Browsing by Author "Karaca, Yeliz"

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Citation - WoS: 17
Citation - Scopus: 19
Achieving More Precise Bounds Based on Double and Triple Integral as Proposed by Generalized Proportional Fractional Operators in the Hilfer Sense
(World Scientific Publ Co Pte Ltd, 2021) Rashid, Saima; Karaca, Yeliz; Hammouch, Zakia; Baleanu, Dumitru; Chu, Yu-Ming; Al-Qurashi, Maysaa; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
A user-friendly approach depending on nonlocal kernel has been constituted in this study to model nonlocal behaviors of fractional differential and difference equations, which is known as a generalized proportional fractional operator in the Hilfer sense. It is deemed, for differentiable functions, by a fractional integral operator applied to the derivative of a function having an exponential function in the kernel. This operator generalizes a novel version of Cebysev-type inequality in two and three variables sense and furthers the result of existing literature as a particular case of the Cebysev inequality is discussed. Some novel special cases are also apprehended and compared with existing results. The outcome obtained by this study is very broad in nature and fits in terms of yielding an enormous number of relating results simply by practicing the proportionality indices included therein. Furthermore, the outcome of our study demonstrates that the proposed plans are of significant importance and computationally appealing to deal with comparable sorts of differential equations. Taken together, the results can serve as efficient and robust means for the purpose of investigating specific classes of integrodifferential equations.
Citation - WoS: 28
Citation - Scopus: 28
Advanced Fractional Calculus, Differential Equations and Neural Networks: Analysis, Modeling and Numerical Computations
(Iop Publishing Ltd, 2023) Karaca, Yeliz; Vazquez, Luis; Macias-Diaz, Jorge E.; Baleanu, Dumitru; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
Most physical systems in nature display inherently nonlinear and dynamical properties; hence, it would be difficult for nonlinear equations to be solved merely by analytical methods, which has given rise to the emerging of engrossing phenomena such as bifurcation and chaos. Conjointly, due to nonlinear systems' exhibiting more exotic behavior than harmonic distortion, it becomes compelling to test, classify and interpret the results in an accurate way. For this reason, avoiding preconceived ideas of the way the system is likely to respond is of pivotal importance since this facet would have effect on the type of testing run and processing techniques used in nonlinear systems. Paradigms of nonlinear science may suggest that it is 'the study of every single phenomenon' due to its interdisciplinary nature, which is another challenge encountered and needs to be addressed by generating and designing a systematic mathematical framework where the complexity of natural phenomena hints the requirement of identifying their commonalties and classifying their various manifestations in different nonlinear systems. Studying such common properties, concepts or paradigms can enable one to gain insight into nonlinear problems, their essence and consequences in a broad range of disciplines all forthwith. Fractional differential equations associated with non-local phenomena in physics have arisen as a powerful mathematical tool within a multidisciplinary research framework. Fractional differential equations, as one extension of the fractional calculus theory, can yield the evolution of various systems properly, which reinforces its position in mathematics and science while setting stage for the description of dynamic, complicated and nonlinear events. Through the reflection of the systems' actual properties, fractional calculus manifests unforeseeable and hidden variations, and thus, enables integration and differentiation, with the solutions to be approximated by numerical methods along with modeling and predicting the dynamics of multiphysics, multiscale and physical systems. Neural Networks (NNs), consisting of hidden layers with nonlinear functions that have vector inputs and outputs, are also considerably employed owing to their versatile and efficient characteristics in classification problems as well as their sophisticated neural network architectures, which make them capable of tackling complicated governing partial differential equation problems. Furthermore, partial differential equations are used to provide comprehensive and accurate models for many scientific phenomena owing to the advancements of data gathering and machine learning techniques which have raised opportunities for data-driven identification of governing equations derived from experimentally observed data. Given these considerations, while many problems are solvable and have been solved, efforts are still needed to be able to respond to the remaining open questions in the fields that have a broad range of spectrum ranging from mathematics, physics, biology, virology, epidemiology, chemistry, engineering, social sciences to applied sciences. With a view of different aspects of such questions, our special issue provides a collection of recent research focusing on the advances in the foundational theory, methodology and topical applications of fractals, fractional calculus, fractional differential equations, differential equations (PDEs, ODEs, to name some), delay differential equations (DDEs), chaos, bifurcation, stability, sensitivity, machine learning, quantum machine learning, and so forth in order to expound on advanced fractional calculus, differential equations and neural networks with detailed analyses, models, simulations, data-driven approaches as well as numerical computations.
