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Stress is an important external element influencing effective thermal conductivity (ETC). However, previous theoretical investigations of stress-dependent effective thermal conductivity have used a simplified parallel plate model, overlooking the complex structure of rock fracture networks. Therefore, this paper establishes a new fractal model for the stress-dependent ETC of a rectangular cross-section tree-like microfracture network. The model derives a constitutive equation between the stress-dependent ETC and the microscopic geometry structural parameters of the microfracture network. The model’s validity is confirmed by the error of less than 0.291% between the theoretical predictions and the experimental data. The influence of geometry structural parameters of the microfracture network (length ratio, width ratio, height ratio, angle, total number of branches and ratios of soft part, hard part, etc.) on the ETC under the low-stress state has been analyzed. It was discovered that the soft part of the rock microfracture network has the most impact on ETC. The fractal pore-scale model clarifies heat transfer mechanism in rock microfracture network under effective stress, with each parameter physically defined and independent of empirical constants. [ABSTRACT FROM AUTHOR]

Thermal shock behaviors of porous alumina samples with different porosities (4.6–16.0 %) and mean grain sizes (2.72–5.02 μm) were investigated under different quenching temperatures. The slit island method was used to analyze the structures of the pores. The effect of the pore structure on the thermal shock resistance of alumina ceramics was described quantitatively. The results revealed that the thermal shock resistance decreased when the fractal dimension of the pores increased. Alumina ceramic strips with a porosity and mean grain size of 4.6 % and 5.02 μm, respectively, were fabricated using raw powders with a mean particle size of ∼0.3 μm. These samples possessed the highest residual strength ratio (∼46.16 % at 600 °C) and critical temperature difference (∼262 °C). In addition, the fractal characterization of cracks on the surfaces of the alumina ceramics after thermal shock was carried out using the box-counting dimension method. In addition, we investigated the correlation between the mechanical properties and fractal dimensions of the surface cracks. The box-counting dimension increased with crack propagation and negatively correlated with the residual strength. Furthermore, the propagation rate of the surface cracks decreased as the temperature difference increased, resulting in a decrease in the growth rate of the fractal dimension. [ABSTRACT FROM AUTHOR]

Here, we report room temperature deposition of nickel oxide (NiO) thin films on silicon and glass substrates by direct current (dc) magnetron sputtering using a metallic nickel target. The effect of sputtering power (20 W, 25 W, and 30 W) on the thin films, their surface scaling, fractal dimension, and optical properties are extensively investigated. Autocorrelation and height–height correlation functions were applied to AFM images to extract deep insights about the thin films' surfaces. Fractal dimension (D f) was extracted through the power spectral density (PSD) function. Various scaling exponents, including α, β, and 1/z, of the NiO film's surface were independently observed. The local roughness exponent, α, was approximately 0.81 for films deposited with 20 W sputtering power and decreased to 0.71 with higher sputtering power. The interface width (σ) scales with sputtering power (Sp) as ∼ Spβ, with a growth exponent (β) value of 1.17. The lateral correlation length (ξ) follows as ∼ Sp1/z with a 1/z value of 0.703. Additionally, optical parameters were recorded through UV–Vis. optical spectroscopy, and an attempt was made to correlate them with fractal parameters (D f & α). Optical absorption (reflection) increased (decreased) with increasing D f values. The minimum (maximum) reflection (absorption) was observed on the roughest surface (D f = 2.29). The calculated band gap decreased with increasing fractal dimension. This investigation suggests that sputtered surfaces with minimal reflectivity, band gap, and enhanced light-absorbing capacity could potentially be used as active solar layers for advanced optoelectronic devices. [ABSTRACT FROM AUTHOR]

Gesture recognition for Arabic speech translation includes developing advanced technologies that correctly translate body and hand movements corresponding to Arabic sign language (ArSL) into spoken Arabic. This leverages machine learning and computer vision techniques in complex systems simulation platforms to scrutinize the gestures utilized in ArSL, detecting mild differences in facial expressions, hand shapes, and movements. Sign Language Recognition (SLR) is paramount in assisting communication for the Deaf and Hard-of-Hearing communities. It includes using vision-based methods and Surface Electromyography (sEMG) signals. The sEMG signal is crucial for recognizing hand gestures and capturing muscular activities in sign language. Researchers have comprehensively shown the capability of EMG signals to approach specific details, mainly in classifying hand gestures. This progression is a stimulating feature in extracting the interpretation and recognition of sign languages and investigating the phonology of signed language. Leveraging machine learning algorithms and signal processing techniques in complex systems simulation platforms, researchers aim to extract relevant traits from the sEMG signals that correspond to different ArSL gestures. This study introduces an Enhanced Dwarf Mongoose Algorithm with a Deep Learning-Driven Arabic Sign Language Detection (EDMODL-ASLD) technique on sEMG data. In the initial phase, the presented EDMODL-ASLD model is subjected to data preprocessing to change the input sEMG data into an attuned format. In the next stage, feature extraction with fractal theories is used to gather relevant and nonredundant data from the EMG window to construct a feature vector. In this study, the absolute envelope (AE), energy (E), root-mean square (RMS), standard deviation (STD), and mean absolute value (MAV) are the five time-domain extracted features for the EMG window observation. Meanwhile, the dilated convolutional long short-term memory (ConvLSTM) technique is used to identify distinct sign languages. To improve the results of the dilated ConvLSTM model, the hyperparameter selection process is executed using the EDMO model. To illustrate the significance of the EDMODL-ASLD technique, a brief experimental validation is made on the Arabic SLR database. The experimental validation of the EDMODL-ASLD technique portrayed a superior accuracy value of 96.47% over recent DL approaches. [ABSTRACT FROM AUTHOR]

AbstractBased on fractal theory, the geometric size, surface morphology, and spatial structure of flocs in the hydrophobic flocculation process of coal particles were examined via particle size distribution detection, image analysis technology, and numerical simulation. The floc size distribution curve was classified and discussed via the dual-domain fractal rule, and the variation law of the composition and distribution of the coarse- and fine-grained coal particle flocs with the flocculation process was clarified. The various levels and characteristics of the floc growth geometry were explained by the analysis of the fractal dimension of the individual floc surface and the multiple spectra of the floc groups in the metallographic microscopy image. The hydrophobic flocculation process of coal particles was simulated via the diffusion-limited cluster aggregation model. The gyration fractal dimension was used to examine floc fragmentation and reconstruction and clarify the growth law of the floc spatial structure during the hydrophobic flocculation process. [ABSTRACT FROM AUTHOR]

