Multi-Chaos, Fractal and Multi-Fractional Artificial Intelligence of Different Complex Systems

By Dumitru Baleanu and Osvaldo Gervasi

Multi-Chaos, Fractal and Multi-Fractional Artificial Intelligence of Different Complex Systems addresses different uncertain processes inherent in the complex systems, attempting to provide global and robust optimized solutions distinctively through multifarious methods, technical analyses, modeling, optimization processes, numerical simulations, case studies as well as applications including theoretical aspects of complexity. Foregrounding Multi-chaos, Fractal and Multi-fractional in the era of Artificial Intelligence (AI), the edited book deals with multi- chaos, fractal, multifractional, fractional calculus, fractional operators, quantum, wavelet, entropy-based applications, artificial intelligence, mathematics-informed and data driven processes aside from the means of modelling, and simulations for the solution of multifaceted problems characterized by nonlinearity, non-regularity and self-similarity, frequently encountered in different complex systems. The fundamental interacting components underlying complexity, complexity thinking, processes and theory along with computational processes and technologies, with machine learning as the core component of AI demonstrate the enabling of complex data to augment some critical human skills. Appealing to an interdisciplinary network of scientists and researchers to disseminate the theory and application in medicine, neurology, mathematics, physics, biology, chemistry, information theory, engineering, computer science, social sciences and other far-reaching domains, the overarching aim is to empower out-of-the-box thinking through multifarious methods, directed towards paradoxical situations, uncertain processes, chaotic, transient and nonlinear dynamics of complex systems.

• Constructs and presents a multifarious approach for critical decision-making processes embodying paradoxes and uncertainty.
• Includes a combination of theory and applications with regard to multi-chaos, fractal and multi-fractional as well as AI of different complex systems and many-body systems.
• Provides readers with a bridge between application of advanced computational mathematical methods and AI based on comprehensive analyses and broad theories.

• Language: English
• Publisher: Academic Press
• Release date: Jun 22, 2022
• ISBN: 9780323886161

Book preview

Multi-Chaos, Fractal and Multi-Fractional Artificial Intelligence of Different Complex Systems

Editor

Yeliz Karaca

University of Massachusetts Medical School, Worcester, MA, United States

Dumitru Baleanu

Çankaya University, Ankara, Turkey and Institute of Space Sciences, Magurele-Bucharest, Romania

Yu-Dong Zhang

University of Leicester, Leicester, United Kingdom

Osvaldo Gervasi

Perugia University, Perugia, Italy

Majaz Moonis

University of Massachusetts Medical School, Worcester, MA, United States

Table of Contents

Cover image

Title page

Copyright

List of contributors

Preface

Acknowledgment

Chapter 1. Introduction

Chapter 2. Theory of complexity, origin and complex systems

1. Introduction

2. Theory of complexity, origin and complex systems

3. Complex order processes toward modern scientific path: from Darwin and onwards

4. Concluding remarks and future directions

Chapter 3. Multi-chaos, fractal and multi-fractional AI in different complex systems

1. Introduction

2. Challenging dimensions of modern science, complexity and complex systems

3. Artificial intelligence way of thinking, processes, complexity and complex systems

4. Concluding remarks and future directions

Chapter 4. High-performance computing and computational intelligence applications with a multi-chaos perspective

1. Introduction

2. Related works

3. High-performance computing approaches to solving complex problems

4. Quantum computing to treat multi-chaos scenarios

5. Techniques enabling the solution of complex problems based on computational intelligence

6. The dilemma of respecting privacy in multi-chaos situations

7. Conclusions

8. Acronyms

Chapter 5. Human hypercomplexity. Error and unpredictability in complex multichaotic social systems

1. Introduction

2. The complexity of living energy and living beings

3. Complicated, complex, and hypercomplex systems

4. Taking a step back: a brief history of complexity

5. An epistemology of error

6. Objects are relations

7. Everything depends on everything else

8. Cognitive cages

9. è troppo, o troppo ravvicinato?

Chapter 6. Multifractal complexity analysis-based dynamic media text categorization models by natural language processing with BERT

1. Introduction

2. Data and methodology

3. Experimental results and discussion

4. Conclusion and future directions

Chapter 7. Mittag-Leffler functions with heavy-tailed distributions' algorithm based on different biology datasets to be fit for optimum mathematical models' strategies

1. Introduction

2. Complex biological datasets and methodology

3. Experimental results and discussion: computational application of Mittag-Leffler function based on heavy-tailed distributions for different biological datasets

4. Conclusion and future directions

Chapter 8. Artificial neural network modeling of systems biology datasets fit based on Mittag-Leffler functions with heavy-tailed distributions for diagnostic and predictive precision medicine

1. Introduction

2. Complex biological datasets and methodology

3. Experimental results and discussions: artificial neural network modeling of complex biological datasets to be fit based on Mittag-Leffler function with heavy-tailed distributions for diagnosis and prediction

4. Conclusion and future directions

Chapter 9. Computational fractional-order calculus and classical calculus AI for comparative differentiability prediction analyses of complex-systems-grounded paradigm