Citation - WoS: 1
Citation - Scopus: 1
Editorial Special Issue Section on Fractal Ai-Based Analyses and Applications To Complex Systems: Part Ii
(World Scientific Publ Co Pte Ltd, 2022) Karaca, Yeliz; Baleanu, Dumitru; Moonis, Majaz; Muhammad, Khan; Zhang, Yu-Dong; Gervasi, Osvaldo; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
Citation - Scopus: 11
Evolutionary Mathematical Science, Fractional Modeling and Artificial Intelligence of Nonlinear Dynamics in Complex Systems
(Akif AKGUL, 2022) Karaca, Yeliz; Baleanu, Dumitru; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
Complex problems in nonlinear dynamics foreground the critical support of artificial phenomena so that each domain of complex systems can generate applicable answers and solutions to the pressing challenges. This sort of view is capable of serving the needs of different aspects of complexity by minimizing the problems of complexity whose solutions are based on advanced mathematical foundations and analogous algorithmic models consisting of numerous applied aspects of complexity. Evolutionary processes, nonlinearity and all the other dimensions of complexity lie at the pedestal of time, reveal time and occur within time. In the ever-evolving landscape and variations, with causality breaking down, the idea of complexity can be stated to be a part of unifying and revolutionary scientific framework to expound complex systems whose behavior is perplexing to predict and control with the ultimate goal of attaining a global understanding related to many branches of possible states as well as high-dimensional manifolds, while at the same time keeping abreast with actuality along the evolutionary and historical path, which itself, has also been through different critical points on the manifold. In view of these, we put forth the features of complexity of varying phenomena, properties of evolution and adaptation, memory effects, nonlinear dynamic system qualities, the importance of chaos theory and applications of related aspects in this study. In addition, processes of fractional dynamics, differentiation and systems in complex systems as well as the dynamical processes and dynamical systems of fractional order with respect to natural and artificial phenomena are discussed in terms of their mathematical modeling. Fractional calculus and fractional-order calculus approach to provide novel models with fractional-order calculus as employed in machine learning algorithms to be able to attain optimized solutions are also set forth besides the justification of the need to develop analytical and numerical methods. Subsequently, algorithmic complexity and its goal towards ensuring a more effective handling of efficient algorithms in computational sciences is stated with regard to the classification of computational problems. We further point out the neural networks, as descriptive models, for providing the means to gather, store and use experiential knowledge as well as Artificial Neural Networks (ANNs) in relation to their employment for handling experimental data in different complex domains. Furthermore, the importance of generating applicable solutions to problems for various engineering areas, medicine, biology, mathematical science, applied disciplines and data science, among many others, is discussed in detail along with an emphasis on power of predictability, relying on mathematical sciences, with Artificial Intelligence (AI) and machine learning being at the pedestal and intersection with different fields which are characterized by complex, chaotic, nonlinear, dynamic and transient components to validate the significance of optimized approaches both in real systems and in related realms.
Fractal and multifractional-based predictive optimization model for stroke subtypes’ classification
(2020) Karaca, Yeliz; Moonis, Majaz; Baleanu, Dumitru; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
Numerous natural phenomena display repeating self-similar patterns. Fractal is used when a pattern seems to repeat itself. Fractal and multifractal methods have extensive applications in neurosciences in which the prevalence of fractal properties like self-similarity in the brain, equipped with a complex structure, in medical data analysis at various levels of observation is admitted. The methods come to the fore since subtle details are not always detected by physicians, but these are critical particularly in neurological diseases like stroke which may be life-threatening. The aim of this paper is to identify the self-similar, significant and efficient attributes to achieve high classification accuracy rates for stroke subtypes. Accordingly, two approaches were implemented. The first approach is concerned with application of the fractal and multifractal methods on the stroke dataset in order to identify the regular, self-similar, efficient and significant attributes from the dataset, with these steps: a) application of Box-counting dimension generated BC_stroke dataset b) application of Wavelet transform modulus maxima generated WTMM_stroke dataset. The second approach involves the application of Feed Forward Back Propagation (FFBP) for stroke subtype classification with these steps: (i) FFBP algorithm was applied on the stroke dataset, BC_stroke dataset and WTMM_stroke dataset. (ii) Comparative analyses were performed based on accuracy, sensitivity and specificity for the three datasets. The main contribution is that the study has obtained the identification of self-similar, regular and significant attributes from the stroke subtypes datasets by following multifarious and integrated methodology. The study methodology is based on the singularity spectrum which provides a value concerning how fractal a set of points are in the datasets (BC_stroke dataset and WTMM_stroke dataset). The experimental results reveal the applicability, reliability and accuracy of our proposed integrated method. No earlier work exists in the literature with the relevant stroke datasets and the methods employed. Therefore, the study aims at pointing a new direction in the relevant fields concerning the complex dynamic systems and structures which display multifractional nature. © 2020 Elsevier Ltd
