Fractals

The complexity of spontaneous cerebral blood volume (CBV) fluctuations can emerge from random, fractal, or chaotic processes. Our aims were to define the contribution of these patterns to the observed complexity and to evaluate the effect of age and gender on it. The total hemoglobin content as the measure of CBV was monitored by near-infrared spectroscopy on volunteers (men n = 19, age = 20 to 78 years; women n = 23, age = 21 to 79 years). Random and fractal patterns were distinguished by the spectral index ( β). Chaos was identified by surrogate analysis of the correlation dimension (a static chaotic parameter, the dimension of the correlation integral) and the largest Lyapunov exponent (a dynamic chaotic parameter, the rate of exponential divergence of the system states from a perturbed initial condition over the chaotic attractor). In spontaneous CBV fluctuations, both fast random and slow fractal dynamics are present separately in their spectra by a cutoff frequency, f′. Below ...

Herein, a spectral scheme is implemented and analyzed for numerically handling general Volterra–Fredholm integral equations (VFIEs), for this purpose, the linearly independent Fibonacci polynomials are utilized as basis functions for the solution, then the spectral collocation process is used to transform the integral equation into a system of algebraic equations with undetermined coefficients. The error, convergence and stability analyses of the scheme are discussed in-depth, some numerical examples are exhibited to ensure the applicability, efficiency and accuracy of the solver.

Both nonlinear and fractal properties of beat-to-beat R-R interval variability signal (RRV) of freely moving lizards ( Gallotia galloti) were studied in baseline and under autonomic nervous system blockade. Nonlinear techniques allowed us to study the complexity, chaotic behavior, nonlinearity, stationarity, and regularity over time of RRV. Scaling behavior of RRV was studied by means of fractal techniques. The autonomic nervous system blockers used were atropine, propranolol, prazosin, and yohimbine. The nature of RRV was linear in baseline and under β-, α1- and α2-adrenoceptor blockades. Atropine changed the linear nature of RRV to nonlinear and increased its stationarity, regularity and fractality. Propranolol increased the complexity and chaotic behavior, and decreased the stationarity, regularity, and fractality of RRV. Both prazosin and yohimbine did not change any of the nonlinear and fractal properties of RRV. It is suggested that 1) the use of both nonlinear and fractal ana...

Artificial Neural Network (ANN) is a supervised learning nonlinear complex model. This characteristic enables ANN to be used in nonlinear system modeling and classification applications. This research work proposed a technique called Wavelet Neural Network (WNN), and in the hidden layers of WNN, Morlet and Mexican are used as an activation function. During the processing, the WNN gets stuck in the local minimum causing slow convergence. For evaluating such kinds of problems, numerous algorithms have been tried and used. Consequently, this proposed research work used a novel meta-heuristic search technique called Accelerated Particle Swarm Optimization (APSO) algorithm combined with the WNN. Due to the effective convergence and fast searching toward an optimal solution, the APSO algorithm is used. In the proposed APSOWNN algorithm, APSO searches for the best sub-search solution. In conclusion, this model is assessed on the basis of total of three different datasets like the 4-bit OR,...

يهدف البحث إلى تطبيق نظام التعليم الهجين ومدي فاعليته في رفع مهارات الطالبات بمادة التفصيل والحياکة في ظل جائحة کورونا. حيث عانا أکثر من مليار ونصف طالب وطالبة من جميع الأعمار وتأثرت طريقة التعليم حول العالم بسبب جائحة کورونا التي جعلت التعليم عن بعد خيارا لا مفر منه. فأعلنت وزارة التعليم العالي، خطة تطبيق نظام التعليم الهجين، حيث تعتمد على الدمج بين التعلم وجها لوجه والتعلم عن بعد. وهنا قام فريق البحث ، على إنشاء مجموعه على (الواتس آب) و إعداد قناة يوتيوب تعليمية عرض من خلالها البرنامج التعليمي على طالبات الفرقة الثانية قسم التربوي لتطبيق التعليم الهجين لمادة التفصيل و الحياکة وقد توصلت نتائج الدراسة إلى زيادة التحصيل المعرفي للمجموعة التجريبية، حيث أظهرت النتائج أن المعلومات المقدمة بواسطة البرنامج التعليمي من خلال شبکات التواصل الإجتماعي تکون أسهل في فهمها وتحصيلها ومن ثم يسهل مراجعتها، مما أدى الى رفع مستوى الأداء المهارى لأفراد المجموعة التجريبية عينة البحث ويسر على الطالبات (عينة البحث) تنفيذ مهارات التفصيل .