A compressed small width circular in shape aerial with fractal characteristics that exhibits minimal delay, cost and better speed with wide band characteristics is modeled. Simulation analysis has been done with software named CST Microwave studio after that it has been verified by experimental analysis. Substrate material used for fabrication is easily available FR-4 (εr = 4.4) with 1.59 mm as thickness of sheet. The dimensions are 24 × 40 mm (W × L). Aerial finds its applications in mobile services. The 5 GHz band is perfect for high-bandwidth devices or activities such as online video games, conference calls and streaming. 6 GHz Wi-Fi range is applicable for recently used short-range, better efficiency, and low delay applications. Proposed antenna covers C, X and Ku bands and conducting from 2.93 to 9.53 GHz with VSWR ≤ 2. This aerial is also performing in ultra wideband (UWB), S, C and partial of the X range. [ABSTRACT FROM AUTHOR]

Since the internal structure of actual porous media has irregularity and complexity and is rough on the surface, it cannot be characterized accurately by traditional theoretical analytical methods. In this paper, the mathematical formalism of the effective diffusion coefficient of gas on rough porous surfaces is established by employing fractal geometry theory, utilizing the rough capillary tube bundle model, and introducing the penetration correction factor. The effective gas diffusion coefficient is investigated as a function relation of the rough porous media structural parameters and gas parameters. The results show that the effective diffusion coefficient of gas is positively correlated to the porosity, maximum pore diameter, and area fractal dimension of porous media and negatively correlated to the relative roughness, tortuous fractal dimension, the molar mass of gas, and gas density. The correctness and reliability of the present model have been confirmed, by the comparative analysis of the model predictive values in this paper and the available experimental data. [ABSTRACT FROM AUTHOR]

The shale formation, a common carbon-hydrogen reservoir, has numerous nanoscale pores that facilitate multiple gas transport mechanisms, including viscous flow, slip flow, Knudsen diffusion, and surface diffusion. Additionally, various action mechanisms involving effective stress, real gas effect, gas adsorption and desorption, and fracture-pore characteristics significantly influence gas transport. In this study, we conceptualize shale as a triple porosity medium comprising organic matrix, inorganic matrix, and microfractures. For each system, its hydraulic-mechanical coupled model with action mechanisms and gas transport mechanisms is derived based on fractal theory. After validating the model with Barnett and Marcellus data, the evolution of apparent permeability and gas pressure is studied, as well as the influences of pore fractal features, the real gas effect, and the number of hydraulic fractures on gas extraction. Simulation results indicate that, in comparison to organic matrix, inorganic pore fractal features exert a more noticeable effect on cumulative production. The real gas effect is critical in gas transport and reservoir reserve estimation; disregarding this effect results in a 17.4% underestimation of cumulative gas production by the 1600th day. Fracture interference attenuates the improvement in cumulative production gains from increased hydraulic fracture numbers. • A hydraulic-mechanical coupled triple porosity fractal model is established. • Inorganic matrix pore fractal features have a greater impact on gas transport than organic matrix. • Ignoring the real gas effect leads to an underestimation of gas productivity. • The hydraulic fracture interference significantly reduces gas productivity in the late stage of shale gas exploitation. [ABSTRACT FROM AUTHOR]

This paper reports fractal patterns identified in the complex musical composition DIAPHONIES by Michael Paouris via power-law fractal analysis with sliding-windows of size 1024. From 7,647,232 analysed musical segments of DIAPHONIES, 3,222,832 (42.4%) are fractional Brownian motion (fBm) fractal segments and 4,424,400 (57.6%) are fractional Gaussian noise (fGn) stochastic ones. From the fBm fractal segments 295,294 (9.1%) exhibit strong persistency-P with power-law segments in the range of 2.3 ≤ b ≤ 3 . These are the very strong fractal areas in DIAPHONIES. Numerous segments with strong antipersistency 1.7 ≤ b < 2 are reported together with segments with AP changes ( 1.7 ≤ b < 2.3 ). In DIAPHONIES continuous fractal fBm areas are dipped in non-fractal fGn areas of deterministic music. The results are within the fBm fractal areas reported in existing papers. Very importantly, the simple composition called Nocturnal-Angel by Michael Paouris, exhibited limited fBm areas of average b ¯ = 1.98 ( σ = 0.3 ), namely of pure statistical, deterministic music, while simultaneously, the fractal analysis profile was completely different from the profiles of DIAPHONIES, hence reinforcing, the fractal findings of DIAPHONIES in relation to trivial music harmony. [ABSTRACT FROM AUTHOR]

Flow of suspensions through the complex porous network is typically characterized by the initial spurt and then the formation of internal/ external filter cake which impedes the flow velocity. The transient mechanisms involved during the particle migration phenomenon need to be studied carefully as it is crucial for effectively managing the flow characteristics of drilling fluids and their impact on subsurface reservoirs. In this study, constant pressure permeation experiments are carried out using a specially designed apparatus to quantify the formation and evolution of particle migration zones using advanced image processing algorithms. Additionally, a comprehensive pre-test and post-test characterization of drilling fluids/ filtrates and the porous medium revealed intricate insights into the dynamics of particle migration. Four distinct particle migration/ filtration zones such as internal filter cake, primary filtration, secondary filtration and fluid loss are identified based on the change in the concentration gradient. The influence of additives on the growth of these zones is quantified during the filtration process. The concentration of barite/ micronized calcium carbonate and xanthan gum predominantly controls the filtration process by enhancing the particle plugging and retention time, respectively. In addition to the in-depth understanding of the particle migration zones, the transition from kinetic to capillary flow is identified by performing the fractal analysis. The analysis revealed that drilling fluid containing more barite exhibits a dominant capillary flow. Finally, an analytical model has been modified by considering the influence of different additives to predict the depth of penetration, which is comparable with the experimental results. [ABSTRACT FROM AUTHOR]