Citation - WoS: 20
Citation - Scopus: 29
Fractal and Multifractional-Based Predictive Optimization Model for Stroke Subtypes? Classification
(Pergamon-elsevier Science Ltd, 2020) Moonis, Majaz; Baleanu, Dumitru; Karaca, Yeliz; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
Fractional Order Computing and Modeling with Portending Complex Fit Real-World Data
(2023) Karaca, Yeliz; Rahman, Mati ur; Baleanu, Dumitru; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
Fractional computing models identify the states of different systems with a focus on formulating fractional order compartment models through the consideration of differential equations based on the underlying stochastic processes. Thus, a systematic approach to address and ensure predictive accuracy allows that the model remains physically reasonable at all times, providing a convenient interpretation and feasible design regarding all the parameters of the model. Towards these manifolding processes, this study aims to introduce new concepts of fractional calculus that manifest crossover effects in dynamical models. Piecewise global fractional derivatives in sense of Caputo and Atangana-Baleanu-Caputo (ABC) have been utilized, and they are applied to formulate the Zika Virus (ZV) disease model. To have a predictive analysis of the behavior of the model, the domain is subsequently split into two subintervals and the piecewise behavior is investigated. Afterwards, the fixed point theory of Schauder and Banach is benefited from to prove the existence and uniqueness of at least one solution in both senses for the considered problem. As for the numerical simulations as per the data, Newton interpolation formula has been modified and extended for the considered nonlinear system. Finally, graphical presentations and illustrative examples based on the data for various compartments of the systems have been presented with respect to the applicable real-world data for different fractional orders. Based on the impact of fractional order reducing the abrupt changes, the results obtained from the study demonstrate and also validate that increasing the fractional order brings about a greater crossover effect, which is obvious from the observed data, which is critical for the effective management and control of abrupt changes like infectious diseases, viruses, among many more unexpected phenomena in chaotic, uncertain and transient circumstances.
Citation - Scopus: 1
Fractional Order Computing and Modeling With Portending Complex Fit Real-World Data
(Springer international Publishing Ag, 2023) Rahman, Mati Ur; Baleanu, Dumitru; Karaca, Yeliz; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
Fractional computing models identify the states of different systems with a focus on formulating fractional order compartment models through the consideration of differential equations based on the underlying stochastic processes. Thus, a systematic approach to address and ensure predictive accuracy allows that the model remains physically reasonable at all times, providing a convenient interpretation and feasible design regarding all the parameters of the model. Towards these manifolding processes, this study aims to introduce new concepts of fractional calculus that manifest crossover effects in dynamical models. Piecewise global fractional derivatives in sense of Caputo and Atangana-Baleanu-Caputo (ABC) have been utilized, and they are applied to formulate the Zika Virus (ZV) disease model. To have a predictive analysis of the behavior of the model, the domain is subsequently split into two subintervals and the piecewise behavior is investigated. Afterwards, the fixed point theory of Schauder and Banach is benefited from to prove the existence and uniqueness of at least one solution in both senses for the considered problem. As for the numerical simulations as per the data, Newton interpolation formula has been modified and extended for the considered nonlinear system. Finally, graphical presentations and illustrative examples based on the data for various compartments of the systems have been presented with respect to the applicable real-world data for different fractional orders. Based on the impact of fractional order reducing the abrupt changes, the results obtained from the study demonstrate and also validate that increasing the fractional order brings about a greater crossover effect, which is obvious from the observed data, which is critical for the effective management and control of abrupt changes like infectious diseases, viruses, among many more unexpected phenomena in chaotic, uncertain and transient circumstances.
