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The interaction-dominant approach to perception and action, originally formulated in the mid-1990s, has matured and gained remarkable momentum as an entailment of the dynamical hypotheses proposed at that time. This framework seeks to explain the fluid and intricate interplay of causality spanning the entire organism by integrating high-dimensional details with low-dimensional constraints across various scales of behavior. Both Chemero (2024) and Wallot et al. (2024) have skillfully explored the theoretical implications and methodological challenges this perspective introduces. We echo Chemero's (2024) and Wallot et al.'s (2024) focus on multifractality, while also underscoring new efforts to model the synergetic relationships and cascading dynamics inherent in this interaction-dominant approach., (© 2024 Cognitive Science Society LLC.)

Lung cancer is the leading cause of cancer-related death. The use of computational methods to quantify changes that are not perceptible to the human eye is increasing in digital pathology imaging and has quickly improved detection rates at a low cost. Therefore, the present study aims to use complex computational shape markers as tools for automated analysis of the spatial distribution of cells in microscopy images of squamous cell lung carcinoma (SqCC). Photomicrographs from pathology glass slides in the LC25000 dataset were used in this study. Compared with those of the control, the fractal dimension (28%) and lacunarity (41%) of the cell nuclei changed in SqCC. The multifractal analysis revealed a significant difference in parameters Dq, α, and f(α) for all values of q (-10 to + 10), with a greater increase for more positive q values. The values at q + 10 increased by 34% for Dq, 36% for α, and 53% for f(α) in the SqCC images. The circularity, area, and perimeter also changed in the SqCC images. However, the parameters of aspect ratio, roundness, and solidity did not significantly differ between SqCC and benign tissue. The complex shape markers with the greatest changes in this study were the f(α) values for multifractality (53%) and lacunarity (41%). In conclusion, automated quantification of the spatial distribution of cell nuclei can be a fast, low-cost tool for evaluating the microscopic characteristics of SqCC; therefore, complex shape markers could be useful tools for software and artificial intelligence to detect lung carcinoma., (© 2024. The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.)

Fingering front morphologies for water and non-aqueous phase liquids (NAPLs) infiltrating into homogeneous unsaturated porous media were quantitatively described based on the fractal assumption. Correlations of fractal dimensions with physical properties of the fluids were studied. The implications of fractal dimensions for environmental systems are further discussed. Fingering front morphologies had fractal properties, and diesels which with high capillary numbers experienced high fractal dimensions than water. Fractal dimension was suggested as an indicator for dye coverage and infiltration depth, which represent pollution area and depth, respectively. The pollution areas showed positive correlations with fractal dimensions while the infiltration depths showed negative correlations. This information is useful for contaminated soil risk management and important in the effective design of recovery and remediation schemes., Competing Interests: Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2023. Published by Elsevier B.V.)

Neuro-electrophysiological recordings contain prominent aperiodic activity - meaning irregular activity, with no characteristic frequency - which has variously been referred to as 1/f (or 1/f-like activity), fractal, or 'scale-free' activity. Previous work has established that aperiodic features of neural activity is dynamic and variable, relating (between subjects) to healthy aging and to clinical diagnoses, and also (within subjects) tracking conscious states and behavioral performance. There are, however, a wide variety of conceptual frameworks and associated methods for the analyses and interpretation of aperiodic activity - for example, time domain measures such as the autocorrelation, fractal measures, and/or various complexity and entropy measures, as well as measures of the aperiodic exponent in the frequency domain. There is a lack of clear understanding of how these different measures relate to each other and to what extent they reflect the same or different properties of the data, which makes it difficult to synthesize results across approaches and complicates our overall understanding of the properties, biological significance, and demographic, clinical, and behavioral correlates of aperiodic neural activity. To address this problem, in this project we systematically survey the different approaches for measuring aperiodic neural activity, starting with an automated literature analysis to curate a collection of the most common methods. We then evaluate and compare these methods, using statistically representative time series simulations. In doing so, we establish consistent relationships between the measures, showing that much of what they capture reflects shared variance - though with some notable idiosyncrasies. Broadly, frequency domain methods are more specific to aperiodic features of the data, whereas time domain measures are more impacted by oscillatory activity. We extend this analysis by applying the measures to a series of empirical EEG and iEEG datasets, replicating the simulation results. We conclude by summarizing the relationships between the multiple methods, emphasizing opportunities for reexamining previous findings and for future work., Competing Interests: Conflicts of Interest The authors declare no competing interests.

Interparticle pore space and vugs are two different scales of pore space in vuggy porous media. Vuggy porous media widely exists in carbonate reservoirs, and the permeability of this porous media plays an important role in many engineering fields. It has been shown that the change of effective stress has important effects on the permeability of vuggy porous media. In this work, a fractal permeability model for vuggy porous media is developed based on the fractal theory and elastic mechanics. Besides, a Monte Carlo simulation is also implemented to obtain feasible values of permeability. The proposed model can predict the elastic deformation of the fractal vuggy porous media under loading stress, which plays a crucial role in the variations of permeability. The predicted permeability data based on the present fractal model are compared with experimental data, which verifies the validity of the present fractal permeability model for vuggy porous media. The parameter sensitivity analysis indicates that the permeability of stress-sensitivity vuggy porous media is related to the capillary fractal dimension, capillary fractal tortuosity dimension, Young's modulus, and Poisson's ratio., (© 2024. The Author(s).)

Smartphones, with embedded accelerometers, may be a viable method to monitor gait variability in the free-living environment. However, measurements estimated using smartphones must first be compared to known quantities to ensure validity. This study assessed the validity and reliability of smartphone-derived gait measures compared to a gold-standard footswitch system during overground walking. Seventeen adults completed three 8-minute overground walking trials during 3 separate visits. The stride time series was calculated as the time difference between consecutive right heel contact events within the footswitch and smartphone-accelerometry signals. Linear (average stride time, stride time standard deviation, and stride time coefficient of variation) and nonlinear (fractal scaling index, approximate entropy, and sample entropy) measures were calculated for each stride time series. Bland-Altman plots with 95% limits of agreement assessed agreement between systems. Intraclass correlation coefficients assessed reliability across visits. Bland-Altman plots revealed acceptable limits of agreement for all measures. Intraclass correlation coefficients revealed good-to-excellent reliability for both systems, except for fractal scaling index, which was moderate. The smartphone system is a valid method and performs similarly to gold-standard research equipment. These findings suggest the development and implementation of an inexpensive, easy-to-use, and ubiquitous telehealth instrument that may replace traditional laboratory equipment for use in the free-living environment.