We study random recursive constructions with finite "memory" in complete metric spaces and the Hausdorff dimension of the generated random fractals. With each such construction and any positive number β we associate a linear operator V (β) in a finite dimensional space. We prove that under some conditions on the random construction the Hausdorff dimension of the fractal coincides with the value of the parameter β for which the spectral radius of V (β) equals 1.

In this paper, we use the $\tilde{q}$-homotopy analysis transform method ($\tilde{q}$-HATM) to investigate the explicit solutions of the Kundu-Eckhaus equation and the massive Thirring model. Kundu-Eckhaus equation is a nonlinear partial differential equation found in quantum field theory, weakly nonlinear dispersive water waves, and nonlinear optics, as well as massive Thirring model, an exactly solvable quantum field theory that defines the self-interactions of a Dirac field in $(1+1)$ dimensions. The presented method combines the Yang transform methodology with the $\tilde{q}$-homotopy analysis technique and the fractional derivative described by the Caputo-Fabrizio (CF) operator in an intriguing way. The fixed point postulate is addressed in an attempt to illustrate that the resulting solution for the presented fractional order framework exists and is unique. We assess the predicted framework in the context of fractional order reinforcement and exhibit the performance of the pro...

Abstract

In this paper, I predict the existence of a 4-dimensional F-theory fractal universal wavefunction provided that strings exist. I begin by reviewing the basic concepts of F-theory and fractals. I then attempt to show that the wavefunction of a string in 4-dimensional F-theory can be written as a fractal wavefunction. I then show that the fractal dimension of this wavefunction can be made arbitrarily large by taking the limit of the string coupling constant approaching zero. In this limit, the wavefunction becomes smooth and can be described by a single wavefunction. This wavefunction is proposed to be the universal wavefunction of the 4-dimensional universe.

Through the ever-increasing sophistication of modern computer visualization and analysing techniques, a greater and more insightful comprehension has emerged regarding the fertile, self-organizing and regulatory processes lurking within natural phenomena. Throughout these systems, the complex behaviour and emergent properties of matter evolve from initially simple starting conditions that eventually generate unpredictable behaviour. These developments directly relate to the radical re-conceptualisation that occurred in the first decades of the twentieth century regarding the nature of matter, its organization and its constituent parts. They also offer new possibilities towards achieving the integrative design strategies aspired to by key central figures and institutions in the history of modern architecture. The comprehensive design goals of the formative period of modern architecture and design were inspired by a reverence towards nature’s integrative and adaptive capabilities. Ins...

Examining retinal image continuously plays an important role in determining human eye health; with any variation present in this image, it may be resulting from some disease. Therefore, there is a need for computer-aided scanning for retinal image to perform this task automatically and accurately. The fundamental step in this task is identification of the retina elements; optical disk localization is the most important one in this identification. Different optical disc localization algorithms have been suggested, such as an algorithm that would be proposed in this paper. The assumption is based on the fact that optical disc area has rich information, so its entropy value is more significant in this area. The suggested algorithm has recursive steps for testing the entropy of different patches in image; sliding window technique is used to get these patches in a specific way. The results of practical work were obtained using different common data set, which achieved good accuracy in tr...

In this paper, first we equip the automorphism group of the p-ary rooted tree X* with a natural metric and define a family of contractions on Aut(X*). Then, we construct an iterated function system (IFS) whose attractor is the closure of the adding machine group on Aut(X*). Finally, we show that this group is a strong self-similar group in the sense of IFS.

A pesquisa de intervenção aqui relatada, de natureza aplicada e abordagem qualitativa, tem como objetivo analisar as contribuições das adaptações materiais, táteis e descritivas, no processo de ensino e aprendizagem de Geometria Fractal para estudantes com deficiência visual, a fim de possibilitar-lhes acesso ao conteúdo escolar sobre esse tema. Esses sujeitos necessitam de ferramentas adequadas que lhes permitam o acesso e a apropriação dos conhecimentos científicos matemáticos. Dessa forma, desenvolveu-se um estudo prático, em um centro de atendimento educacional especializado na área da deficiência visual, em um município do Centro-Oeste do Paraná, com um grupo de cinco pessoas cegas e com baixa visão, já concluintes do Ensino Médio. A coleta de dados da intervenção pedagógica deu-se por meio de observações, registros em filmes e diário de campo, examinados por meio da análise da conversação. Os resultados indicaram lacunas na formação escolar dos estudantes em relação aos concei...