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.

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 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.

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.

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.

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.

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.

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.

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.

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.

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.

Delineating cognitive resilience using fractal regulation: Cross-sectional and longitudinal evidence from the Rush Memory and Aging Project.

INTRODUCTION: Degradation of fractal patterns in actigraphy independently predicts dementia risk. Such observations motivated the study to understand the role of fractal regulation in the context of neuropathologies. METHODS: We examined associations of fractal regulation with neuropathologies and longitudinal cognitive changes in 533 older participants who were followed annually with actigraphy and cognitive assessments until death with brain autopsy performed. Two measures for fractal patterns were extracted from actigraphy, namely, α1 (representing the fractal regulation at time scales of <90 min) and α2 (for time scales 2 to 10 h). RESULTS: We found that larger α1 was associated with lower burdens of Lewy body disease or cerebrovascular disease pathologies; both α1 and α2 were associated with cognitive decline. They explained an additional significant portion of the variance in the rate of cognitive decline above and beyond neuropathologies. DISCUSSION: Fractal patterns may be used as a biomarker for cognitive resilience against dementia-related neuropathologies.

Fractal Analysis in Clinical Neurosciences: An Overview.

Over the last years, fractals have entered into the realms of clinical neurosciences. The whole brain and its components (i.e., neurons and astrocytes) have been studied as fractal objects, and even more relevant, the fractal-based quantification of the geometrical complexity of histopathological and neuroradiological images as well as neurophysiopathological time series has suggested the existence of a gradient in the pattern representation of neurological diseases. Computational fractal-based parameters have been suggested as potential diagnostic and prognostic biomarkers in different brain diseases, including brain tumors, neurodegeneration, epilepsy, demyelinating diseases, cerebrovascular malformations, and psychiatric disorders as well. This chapter and the entire third section of this book are focused on practical applications of computational fractal-based analysis into the clinical neurosciences, namely, neurology and neuropsychiatry, neuroradiology and neurosurgery, neuropathology, neuro-oncology and neurorehabilitation, neuro-ophthalmology, and cognitive neurosciences, with special emphasis on the translation of the fractal dimension and other fractal parameters as clinical biomarkers useful from bench to bedside.

Fractal Dimension Analysis in Neurological Disorders: An Overview.

Fractal analysis has emerged as a powerful tool for characterizing irregular and complex patterns found in the nervous system. This characterization is typically applied by estimating the fractal dimension (FD), a scalar index that describes the topological complexity of the irregular components of the nervous system, both at the macroscopic and microscopic levels, that may be viewed as geometric fractals. Moreover, temporal properties of neurophysiological signals can also be interpreted as dynamic fractals. Given its sensitivity for detecting changes in brain morphology, FD has been explored as a clinically relevant marker of brain damage in several neuropsychiatric conditions as well as in normal and pathological cerebral aging. In this sense, evidence is accumulating for decreases in FD in Alzheimer's disease, frontotemporal dementia, Parkinson's disease, multiple sclerosis, and many other neurological disorders. In addition, it is becoming increasingly clear that fractal analysis in the field of clinical neurology opens the possibility of detecting structural alterations in the early stages of the disease, which highlights FD as a potential diagnostic and prognostic tool in clinical practice.

Point of Care Testing (POCT) in Psychopathology Using Fractal Analysis and Hilbert Huang Transform of Electroencephalogram (EEG).

Research has shown that relying only on self-reports for diagnosing psychiatric disorders does not yield accurate results at all times. The advances of technology as well as artificial intelligence and other machine learning algorithms have allowed the introduction of point of care testing (POCT) including EEG characterization and correlations with possible psychopathology. Nonlinear methods of EEG analysis have significant advantages over linear methods. Empirical mode decomposition (EMD) is a reliable nonlinear method of EEG pre-processing. In this chapter, we compare two existing EEG complexity measures - Higuchi fractal dimension (HFD) and sample entropy (SE), with our newly proposed method using Higuchi fractal dimension from the Hilbert Huang transform (HFD-HHT). We present an example using the three complexity measures on a 2-minute EEG recorded from a healthy 20-year-old male after signal pre-processing. Furthermore, we showed the usefulness of these complexity measures in the classification of major depressive disorder (MDD) with healthy controls. Our study is in line with previous research and has shown an increase in HFD and SE values in the full, alpha and beta frequency bands suggestive of an increase in EEG irregularity. Moreover, the HFD-HHT values decreased in those three bands for majority of electrodes which is suggestive of a decrease in irregularity in the frequency-time domain. We conclude that all three complexity measures can be vital features useful for EEG analysis which could be incorporated in POCT systems.