Introduction: Electrical stimulation of the brain has shown promising prospects in treating various brain diseases. Although biphasic pulse stimulation remains the predominant clinical approach, there has been increasing interest in exploring alternative stimulation waveforms, such as sinusoidal stimulation, to improve the effectiveness of brain stimulation and to expand its application to a wider range of brain disorders. Despite this growing attention, the effects of sinusoidal stimulation on neurons, especially on their nonlinear firing characteristics, remains unclear., Methods: To address the question, 50 Hz sinusoidal stimulation was applied on Schaffer collaterals of the rat hippocampal CA1 region in vivo . Single unit activity of both pyramidal cells and interneurons in the downstream CA1 region was recorded and analyzed. Two fractal indexes, namely the Fano factor and Hurst exponent, were used to evaluate changes in the long-range correlations, a manifestation of nonlinear dynamics, in spike sequences of neuronal firing., Results: The results demonstrate that sinusoidal electrical stimulation increased the firing rates of both pyramidal cells and interneurons, as well as altered their firing to stimulation-related patterns. Importantly, the sinusoidal stimulation increased, rather than decreased the scaling exponents of both Fano factor and Hurst exponent, indicating an increase in the long-range correlations of both pyramidal cells and interneurons., Discussion: The results firstly reported that periodic sinusoidal stimulation without long-range correlations can increase the long-range correlations of neurons in the downstream post-synaptic area. These results provide new nonlinear mechanisms of brain sinusoidal stimulation and facilitate the development of new stimulation modes., Competing Interests: The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest. The reviewer LZ declared a past collaboration with the authors YY, XY, and ZW to the handling editor., (Copyright © 2024 Yuan, Ye, Cui, Zhang and Wang.)

Objectives: The present study aimed to investigate the incremental prognostic value of the right ventricular fractal dimension (FD), a novel marker of myocardial trabecular complexity by cardiac magnetic resonance (CMR) in patients with arrhythmogenic cardiomyopathy (ACM)., Methods: Consecutive patients with ACM undergoing CMR were followed up for major cardiac events, including sudden cardiac death, aborted cardiac arrest, and appropriate implantable cardioverter defibrillator intervention. Prognosis prediction was compared by Cox regression analysis. We established a multivariable model supplemented with RV FD and evaluated its discrimination by Harrell's C-statistic. We compared the category-free, continuous net reclassification improvement (cNRI) and integrated discrimination index (IDI) before and after the addition of FD., Results: A total of 105 patients were prospectively included from three centers and followed up for a median of 60 (48, 66) months; experienced 36 major cardiac events were recorded. Trabecular FD displayed a strong unadjusted association with major cardiac events (p < 0.05). In the multivariable Cox regression analysis, RV maximal apical FD maintained an independent association with major cardiac events (hazard ratio, 1.31 (1.11-1.55), p < 0.002). The Hosmer-Lemeshow goodness of fit test displayed good fit (X 2  = 0.68, p = 0.99). Diagnostic performance was significantly improved after the addition of RV maximal apical FD to the multivariable baseline model, and the continuous net reclassification improvement increased 21% (p = 0.001), and the integrated discrimination index improved 16% (p = 0.045)., Conclusions: In patients with ACM, CMR-assessed myocardial trabecular complexity was independently correlated with adverse cardiovascular events and provided incremental prognostic value., Clinical Relevance Statement: The application of FD values for assessing RV myocardial trabeculae may become an accessible and promising parameter in monitoring and early diagnosis of risk factors for adverse cardiovascular events in patients with ACM., Key Points: • Ventricular trabecular morphology, a novel quantitative marker by CMR, has been explored for the first time to determine the severity of ACM. • Patients with higher maximal apical fractal dimension of RV displayed significantly higher cumulative incidence of major cardiac events. • RV maximal apical FD was independently associated with major cardiac events and provided incremental prognostic value in patients with ACM., (© 2024. The Author(s), under exclusive licence to European Society of Radiology.)

Underground coal seam mining significantly alters the stress and energy distribution within the overlying rock, leading to eventual structural degradation. Therefore, it is imperative to quantitatively identify the temporal and spatial characteristics of stress evolution of overlying rock caused by mining. This paper introduces a novel rock stress model integrating entropy and a spatial-temporal cube. Similar material model tests are used to identify the abrupt entropy changes within the mining rock, and the trend analysis is carried out to describe the spatial-temporal evolution law of stress during mining. Experimental findings indicate elevated stress levels in the unmined rock preceding and following the panel, as well as within specific rock strata above it. Definitively, dynamic stress arches within the surrounding rock of the stope predominantly bear and distribute the load and pressure from the overlying rock, and each stress mutation is accompanied by a sudden stress entropy change. Over time, z-score shows that the noticeable reduction in mining-induced overburden stress becomes increasingly pronounced, especially in the water-conducting fracture zone. The model's bifurcation set serves as the comprehensive criterion for the entropy-induced sudden changes in the rock system, signifying overall failure., (© 2024. The Author(s).)

Background: The aim of the study was to investigate the changes occurring in the mandibular condyle by using mentoplate together with rapid maxillary expansion (MP-RME) treatment in the correction of skeletal class III relationship, using fractal analysis (FA)., Methods: The sample consisted of 30 individuals (8-11 years) diagnosed with skeletal Class III malocclusion who underwent MP-RME treatment. Archival records provided cone-beam computed tomography (CBCT) images taken at two intervals: before MP-RME treatment (T0) and after treatment (T1). The CBCT images were obtained using standardized settings to ensure consistency in image quality and resolution. The trabecular structures in the bilateral condyles at both T0 and T1 were analyzed using FA. The FA was performed on these condylar images using the Image J software. The region of interest (ROI) was carefully selected in the condyle to avoid overlapping with cortical bone, and the box-counting method was employed to calculate the fractal dimension (FD). Statistical analysis was conducted to compare the FD values between T0 and T1 and to evaluate gender differences. The statistical significance was determined using paired t-tests for intra-group comparisons and independent t-tests for inter-group comparisons, with a significance level set at p < 0.05., Results: The analysis revealed no statistically significant differences in the trabecular structures of the condyles between T0 and T1 (p > 0.05). However, a significant gender difference was observed in FA values, with males exhibiting higher FA values in the left condyle compared to females at both T0 and T1 (p < 0.05). Specifically, the FA values in the left condyle increased from a mean of 1.09 ± 0.09 at T0 to 1.13 ± 0.08 at T1 in males, whereas in females, the FA values remained relatively stable with a mean of 1 ± 0.09 at T0 and 1.03 ± 0.11 at T1., Conclusion: The findings indicate that MP-RME therapy does not induce significant alterations in the trabecular structure of the mandibular condyle. These results suggest the treatment's safety concerning the structural integrity of the condyle, although the observed gender differences in FA values warrant further investigation., (© 2024. The Author(s).)

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., Competing Interests: Declaration of Competing Interest None, (Copyright © 2024 Elsevier B.V. All rights reserved.)