1. Introduction

2. Datasets and methodology

3. Experimental results and discussion

4. Conclusion and future directions

Chapter 10. Pattern formation induced by fractional-order diffusive model of COVID-19

1. Introduction

2. Model

3. Spatiotemporal model

4. Weakly nonlinear analysis

5. Numerical simulation

6. Conclusion

Chapter 11. Prony's series and modern fractional calculus: Rheological models with Caputo-Fabrizio operator

1. Introduction

2. Prony's method

3. Exponential sums approximation of functions

4. Fractional operators in applied rheology

5. Modeling linear viscoelastic responses

6. Prony's series in linear viscoelasticity

7. Final comments

Chapter 12. A chain of kinetic equations of Bogoliubov–Born–Green–Kirkwood–Yvon and its application to nonequilibrium complex systems

1. Introduction

2. Formulation of the problem

3. The solution of the BBGKY hierarchy for many-type particle systems

4. Derivation of the Gross–Pitaevskii equation from the BBGKY hierarchy

5. Summary

Chapter 13. Hearing loss detection in complex setting by stationary wavelet Renyi entropy and three-segment biogeography-based optimization

1. Introduction

2. Dataset

3. Methods

4. Implementation

5. Measure

6. Experiment results and discussions

7. Conclusions

Appendix

Chapter 14. Shannon entropy-based complexity quantification of nonlinear stochastic process: diagnostic and predictive spatiotemporal uncertainty of multiple sclerosis subgroups

1. Introduction

2. Materials and methods

3. Experimental results

4. Conclusion and future directions

Chapter 15. Chest X-ray image detection for pneumonia via complex convolutional neural network and biogeography-based optimization

1. Introduction

2. Dataset

3. Methodology

4. Experiment results and discussions

5. Conclusions

Chapter 16. Facial expression recognition by DenseNet-121

1. Introduction

2. Dataset

3. Methodology

4. Experiment result and discussions

5. Conclusions

Chapter 17. Quantitative assessment of local warming based on urban dynamics

1. Introduction

2. Study areas

3. Materials and methods

4. Results and discussion

5. Conclusions

Chapter 18. Managing information security risk and Internet of Things (IoT) impact on challenges of medicinal problems with complex settings: a complete systematic approach

1. Introduction to information security

2. Information security in healthcare

3. Impact of IoT in medical problems

4. Medical problems with complex settings

5. IoT and information security

6. Challenges of medicinal problems using IoT: a case study

7. Conclusion

Chapter 19. An extensive discussion on utilization of data security and big data models for resolving healthcare problems

1. Information security

2. Internet of Things

3. Information security and IoT

4. Data security and IoT in medicine

5. Big data and its applications

6. IoT and big data applications in medicine

7. Complex system in healthcare

8. Role of IoT and big data applications in medicine

9. Conclusion

Index

Copyright

Academic Press is an imprint of Elsevier

125 London Wall, London EC2Y 5AS, United Kingdom

525 B Street, Suite 1650, San Diego, CA 92101, United States

50 Hampshire Street, 5th Floor, Cambridge, MA 02139, United States

The Boulevard, Langford Lane, Kidlington, Oxford OX5 1GB, United Kingdom

Copyright © 2022 Elsevier Inc. All rights reserved.

No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or any information storage and retrieval system, without permission in writing from the publisher. Details on how to seek permission, further information about the Publisher’s permissions policies and our arrangements with organizations such as the Copyright Clearance Center and the Copyright Licensing Agency, can be found at our website: www.elsevier.com/permissions.

This book and the individual contributions contained in it are protected under copyright by the Publisher (other than as may be noted herein).

Notices

Knowledge and best practice in this field are constantly changing. As new research and experience broaden our understanding, changes in research methods, professional practices, or medical treatment may become necessary.

Practitioners and researchers must always rely on their own experience and knowledge in evaluating and using any information, methods, compounds, or experiments described herein. In using such information or methods they should be mindful of their own safety and the safety of others, including parties for whom they have a professional responsibility.

To the fullest extent of the law, neither the Publisher nor the authors, contributors, or editors, assume any liability for any injury and/or damage to persons or property as a matter of products liability, negligence or otherwise, or from any use or operation of any methods, products, instructions, or ideas contained in the material herein.

ISBN: 978-0-323-90032-4

For information on all Academic Press publications visit our website at https://www.elsevier.com/books-and-journals

Publisher: Mara Conner

Acquisitions Editor: Chris Katsaropoulos

Editorial Project Manager: Maria Elaine D. Desamero

Production Project Manager: Niranjan Bhaskaran

Cover Designer: Yeliz Karaca

Typeset by TNQ Technologies

List of contributors

Tohir Vohidovich Akramov

Nuclear Physics, Academy of Sciences of Uzbekistan, Tashkent, Uzbekistan

National University of Uzbekistan, Tashkent, Uzbekistan

Umarbek Avazov,     Nuclear Physics, Academy of Sciences of Uzbekistan, Tashkent, Uzbekistan