We analyze the dynamical behavior of an eighth-order Sharma's iterative scheme, which contains a single parameter, with respect to an arbitrary quadratic polynomial using complex analysis. The eighth-order Sharma's iterative scheme is analytically conjugated to a rational operator on the Riemann sphere. We discuss the strange fixed points of the rational operator and present its stable region graph. Additionally, we briefly investigate the superattracting point and the critical point, which have an impact on the Sharma's iterative scheme discussed. Finally, we present the dynamical planes for different parameter values using the complex dynamics tool, which helps us select more effective members of the Sharma's iterative scheme. Numerical experiments are conducted to verify the theoretical results. [ABSTRACT FROM AUTHOR]

Psychotherapy is a relational process that emerges from the meeting of two people. There is an ontological difference between the individual psychopathology of the patient and relational therapy; the present work aims to overcome the patient-centric conception of psychotherapy, restoring the dyadic nature of the therapy through the interpretation of the psychological interview as a fractal process. Recursion, namely the application of the same logical operator to the result of the operation itself, is presented here as the basic procedural element of psychotherapy. The paper is divided into two parts: The first has epistemological nature and focuses on complexity theory and cybernetics: Edgar Morin and recursion as a process of existence, Heinz von Foerster and epistemology as second-order praxis. From the thought of Gregory Bateson, it is here postulated the self-similarity of the content and structure of the mind, to the point of conceptualizing the dyadic relationship as a Mind of a different logical type compared to the individual mind. The second part of the present work introduces two intellectual tools designed to conceptualize psychotherapy as a fractal process: the psychopathological hologram, useful for clinical work although of a non-clinical nature, that consists in a fraction of the patient's experiential flow, while the psychotherapeutic string is presented here as the basic recursive element of psychotherapeutic process. [ABSTRACT FROM AUTHOR]

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Featured Application: The proposed antenna is potentially suitable for Wi-MAX (3.5 GHz) and sub-6 GHz n77 (3300–3800 MHz), n78 (3300–4200 MHz), and n79 (4400–4990 MHz), in addition to C-band applications. This study introduces a novel antenna based on the binary operation of a modified circular patch in conjunction with the Koch fractal. The antenna is intended for applications in the sub-6 GHz band, partial C-band, and X-band. The low-cost antenna is fabricated on a 1.6-mm-thick FR-4 substrate. A frequency-selective surface (FSS) is used to overcome the decreased values of the gain and bandwidth due to the fractal operations. The introduced split ring resonator (SRR) and the antenna substrate dimension reduction reduce the bandwidth and antenna gain. The air gap between the FSS and the antenna not only enhances the antenna gain but also controls the frequency tuning at the design frequency. The antenna size is miniaturized to 36.67%. A monopole antenna ground loaded with an SRR results in improved closest tuning (3.44 GHz) near the design frequency. The antenna achieves a peak gain of 9.37 dBi in this band. The FSS-based antenna results in a 4.65 dBi improvement in the gain value with the FSS. The measured and simulated plots exhibit an excellent match with each other in all three frequency bands at 2.96–4.72 GHz. These bands cover Wi-MAX (3.5 GHz), sub-6 GHz n77 (3300–3800 MHz), n78 (3300–4200 MHz), and approximately n79 (4400–4990 MHz), in addition to C-band applications. [ABSTRACT FROM AUTHOR]

This paper presents discontinuous Riemann integrable functions on the unit interval $ [0, 1] $ derived from the dynamics of two-dimensional elementary cellular automata. Based on the self-similarities of their orbits, we write down the numbers of nonzero states in the spatial and spatio-temporal patterns and obtain discontinuous Riemann integrable functions by normalizing the values. We calculate the integrals of the two obtained functions over $ [0, 1] $ and demonstrate the relationship between them. [ABSTRACT FROM AUTHOR]

In this study, we aim to explore the birth mechanism of coexisting Strange Nonchaotic Attractors (SNAs) in a multistability system. The underlying mechanism behind the emergence of coexisting SNAs is understood by examining the interruption of coexisting torus-doubling bifurcations. We identify three different routes that lead to the creation of coexisting SNAs, namely, the intermittent route, Heagy–Hammel route, and fractalization route. To effectively characterize SNAs, we employ several metrics, including the nontrivial largest Lyapunov exponents, phase sensitivity exponents, and power spectrum analysis. Notably, SNAs exhibit a fractal (strange) nature, which has inspired us to develop a novel optimization algorithm termed the Strange Nonchaotic Optimization (SNO) algorithm. This algorithm is used to optimize the Proportional-Integral-Derivative (PID) controller parameters in time-delay systems based on a defined objective function. Simulation results validate that the proposed SNO algorithm presents better performance than the available algorithms in the literature for time-delay systems. [ABSTRACT FROM AUTHOR]

In this paper, we obtain the average geodesic distance of the (2 × 3)-type hybrid Sierpinski gasket, using the method of finite pattern. [ABSTRACT FROM AUTHOR]

In order to study the influence of friction coefficient on the stiffness of disc spring, A series of disc springs (D = 71 mm) were selected in this paper. The tension and compression experiments of disc spring components were carried out by universal testing machine. The load-displacement characteristic curves of disc springs with different friction surfaces were obtained. The results show that in the loading process, the friction effect hinders the increase of the deformation of the disc spring, so that the actual stiffness of the disc spring is improved and the actual compensation amount is reduced, so this result is worthy of attention. In order to further study the influence of friction coefficient on the loading process of disc spring, according to the load-deformation formula of disc spring in A-L method, the tangential stress caused by friction is added, and the stiffness calculation model of corresponding disc spring is established by Workbench finite element software. The coefficients of different friction surfaces are used as variables for numerical calculation. The results show that the theoretical calculation, numerical calculation and experimental results of stiffness increase with the increase of friction coefficient under 0.55 h (the compensation displacement of A71 disc spring under the working displacement of corrugated tube ±10 mm). Among them, the numerical calculation results are close to the experimental results, and the error value is less than 1%. The numerical calculation results are corrected by using the experimental data, and the corrected model calculation results are in good agreement with the measured results. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