Citation - WoS: 8
Citation - Scopus: 10
Hidden Markov Model and Multifractal Method-Based Predictive Quantization Complexity Models Vis-A the Differential Prognosis and Differentiation of Multiple Sclerosis' Subgroups
(Elsevier, 2022) Baleanu, Dumitru; Karabudak, Rana; Karaca, Yeliz; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
Hidden Markov Model (HMM) is a stochastic process where implicit or latent stochastic processes can be inferred indirectly through a sequence of observed states. HMM as a mathematical model for uncertain phenomena is applicable for the description and computation of complex dynamical behaviours enabling the mathematical formulation of neural dynamics across spatial and temporal scales. The human brain with its fractal structure demonstrates complex dynamics and fractals in the brain are characterized by irregularity, singularity and self-similarity in terms of form at different observation levels, making detection difficult as observations in real-time occurrences can be time variant, discrete, continuous or noisy. Multiple Sclerosis (MS) is an autoimmune degenerative disease with time and space related dissemination, leading to neuronal apoptosis, coupled with some subtle features that could be overlooked by physicians. This study, through the proposed integrated approach with multi-source complex spatial data, aims to attain accurate prediction, diagnosis and prognosis of MS subgroups by HMM with Viterbi algorithm and Forward-Backward algorithm as the dynamic and efficient products of knowledge-based and Artificial Intelligence (AI)-based systems within the framework of precision medicine. Multifractal Bayesian method (MFM) accordingly applied to identify and eliminate "insignificant "irregularities while maintaining "significant "singularities. An efficient modelling of HMM is proposed to diagnose and predict the course of MS while using MFM method. Unlike the methods employed in previous studies, our proposed integrated novel method encompasses the subsequent approaches based on reliable MS dataset ((X) over cap) collected: (i) MFM method was applied ((X) over cap) to MS dataset to characterize the irregular, self-similar and significant attributes, thus, attributes with "insignificant " irregularities were eliminated and "significant " singularities were maintained. MFM-MS dataset ((X) over cap) was generated. (ii) The continuous values in the MS dataset ((X) over cap) and MFM-MS dataset ((X) over cap) were converted into discrete values through vector quantization method of the HMM (iii) Through transitional matrices, different observation matrices were computed from the both datasets. (v) Computational complexity has been computed for both datasets. (vi) The results of the HMM models based on observation matrices obtained from both datasets were compared. In terms of the integrated HMM model proposed and the MS dataset handled, no earlier work exists in the literature. The experimental results demonstrate the applicability and accuracy of our novel proposed integrated method, HMM and Multifractal (HMM-MFM) method, for the application to the MS dataset (X). Compared with conventional methods, our novel method has achieved more superiority regarding extracting subtle and hidden details, which are significant for distinguishing different dynamic and complex systems including engineering and other related applied sciences. Thus, we have aimed at pointing a new frontier by providing a novel alternative mathematical model to facilitate the critical decision-making, management and prediction processes among the related areas in chaotic, dynamic complex systems with intricate and transient states. (C)2022 Elsevier B.V. All rights reserved.
Citation - Scopus: 2
Multifractional Gaussian Process Based on Self-Similarity Modelling for Ms Subgroups' Clustering With Fuzzy C-Means
(Springer international Publishing Ag, 2020) Baleanu, Dumitru; Karaca, Yeliz; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
Multifractal analysis is a beneficial way to systematically characterize the heterogeneous nature of both theoretical and experimental patterns of fractal. Multifractal analysis tackles the singularity structure of functions or signals locally and globally. While Holder exponent at each point provides the local information, the global information is attained by characterization of the statistical or geometrical distribution of Holder exponents occurring, referred to as multifractal spectrum. This analysis is time-saving while dealing with irregular signals; hence, such analysis is used extensively. Multiple Sclerosis (MS), is an auto-immune disease that is chronic and characterized by the damage to the Central Nervous System (CNS), is a neurological disorder exhibiting dissimilar and irregular attributes varying among patients. In our study, the MS dataset consists of the Expanded Disability Status Scale (EDSS) scores and Magnetic Resonance Imaging (MRI) (taken in different years) of patients diagnosed with MS subgroups (relapsing remitting MS (RRMS), secondary progressive MS (SPMS) and primary progressive MS (PPMS)) while healthy individuals constitute the control group. This study aims to identify similar attributes in homogeneous MS clusters and dissimilar attributes in different MS subgroup clusters. Thus, it has been aimed to demonstrate the applicability and accuracy of the proposed method based on such cluster formation. Within this framework, the approach we propose follows these steps for the classification of the MS dataset. Firstly, Multifractal denoising with Gaussian process is employed for identifying the critical and significant self-similar attributes through the removal of MS dataset noise, by which, mFd MS dataset is generated. As another step, Fuzzy C-means algorithm is applied to the MS dataset for the classification purposes of both datasets. Based on the experimental results derived within the scheme of the applicable and efficient proposed method, it is shown that mFd MS dataset yielded a higher accuracy rate since the critical and significant self-similar attributes were identified in the process. This study can provide future direction in different fields such as medicine, natural sciences and engineering as a result of the model proposed and the application of alternative mathematical models. As obtained based on the model, the experimental results of the study confirm the efficiency, reliability and applicability of the proposed method. Thus, it is hoped that the derived results based on the thorough analyses and algorithmic applications will be assisting in terms of guidance for the related studies in the future.