Dumitru Baleanu

Çankaya University, Ankara, Turkey

Institute of Space Science, Magurele, Bucharest, Romania

Debnath Bhattacharyya,     Koneru Lakshmaiah Education Foundation, Vaddeswaram, Guntur, Andhra Pradesh, India

Nikolai (Jr) Bogoliubov,     Steklov Institute of Mathematics of the Russian Academy of Sciences, Moscow, Russia

Piero Dominici

CHAOS–International Research and Education Programme Complex Human Adaptive Organizations and Systems, Perugia University, Italy

Department of Philosophy, Social, Human and Educational Sciences, University of Perugia, Italy

WAAS - World Academy of Art and Science, Rome, Italy

Ahu Dereli Dursun,     Institute of Social Sciences, Communication Studies, Istanbul Bilgi University, Istanbul, Turkey

Osvaldo Gervasi,     University of Perugia, Perugia, Italy

Jordan Hristov,     University of Chemical Technology and Metallurgy, Sofia, Bulgaria

Naveed Iqbal,     University of Ha'il, Ha'il, Saudi Arabia

Yeliz Karaca,     University of Massachusetts Medical School, Worcester, MA, United States

Xiang Li,     Henan Polytechnic University, Jiaozuo, Henan, PR China

Yabei Li,     Henan Polytechnic University, Jiaozuo, Henan, PR China

Bin Li,     Henan Polytechnic University, Jiaozuo, Henan, PR China

Majaz Moonis,     University of Massachusetts Medical School, Worcester, MA, United States

Beniamino Murgante,     University of Basilicata, Via dell'Ateneo Lucano, Potenza, Italy

Eali Stephen Neal Joshua,     Vignan's Institute of Information Technology (A), Visakhapatnam, Andhra Pradesh, India

Gabriele Nolè,     CNR-IMAA, C.da Santa Loja Zona Industriale Tito Scalo, Potenza, Italy

Damiano Perri

University of Florence, Firenze, Italy

University of Perugia, Perugia, Italy

Angela Pilogallo,     University of Basilicata, Via dell'Ateneo Lucano, Potenza, Italy

N. Thirupathi Rao,     Vignan's Institute of Information Technology (A), Visakhapatnam, Andhra Pradesh, India

Mukhayo Yunusovna Rasulova,     Nuclear Physics, Academy of Sciences of Uzbekistan, Tashkent, Uzbekistan

Lucia Saganeiti,     University of L’Aquila, L’Aquila, Italy

Valentina Santarsiero

University of Basilicata, Via dell'Ateneo Lucano, Potenza, Italy

CNR-IMAA, C.da Santa Loja Zona Industriale Tito Scalo, Potenza, Italy

Francesco Scorza,     University of Basilicata, Via dell'Ateneo Lucano, Potenza, Italy

Marco Simonetti

University of Florence, Firenze, Italy

University of Perugia, Perugia, Italy

Junding Sun,     Henan Polytechnic University, Jiaozuo, Henan, PR China

Sergio Tasso,     University of Perugia, Perugia, Italy

Shui-Hua Wang,     University of Leicester, Leicester, United Kingdom

Chong Yao,     Henan Polytechnic University, Jiaozuo, Henan, PR China

Mengyao Zhai,     Hebi Polytechnic, Hebi, Henan, PR China

Yu-Dong Zhang,     University of Leicester, Leicester, United Kingdom

Preface

Multi -Chaos, Fractal and Multi-Fractional Artificial Intelligence of Different Complex Systems is an edited book that addresses different uncertain processes inherent in the complex systems, attempting to provide global and robust optimized solutions distinctively through multifarious methods, technical analyses, modeling, optimization processes, numerical simulations, case studies and applications not excluding theoretical aspects of complexity. Based on advanced mathematical foundation, our edited book foregrounds multichaos, fractal, multifractional, fractional calculus, fractional operators, quantum, wavelet, entropy-based applications and artificial intelligence (AI) mathematics-informed and data-driven processes. The primary focus and purpose, herein, is related to the needs and solutions for new analytic strategies and mathematical modeling to attain accurate, timely and optimized solutions.

Appealing to an interdisciplinary network of scientists and researchers to disseminate the theory and application of multichaos, fractal and multifractional AI of different complex systems in medicine, neurology, mathematics, physics, biology, chemistry, information theory, engineering, computer science, social sciences and other far-reaching domains, the overarching aim is to enable the provision of global and optimized robust solutions distinctively with a perspective through multifarious methods, different from the conventional perspective, as directed toward paradoxical situations, different uncertain processes, nonlinear dynamic systems inherent in complex systems. Elaborating on the most intriguing theoretical aspects, modeling and applications of multichaos, fractal, multifractional, fractional calculus, fractional operators, quantum, wavelet, entropy-based applications and AI mathematics-informed and data-driven processes around the common theme of complexity and nonlinearity under consideration, current applications, future directions and perspectives, limitations, strengths and opportunities are provided in our edited book for scientists, researchers, students, and anyone who is interested in the enigma of complexity. The invaluable inputs of 31 experts worldwide specialized in mathematics, physics, biology, chemistry, neurology, information theory, computer science, engineering, applied sciences, sociology, philosophy and communication, among others, from 11 countries, are significant to establish a holistic body of work and spectrum, owing to their personal contributions in their respective fields. The edited book includes a total of 19 chapters, as has been inspired by the aforesaid considerations; the chapters along the book are outlined in terms of their content as follows.