Dexterous postural control subtly complements movement variability with sensory correlations at many scales. The expressive poise of gymnasts exemplifies this lyrical punctuation of release with constraint, from coarse grain to fine scales. Dexterous postural control upon a 2D support surface might collapse the variation of center of pressure (CoP) to a relatively 1D orientation-a direction often oriented towards the focal point of a visual task. Sensory corrections in dexterous postural control might manifest in temporal correlations, specifically as fractional Brownian motions whose differences are more and less correlated with fractional Gaussian noises ( fGn s) with progressively larger and smaller Hurst exponent H . Traditional empirical work examines this arrangement of lower-dimensional compression of CoP along two orthogonal axes, anteroposterior (AP) and mediolateral (ML). Eyes-open and face-forward orientations cultivate greater variability along AP than ML axes, and the orthogonal distribution of spatial variability has so far gone hand in hand with an orthogonal distribution of H , for example, larger in AP and lower in ML. However, perturbing the orientation of task focus might destabilize the postural synergy away from its 1D distribution and homogenize the temporal correlations across the 2D support surface, resulting in narrower angles between the directions of the largest and smallest H . We used oriented fractal scaling component analysis (OFSCA) to investigate whether sensory corrections in postural control might thus become suborthogonal. OFSCA models raw 2D CoP trajectory by decomposing it in all directions along the 2D support surface and fits the directions with the largest and smallest H . We studied a sample of gymnasts in eyes-open and face-forward quiet posture, and results from OFSCA confirm that such posture exhibits the classic orthogonal distribution of temporal correlations. Head-turning resulted in a simultaneous decrease in this angle Δ θ , which promptly reversed once gymnasts reoriented their heads forward. However, when vision was absent, there was only a discernible negative trend in Δ θ , indicating a shift in the angle's direction but not a statistically significant one. Thus, the narrowing of Δ θ may signify an adaptive strategy in postural control. The swift recovery of Δ θ upon returning to a forward-facing posture suggests that the temporary reduction is specific to head-turning and does not impose a lasting burden on postural control. Turning the head reduced the angle between these two orientations, facilitating the release of postural degrees of freedom towards a more uniform spread of the CoP across both dimensions of the support surface. The innovative aspect of this work is that it shows how fractality might serve as a control parameter of adaptive mechanisms of dexterous postural control., Competing Interests: The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest., (Copyright © 2024 Mangalam, Seleznov, Kolosova, Popov, Kelty-Stephen and Kiyono.)

Individuals with Parkinson's disease exhibit tremors, rigidity, and bradykinesia, disrupting normal movement variability and resulting in postural instability. This comprehensive study aimed to investigate the link between the temporal structure of postural sway variability and Parkinsonism by analyzing multiple datasets from young and older adults, including individuals with Parkinson's disease, across various task conditions. We used the Oriented Fractal Scaling Component Analysis (OFSCA), which identifies minimal and maximal long-range correlations within the center of pressure time series, allowing for detecting directional changes in postural sway variability. The objective was to uncover the primary directions along which individuals exerted control during the posture. The results, as anticipated, revealed that healthy adults predominantly exerted control along two orthogonal directions, closely aligned with the anteroposterior (AP) and mediolateral (ML) axes. In stark contrast, older adults and individuals with Parkinson's disease exhibited control along suborthogonal directions that notably diverged from the AP and ML axes. While older adults and those with Parkinson's disease demonstrated a similar reduction in the angle between these two control directions compared to healthy older adults, their reliance on this suborthogonal angle concerning endogenous fractal correlations exhibited significant differences from the healthy aging cohort. Importantly, individuals with Parkinson's disease did not manifest the sensitivity to destabilizing task settings observed in their healthy counterparts, affirming the distinction between Parkinson's disease and healthy aging., Competing Interests: The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (© 2024 The Author(s).)

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

Mixed matrix materials (MMMs) containing metal-organic framework (MOF) nanoparticles are attractive for membrane carbon capture. Particularly, adding <5 mass % MOFs in polymers dramatically increased gas permeability, far surpassing the Maxwell model's prediction. However, no sound mechanisms have been offered to explain this unusual low-loading phenomenon. Herein, we design an ideal series of MMMs containing polyethers (one of the leading polymers for CO 2 /N 2 separation) and discrete metal-organic polyhedra (MOPs) with cage sizes of 2-5 nm. Adding 3 mass % MOP-3 in a polyether increases the CO 2 permeability by 100% from 510 to 1000 Barrer at 35 °C because of the increased gas diffusivity. No discernible changes in typical physical properties governing gas transport properties are detected, such as glass transition temperature, fractional free volume, d -spacing, etc. We hypothesize that this behavior is attributed to fractal-like networks formed by highly porous MOPs, and for the first time, we validate this hypothesis using small-angle X-ray scattering analysis.

Introduction The cysts of the maxillofacial region account for one of the most common pathologies of the head and neck region after the mucosal pathologies. Radiography provides an essential clue in early diagnosis and triaging, but it continues further as it is used to evaluate the post-treatment outcome. However, manual analysis is prone to errors. In this scenario, fractal analysis (FA) in radiographs uses mathematical methods to analyse the changes in grey scales in a given radiographic image. FA in odontogenic cysts is used to characterise their complexity, uncover hidden patterns, monitor treatment response, and potentially provide prognostic information. This paper aimed to assess the fractal characteristics of the radicular cyst (RC), dentigerous cyst (DC), and odontogenic keratocyst (OKC) using cone beam computed tomography (CBCT). The objective was to calculate fractal dimension (FD) values expressed in each of these cysts, which could prove to be a radiological adjunct in diagnosing the above cysts. Materials and methods As this is a retrospective study, the archives of CBCT images from June 2021 to December 2023 were obtained from patients diagnosed and confirmed with a histopathological diagnosis with RC, DC, and OKC. The FA was performed using Image J Software (Ver 1.51, National Institute of Health Bethesda, Fiji). The cortical and cancellous bones were segmented using thresholding techniques and converted to binary images. The mean FD of the three planes was then compared to establish the distinctive fractal characteristic for the specific odontogenic cysts. A one-way ANOVA was performed using the Statistical Product and Service Solutions (SPSS) (version 23.0; IBM SPSS Statistics for Windows, Armonk, NY) to determine the difference between FD values of RC, DC, and OKC with a significance level less than 0.05. Results The FD values of DC, RC, and OKC were 1.33 ± 0.17, 1.08 ± 0.16, and 1.65 ± 0.12, respectively. The results indicated that OKC had higher FD values than DC and RC, which means that OKC had lesser bone destruction compared to DC and RC. Inferential statistics showed that the one-way ANOVA was used to compare the means of the three groups of FD data. When calculated for the three groups, the F-statistic value was at 7.29, which yielded a P value of 0.03, making it statistically significant for a 95% confidence interval (p<0.05). Conclusion Our CBCT study on bone trabecular pattern analysis using FD and FA in odontogenic cysts reveals distinct alterations in bone parameters among different cyst types. The probability of higher FD values in OKC is because of lesser cortical bone destruction in OKC compared to the other cyst types. These findings have potential implications for diagnosing, treating, and prognosticating odontogenic cysts., Competing Interests: The authors have declared that no competing interests exist., (Copyright © 2024, Murugesan et al.)