NEW MULTI-FUNCTIONAL APPROACH for κ TH-ORDER DIFFERENTIABILITY GOVERNED by FRACTIONAL CALCULUS VIA APPROXIMATELY GENERALIZED (ψ, ?) -CONVEX FUNCTIONS in HILBERT SPACE
(2021) Wang, Miao-Kun; Rashid, Saima; Karaca, Yeliz; Baleanu, Dumitru; Chu, Yu-Ming; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
This work addresses several novel classes of convex function involving arbitrary non-negative function, which is known as approximately generalized (ψ, ?)-convex and approximately ψ-quasiconvex function, with respect to Raina's function, which are elaborated in Hilbert space. To ensure the feasibility of the proposed concept and with the discussion of special cases, it is presented that these classes generate other classes of generalized (ψ, ?)-convex functions such as higher-order strongly (HOS) generalized (ψ, ?)-convex functions and HOS generalized ψ-quasiconvex function. The core of the proposed method is a newly developed Simpson's type of identity in the settings of Riemann-Liouville fractional integral operator. Based on the HOS generalized (ψ, ?)-convex function representation, we established several theorems and related novel consequences. The presented results demonstrate better performance for HOS generalized ψ-quasiconvex functions where we can generate several other novel classes for convex functions that exist in the relative literature. Accordingly, the assortment in this study aims at presenting a direction in the related fields. © 2021 The Author(s).
Citation - WoS: 13
Citation - Scopus: 14
New Multi-Functional Approach for Κth-Order Differentiability Governed by Fractional Calculus Via Approximately Generalized (Ψ, (h)over-Bar) Functions in Hilbert Space
(World Scientific Publ Co Pte Ltd, 2021) Wang, Miao-Kun; Rashid, Saima; Karaca, Yeliz; Baleanu, Dumitru; Chu, Yu-Ming; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
This work addresses several novel classes of convex function involving arbitrary non-negative function, which is known as approximately generalized (psi, PLANCK CONSTANT OVER TWO PI)-convex and approximately psi-quasiconvex function, with respect to Raina's function, which are elaborated in Hilbert space. To ensure the feasibility of the proposed concept and with the discussion of special cases, it is presented that these classes generate other classes of generalized (psi, PLANCK CONSTANT OVER TWO PI)-convex functions such as higher-order strongly (HOS) generalized (psi, PLANCK CONSTANT OVER TWO PI)-convex functions and HOS generalized psi-quasiconvex function. The core of the proposed method is a newly developed Simpson's type of identity in the settings of Riemann-Liouville fractional integral operator. Based on the HOS generalized (psi, PLANCK CONSTANT OVER TWO PI)-convex function representation, we established several theorems and related novel consequences. The presented results demonstrate better performance for HOS generalized psi-quasiconvex functions where we can generate several other novel classes for convex functions that exist in the relative literature. Accordingly, the assortment in this study aims at presenting a direction in the related fields.