Chapter 1 is the Introduction (by Yeliz Karaca and Dumitru Baleanu), which provides the basic motivations underlying complexity, complexity thinking and theory along with the important role of computational processes with extensive applications in integration with fractals, multifractals, fractional methods, chaos, nonlinear dynamical properties and stochastic elements. Computational technologies, with machine learning as the core component of AI, is stated to have broad use and transformative impacts, enabling the training of complex data to automate or augment some of the critical human skills. Thus, it is presented that our edited book foregrounds multichaos, fractal, and multifractional in the era of AI, which requires the integration of advanced mathematical models and mathematics-informed frameworks as well as AI addressing fractal, fractional calculus, fractional operators, quantum, wavelet, entropy-based applications aside from the means of modeling, technical analyses and numerical simulations as some of the most broadly employed methods for the solution of multifaceted problems characterized by nonlinearity, nonregularity, self-similarity and many other properties, frequently encountered in different complex systems. Accordingly, the chapter presents the overarching aim of the edited book of ours, its key objectives, motivational aspects and the detailed content of all other chapters presented herein.

Chapter 2 entitled Theory of Complexity, Origin and Complex Systems (by Yeliz Karaca) attempts to touch on the possible dimensions of complex systems in different fields with a focus on origin-related, historical, evolutionary and epistemological viewpoints of complexity by taking into consideration the various multiple interacting factors of systems with the goal of providing a global understanding between variables, sensitivity to initial control, and strange, nonperiodic and unpredictable time evolution. The detailed presentation in the chapter tries to ensure that the foundation for the complex systems' interpretations can be explored in different related areas of complexity.

Chapter 3 Multichaos, Fractal and Multifractional AI in Different Complex Systems (by Yeliz Karaca) provides an overview including multichaos, fractal, fractional and AI way of thinking with regard to the solutions of the complex system problems concerned with natural and social sciences. Ethical decision-making frameworks and strategies related to big data and AI applications are also presented in detail to enable assistance for the identification of the related problems in different settings and thinking methodically so that tensions between conflicting aspects can be managed systematically.

Chapter 4, High-Performance Computing and Computational Intelligence Applications with Multichaos Perspective (by Damiano Perri, Marco Simonetti, Osvaldo Gervasi and Sergio Tasso), addresses the experience of the COVID-19 pandemic, which has accelerated many chaotic processes in modern society besides revealing the need to understand complex processes to achieve common well-being in a very serious and emergent way. A set of best practices and case studies, which provide assistance to the researchers while handling computationally complex problems, are presented in the chapter, providing a general sketch of various topics, which could be of help to researchers and developers to deal with complex and chaotic situations within the scope of machine learning and the issue of privacy including the recent related regulations.

Chapter 5 Human Hypercomplexity. Error and Unpredictability in Complex Multichaotic Social Systems (by Piero Dominici) has the perspective that traditional linear models and deterministic approaches can no longer be capable of the analyzing the dynamics of unstable dynamics. The chapter provides perspectives on the complexity of living energy and living beings, along with 12 essential planes of awareness, the characteristics of complicated, complex and hypercomplex systems, epistemology of error and complex and chaotic characteristics of social systems.

Chapter 6 Multifractal Complexity Analysis-Based Dynamic Media Text Categorization Models by Natural Language Processing with BERT (by Yeliz Karaca, Yu-Dong Zhang, Ahu Dereli Dursun and Shui-Hua Wang) addresses the challenges and complexity inherent in digital-based complex media texts. The study puts forth the significance of the fractal behavior while articulating the distinguishing quality of BERT owing to its capability of classification accuracy and adaptiveness into integrated methodologies.

Chapter 7 (Part I) Mittag-Leffler Functions With Heavy-Tailed Distributions' Algorithm Based on Different Biology Datasets to be Fit for Optimum Mathematical Models' Strategies (by Dumitru Baleanu and Yeliz Karaca) addresses the challenges of integrating fractional calculus in cases of complexity, which necessitates an effective use of empirical, numerical, experimental, and analytical methods to tackle complexity. The proposed integrated approach in this chapter uses the Mittag–Leffler function with two parameters (a, fl) for the purpose of investigating the dynamics of two diseases: cancer cell and diabetes.