A multifunctional, multiphase-supported photocatalyst was fabricated via the combination of LCD three-dimensional (3D) printing, cold plasma discharge (CPD) technology, and surface chemistry to be used for the degradation of organic pollutants in water and for the generation of hydrogen gas. BiOBr was chosen as the main catalytic phase and was used in association with a phosphor, SrAl2O4:Eu2+,Dy3+ (SAED), and a metal–organic framework, Ni-BDC. Their immobilization was realized thanks to polydopamine (PDA), which is used as a coupling agent. While BiOBr was the most active photocatalytic phase, the phosphor acted as a light-storing component for photodegradation in the dark and overall, as a boost for photoactivity. PDA also boosted the photoactivity, in parallel with its crucial role in the immobilization of the SAED/Ni-MOF/BiOBr catalyst on fractal polymer support. An in situ complexation-assisted precipitation (ISCAP) process was used, allowing the formation of the catalytic phases with nano features. The resulting hybrid photocatalysts were tested through rhodamine B (RhB) dye photodegradation upon visible light irradiation or light/dark alternating conditions to simulate more realistic variable light illumination. We found that, although used in a very small amount, the Ni-MOF had a significant impact on the photoactivity, forming a Z-scheme heterojunction with BiOBr. Finally, H2 evolution testing further established the photocatalytic activity and versatility of the supported catalysts. [ABSTRACT FROM AUTHOR]

The growing demand for space-efficient antennas compatible with portable electronic gadgets inspired the integration of recursively iterated fractal geometries (characterized by self-similarity, space-filling, and multiband/wideband capabilities) in antenna designs. Therefore, this article conducts an extensive survey on fractal-based single-port and multi-port patch antenna designs with multiband and ultrawideband characteristics for their implementation in 5G/IoT (Internet of Things) devices. The survey begins with a basic overview of fractal geometries and the iterated function system (IFS) technique employed for their generation. Further, it highlights the limitation of multipath fading prevalent in single-port antenna arrays that can be overcome by adopting multiple-input multiple-output (MIMO) technology. The MIMO antenna systems are vital for 5G networks to enhance data transmission rate, network capacity, and system reliability. Apart from these admirable attributes, the closely packed antenna elements in the MIMO configuration result in a severe mutual coupling. To address this limitation, various isolation enhancement techniques developed by distinguished researchers are thoroughly discussed in this article, detailing their merits and demerits. At last, this article portrays diverse band-notch structures integrated into the antenna designs to eradicate the existing interfering narrow bands in the ultrawideband (UWB) spectrum. The underlying reason for conducting this survey is to aid antenna designers and academicians with a thorough knowledge of distinct fractal geometries, various isolation improvement approaches, and band-notch techniques on a single platform, desired for designing 5G/IoT-based antenna systems. [ABSTRACT FROM AUTHOR]

In this paper, a novel class of rational cubic fractal interpolation function (RCFIF) has been proposed, which is characterized by one shape parameter and a linear denominator. In interpolation for shape preservation, the proposed rational cubic fractal interpolation function provides a simple but effective approach. The nature of shape preservation of the proposed rational cubic fractal interpolation function makes them valuable in the field of data visualization, as it is crucial to maintain the original data shape in data visualization. Furthermore, we discussed the upper bound of error and explored the mathematical framework to ensure the convergence of RCFIF. Shape parameters and scaling factors are constraints to obtain the desired shape-preserving properties. We further generalized the proposed RCFIF by introducing the concept of signature, giving its construction in the form of a zipper-rational cubic fractal interpolation function (ZRCFIF). The positivity conditions for the rational cubic fractal interpolation function and zipper-rational cubic fractal interpolation function are found, which required a detailed analysis of the conditions where constraints on shape parameters and scaling factor lead to the desired shape-preserving properties. In the field of shape preservation, the proposed rational cubic fractal interpolation function and zipper fractal interpolation function both represent significant advancement by offering a strong tool for data visualization. [ABSTRACT FROM AUTHOR]

Many physical processes feature random telegraph signals, e.g., a time signal c (t) that randomly switches between two values over time. The present study focuses on the class of telegraphic processes for which the transition rates are formulated by using fractal-like expressions. By considering various restrictive hypotheses regarding the statistics of the waiting times, the present analysis provides the corresponding expressions of the unconditional and conditional probabilities, the mean waiting times, the mean phase duration, the autocorrelation function and the associated integral time scale, the spectral density, and the mean switching frequency. To assess the relevance of the various hypotheses, synthetically generated signals were constructed and used as references to evaluate the predictive quality of the theoretically derived expressions. The best predictions were obtained by considering that the waiting times probability density functions were Dirac peaks centered on the corresponding mean values. [ABSTRACT FROM AUTHOR]

The article presents a theoretical analysis of the extramural polemic between Slavoj Žižek and Evald Ilyenkov, undertaken in the context of the search for the foundational underpinnings of the two philosophers' perspectives on the limit-logical definitions of being. It shows how this apparently "abstract" search grows out of the socio-historical circumstances of the thinkers' lives, which are inscribed in the dramatic conditions of existence of the political events of the twentieth century. The active life-political position of the follower of Marx's ideas, figuratively expressed in the text by Lenin's term "tactics of social democracy" (Lenin 1962), is justified by one or another cognitive position: the unified attitude "not to explain but to transform the world" breaks down into various "tactics" precisely in the attempt to solve the problem of radical negativity (as Žižek formulates it). This is expressed in the division of Marxism into "Western" and "Eastern". This article analyzes the legitimacy of such a division and shows the conditions for a disintegration of the divide. The relation of Ilyenkov and Žižek to Hegel's works turns out to be the key to understanding this division, and consequently to the essential difference in socio-political attitudes and "tactics", of which they are creative representatives. The analysis leads to the formulation of the "germ cell" of disagreement between Ilyenkov and Žižek—the problem of the universal—which unfolds in the difference between the thinkers' positions on certain theoretical points. The limitation of Ilyenkov's position, established under the fire of Žižek's criticism, is removed, according to the author, by the development of a new category of "fractality", which acts as a counterpart to the main dialectical category of "totality" and provides a concrete (in the Hegelian sense) solution to the problem of radical negativity in the spirit of the classical philosophical tradition. [ABSTRACT FROM AUTHOR]