Fractals in Neuroanatomy and Basic Neurosciences: An Overview.

The introduction of fractal geometry to the neurosciences has been a major paradigm shift over the last decades as it has helped overcome approximations and limitations that occur when Euclidean and reductionist approaches are used to analyze neurons or the entire brain. Fractal geometry allows for quantitative analysis and description of the geometric complexity of the brain, from its single units to the neuronal networks.As illustrated in the second section of this book, fractal analysis provides a quantitative tool for the study of the morphology of brain cells (i.e., neurons and microglia) and its components (e.g., dendritic trees, synapses), as well as the brain structure itself (cortex, functional modules, neuronal networks). The self-similar logic which generates and shapes the different hierarchical systems of the brain and even some structures related to its "container," that is, the cranial sutures on the skull, is widely discussed in the following chapters, with a link between the applications of fractal analysis to the neuroanatomy and basic neurosciences to the clinical applications discussed in the third section.

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.

Analysis of the quality of tunnel roof topography by automatic cutting control under the coupling of multiple factors.

The automatic cutting of coal and rock surface morphology modeling based on the actual geological environment of coal mine underground excavation and mining is of great significance for improving the surface quality of coal and rock after cutting and enhancing the safety and stability of advanced support. To this end, using the principle of coordinate transformation, the kinematic trajectory of the cutting head of the tunneling machine is established, and the contour morphology of the cutting head under variable cutting technology is obtained. Then, based on the regenerative vibration theory of the cutting head, a dynamic model of the cutting head coal wall is established, and the coordinate relationship of the cutting head in the tunnel coordinate system under vibration induction is analyzed. Based on fractal theory and Z-MAP method, a simulation method for the surface morphology of coal and rock after cutting is proposed, which is driven by the cutting trajectory Under the coupling effect of cutting vibration induction and random fragmentation of coal and rock, simulation of the surface morphology of comprehensive excavation tunnels was conducted, and relevant experiments were conducted to verify the results. A 1:3 similarity experimental model of EBZ160 tunneling machine was used to build a cutting head coal and rock system cutting experimental platform for comparative experiments of cutting morphology. Furthermore, statistical methods were used to compare and evaluate the simulated roof with the actual roof. The results show that the relative errors between the maximum range of peaks and valleys, the peak skewness coefficient of height standard deviation, and the kurtosis coefficient of the actual roof are 1.3%, 24.5%, 16%, and 2.9%, respectively. Overall, this indicates that the surface morphology distribution characteristics of the simulated roof and the actual roof are similar, verifying the effectiveness of the modeling and simulation method proposed in this paper, and providing theoretical support for the design and optimization of advanced support in the future.

Fundamentals of sleep regulation: Model and benchmark values for fractal and oscillatory neurodynamics.

Homeostatic, circadian and ultradian mechanisms play crucial roles in the regulation of sleep. Evidence suggests that ratios of low-to-high frequency power in the electroencephalogram (EEG) spectrum indicate the instantaneous level of sleep pressure, influenced by factors such as individual sleep-wake history, current sleep stage, age-related differences and brain topography characteristics. These effects are well captured and reflected in the spectral exponent, a composite measure of the constant low-to-high frequency ratio in the periodogram, which is scale-free and exhibits lower interindividual variability compared to slow wave activity, potentially serving as a suitable standardization and reference measure. Here we propose an index of sleep homeostasis based on the spectral exponent, reflecting the level of membrane hyperpolarization and/or network bistability in the central nervous system in humans. In addition, we advance the idea that the U-shaped overnight deceleration of oscillatory slow and fast sleep spindle frequencies marks the biological night, providing somnologists with an EEG-index of circadian sleep regulation. Evidence supporting this assertion comes from studies based on sleep replacement, forced desynchrony protocols and high-resolution analyses of sleep spindles. Finally, ultradian sleep regulatory mechanisms are indicated by the recurrent, abrupt shifts in dominant oscillatory frequencies, with spindle ranges signifying non-rapid eye movement and non-spindle oscillations - rapid eye movement phases of the sleep cycles. Reconsidering the indicators of fundamental sleep regulatory processes in the framework of the new Fractal and Oscillatory Adjustment Model (FOAM) offers an appealing opportunity to bridge the gap between the two-process model of sleep regulation and clinical somnology.