Chapter 8 (Part II) Artificial Neural Network Modeling of Systems Biology Datasets Fit Based on Mittag-Leffler Functions with Heavy-Tailed Distributions for Diagnostic and Predictive Precision Medicine (by Yeliz Karaca and Dumitru Baleanu) obtains the generation of optimum model strategies for different biology datasets along with the Mittag-Leffler functions with heavy-tailed distributions. The integrative modeling scheme proposed in the chapter is concerned with the applicability and reliability of the solutions obtained by the two-parametric Mittag-Leffler functions with heavy-tailed distributions. Accordingly, the proposed integrated approach in this chapter investigates the dynamics of diseases related to biological elements. The application of multilayer perceptron, as one of the Artificial Neural Network (ANN) algorithms, is directed for the diagnostic and predictive purpose of the disease. The content of the chapter intends to enable the building of precise models to avoid unpredictable risks and identify opportunities in nonlinear complex situations, along with the integration of precision medicine.

Chapter 9 Computational Fractional Order Calculus and Classical Calculus AI for Comparative Differentiability Prediction Analyses of Complex Systems-grounded Paradigm (by Yeliz Karaca and Dumitru Baleanu) intends to provide an intermediary facilitating function for both the physicians and individuals through establishing an accurate and robust model based on the integration of fractional order calculus and ANN in terms of the diagnostic and differentiability predictive purposes with the diseases, which display highly complex properties. The integrative and multistaged approach proposed includes the application of the Caputo fractional derivative with two-parametric Mittag-Leffler function on the stroke dataset and cancer cell dataset. The chapter reveals that modeling many complex systems can be possible by fractional order derivatives based on fractional calculus and computational complexity is shown to provide us with applicable sets of ideas or integrative paradigms to understand the intricate properties of complex systems.

Chapter 10 Pattern Formation Induced by Fractional Order Diffusive Model of COVID-19 (by Naveed Iqbal and Yeliz Karaca) presents the investigation of the Turing instability produced by fractional diffusion in a COVID-19 model. Differential equations with complex order fractional derivatives enable the regulation of complicated fractional systems, positive equilibrium points have been initially specified, and Routh-Hurwitz criteria have been used to assess the stability of positive equilibrium point. Local equilibrium points and stability analysis have been employed to find the conditions for Turing instability. The analysis, by exploring the system's dynamical behavior and the bifurcation point centered on the death rate, anticipates to serve as a leverage in different disciplines concerning COVID-19 model through the lenses of distinct viewpoints; and within that framework, fractional calculus is known to unfold the fundamental mechanisms and multiscale dynamic phenomena.

Chapter 11 Prony's Series in Time and Frequency Domains and Relevant Fractional Models (by Jordan Hristov) deals with Prony's series approximation of monotonically responses in material viscoelastic rheology and the possibilities of implementation on this sort of basis relying on modern fractional operations with nonsingular kernels, which is to say the Caputo-Fabrizio operator. The chapter provides the origins of Prony's series in time and frequency domains together with the relevant approximation and calculation techniques. In this way, contributions in pure mathematics and experimental aspects are put forth, while the elaboration and application of Prony's series are said to have the extension possibility to modeling problems emerging in mechanical engineering, chemical engineering and other related disciplines.

Chapter 12 A Chain of Kinetic Equations of Bogoliubov-Born-Green-Kirkwood-Yvon and Its Application to Nonequilibrium Complex Systems (by Nicolai (Jr) Bogoliubov, Mukhayo Yunusovna Rasulova, Tohir Akramov and Umarbek Avazov) is directed to the study of the Bogoliubov-Born-Green-Kirkwood-Yvon chain of kinetic equations (BBGKYchke) and its applications to modern problems of physics. The chapter has the focus on the need of creating a mathematical apparatus fulfilling the existing theory of one-particle systems and systems made up of a huge number of particles. Two types of BBGKY chains are addressed for both classical and quantum particle systems. The solution of the BBGKYchqke for generalized Yukawa potential (gYp) is provided, solving of the BBGKYchqke with the gYp for systems of many type particles is also elaborated on, and the Gross-Pitaevskii equation derived based on the BBGKYchqke is presented.

Chapter 13 Hearing Loss Detection in Complex Setting by Stationary Wavelet Renvi Entropy and Three-Segment Biogeography-Based Optimization (by Yabei Li) addresses hearing loss with the main objective of improving the accuracy and efficiency of detecting images in sensorineural hearing loss through a new solution. To this end, an improved feature extraction method stationary wavelet Renvi entropy as well as optimization algorithm for model and feature extraction, namely three-segment biogeography-based optimization have been proposed.

Chapter 14 Shannon Entropy-Based Complexity Quantification of Nonlinear Stochastic Process: Diagnostic and Predictive Spatio-temporal Uncertainty of Multiple Sclerosis Subgroups (by Yeliz Karaca and Majaz Moonis) aims at facilitating the accurate classification and course of three subgroups of multiple sclerosis (MS) (relapsing remitting MS, secondary progressive MS, primary progressive MS), which is a debilitating neurological disease. An entropy-based feature selection method (Shannon entropy and minimum redundancy maximum relevance) as well as linear transformation methods (principal component analysis and linear discriminant analysis) have been applied. Each new dataset obtained has been addressed as input for the training procedure of k-nearest neighbor and decision tree algorithms. The accuracy rates for the MS subgroups' classification have also been analyzed comparatively based on the optimized experimental results, which demonstrate that Shannon entropy, as a distinctive entropy method, has proven to be higher in terms of accuracy compared with the other feature selection methods. Accordingly, a new perspective with a multilevel aspect has been presented to cope with the complex dynamic systems where uncertainty and heterogeneity prevail for critical decision-making and manageable tracking in medicine and relevant fields.