The dynamics of thin-walled parts are highly affected by the clamping conditions. Clamping stiffness is a function of c lamping force and surface roughness profiles of the clamp and part. Since the surface profiles cannot be altered, estimating clamping stiffness as a function of the clamping force is essential to simulate vibrations of the machined thin-walled parts. This paper presents the modeling of clamping stiffness as a function of the applied clamping force and material properties. Surface profile parameters are estimated from the identified contact stiffnesses evaluated using the Finite Element (FE) model. The contact stiffnesses are either predicted directly from the proposed mechanics model of the part or estimated from the Fractal surface parameters. It is shown that an average clamping stiffness can be predicted from the Fractal surface parameters, or directly and more accurately from the static model of the clamped part. [ABSTRACT FROM AUTHOR]

A fractal, a self-similar organic or geometric pattern that repeats at varying scales, is one of the most compelling characteristics found in nature. Previous studies on fractal patterns have demonstrated consistent trends in potential psychological benefits, such as stress reduction. However, we fall short of understanding one of the essential properties of fractals found in nature, i.e., the three-dimensionality of their appearance. In this study, we aimed at understanding the role of the three-dimensionalization of fractal patterns in spatial structures on human subjective perceptual experience. Two hundred seventy three-dimensional spatial prototype models were created for this study, spanning two dimensions: (1) the application of spatial depth (shallow; medium; deep) and (2) fractal complexity (low; medium; high). The participants rated each space on six psychological dimensions (bad–good; stressful–relaxing; ugly–beautiful; boring–interesting; leave–enter; ignore–explore). Significant effects of the application depth of fractals were observed primarily for "boring-interesting", "ignore-explore", and "leave-enter" dimensions and were primarily manifested within spaces with medium and high D-values. The results suggest that spatial depth plays a significant role in individuals' experiences of fractal spaces, arguably by making the space more engaging and interesting. [ABSTRACT FROM AUTHOR]

Subject and Purpose. At the beginning of the 21st century, a fundamentally new scientific direction was formed in radiophysics — fractal radiophysics. The subject of this review is the main practical ideas of "fractalization" in radio physics. The purpose of the work is a systematic presentation of the main results of the practical application of fractal theory in radiophysics, as well as a detailed analysis of the originality, novelty, and practical value of the obtained results. Methods and Methodology. The results of using the fractal approach in various fields of modern radiophysics are presented. The results of the application of fractal and multifractal analysis methods for various radiophysical objects, phenomena and processes are considered. The main features, advantages and disadvantages of this approach, as well as existing problems, are highlighted. Results. The main practical results of applying the fractal approach in radio physics are considered. The main features of solving the problem of radio wave propagation in fractal media are also discussed. The usage of fractals in applied electrodynamics is demonstrated by the example of fractal antennas, resonators, filters, capacitors, transistors, diplexers, frequency-selective surfaces and metamaterials, etc. Fractals in semiconductor and vacuum electronics are described by the example of the fractal structures of the cathode spot and the cathodes themselves, fractal electrodes and diffusers, as well as the avalanche breakdown of the p-n junction. The features of the application of fractal ideas in statistical and nonlinear radiophysics are considered. To illustrate the "fractalization" of physics and radiophysics of the geospace, the fractal processes that occur during earthquakes, in the atmosphere, ionosphere and magnetosphere, etc., are used. Conclusions. The main directions of practical application of the theory of fractals in modern radiophysics are analyzed, as well as the features of the new results obtained, which reflect one of the main properties of the surrounding world — its fractality, are discussed.

Abstract 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.

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. [ABSTRACT FROM AUTHOR]

The paper presents a novel fractal antenna in millimetre wavebands for 5G applications involving the fusion of Koch and Sierpinski methods. A four-element MIMO antenna is designed using a unique fractal structure. The proposed four-element MIMO antenna operates from 27.55 GHz to 28.6 GHz with a resonant frequency at 28 GHz and the obtained mutual coupling between the MIMO elements is well below −25 dB. The performance of the antenna is characterised in MIMO environment by studying the important MIMO parameters like Envelope Correlation Coefficient (ECC), Channel Capacity Loss (CCL), Mean Effective Gain (MEG) and Total Active Reflection Coefficient (TARC). The proposed antenna is highly suitable for 5G applications in the mmWave spectrum owing to its stable and directional radiation patterns on both the E and H planes. A prototype of the proposed model is fabricated and measured results are obtained with good matching to the simulated results. [ABSTRACT FROM AUTHOR]

Due to the recent expansion in the generations of the communications systems, it is utmost priority to transmit a large amount of data over a wideband frequency spectrum. For this single ultra-wideband (UWB) antennas are the prime choice as compared to the multiple narrow band antennas. A modified pentagonal fractal patch antenna with a modified ground plane covering ultra-wideband has been proposed. The antenna has a compact size of 25 mm × 25 mm × 1.6 mm with peak gain of 2.2 dB. The UWB coverage of the design is achieved by implementing modified co-planar ground, modified fractal geometry and coplanar feed. The proposed design possesses the significant resonance and radiation performance with very compact size on low-cost substrate while covering the whole UWB. Finally, the simulated resonating and radiation characteristics have been validated with the measured characteristics of the fabricated prototype and the results are quite promising. [ABSTRACT FROM AUTHOR]

Great attention has been focused on uncovering the physics of seismic wave attenuation in rocks in the past few decades. However, the contribution of different attenuation mechanisms on attenuation is not completely clear in coal. We use the fractal viscoelastic model to describe the P-wave attenuation in coal, and the model has a good approximation to the constant-Q model when choosing lower fractional order α . We experimentally measured attenuation in dry and water-saturated coal samples in the frequency range of 10–250 Hz, at room temperature, and approximately room pressure. Attenuation in the dry sample is frequency independent and the fractal viscoelastic model curves fit well with the data when α = 0.056 . For the partial water saturation cases, attenuation is frequency dependent, and the simple viscoelastic attenuation theory cannot describe the strong attenuation in seismic band; when water saturation is high ( ≥ 80 % ), we need wave-induced fluid flow mechanism to explain the high Q - 1 values. The final contribution of viscoelasticity to attenuation is about 63%, while the final contribution of wave-induced fluid flow mechanism to attenuation is about 37% in the test. [ABSTRACT FROM AUTHOR]