In this paper we discuss the details, limitations, and difficulties of the implementation in hardware of a memristor-based random number generator that exhibits monofractal/multifractal behavior. To do so, the components and selection criteria of a reference memristor and one proposed by the authors, the chaotic circuit leveraging them, and the processing that is performed on the chaotic signals to achieve the random discrete sequences are described. After applying the estimation tools, findings indicate that more than 60% of the proposed combinations allow generating random discrete sequences, with long-range dependence, and that both monofractal and multifractal behaviors can also be obtained. Consequently, a hardware system was achieved that can be used as a source of entropy in future synthetic biological signal generators., Competing Interests: The authors declare the following financial interests/personal relationships which may be considered as potential competing interests:Cesar Hernandez reports administrative support and equipment, drugs, or supplies were provided by District University Francisco José de Caldas., (© 2024 The Authors.)

With the rapid advancement of wearable electronics, there is an increasing demand for high-performance flexible strain sensors. In this work, a flexible strain sensor based on liquid metal (LM)-integrated into a microfluidic device is developed with Peano-type fractal structure design. Compared with the microfluidic sensors with straight and wavy microchannels, the sensor with Peano-shaped channels shows lower hysteresis and improved stretchability. Furthermore, the increase of the fractal order can further improve the sensing performances. The third-order Peano sensor exhibits excellent mechanical and electrical properties, including high tensile capability (490.3%), minimal hysteresis (DH = 0.86%), ultra-low detection limit (0.1%), low overshoot, rapid response time (117 ms), as well as good stability and durability. By adding two independent and perpendicular straight channels to the Peano sensing unit, the feasibility of multi-directional strain recognition is demonstrated. To further improve the sensitivity of the Peano-shaped sensor, a multi-layer Peano sensor is developed, exhibiting remarkably enhanced sensitivity while maintaining low hysteresis. Overall, the developed LM-based microfluidic strain sensors enrolling Peano fractal geometry hold high potential for various wearable electronics applications., Competing Interests: Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2023 Elsevier B.V. All rights reserved.)

In the study of liver cancer, invasive techniques such as computed tomography (CT) and magnetic resonance imaging (MRI) are used. In the present work, an in vivo 3D study will be carried out using MRI and CT images, using scaling dynamics, that is, calculating critical exponents of local roughness and fractal dimension. The results obtained for stages IA, IIA, and IIIA in liver cancer correspond to what was proposed by F. Family and T. Vicsek (1991)., Competing Interests: Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2023 Elsevier Ltd. All rights reserved.)

Specifying the role of genetic mutations in cancer development is crucial for effective screening or targeted treatments for people with hereditary cancer predispositions. Our goal here is to find the relationship between a number of cancerogenic mutations and the probability of cancer induction over the lifetime of cancer patients. We believe that the Avrami-Dobrzyński biophysical model can be used to describe this mechanism. Therefore, clinical data from breast and ovarian cancer patients were used to validate this model of cancer induction, which is based on a purely physical concept of the phase-transition process with an analogy to the neoplastic transformation. The obtained values of model parameters established using clinical data confirm the hypothesis that the carcinogenic process strongly follows fractal dynamics. We found that the model's theoretical prediction and population clinical data slightly differed for patients with the age below 30 years old, and that might point to the existence of an ancillary protection mechanism against cancer development. Additionally, we reveal that the existing clinical data predict breast or ovarian cancers onset two years earlier for patients with BRCA1/2 mutations.

The integration of biology, computer science, and statistics has given rise to the interdisciplinary field of bioinformatics, which aims to decode biological intricacies. It produces extensive and diverse features, presenting an enormous challenge in classifying bioinformatic problems. Therefore, an intelligent bioinformatics classification system must select the most relevant features to enhance machine learning performance. This paper proposes a feature selection model based on the fractal concept to improve the performance of intelligent systems in classifying high-dimensional biological problems. The proposed fractal feature selection (FFS) model divides features into blocks, measures the similarity between blocks using root mean square error (RMSE), and determines the importance of features based on low RMSE. The proposed FFS is tested and evaluated over ten high-dimensional bioinformatics datasets. The experiment results showed that the model significantly improved machine learning accuracy. The average accuracy rate was 79% with full features in machine learning algorithms, while FFS delivered promising results with an accuracy rate of 94%., (© 2024. The Author(s).)

When describing the tribological behaviour of technical surfaces, the need for full-length scale microtopographic characterization often arises. The self-affine of surfaces and the characterisation of self-affine using a fractal dimension and its implantation into tribological models are commonly used. The goal of our present work was to determine the frequency range of fractal behaviour of surfaces by analysing the microtopographic measurements of an anodised aluminium brake plunger. We also wanted to know if bifractal and multifractal behaviour can be detected in real machine parts. As a result, we developed a new methodology for determining the fractal range boundaries to separate the nano- and micro-roughness. To reach our goals, we used an atomic force microscope (AFM) and a stylus instrument to obtain measurements in a wide frequency range (19 nm-3 mm). Power spectral density (PSD)-based fractal evaluation found that the examined surface could not be characterised by a single fractal dimension. A new method capable of separating nano- and micro-roughness has been developed for investigating multifractal behaviour. The presented procedure separates nano- and micro-roughness based on the geometric characteristics of surfaces. In this way, it becomes possible to specifically examine the relationship between the micro-geometry that can be measured in each wavelength range and the effects of cutting technology and the material structure that creates them.

A review of the most important concepts of the last 100 years on the topic of fascia and its fundamental importance to tissue and organ structure and function is provided as a basis for the author's commentary on the self-organizing nature of fascia. Implications for clinical applications in medicine, in both pathophysiology and the treatment of disease, follow from these anatomic insights. Organizing principles of nature put forth by D'Arcy Thompson, Buckminster Fuller, Benoit Mandelbrot, and Adrian Bejan set the stage for understanding tissue and fascial form. The author presents videos from the operating room of living anatomy illustrating the concept of a basic fascia segment, which differentiates according to need in the various locations of the body.

Fractal geometry is a branch of mathematics used to characterize and quantify the geometrical complexity of natural objects, with many applications in different fields, including physics, astronomy, geology, meteorology, finances, social sciences, and computer graphics. In the biomedical sciences, the use of fractal parameters has allowed the introduction of novel morphometric parameters, which have been shown to be useful to characterize any biomedical images as well as any time series within different domains of applications. Specifically, in the neurosciences and neurosurgery, the use of the fractal dimension and other computationally inferred fractal parameters has offered robust morphometric quantitators to characterize the brain in its wholeness, from neurons to the cortical structure and connections, and introduced new prognostic, diagnostic, and eventually therapeutic markers of many diseases of neurosurgical interest, including brain tumors and cerebrovascular malformations, as summarized in this chapter., (© 2024. The Author(s), under exclusive license to Springer Nature Switzerland AG.)

This chapter lays out the elementary principles of fractal geometry underpinning much of the rest of this book. It assumes a minimal mathematical background, defines the key principles and terms in context, and outlines the basics of a fractal analysis method known as box counting and how it is used to perform fractal, lacunarity, and multifractal analyses. As a standalone reference, this chapter grounds the reader to be able to understand, evaluate, and apply essential methods to appreciate and heal the exquisitely detailed fractal geometry of the brain., (© 2024. The Author(s), under exclusive license to Springer Nature Switzerland AG.)