Chapter 15 Chest X-ray Image Detection for Pneumonia via Complex Convolutional Neural Network and Biogeography-Based Optimization (by Xiang Li, Mengvao Zhai and Junding Sun) proposes a novel chest X-ray image detection for pneumonia. The detection model proposed is reliant on the combination of complex convolutional neural network (CNN) and biogeography-based optimization. It has been proven that the model has higher sensitivity and accuracy in terms of detecting the pneumonia-related chest X-ray images with a detection performance being significantly better than that of advanced approaches in complex medical settings. The utilization of BBO, employed as the global optimization algorithm of the related model, also provides the benefit of optimizing the stride size of the convolution kernel on CNN to obtain better detection effects with less model training cost.

Chapter 16 Complex Facial Expression Recognition by DenseNet-121 (by Bin Li) is concerned with facial expression recognition system, which has gradually been integrated into different fields of our lives with the advent of AI era. The application prospects of intelligent face recognition via computer technology are very broad, which can also be applied to the diagnosis of facial paralysis in medicine. Handling the complex nature of facial expression since it involves emodiversity and emotional complexity, the chapter shows that facial expression recognition is a difficult task bringing about some problems such as low accuracy and poor generalization ability of network model recognition. To address these challenges, the authors have proposed a DenseNet-121 image feature extraction method, combined with CNN for facial expression recognition. The presentation of an improved face emotion recognition system proposed employing a method based on densely connected neural network also facilitates the avoiding of complex feature extraction required by traditional deep learning while saving on the training time.

Chapter 17 Quantitative Assessment of Local Warming Based on Complex Urban Dynamics Using Remote Sensing Techniques (by L. Saganeiti, Angela Pilogallo, Francesco Scorza, Valentina Santarsiero, Gabriele Nole and Beniamino Murgante) is concerned with urban growth, which is one of the cornerstones of sustainable development policies that require to be implemented at initial states for a well-managed urbanization process and experience. The chapter provides a simultaneous analysis of the variations of land surface temperature and urbanized environment over a period of 15 years within two regions that differ in size, population density, and growth dynamics. The research also provides an appealing and innovative contribution to grasp the relationships between urban growth spatial patterns and the urban thermal environment. Detailed analyses presented in the chapter are beneficial in supporting decision-making processes underlying future urban policies and assessment of development scenarios with regard to quality of life, environmental sustainability and preservation of ecosystems.

Chapter 18 Managing Information Security Risk and Internet of Things Impact on Challenges of Medicinal Problems with Complex Settings: a Complete Systematic Approach (by Eali Stephen Neal Joshua, Debnath Bhattacharyya and N. Thirupathi Rao), discovers the crossway of healthcare and significant data, providing details with respect to information security, different vulnerabilities in healthcare, data breaches, distributed denial of service assaults, insider threats, information security in healthcare, health information privacy and security, and various information threat elements regarding medical health reports. The chapter also points out the impact of IoT in medical problems, IoT in healthcare, and challenges in IoT in medical problems. The information threats are outlined in detail in the chapter, which presents the challenges of medicinal problems using IoT through a case study that shows the efficiency of IoT owing to exponentially increasing patient monitoring (blood pressure monitoring, glucose monitoring, and pulse rate monitoring) in the healthcare plans.

Chapter 19 is entitled An Extensive Discussion on Utilization of Data Security and Big Data Models for Resolving Complex Healthcare Problems (by N. Thirupathi Rao, Debnath Bhattacharyya and Eali Stephen Neal Joshua), and it is concerned with the utilization of technology in the healthcare settings with a focus on the employment of the IoT technology, providing an extensive elaboration of its opportunities, benefits, impacts, existing gaps, security threats and adaptive frameworks that need to be developed. The chapter, with updated information for our current time, presents detailed discussions on big data in healthcare, information security, confidentiality, integrity, and availability by considering the related stakeholders in the area that are the physicians, patients, hospitals and insurance companies. The chapter presents the complex system with its components in various healthcare domains, and this attribute concerns many different disciplines including but not limited to medicine, microbiology, biomedical engineering, computer science and big data analytics. Awareness into and efficient management of all the components involved is noted to have benefits for the patients who will be knowledgeable in terms of pertinent medical resources and faith in healthcare professionals. In addition, access into a variety of medical services based on technological devices will be of great benefit to all the stakeholders and complex settings.

We are of the opinion and anticipation that our edited book will provide new dimensions into layers of complexity thinking, momentum to progressive ideas into complexity, complexity thinking and processes, and above all out-of-the-box way of thinking for everyone interested in the theory, applications and modeling of complexity and different complex systems.