Citation - WoS: 32
Citation - Scopus: 39
A Novel R/S Fractal Analysis and Wavelet Entropy Characterization Approach for Robust Forecasting Based on Self-Similar Time Series Modeling
(World Scientific Publ Co Pte Ltd, 2020) Baleanu, Dumitru; Karaca, Yeliz; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
It has become vital to effectively characterize the self-similar and regular patterns in time series marked by short-term and long-term memory in various fields in the ever-changing and complex global landscape. Within this framework, attempting to find solutions with adaptive mathematical models emerges as a major endeavor in economics whose complex systems and structures are generally volatile, vulnerable and vague. Thus, analysis of the dynamics of occurrence of time section accurately, efficiently and timely is at the forefront to perform forecasting of volatile states of an economic environment which is a complex system in itself since it includes interrelated elements interacting with one another. To manage data selection effectively and attain robust prediction, characterizing complexity and self-similarity is critical in financial decision-making. Our study aims to obtain analyzes based on two main approaches proposed related to seven recognized indexes belonging to prominent countries (DJI, FCHI, GDAXI, GSPC, GSTPE, N225 and Bitcoin index). The first approach includes the employment of Hurst exponent (HE) as calculated by Rescaled Range (R/S) fractal analysis and Wavelet Entropy (WE) in order to enhance the prediction accuracy in the long-term trend in the financial markets. The second approach includes Artificial Neural Network (ANN) algorithms application Feed forward back propagation (FFBP), Cascade Forward Back Propagation (CFBP) and Learning Vector Quantization (LVQ) algorithm for forecasting purposes. The following steps have been administered for the two aforementioned approaches: (i) HE and WE were applied. Consequently, new indicators were calculated for each index. By obtaining the indicators, the new dataset was formed and normalized by min-max normalization method' (ii) to form the forecasting model, ANN algorithms were applied on the datasets. Based on the experimental results, it has been demonstrated that the new dataset comprised of the HE and WE indicators had a critical and determining direction with a more accurate level of forecasting modeling by the ANN algorithms. Consequently, the proposed novel method with multifarious methodology illustrates a new frontier, which could be employed in the broad field of various applied sciences to analyze pressing real-world problems and propose optimal solutions for critical decision-making processes in nonlinear, complex and dynamic environments.
Citation - WoS: 4
Special Issue Section on Fractal Ai-Based Analyses and Applications To Complex Systems: Part I
(World Scientific Publ Co Pte Ltd, 2021) Baleanu, Dumitru; Moonis, Majaz; Muhammad, Khan; Zhang, Yu-Dong; Gervasi, Osvaldo; Karaca, Yeliz; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
Citation - WoS: 1
Citation - Scopus: 2
Special Issue Section on Fractal Ai-Based Analyses and Applications To Complex Systems: Part Iii
(World Scientific Publ Co Pte Ltd, 2022) Baleanu, Dumitru; Moonis, Majaz; Zhang, Yu-Dong; Gervasi, Osvaldo; Karaca, Yeliz; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
Citation - Scopus: 2
Theory, Analyses and Predictions of Multifractal Formalism and Multifractal Modelling for Stroke Subtypes' Classification
(Springer international Publishing Ag, 2020) Baleanu, Dumitru; Moonis, Majaz; Zhang, Yu-Dong; Karaca, Yeliz; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
Fractal and multifractal analysis interplay within complementary methodology is of pivotal importance in ubiquitously natural and man-made systems. Since the brain as a complex system operates on multitude of scales, the characterization of its dynamics through detection of self-similarity and regularity presents certain challenges. One framework to dig into complex dynamics and structure is to use intricate properties of multifractals. Morphological and functional points of view guide the analysis of the central nervous system (CNS). The former focuses on the fractal and self-similar geometry at various levels of analysis ranging from one single cell to complicated networks of cells. The latter point of view is defined by a hierarchical organization where self-similar elements are embedded within one another. Stroke is a CNS disorder that occurs via a complex network of vessels and arteries. Considering this profound complexity, the principal aim of this study is to develop a complementary methodology to enable the detection of subtle details concerning stroke which may easily be overlooked during the regular treatment procedures. In the proposed method of our study, multifractal regularization method has been employed for singularity analysis to extract the hidden patterns in stroke dataset with two different approaches. As the first approach, decision tree, Naive bayes, kNN and MLP algorithms were applied to the stroke dataset. The second approach is made up of two stages: i) multifractal regularization (kulback normalization) method was applied to the stroke dataset and mFr stroke dataset was generated. ii) the four algorithms stated above were applied to the mFr stroke dataset. When we compared the experimental results obtained from the stroke dataset and mFr stroke dataset based on accuracy (specificity, sensitivity, precision, F1-score and Matthews Correlation Coefficient), it was revealed that mFr stroke dataset achieved higher accuracy rates. Our novel proposed approach can serve for the understanding and taking under control the transient features of stroke. Notably, the study has revealed the reliability, applicability and high accuracy via the methods proposed. Thus, the integrated method has revealed the significance of fractal patterns and accurate prediction of diseases in diagnostic and other critical-decision making processes in related fields.