After the previous sections on "Fractals: What and Why?," the last section of this book covers the software tools necessary to perform computational fractal-based analysis, with special emphasis on its applications into the neurosciences. The use of ImageJ and MATLAB, as well as other software packages, is reviewed. The current and future applications of fractal modeling in bioengineering and biotechnology are discussed as well. Perspectives on the translation of merging fractals with artificial intelligence-based methods with the final aim of pattern discrimination in neurological diseases by means of a unified fractal model of the brain are also given. Moreover, some new translational applications of fractal analysis to the neurosciences are presented, including eye tracking analysis, cognitive neuroscience, and music., (© 2024. The Author(s), under exclusive license to Springer Nature Switzerland AG.)

In this chapter, we review the research that has applied fractal measures to the study of the most common psychological disorders, that is, affective and anxiety disorders. Early studies focused on heart rate, but diverse measures have also been examined, from variations in subjective mood, or hand movements, to electroencephalogram or magnetoencephalogram data. In general, abnormal fractal dynamics in different physiological and behavioural outcomes have been observed in mental disorders. Despite the disparity of variables measured, fractal analysis has shown high sensitivity in discriminating patients from healthy controls. However, and because of this heterogeneity in measures, the results are not straightforward, and more studies are needed in this promising line., (© 2024. The Author(s), under exclusive license to Springer Nature Switzerland AG.)

Visual patterns reflect the anatomical and cognitive background underlying process governing how we perceive information, influenced by stimulus characteristics and our own visual perception. These patterns are both spatially complex and display self-similarity seen in fractal geometry at different scales, making them challenging to measure using the traditional topological dimensions used in Euclidean geometry.However, methods for measuring eye gaze patterns using fractals have shown success in quantifying geometric complexity, matchability, and implementation into machine learning methods. This success is due to the inherent capabilities that fractals possess when reducing dimensionality using Hilbert curves, measuring temporal complexity using the Higuchi fractal dimension (HFD), and determining geometric complexity using the Minkowski-Bouligand dimension.Understanding the many applications of fractals when measuring and analyzing eye gaze patterns can extend the current growing body of knowledge by identifying markers tied to neurological pathology. Additionally, in future work, fractals can facilitate defining imaging modalities in eye tracking diagnostics by exploiting their capability to acquire multiscale information, including complementary functions, structures, and dynamics., (© 2024. The Author(s), under exclusive license to Springer Nature Switzerland AG.)

Autism spectrum disorder is an increasingly prevalent and debilitating neurodevelopmental condition and an electroencephalogram (EEG) diagnostic challenge. Despite large amounts of electrophysiological research over many decades, an EEG biomarker for autism spectrum disorder (ASD) has not been found. We hypothesized that reductions in complex dynamical system behaviour in the human central nervous system as part of the macroscale neuronal function during cognitive processes might be detectable in whole EEG for higher-risk ASD adults. In three studies, we compared the medians of correlation dimension, largest Lyapunov exponent, Higuchi's fractal dimension, multiscale entropy, multifractal detrended fluctuation analysis and Kolmogorov complexity during resting, cognitive and social skill tasks in 20 EEG channels of 39 adults over a range of ASD risk. We found heterogeneous complexity distribution with clusters of hierarchical sequences pointing to potential cognitive processing differences, but no clear distinction based on ASD risk. We suggest that there is indication of statistically significant differences between complexity measures of brain states and tasks. Though replication of our studies is needed with a larger sample, we believe that our electrophysiological and analytic approach has potential as a biomarker for earlier ASD diagnosis., (© 2024. The Author(s), under exclusive license to Springer Nature Switzerland AG.)

Synapse formation is a unique biological phenomenon. The molecular biological perspective of this phenomenon is different from the fractal geometrical one. However, these perspectives are not mutually exclusive and supplement each other. The cornerstone of the first one is a chain of biochemical reactions with the Markov property, that is, a deterministic, conditional, memoryless process ordered in time and in space, in which the consecutive stages are determined by the expression of some regulatory proteins. The coordination of molecular and cellular events leading to synapse formation occurs in fractal time space, that is, the space that is not only the arena of events but also actively influences those events. This time space emerges owing to coupling of time and space through nonlinear dynamics. The process of synapse formation possesses fractal dynamics with non-Gaussian distribution of probability and a reduced number of molecular Markov chains ready for transfer of biologically relevant information., (© 2024. The Author(s), under exclusive license to Springer Nature Switzerland AG.)

Increase of collagen content and reorganization characterizes fibrosis but quantifying the latter remains challenging. Spatially complex structures are often analyzed via the fractal dimension; however, established methods for calculating this quantity either provide a single dimension for an entire object or a spatially distributed dimension that only considers binary images. These neglect valuable information related to collagen density in images of fibrotic tissue. We sought to develop a fractal analysis that can be applied to 3-dimensional (3D) images of fibrotic tissue. A fractal dimension map for each image was calculated by determining a single fractal dimension for a small area surrounding each image pixel, using fiber thickness as the third dimension. We found that this local fractal dimension increased with age and with progression of fibrosis regardless of collagen content. Our new method of distributed 3D fractal analysis can thus distinguish between changes in collagen content and organization induced by fibrosis., (© 2023. The Author(s).)

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., (© 2024. The Author(s), under exclusive license to Springer Nature Switzerland AG.)

Living systems are hierarchical control systems that display a small world network structure. In such structures, many smaller clusters are nested within fewer larger ones, producing a fractal-like structure with a 'power-law' cluster size distribution (a mereology). Just like their structure, the dynamics of living systems shows fractal-like qualities: the timeseries of inner message passing and overt behavior contain high frequencies or 'states' (treble) that are nested within lower frequencies or 'traits' (bass), producing a power-law frequency spectrum that is known as a 'state-trait continuum' in the behavioral sciences. Here, we argue that the power-law dynamics of living systems results from their power-law network structure: organisms 'vertically encode' the deep spatiotemporal structure of their (anticipated) environments, to the effect that many small clusters near the base of the hierarchy produce high frequency signal changes and fewer larger clusters at its top produce ultra-low frequencies. Such ultra-low frequencies exert a tonic regulatory pressure that produces morphological as well as behavioral traits (i.e., body plans and personalities). Nested-modular structure causes higher frequencies to be embedded within lower frequencies, producing a power-law state-trait continuum. At the heart of such dynamics lies the need for efficient energy dissipation through networks of coupled oscillators, which also governs the dynamics of non-living systems (e.q., earthquakes, stock market fluctuations). Since hierarchical structure produces hierarchical dynamics, the development and collapse of hierarchical structure (e.g., during maturation and disease) should leave specific traces in system dynamics (shifts in lower frequencies, i.e. morphological and behavioral traits) that may serve as early warning signs to system failure. The applications of this idea range from (bio)physics and phylogenesis to ontogenesis and clinical medicine., (Copyright © 2023 The Authors. Published by Elsevier Ltd.. All rights reserved.)