September, 2021

Yeliz Karaca

University of Massachusetts Medical School, Worcester, United States

Dumitru Baleanu

Çankaya University, Ankara, Turkey and Institute of Space Sciences, Magurele-Bucharest, Romania

Yu-Dong Zhang

University of Leicester, Leicester, United Kingdom

Osvaldo Gervasi

University of Perugia, Perugia, Italy

Majaz Moonis

University of Massachusetts Medical School, Worcester, MA, United States

Acknowledgment

Yeliz Karaca would like to express her deep respect and gratitude to her family members: her mother, Fahrive Ekecik Karaca; her father, Emin Karaca; and her brother, Mehmet Karaca and his family who have always provided unconditional true love, offering all kinds of support all the way through. Yeliz Karaca is also sincerely indebted to her ancestor, late grandfather, Hasan Hüseyin Ekecik, holding the superiority service award by the Turkish Grand National Assembly for his beneficial contributions in public welfare, education and social development both at national and international scales, whom she has taken as an esteemed role model in her life.

Dumitru Baleanu would like to thank his wife Mihaela-Cristina for her continuous support.

Yu-Dong Zhang would like to express his acknowledgment to all his family members, including his wife and son, who support his research work all the time.

Osvaldo Gervasi would like to express his deepest thanks for the continuous support in the course of his work to his wife Lorella Giovannelli and his children Marta, Andrea and Damiano and to his parents Loretta Pucci and Angelo Gervasi for the profound values that Osvaldo Gervasi was able to transmit to his children.

Majaz Moonis is deeply grateful to his father Professor Moonis Raza who taught and encouraged the idea of research, his mother and wife who in all adversities stood behind him and made it possible to continue his work.

Chapter 1: Introduction

Yeliz Karaca ¹ , and Dumitru Baleanu ² , ³       ¹ University of Massachusetts Medical School, Worcester, MA, United States      ² Çankaya University, Ankara, Türkiye      ³ Institute of Space Science, Magurele, Bucharest, Romania

Complexity, having existed since antiquity, entails the understanding of the complex components' origin, with meticulous computations and causal processes. Nonlinearity, self-organization, adaptation, synchronization, noise, a high number of descriptive variables or dimensions involved in the description of differential equation systems, and reaction to responses in the external environment are some of the numerous characteristics of a complex system in which multiple interactions emerge. Along these lines, complexity thinking and theory, one of the basic premises of which is the acknowledging of the existence of a hidden order to the behavior and evolution of complex systems, requires a horizon that takes the subtle and hidden properties of different domains into account, necessitating their own means of optimized solutions and applicability. Bearing in mind the quote by Stephen Hawking: I think the next [21st] century will be the century of complexity is critically significant not only for this era but also for onwards. Accordingly, the idea of complexity is stated to be part of a new unifying framework for science and a revolution in our understanding of systems the behavior of which has proved to be difficult in terms of prediction, management and control.

In a complex system, different and multiple ways need to be contemplated for the provision of solutions and sorting out the problems. The system is likely to change depending on these selections, which shows us the complex systems' adaptiveness. And, the more insight is developed, the answers to the problems keep changing which enables more learning in the process. Given this, modern science has embarked on the attempts for a thorough, holistic, multifaceted and accurate interpretation of natural and physical phenomena, which has proven to provide successful models for the analysis of complex systems and harnessing of control over the various related processes. Computational complexity, in this regard, comes to the foreground by providing the applicable sets of ideas and/or integrative paradigms to recognize and understand the intricate properties and dynamics of many different complex systems. The lenses of such transformative thinking in conjunction with mathematics-informed frameworks encompass chaos, fractal and multi-fractional ways as well as the indispensable incorporation of technology, with Artificial Intelligence, as a far-reaching leg, which are all essentially required to be capable of addressing and tackling complexity manifesting chaotic, nonlinear, and dynamic characteristics.

Chaos refers to irregular and unpredictable behavior characterized by sensitive reliance on initial conditions. The tendency of nature toward pattern formation, iteration and creation of order out of chaos all point to the generation of expectations of predictability. Chaos and its study in consort with the advances in scientific realm are important roots of modern study of complex systems that display dynamic, nonlinear, open qualities and interconnection with the environment constituting many interacting components, with new unanticipated patterns emerging. Chaos, in this context, is said to have somehow strict definitions portraying a nonlinear world, addressing deterministic systems with trajectories diverging exponentially in time, which is also among the properties of behaviors in complex systems. In mathematics and physics, chaos theory is concerned with the nonlinear dynamical systems' behavior, which under certain circumstances exhibits a phenomenon referred to as chaos marked by sensitivity to initial conditions.

Fractals are also components of dynamic systems, being the images thereof, driven by recursion, which is to say the image of chaos. Accordingly, fractals are used for modeling structures where patterns recur repeatedly and describe random or chaotic phenomena. For the handling of complex systems, the concept of progressive smoothness on finer scales may not always prove to be useful as a starting point from mathematical point of view. This acknowledgment is important as a fundamental change in outlook when traditional geometry studying the properties of objects and spaces with integral dimensions is not useful. Effective fractional dimensions of objects, named as fractals, are integrated into an integral dimension space. Being never-ending patterns, fractals can be curves or geometric figures, with each part appearing to be the same as the whole pattern, which is called self-similarity brought about by a process or function's iterative repetition. Fractals are, in other words, images of dynamic systems driven by recursion, namely the image of chaos. Fractals are employed to model structures in which patterns recur in a repeated way and to describe random or chaotic phenomena.