Interpolation techniques can be used to determine the approximate value of a parameter if it is known that two values are bound to a certain interval. Interpolation can be done numerically or fractal. The fractal interpolation value is influenced by the vertical scale factor and the fractal interpolation function (FIF). This research introduces fractal interpolation technique with FIF which is constructed from Sierspinski triangles. As an example of application, the interpolation technique is applied to determine the approximate value of the rice demand parameter in the inventory model. The accuracy of the interpolation results is determined using the mean absolute percentage error (MAPE). The number of triangles obtained and the interpolation values for each successive iteration are 3n and 3n+1. MAPE values from 6 to 9 iteration were 24.603%, 24.603%, 23.858%, 23.772% respectively. There is a decrease in the value of MAPE, this indicates an increase in the value of the accuracy of the interpolation results. It can be concluded that the MAPE value is also influenced by the number of iterations of the interpolation technique. [ABSTRACT FROM AUTHOR]

A fractal, a self-similar organic or geometric pattern that repeats at varying scales, is one of the most compelling characteristics found in nature. Previous studies on fractal patterns have demonstrated consistent trends in potential psychological benefits, such as stress reduction. However, we fall short of understanding one of the essential properties of fractals found in nature, i.e., the three-dimensionality of their appearance. In this study, we aimed at understanding the role of the three-dimensionalization of fractal patterns in spatial structures on human subjective perceptual experience. Two hundred seventy three-dimensional spatial prototype models were created for this study, spanning two dimensions: (1) the application of spatial depth (shallow; medium; deep) and (2) fractal complexity (low; medium; high). The participants rated each space on six psychological dimensions (bad–good; stressful–relaxing; ugly–beautiful; boring–interesting; leave–enter; ignore–explore). Significant effects of the application depth of fractals were observed primarily for “boring-interesting”, “ignore-explore”, and “leave-enter” dimensions and were primarily manifested within spaces with medium and high D-values. The results suggest that spatial depth plays a significant role in individuals’ experiences of fractal spaces, arguably by making the space more engaging and interesting.

The Mandelbrot and Julia sets are generated through iterative mathematical functions applied to points in the complex plane. These operations enable the detailed and intricate patterns characteristic of these fractals, allowing for modifications and zooming to explore different regions of the sets. TThe Mojokerto Surya Majapahit batik motif is a motif that has eight corners. One way to develop a Mojokerto batik motif that is similar to Surya Majapahit is by applying the science of fractal geometry. Fractal geometry studies a fractal pattern that can change shape according to input parameters and the number of iterations carried out. This research was conducted to determine the application of Mandelbrot and Julia’s fractal geometry using geometric transformations to obtain batik motif variants that is similar to Surya Majapahit. There are three steps in forming this motif variant. First, generating Mandelbrot fractals and Julia fractals. Second, the patterns generated by Mandelbrot and Julia are applied using geometric transformations. The geometric transformations that will be used are rotation, dilation, and translation. Finally, these patterns will be modified by combining patterns implementing logic operations using Python computer applications. The results of this research obtained four variants of batik motif that is similar to Surya Majapahit. The difference in each variant lies in the order of transformation. Variant 1 and variant 3 can be carried out by changing the sequence of geometric transformations, namely rotation, translation and dilationVariant 1 is obtained by applying rotation, dilation, and translation to the Mandelbrot and Julia pattern. Variant 2 is obtained with the Mandelbrot pattern applying rotation, dilation with two different scales, and translation, while the Julia pattern only applied rotation and translation. Variant 3 is obtained by applying rotation, dilation and translation to the Mandelbrot and Julia pattern. Variant 4 is obtained with the Mandelbrot pattern applied by rotation, dilation with three different scales, and translation, while the Julia pattern was applied only by rotation and translation. Meanwhile variants 2 and 4 apply different rotations, dilation scales, namely 0.451 and 0.318, and translation to the Mandelbrot pattern.

Abstract 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.

Abstract 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). 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

The manuscript investigates the utilization of Koch curves and hexagonal ring-shaped geometry for an ultra-wideband fractal antenna, achieved through a combination of DGS, parasitic elements, and EC-SRR. The antenna's properties are investigated without and with DGS, Parasitic element, and EC-SRR in the hexagonal ring-shaped geometries for broader band characteristics. Simulation results show that the antenna designed without DGS resonates at five distinct frequencies, while with DGS, Parasitic element, and SRR, it resonates at six frequencies. An enhanced bandwidth of 10.42 GHz (99.43%) is revealed in the final antenna geometry, and the proposed antenna resonates at six frequencies, 3.4, 5.8, 8.5, 11, 14.2, and 15 GHz, with reflection coefficients of − 24.33, − 38.10, − 28.35, − 27.39, − 32.32, and − 15.93 dB, respectively. Combining a defected ground structure, parasitic element, and EC-SRR increases frequency bands and enhances the BW and reflection coefficient. With an overall dimension of 30 mm × 24 mm, the proposed antenna is suitable for wireless applications in the frequency ranges of 2.40–3.89 GHz and 5.33–15.75 GHz. The proposed antenna is fabricated, and the results are measured. It is found that simulated and measured results are in good agreement with each other. [ABSTRACT FROM AUTHOR]

In this paper, an analytical approach has been developed for electromagnetic field enhancement in fractal nanostructure under the quasi-static limit. A metallic fractal embedded in an unbounded, isotropic, and lossless chiral medium has been treated under this approach. In addition, the field enhancement is also noted by imposing surface plasmon resonance condition. To achieve the desired objective, Maxwell divergence equations are considered and written in an appropriate form by mean of fractional calculus. [ABSTRACT FROM AUTHOR]

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 (X2 = 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. [ABSTRACT FROM AUTHOR]