Protecting digital data, especially digital images, from unauthorized access and malicious activities is crucial in today's digital era. This paper introduces a novel approach to enhance image encryption by combining the strengths of the RSA algorithm, homomorphic encryption, and chaotic maps, specifically the sine and logistic map, alongside the self-similar properties of the fractal Sierpinski triangle. The proposed fractal-based hybrid cryptosystem leverages Paillier encryption for maintaining security and privacy, while the chaotic maps introduce randomness, periodicity, and robustness. Simultaneously, the fractal Sierpinski triangle generates intricate shapes at different scales, resulting in a substantially expanded key space and heightened sensitivity through randomly selected initial points. The secret keys derived from the chaotic maps and Sierpinski triangle are employed for image encryption. The proposed scheme offers simplicity, efficiency, and robust security, effectively safeguarding against statistical, differential, and brute-force attacks. Through comprehensive experimental evaluations, we demonstrate the superior performance of the proposed scheme compared to existing methods in terms of both security and efficiency. This paper makes a significant contribution to the field of digital image encryption, paving the way for further exploration and optimization in the future.

A common basis to address the dynamics of directly transmitted infectious diseases, such as COVID-19, are compartmental (or SIR) models. SIR models typically assume homogenous population mixing, a simplification that is convenient but unrealistic. Here we validate an existing model of a scale-free fractal infection process using high-resolution data on COVID-19 spread in São Caetano, Brazil. We find that transmission can be described by a network in which each infectious individual has a small number of susceptible contacts, of the order of 2-5. This model parameter correlated tightly with physical distancing measured by mobile phone data, such that in periods of greater distancing the model recovered a lower average number of contacts, and vice versa. We show that the SIR model is a special case of our scale-free fractal process model in which the parameter that reflects population structure is set at unity, indicating homogeneous mixing. Our more general framework better explained the dynamics of COVID-19 in São Caetano, used fewer parameters than a standard SIR model and accounted for geographically localized clusters of disease. Our model requires further validation in other locations and with other directly transmitted infectious agents., (© 2023 Published by Elsevier Inc.)

The creativity and emergence of biological and psychological behavior tend to be nonlinear, and correspondingly, biological and psychological measures contain degrees of irregularity. The linear model might fail to reduce these measurements to a sum of independent random factors (yielding a stable mean for the measurement), implying nonlinear changes over time. The present work reviews some of the concepts implicated in nonlinear changes over time and details the mathematical steps involved in their identification. It introduces multifractality as a mathematical framework helpful in determining whether and to what degree the measured series exhibits nonlinear changes over time. These mathematical steps include multifractal analysis and surrogate data production for resolving when multifractality entails nonlinear changes over time. Ultimately, when measurements fail to fit the structures of the traditional linear model, multifractal modeling allows for making those nonlinear excursions explicit, that is, to come up with a quantitative estimate of how strongly events may interact across timescales. This estimate may serve some interests as merely a potentially statistically significant indicator of independence failing to hold, but we suspect that this estimate might serve more generally as a predictor of perceptuomotor or cognitive performance., (© 2022. The Psychonomic Society, Inc.)

Fractals, mathematically defined as "self-similar subsets at different scales", are ubiquitous in nature despite their complexity in assembly and formulation. Fractal geometry formed by simple components has long been applied to many fields, from physics and chemistry to electronics and architecture. The Sierpiński carpet (SC), a fractal with a Hausdorff dimension of approximately 1.8933, has two-dimensional space-filling abilities and therefore provides many structural applications. However, few studies have investigated its mechanical properties and fracture behaviors. Here, utilizing the lattice spring model (LSM), we constructed SC composites with two base materials and simulated tensile tests to show how fractal iterations affect their mechanical properties and crack propagation. From observing the stress-strain responses, we find that, for either the soft-base or stiff-base SC composites, the second iteration has the optimal mechanical performance in the terms of stiffness, strength, and toughness compared to the composites with higher hierarchies. The reason behind this surprising result is that the largest stress intensities occur at the corners of the smallest squares in the middle zone, which consequently induces crack nucleation. We also find that the main crack tends to deflect locally in SC composites with a soft matrix, but in global main crack behavior, SC composites with a stiff matrix have a large equivalent crack deflection. Furthermore, considering the inherent anisotropy of SC composites, we rotated the samples by 45°. The results show that the tensile strength and toughness of rotated SC composites are inferior and the crack propagating behaviors are distinct from the standard SC composites. This finding infers advanced engineering for crack control and deflection by adjusting the orientation of SC composites. Overall, our study opens the door for future engineering applications in stretchable devices, seismic metamaterials, and structural materials with tunable properties and hierarchies.

Jump and pull-in instability are common nonlinear dynamic behaviors leading to the loss of the performance reliability and structural safety of electrostatic micro gyroscopes. To achieve a better understanding of these initial-sensitive phenomena, the dynamics of a micro gyroscope system considering the nonlinearities of the stiffness and electrostatic forces are explored from a global perspective. Static and dynamic analyses of the system are performed to estimate the threshold of the detecting voltage for static pull-in, and dynamic responses are analyzed in the driving and detecting modes for the case of primary resonance and 1:1 internal resonance. The results show that, when the driving voltage frequency is a bit higher than the natural frequency, a high amplitude of the driving AC voltage may induce the coexistence of bistable periodic responses due to saddle-node bifurcation of the periodic solution. Basins of attraction of bistable attractors provide evidence that disturbance of the initial conditions can trigger a jump between bistable attractors. Moreover, the Melnikov method is applied to discuss the condition for pull-in instability, which can be ascribed to heteroclinic bifurcation. The validity of the prediction is verified using the sequences of safe basins and unsafe zones for dynamic pull-in. It follows that pull-in instability can be caused and aggravated by the increase in the amplitude of the driving AC voltage.

