disease models, this research advances our understanding of the course and recurrence of disease. Such type of investigation will be useful to investigate the spread of disease as well as helpful in developing control strategies from our justified outcomes.

Gait variability, fractal dynamics, and statistical regularity of treadmill and overground walking recorded with a smartphone.

BACKGROUND: The nonlinear variability present during steady-state gait may provide a signature of health and showcase one's walking adaptability. Although treadmills can capture vast amounts of walking data required for estimating variability within a small space, gait patterns may be misrepresented compared to an overground setting. Smartphones may provide a low-cost and user-friendly estimate of gait patterns among a variety of walking settings. However, no study has investigated differences in gait patterns derived from a smartphone between treadmill walking (TW) and overground walking (OW). RESEARCH QUESTION: This study implemented a smartphone accelerometer to compare differences in temporal gait variability and gait dynamics between TW and OW. METHODS: Sixteen healthy adults (8F; 24.7 ± 3.8 years) visited the laboratory on three separate days and completed three 8-minute OW and three TW trials, at their preferred speed, during each visit. The inter-stride interval was calculated as the time difference between right heel contact events located within the vertical accelerometery signals recorded from a smartphone while placed in participants front right pant pocket during walking trials. The inter-stride interval series was used to calculate stride time standard deviation (SD) and coefficient of variation (COV), statistical persistence (fractal scaling index), and statistical regularity (sample entropy). Two-way analysis of variance compared walking condition and laboratory visits for each measure. RESULTS: Compared to TW, OW displayed significantly (p < 0.01) greater stride time SD (0.014 s, 0.020 s), COV (1.26 %, 1.82 %), fractal scaling index (0.70, 0.79) and sample entropy (1.43, 1.63). No differences were found between visits for all measures. SIGNIFICANCE: Smartphone-based assessment of gait provides the ability to distinguish between OW and TW conditions, similar to previously established methodologies. Furthermore, smartphones may be a low-cost and user-friendly tool to estimate gait patterns outside the laboratory to improve ecological validity, with implications for free-living monitoring of gait among various populations.

Main role of fractal-like nature of conformational space in subdiffusion in proteins.

Protein dynamics involves a myriad of mechanical movements happening at different time and space scales, which make it highly complex. One of the less understood features of protein dynamics is subdiffusivity, defined as sublinear dependence between displacement and time. Here, we use all-atoms molecular dynamics (MD) simulations to directly interrogate an already well-established theory and demonstrate that subdiffusivity arises from the fractal nature of the network of metastable conformations over which the dynamics, thought of as a diffusion process, takes place.

Evaluation of the Correlation Between the Structural Parameters of Trabecular Bone in CBCT and the Primary Stability of Dental Implants.

PURPOSE: To investigate the relationship between the structural parameters of trabecular bone obtained from CBCT imaging and the primary stability of dental implants. MATERIALS AND METHODS: Sixty patients underwent implant placement followed by primary stability evaluation via measurement of the insertion torque (IT) and the implant stability quotient (ISQ). Gray values (GV) and the fractal dimension (FD) were also measured using pretreatment CBCT images. RESULTS: FD values showed a positive and significant relationship with ISQ and IT values (P = .017 and P = .004, respectively). Additionally, there was a positive and significant correlation between GV and IT (P = .004) as well as between GV and ISQ (P = .010). FD and GV showed a considerable difference between the maxillary and mandibular jaws and were higher in the mandible. Only FD was significantly different between men and women and was higher in men. In the two age groups (older and younger than 45 years), only GV was considerably higher in people older than 45 (P < .05). CONCLUSIONS: Both fractal dimension and gray values obtained from CBCT are efficient methods for predicting the primary stability of the implant due to their relationship with ISQ and IT values.

Investigating the interpretability of schizophrenia EEG mechanism through a 3DCNN-based hidden layer features aggregation framework.

BACKGROUND AND OBJECTIVE: Electroencephalogram (EEG) signals record brain activity, with growing interest in quantifying neural activity through complexity analysis as a potential biological marker for schizophrenia. Presently, EEG complexity analysis primarily relies on manual feature extraction, which is subjective and yields varied findings in studies involving schizophrenia and healthy controls. METHODS: This study aims to leverage deep learning methods for enhanced EEG complexity exploration, aiding early schizophrenia screening and diagnosis. Our proposed approach utilizes a three-dimensional Convolutional Neural Network (3DCNN) to extract enhanced data features for early schizophrenia identification and subsequent complexity analysis. Leveraging the spatiotemporal capabilities of 3DCNN, we extract advanced latent features and employ knowledge distillation to reintegrate these features into the original channels, creating feature-enhanced data. RESULTS: We employ a 10-fold cross-validation strategy, achieving the average accuracies of 99.46% and 98.06% in subject-dependent experiments on Dataset 1(14SZ and 14HC) and Dataset 2 (45SZ and 39HC). The average accuracy for subject-independent is 96.04% and 92.67% on both datasets. Feature extraction and classification are conducted on both the re-aggregated data and the original data. Our results demonstrate that re-aggregated data exhibit superior classification performance and a more stable training process after feature extraction. In the complexity analysis of re-aggregated data, we observe lower entropy features in schizophrenic patients compared to healthy controls, with more pronounced differences in the temporal and frontal lobes. Analyzing Katz's Fractal Dimension (KFD) across three sub-bands of lobe channels reveals the lowest α band KFD value in schizophrenia patients. CONCLUSIONS: This emphasizes the ability of our method to enhance the discrimination and interpretability in schizophrenia detection and analysis. Our approach enhances the potential for EEG-based schizophrenia diagnosis by leveraging deep learning, offering superior discrimination capabilities and richer interpretive insights.