Hidden Markov Model and multifractal method-based predictive quantization complexity models vis-á-vis the differential prognosis and differentiation of Multiple Sclerosis’ subgroups

Karaca, Yeliz; Băleanu, Dumitru; Karabudak, Rana

doi:10.1016/j.knosys.2022.108694

Cited by 6 publications

(2 citation statements)

References 62 publications

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“…"on the order of " is written in an abbreviated form in capital "O". This gives us the more recognized term, that is to say the Big-O notation (Karaca et al 2022).…”

Section: Computational Complexitymentioning

confidence: 99%

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Computational Complexity-based Fractional-Order Neural Network Models for the Diagnostic Treatments and Predictive Transdifferentiability of Heterogeneous Cancer Cell Propensity

Karaca

2023

Chaos Theory and Applications

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Neural networks and fractional order calculus are powerful tools for system identification through which there exists the capability of approximating nonlinear functions owing to the use of nonlinear activation functions and of processing diverse inputs and outputs as well as the automatic adaptation of synaptic elements through a specified learning algorithm. Fractional-order calculus, concerning the differentiation and integration of non-integer orders, is reliant on fractional-order thinking which allows better understanding of complex and dynamic systems, enhancing the processing and control of complex, chaotic and heterogeneous elements. One of the most characteristic features of biological systems is their different levels of complexity. In view of this, chaos theory seems to be one of the most applicable areas of life sciences along with nonlinear dynamic and complex systems of living and non-living environment. Biocomplexity, with multiple scales ranging from molecules to cells and organisms, addresses complex structures and behaviors which emerge from nonlinear interactions of active biological agents. This sort of emergent complexity is concerned with the organization of molecules into cellular machinery by that of cells into tissues as well as that of individuals to communities. Healthy systems sustain complexity in their lifetime and are chaotic, so complexity loss or the chaos loss results in diseases. Within the mathematics-informed frameworks, fractional-order calculus based Artificial Neural Networks (ANNs) can be employed for accurate understanding of complex biological processes. This approach aims at achieving optimized solutions through the maximization of the model’s accuracy and minimization of computational burden and exhaustive methods. Within this framework with highly intricate complex elements, computational complexity becomes prominent. Relying on a transdifferentiable mathematics-informed framework and multifarious integrative methods concerning computational complexity, this study aims at establishing an accurate and robust model based upon integration of fractional-order derivative and ANN for the diagnosis and prediction purposes for cancer cell whose propensity exhibits various transient and dynamic biological properties. The other aim is concerned with showing the significance of computational complexity for obtaining the fractional-order derivative with the least complexity in order that optimized solution could be achieved. The multifarious scheme of the study, by applying fractional-order calculus to optimization methods, the advantageous aspect concerning model accuracy maximization has been demonstrated through the proposed method’s applicability and predictability aspect in various domains manifested by dynamic and nonlinear nature displaying different levels of complexity.

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“…"on the order of " is written in an abbreviated form in capital "O". This gives us the more recognized term, that is to say the Big-O notation (Karaca et al 2022).…”

Section: Computational Complexitymentioning

confidence: 99%

“…Big-O notation depends on the input parameters for whose details (Karaca et al 2022) can be referred to. Figure 2 depicts the order of growth concerning the algorithms stated in Big-O notation.…”

Section: Big-o Notation Is: O (Formula)mentioning

confidence: 99%

Computational Complexity-based Fractional-Order Neural Network Models for the Diagnostic Treatments and Predictive Transdifferentiability of Heterogeneous Cancer Cell Propensity

Karaca

2023

Chaos Theory and Applications

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Urban land use change simulation and spatial responses of ecosystem service value under multiple scenarios: A case study of Wuhan, China

Ren

Hongjie

2022

Ecological Indicators

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Global Attractivity, Asymptotic Stability and Blow-Up Points for Nonlinear Functional-Integral Equations’ Solutions and Applications in Banach Space Bc(r+) With Computational Complexity

Karaca

2022

Fractals

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Nonlinear functional-integral equations contain the unknown function nonlinearly, occurring extensively in theory developed to a certain extent toward different applied problems and solutions thereof. Nonlinear science serves to reveal the nonlinear descriptions of widely different systems, has had a fundamental impact on complex dynamics. Accordingly, this study provides the basic definitions and results regarding Banach spaces with the proof as well as applications. Besides, proving the existence and uniqueness of the solutions by the Banach theorem is carried out. The existence results of the equations are generally obtained based on fundamental methods by which the fixed-point theorems are frequently applied. Subsequently, the definition of the measure pertaining to noncompactness on Banach space along with properties is presented. Hence, the aim is to study nonlinear functional-integral equations in the Banach space [Formula: see text] using the measure of noncompactness. In addition, the proof of the existence of global attractors and asymptotic stabilities, having at least one solution which pertains to [Formula: see text] is looked into. As the last stage, the definitions of global attractivity and asymptotical stability for equations on Banach space [Formula: see text] are given while proving the existence of solutions and global attractivity. Besides these, the existence and asymptotical stability are proven. Furthermore, the proof of the existence of global attractors and asymptotic stabilities, having at least one solution which pertains to [Formula: see text] for an example nonlinear integral equation has been demonstrated by one example premediated and the existence of blow-up point has been examined in one and more than one points regarding the nonlinear integral equation. The example nonlinear integral equation as addressed in this study has been examined in terms of its blow-up point and asymptotic stability with computational complexity for the first time. By doing so, it has been demonstrated that the existence of blow-up point has been the case in one and more than one points and besides this, the examination of its asymptotic stability has shown that it is asymptotically stable at least in one point, yet has no blow-up point pertaining to [Formula: see text]. This has enabled thorough analysis of computational complexity of the related nonlinear functional-integral equations within the example both addressing dimension of input in Banach space and that of dataset with [Formula: see text] dimension. This applicable approach assures the accurate transformation of the complex problems towards optimized solutions through the generation of advanced mathematical models in nonlinear dynamic settings characterized by complexity.

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Hidden Markov Model and multifractal method-based predictive quantization complexity models vis-á-vis the differential prognosis and differentiation of Multiple Sclerosis’ subgroups

Cited by 6 publications

References 62 publications

Computational Complexity-based Fractional-Order Neural Network Models for the Diagnostic Treatments and Predictive Transdifferentiability of Heterogeneous Cancer Cell Propensity

Computational Complexity-based Fractional-Order Neural Network Models for the Diagnostic Treatments and Predictive Transdifferentiability of Heterogeneous Cancer Cell Propensity

Urban land use change simulation and spatial responses of ecosystem service value under multiple scenarios: A case study of Wuhan, China

Global Attractivity, Asymptotic Stability and Blow-Up Points for Nonlinear Functional-Integral Equations’ Solutions and Applications in Banach Space Bc(r+) With Computational Complexity

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