Herein, we explore the potential of innovative manufacturing techniques based on green chemistry principles, for the fabrication of convenient, performant, and stable supported photocatalysts to be used for water depollution. After giving some insight into the use of fractal geometry for the fabrication of tunable polymer supports for photocatalysts, we investigated the use of liquid crystal display (LCD) 3D printing to generate the fractal resin substrates to be used for the immobilization of semiconductor photocatalysts. Notably, confocal laser imaging was used as a first attempt for assessing the surface area of the fractal substrate. Immobilization methods based on cold plasma discharge (CPD) were employed to modify the surface of the polymer substrates and permanently anchor three different phases, namely, nickel-based metal-organic framework (Ni-MOF), BiOI, and AgVO 3 , in a hierarchical configuration. Herein, for the first time, we developed a plasma-initiated condensed in situ complexation-assisted precipitation (c-ISCAP) method that allowed 2D Ni-MOF to be synthesized directly onto the surface of a polymer substrate, in a single step. Not only this MOF coating was found to be strongly bound to the surface of the polymer substrate but also very uniform and fully functional, even when other inorganic phases were immobilized on the top of this layer. This chemical approach opens the way for the fabrication of hybrid materials with complex polymer substrates and MOF coatings that could be used in a range of possible applications, for instance as chemical sensors, electrodes, adsorbents, optical devices, etc. Our hybrid photocatalysts were tested via photodegradation of Rhodamine B (RhB) dye upon visible light activation, with recycling runs to assess their durability. It was found that the hierarchical heterojunction Ni-MOF/BiOI/AgVO 3 showed an outstanding ability for the removal of RhB dye, owing to the activity of the Ni-MOF layer in terms of charge transfer, and also partly because of its adsorbing potential. The three photoactive phases demonstrated a strong synergistic effect through coupling. However, more importantly, our findings show that their immobilization itself, regardless of the method used, significantly modified their optoelectronic properties, hence most likely changing the overall mechanism of charge transfer in the heterojunction. The Ni-MOF phase, notably, was found to display a reduced bandgap when obtained by c-ISCAP, which contributed to enhance its activation by visible light irradiation. Finally, it was established that the fractal geometry had a significant impact on the efficiency of the supported catalysts, probably thanks to an increased immobilization ratio of photocatalyst mostly, owing to the larger surface area available.

Aims: Analysis of colonoscopy images is an important diagnostic procedure in the identification of colorectal cancer. It has been observed that owing to advancements in technology, numerous machine-learning models now excel in the analysis of colorectal polyps classification. This work focused on developing a framework that can classify polyps using images during colonoscopy., Materials and Methods: First, the images were corrected by removing their spectral reflection. Second, feature pools were obtained by applying Radon transform ( θ =45, 90, 135, and 180). From the Radon transform, fractal dimension was calculated as a feature vector combined with Zernike moment obtained from the Zernike features. Finally, Extreme Gradient Boosting (XGBoost) algorithm was applied for the classification and to compare it with state-of-the-art methods., Results: The experimental results obtained with the proposed framework have been reported, cross-validated, and discussed. The proposed method gives a classification accuracy of 93% for light XGBoost and 92% for XGBoost., Conclusion: This study shows that by applying scale invariant features over a small dataset, XGBoost outperforms state-of-the-art methods when it comes to polyp classification., Competing Interests: There are no conflicts of interest., (Copyright: © 2023 Journal of Medical Physics.)

Vagus nerve stimulation (VNS) has the potential to treat various peripheral dysfunctions, but the traditional cuff electrodes for VNS are susceptible to off-target effects. Microelectrodes may enable highly selective VNS that can mitigate off-target effects, but they suffer from the increased impedance. Recent studies on microelectrodes with non-Euclidean geometries have reported higher energy efficiency in neural stimulation applications. These previous studies use electrodes with mm/cm-scale dimensions, mostly targeted for myelinated fibers. This study evaluates fractal microelectrodes for VNS in a rodent model (N = 3). A thin-film device with fractal and circle microelectrodes is fabricated to compare their neural stimulation performance on the same radial coordinate of the nerve. The results show that fractal microelectrodes can activate C-fibers with up to 52% less energy (p = 0.012) compared to circle microelectrodes. To the best of the knowledge, this work is the first to demonstrate a geometric advantage of fractal microelectrodes for VNS in vivo., (© 2023 The Authors. Advanced Healthcare Materials published by Wiley-VCH GmbH.)

The random lamellae of the synthetic CP were synthesized with a hydrothermal approach using o-Phenylenediamine (OPD) as a modifier. The decreases in the order degree of the CP synthesized in the presence of the OPD resulted from the loss of long-range order in a certain direction. Subsequently, the ultrasonic treatment and washing were conducive to further facilitate the disordered arrangements of its lamellae. The possible promotion mechanism regarding the nucleation and growth behaviors of the sol-gel particles was proposed. The fractal evolutions of the aluminosilicate species with crystallization time implied that the aluminosilicate species became gradually smooth to rough during the crystallization procedures since the amorphous structures transformed into flower-like morphologies. Their gas adsorption and separation performances indicated that the adsorption capacity of CO 2 at 273 K reached up to 2.14 mmol·g -1 at 1 bar, and the selective factor (CO 2 /CH 4 ) up to 3.4, much higher than that of the CPs synthesized without additive OPD. The breakthrough experiments displayed a longer breakthrough time and enhancement of CO 2 uptake, showing better performance for CO 2 /CH 4 separation. The cycling test further highlighted their efficiency for CO 2 /CH 4 separation.

Background: The treatment of transversal maxillary deficiency usually aims at skeletal expansion. The treatment option highly depends on the maturation stage of the midpalatal suture (MPS), which may vary between individuals at the same chronological age. Therefore, the individual determination of the MPS maturation is crucial., Aims: Our aim was to investigate the applicability of fractal analysis for the quantitative evaluation of MPS maturation., Methods: Nine experienced orthodontists were asked to evaluate the MPS maturation on 51 cone beam computed tomography (CBCT) scans according to the Angelieri classification method. Intra- and inter-examiner reliability was measured using Cohen's Kappa coefficient. The stages were agreed upon according to the results of the examiners with the highest strength of agreement. Fractal analysis was then performed on the CBCTs and the correlation between the fractal dimension values and maturation stages was then evaluated. Optimal fractal dimension cut-off values were determined using a receiver operating characteristic curve., Results: The cut-off point was found at 1.073, at which the use of fractal dimension for predicting MPS maturation showed 100% sensitivity, 93.7% specificity, 9.5% false positive, 0% false negative rate., Conclusion: Our results provided further evidence that fractal analysis is a reliable tool to determine MPS maturation stage.

Objective: To examine whether artificial intelligence can achieve discoveries regarding fetal brain activity., Methods: In this observational study, the authors collected images of fetal faces using a four-dimensional ultrasound technique obtained from singleton pregnancies of outpatients in routine practice at 27 to 37 weeks of gestation between February 1 and December 31, 2021. The authors developed an artificial intelligence classifier to recognize seven facial expressions of fetuses, then applied it to video files of fetal facial images to generate the probabilities, as confidence scores, of each expression category. Discrete Fourier transform and chaotic analysis were used to investigate the scores. Mann-Whitney test, t test, variance test, and one-way analysis of variance were used for statistical analysis., Results: Facial expression changes were observed in cycles averaging 66 to 73 s. The power spectrum showed that mouthing and neutral expressions were the most prevalent. There was a difference between categories for the spectrum (p = 0.004). Two different states--dense and sparse--of confidence scores were discovered. The correlation dimension was 1.19 ± 0.22 and 1.33 ± 0.27 for dense and sparse, respectively (p = 0.047)., Conclusion: This method objectively and quantitatively demonstrated fetal brain activity and may provide insight into how the fetus spends its time in utero., (© 2022 The Authors. International Journal of Gynecology & Obstetrics published by John Wiley & Sons Ltd on behalf of International Federation of Gynecology and Obstetrics.)