We propose and theoretically substantiate an algorithm for conducting a generalized Chaos game with an arbitrary jump on finite convex polygons of the extended hyperbolic plane whose components in the Cayley–Klein projective model are the Lobachevsky plane and its ideal domain. In particular, the defining identities for a point dividing an elliptic, hyperbolic, or parabolic segment in a given ratio are proved, and formulas for calculating the coordinates of such a point at a canonical frame of the first type are obtained. The results of a generalized Chaos game conducted using the advanced software package pyv are presented. [ABSTRACT FROM AUTHOR]

Most information systems, especially on the Internet, have a distributed architecture with remote access and an insecure communication channel. In such systems, the tasks of permanent authorization mean implementing time intervals of user work without re-authentication are especially actual. The problem is that repeatedly sending a password increases the likelihood of it corruption. One solution is to use zero-knowledge protocols. In these protocols, passwords are not transmitted over the channel but are included in the algorithms as parameters. However, the computational complexity, as well as the finite number of passwords, limit their use, ensuring the relevance of further research. Focusing on object of the exchange protocols security, the use of algebraic fractal sets has been proposed as a potentially infinite source of data for passwords. In this work, algorithms were developed, implemented, and tested, which proved the higher reliability of fractal protocols in comparison with the reference generator of random bits (with an error probability of 0.5). It was also noted that the calculation operations have an insignificant influence on the overall time complexity of the exchange protocol as a whole. Practical recommendations for the use of fractals with a Hausdorff dimensionally of about 1.6 on the boundary of the Mandelbrot set are given. The paper also highlights the advantages of including color information in fractal sets, which gives about 3 times improving of confidential security indicators of communication protocol. The proposed algorithms do not require specialized software and can be implemented in the majority of network information systems as an additional module. [ABSTRACT FROM AUTHOR]

Earthquakes in the Himalayan region predominantly exhibit tectonic characteristics, stemming from fault slippage caused by the ongoing collision between the Indian plate and the Eurasian plate. The western Nepal and adjoining regions (28.5°N to 31.0°N and 78°E to 82.96°E) have hosted the damaging earthquake namely, the 1905 Kangra earthquake, the 1991 Uttarkashi earthquake, and the 1999 Chamoli earthquake in the past and need to understand the recent seismic activity of the region. In this study, we quantified seismic activity in the region from the fractal approach. The key idea of fractal method is based on the self-similarities of objects at different scales. Twelve windows of 100 seismic events with 25-event shifts were analyzed to observe variations in b-value and Dc value for the earthquakes (Mb ≥ 4.0) transpiring between 1964 and 2021. The three consecutive windows from 1991 to 2006 demonstrate a variation in b-value from 0.80 ± 0.07 to 0.90 ± 0.09 and a decrement in Dc value from 1.24 ± 0.03 to 1.20 ± 0.03, indicating a high clustering of earthquakes during the occurrence of major earthquakes, illustrated by the instances like the 1991 Uttarkashi earthquake, the 1999 Chamoli earthquake, and the magnitude 6.1 Mb earthquake in 2004. In addition, the study shows the negative correlation between b-value and Dc value for spatial and temporal distribution of earthquakes in the study region. This study demonstrates the use of b-value and Dc value for identifying seismicity patterns prior to major earthquakes. Continuous monitoring of these seismic patterns could be valuable for assessing the potential seismic hazard and risk throughout the entire Himalayan region. [ABSTRACT FROM AUTHOR]

3D digital models can facilitate the understanding of micro- and nanoscale pore structures and enhance the permeability prediction accuracy of geological materials. However, the reconstruction of digital models using the conventional Markov chain Monte Carlo (MCMC) algorithm cannot well reflect the microstructure of the heterogenous media and needs to be improved. In this study, referring to the box-counting method (BCM) of fractal theory, the conventional probability distribution function was extended to different scale probability functions, and the concept of value paths was introduced to control the reconstruction quality. Subsequently, a comparison to the conventional MCMC algorithm was conducted based on the statistical function and the pore fractal dimension to verify the effectiveness of the improved algorithm. Finally, the reconstruction model was applied in finite element simulation to predict the permeability of soft soil. The verification results showed that the improved MCMC algorithm can well realize the reconstruction of heterogeneous porous media since the squared correlation coefficients of statistical functions of the 3D reconstruction and the original image are above 0.98, and the pore fractal dimension of reconstructions using the improved MCMC was closer to the original image than that using the conventional MCMC. Furthermore, in permeability prediction, permeability simulations using images reconstructed with an improved MCMC algorithm are closer to the experimental values, with a maximum prediction error of 1.87 times (that of MCMC was 4.21 times) the corresponding experimental value. [ABSTRACT FROM AUTHOR]

Autism spectrum disorder (ASD) is a neurological condition characterized by impaired functional connectivity (FC) networks in the brain. There are several brain networks associated with ASD that have been studied for ASD diagnosis, but the results are inconsistent. A functional magnetic resonance imaging (fMRI) study was performed to address this gap by comparing brain networks among autistic individuals and individuals with typical development (TD) using data from the ABIDE-I and ABIDE-II databases. Blood oxygen level-dependent (BOLD) time series were extracted from 236 regions of interest (ROI) in fMRI data using three atlases: Gordon's, Harvard Oxford, and Diedrichsen. Consequently, 27,730 nonlinear features are extracted from FC matrices, including fractals, non-fractals, and Pearson correlation coefficients (PCC). A parametric and nonparametric classifier was used to analyze the top 0.1%, 0.3%, 0.5%, 0.7%, 1%, 2%, and 3% of features based on the XGBoost feature ranking algorithm. In the study, we found that non-fractal brain FC measures can accurately identify ASD and TD more effectively than fractal and PCC measures. Classifiers performed well, with FC features at the top 0.3%. The classification model at OHSU was more accurate than the model at other sites. There was 100% accuracy at a single site and 96.17% accuracy at all sites using a multilayer perceptron classifier with non-fractal features. The classifier model shows that Cingulo-Parietal Task Control (13.6%), Retro-Splenial Temporal (RST) (13.3%), and Salience (11.6%) are significant contributors. The optimal performance was observed in features derived from networks such as RST and default (4 connections), auditory and Fronto-Parietal Task Control (3 connections), Cingulo-Opercular Task Control (COTC), and ventral attention (3 connections) within COTC (3 connections), visual and COTC (3 connections), and cerebellum and COTC (3 connections). Based on the results, non-fractal-based FC has value in distinguishing ASD from TD using resting-state fMRI. [ABSTRACT FROM AUTHOR]