Coalbed methane (CBM) is primarily stored and transported through the pores in the coal matrix, making it essential to study the development of different scales of pores in coal to better understand the evaluation and exploration of CBM. In this study, four coal samples of varying ranks (R o,max = 0.68%-2.86%) were selected, and different scale pores were obtained through low-pressure CO 2 and Ar adsorption (LP-CO 2 /ArGA) and mercury intrusion porosimetry (MIP) experiments. A full-scale pore evaluation model was established, and the impact of pores on methane adsorption and restriction was analyzed and discussed through high-pressure adsorption experiments. Our results show that (1) at high pressures (> 100 MPa), the MIP technique caused pore compression and overestimated the pore size below 30 nm by up to 47.2%; (2) to obtain a comprehensive pore evaluation, we developed an accurate model that combines LP-CO 2 /ArGA with NLDFT and BJH and NLDFT models to determine micropore (0.3-1.5 nm) and mesopore (1.5-30 nm) parameters. By combining this model with MIP test results, we can obtain a full-scale pore size in the range of 0.3 nm-200 μm; (3) coal rank affected the development of full-scale pore characteristics. As coal rank increased, the specific surface area (SSA) of micropores and adsorption capacity of methane first decreased, then increased. Micropores were found to be the most important storage space for CBM and control gas adsorption, with a microporous SSA and PV to total SSA and total PV ratio of 97.93% and 63.69%, respectively. (4) We also observed a significant linear relationship between the fractal dimension of micropores and the Langmuir volume (V L ) based on fractal theory. As the fractal dimension increased, V L also increased (R 2 = 0.8581), indicating that V L is controlled by the complexity of micropores, which is consistent with the comprehensive evaluation index (D t ) and V L (R 2 = 0.8744). Based on our predicted model, V L can be estimated using the SSA of micropores and D t . Our findings shed light on the relationship between pore morphology and CBM occurrence and have practical implications for fields such as catalytic synthesis, E-CBM, and gas purification., (© 2023. The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.)

Cardiovascular self-organized criticality has recently been demonstrated. We studied a model of autonomic nervous system changes to better characterize heart rate variability self-organized criticality. The model included short and long-term autonomic changes associated with body position and physical training, respectively. Twelve professional soccer players took part in a 5-week training session divided into "Warm-up", "Intensive", and "Tapering" periods. A stand test was carried out at the beginning and end of each period. Heart rate variability was recorded beat by beat (Polar Team 2). Bradycardias, defined as successive heart rates with a decreasing value, were counted according to their length in number of heartbeat intervals. We checked whether bradycardias were distributed according to Zipf's law, a feature of self-organized criticality. Zipf's law draws a straight line when the rank of occurrence is plotted against the frequency of occurrence in a log-log graph. Bradycardias were distributed according to Zipf's law, regardless of body position or training. Bradycardias were much longer in the standing position than the supine position and Zipf's law was broken after a delay of four heartbeat intervals. Zipf's law could also be broken in some subjects with curved long bradycardia distributions by training. Zipf's law confirms the self-organized nature of heart rate variability and is strongly linked to autonomic standing adjustment. However, Zipf's law could be broken, the significance of which remains unclear., Competing Interests: The authors declare no conflict of interest.

Asymmetric damage segregation (ADS) is ubiquitous among unicellular organisms: After a mother cell divides, its two daughter cells receive sometimes slightly, sometimes strongly different fractions of damaged proteins accumulated in the mother cell. Previous studies demonstrated that ADS provides a selective advantage over symmetrically dividing cells by rejuvenating and perpetuating the population as a whole. In this work we focus on the statistical properties of damage in individual lineages and the overall damage distributions in growing populations for a variety of ADS models with different rules governing damage accumulation, segregation, and the lifetime dependence on damage. We show that for a large class of deterministic ADS rules the trajectories of damage along the lineages are chaotic, and the distributions of damage in cells born at a given time asymptotically becomes fractal. By exploiting the analogy of linear ADS models with the Iterated Function Systems known in chaos theory, we derive the Frobenius-Perron equation for the stationary damage density distribution and analytically compute the damage distribution moments and fractal dimensions. We also investigate nonlinear and stochastic variants of ADS models and show the robustness of the salient features of the damage distributions., Competing Interests: Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2023. Published by Elsevier Inc.)

An adaptive response to unexpected perturbations requires near-term and long-term adjustments over time. We used multifractal analysis to test how nonlinear interactions across timescales might support an adaptive response following an unpredictable perturbation. We reanalyzed torque data from 44 young and 24 older adults who performed a single-leg squat task challenged by an unexpected mechanical perturbation and a secondary visual-cognitive task. We report three findings: (a) multifractal nonlinearity interacted with pre-perturbation torque production and task error to presage greater pre-voluntary feedforward increases and greater voluntary reductions, respectively, in post-perturbation task error; (b) multifractal nonlinearity presaged relatively smaller task error than standard deviations of both pre-perturbation torques and pre-perturbation task error; and (c) increased task demand (e.g., age-related changes in dexterity and dual-task settings) led to multifractal nonlinearity presaging reduced task error. All these results were consistent with our expectations, except that a pre-perturbation knee torque-dependent increase in post-perturbation task error appeared later for older than for younger participants. This correlational multifractal modeling offered theoretical clarity on the possible roles of nonlinear interactions across timescales, moderating both feedforward and feedback processes, and presaging greater stability when the standard deviation is relatively large and task demands are strong. Thus, multifractal nonlinearity usefully describes movement variability even when paired with classical descriptors like the standard deviation. We discuss potential insights from these findings for understanding suprapostural dexterity and developing rehabilitative interventions.

During the excavation of underground projects, the rock masses left as the bearing support system are also subjected to dynamic loads from the excavation activities ahead. These rock masses have been damaged and fractured during the initial exposure (dynamic loads) and are subjected to static loads in the subsequent process as the support system. In this study, granite rock samples and specimens with different angles were produced, preloaded with different confining pressure, and under a combination of dynamic and static loading tests using a modified dynamic and static loading system: split Hopkinson pressure bar (SHPB). The peak strain and dynamic modulus of elasticity are weakened by the inclination angle in a similar way to the strength, with the specimens showing an evolutionary pattern from tensile strain to shear damage. The change in the inclination angle of flaws would weaken the dynamic and combined strengths, and a larger inclination flaw results in a significant decrease in its strength. Fractal analysis revealed that the fractural dimension was closely related to the fissure angle and showed a good linear correlation with the strain rate. This study will provide an important security assurance for deep mining.

The authors explore the value of using psychoanalysis in a community and a social justice setting. A so-called Mental Health Marathon Project in South Africa left human wreckage in its wake. Psychoanalysis, as a conjunction between ordinary human interaction and psychoanalytic awareness (Parsons, 2007), provided a way of thinking and intervening in this context so that the families were provided with holding and containment, but forensic goals were also achieved in the form of an expert report. This document, named the "Brick Mother Report" (Steiner, as cited in Rey, 1994), attempts to make psychological sense of the impact of the Marathon Project.