In this paper, we consider a new class of generalized enriched cyclic contraction and establish a related fixed point theorem in the setting of a Banach space. As an application to the fractals, we develop a new iterated function system (IFS) consisting of enriched cyclic (bn, ...n(t), βn(t))-contractions. [ABSTRACT FROM AUTHOR]

Research has demonstrated the significant influence of surface roughness on electrical conductivity and streaming potential. This article presents a model for the flow potential in a porous medium with rough fractures, based on fractal theory and representative elementary volume theory. Expressions for the model's permeability, conductivity, and coupling coefficient between flow and potential are derived. The results indicate that both the relative roughness and structural parameters of the model have certain effects on the conductivity and coupling coefficient. By comparing experimental data from previous literature with the predicted values from the model, the correctness and effectiveness of the model are validated. [ABSTRACT FROM AUTHOR]

Predicting the invasion depth of superficial esophageal neoplasms (SENs) is crucial for an indication toward endoscopic treatment. We aimed to develop imaging biomarkers to predict the invasion depth of SENs using the intrapapillary capillary loop (IPCL) patterns. Texture and fractal analyses were performed on IPCL demarcations. Logistic regression models were built to distinguish narrow‐band images (NBIs) of T1b from T1a and high‐grade dysplasia (HGD). Classification performances of a base model composed of the age, sex, height, and body mass index of the patient, and a morphometric model comprising the texture and fractal metrics along with the base model parameters were compared. NBIs of 39 patients including T staging of 6 HGD, 22 T1a, and 11 T1b were analyzed. In the logistic regression by a multivariable generalized linear model classifying histological depths, only texture entropy was significantly and positively associated with the invasion depth. Lower texture entropy of IPCL demarcations was significantly associated with diagnoses of T1b (odds ratio: 0.144, 95% confidence interval: 0.019–0.687) in comparison to the stratum with higher texture entropy. The performance of the morphometric model represented by areas under the receiver operating curves (0.795) was better than that of the base model (0.562). We suggest morphometric analyses, particularly texture entropy, have the potential as image biomarkers to aid in the prediction of SEN invasion depth using IPCL patterns. [ABSTRACT FROM AUTHOR]

This paper introduces hybrid models designed to analyze daily and weekly bitcoin return spanning the periods from 18 July 2010 to 28 December 2023 for daily data, and from 18 July 2010 to 24 December 2023 for weekly data. Firstly, the fractal and chaotic structure of the selected variables was explored. Asymmetric Cantor set, Boundary of the Dragon curve, Julia set z2 −1, Boundary of the Lévy C curve, von Koch curve, and Brownian function (Wiener process) tests were applied. The R/S and Mandelbrot–Wallis tests confirmed long-term dependence and fractionality. The largest Lyapunov test, the Rosenstein, Collins and DeLuca, and Kantz methods of Lyapunov exponents, and the HCT and Shannon entropy tests tracked by the Kolmogorov–Sinai (KS) complexity test determined the evidence of chaos, entropy, and complexity. The BDS test of independence test approved nonlinearity, and the TeraesvirtaNW and WhiteNW tests, the Tsay test for nonlinearity, the LR test for threshold nonlinearity, and White's test and Engle test confirmed nonlinearity and heteroskedasticity, in addition to fractionality and chaos. In the second stage, the standard ARFIMA method was applied, and its results were compared to the LieNLS and LieOLS methods. The results showed that, under conditions of chaos, entropy, and complexity, the ARFIMA method did not yield successful results. Both baseline models, LieNLS and LieOLS, are enhanced by integrating them with deep learning methods. The models, LieLSTMOLS and LieLSTMNLS, leverage manifold-based approaches, opting for matrix representations over traditional differential operator representations of Lie algebras were employed. The parameters and coefficients obtained from LieNLS and LieOLS, and the LieLSTMOLS and LieLSTMNLS methods were compared. And the forecasting capabilities of these hybrid models, particularly LieLSTMOLS and LieLSTMNLS, were compared with those of the main models. The in-sample and out-of-sample analyses demonstrated that the LieLSTMOLS and LieLSTMNLS methods outperform the others in terms of MAE and RMSE, thereby offering a more reliable means of assessing the selected data. Our study underscores the importance of employing the LieLSTM method for analyzing the dynamics of bitcoin. Our findings have significant implications for investors, traders, and policymakers. [ABSTRACT FROM AUTHOR]

The novelty of this work is that it is the first to introduce complex-valued suprametric spaces and apply it to Fractal Generation and mixed Volterra–Fredholm Integral Equations. In the realm of fuzzy logic, complex-valued suprametric spaces provide a robust framework for quantifying the similarity between fuzzy sets; for instance, utilizing a complex-valued suprametric approach, we compared the similarity between fuzzy sets represented by complex-valued feature vectors, yielding quantitative measures of their relationships. Thereafter, we establish related fixed point results and their applications in algorithmic and numerical contexts. The study then delves into the generation of fractals, exemplified by the Barnsley Fern fractal, utilizing sequences of affine transformations within complex-valued suprametric spaces. Moreover, this article presents two algorithms for soft computing and fractal generation. The first algorithm uses complex-valued suprametric similarity for fuzzy clustering, iteratively assigning fuzzy sets to clusters based on similarity and updating cluster centers until convergence. The distinctive pattern of the Barnsley Fern fractal is produced by the second algorithm's repetitive affine transformations, which are chosen at random. These techniques demonstrate how well complex numbers cluster and how simple procedures can create complicated fractals. Moving beyond fractal generation, the paper addresses the solution of mixed Volterra–Fredholm integral equations in the complex plane using our results, demonstrating numerical illustrations of complex-valued integral equations. [ABSTRACT FROM AUTHOR]