The advent of increasing capacity of computational processes in numerical methods, interest in fractional derivative equations (FDEs) has been on the rise to be able to represent complex physical courses where dynamics may not be as accurately detected through classical differential equations. Fractional dynamics, in this regard, refers to such systems for which derivatives and integrals of fractional orders are employed to describe objects likely to be characterized by power-law nonlocality, fractal properties, or long-range dependence. For this reason, fractional-order system model can be regarded as a key for describing the system performance in a better way, with predictive reliability and applicability. In view of these concepts and challenges, it is important not to disregard data reliability, chaos thinking and processes, fractal thinking and processes, as well as artificial intelligence way of thinking and processes around complexity as the common theme under consideration. The related computational processes with broad applications in integration with fractals, multi-fractals, fractional methods, chaos, nonlinear dynamical properties, stochastic elements and so forth can provide systematic optimized solutions. Furthermore, computational technologies, with machine learning as the core component of AI, enjoy the broad use and transformative impacts enabling us to train complex data to automate or augment some of the critical human skills. Hence, the crosscutting nature of AI provides motivational power to formulize research in a systematic way. Artificial neural networks (ANNs), which are networks of computer systems inspired by the human brain and biological neural networks have the capability of learning and modeling complex, dynamic and nonlinear relationships. As the simplification, abstraction and simulation of the human brain, ANNs also reflect the related fundamental characteristics of this complex organ. Thus, optimized solutions need to be conceived and applied in a facilitating way and efficiently with some required degree of flexibility, too. Considering the impact of data technologies vis-à-vis all aspects of conditions of modern era and life, it becomes highly important to establish a balance between data use and ethical matters. Computational technologies in different complex systems based on mathematical-driven informed frameworks can enable the generation of more realistic, applicable, adaptive models open to learning and flexibility under transient, dynamic, chaotic and ever-evolving conditions of different complex systems.

To put it differently, complexity along with all the variations in networks and systems demonstrates that the decisions made are not based on one single parameter per se, but also on multiple numbers of parameters with hidden and subtle information being at stake. To this end, multifarious adaptive methods within mathematics-informed frameworks have gained prominence for the optimized solution of complex problems. This will enable us to ensure that solution is not superficial or pretentious but reliable, robust, and smooth enabling the maintenance of quality, sustainability and meritocracy.

The overarching aim of this book is to address the need concerning novel analytic strategies and mathematical modeling to achieve reliable and optimized global solutions with regard to Multi-chaos, Fractal, and Multi-fractional in the era of Artificial Intelligence, which requires the indispensable integration of advanced mathematical models and AI for a much smarter level of blended systems in complex settings. Appealing to an interdisciplinary network of scientists and researchers to disseminate the theory and application of Multi-chaos, Fractal, and Multi-fractional AI of Different Complex Systems in medicine, neurology, mathematics, physics, biology, chemistry, information theory, engineering, computer science, social sciences and other far-reaching domains, the primary focus is to enable the provision of global and optimized robust solutions distinctively with a perspective through multifarious methods, different from the conventional perspective, as directed toward paradoxical situations, different uncertain processes, nonlinear dynamic systems inherent in complex systems.

Based on these ideas and consideration, the prominent objectives of our edited book can be outlined as follows:

- Constructing and presenting a multifarious approach for critical decision-making processes embodying paradoxes and uncertainty,

- Combining theory and applications with regard to multi-chaos, fractal and multi-fractional AI of different complex systems and many-body systems,

- Enabling the provision of global and optimized robust solutions distinctively with a perspective through multifarious methods and mathematics-informed frameworks, as different from the conventional perspective,

- Providing an outlook directed toward the prediction and management of paradoxical situations, different uncertain processes, and nonlinear dynamic components inherent in a given complex system,

- Facilitating the dissemination of theory and application of multi-chaos, fractal, and multi-fractional AI in different complex systems of various areas,

- Establishing a balance between data use and ethical matters while employing computational technologies in different complex systems of numerous domains,

- Acting as a bridge between application of advanced computational mathematical methods and AI based on comprehensive analyses and broad theories.

Accordingly, each chapter of this edited book addresses different uncertain processes inherent in the complex systems and attempts to provide accurate, flexible, global, and robust optimized solutions distinctively, with a perspective through the related multifarious methods fit for the content. To this end, this edited book of ours foregrounds Multi-chaos, Fractal and Multi-fractional in the era of Artificial Intelligence, which definitely requires the integration of advanced mathematical models and mathematics-informed frameworks as well as AI addressing fractal, fractional calculus, fractional operators, quantum, wavelet, entropy-based applications apart from the means of modeling, technical analyses, and numerical simulations as some of the most extensively used methods for the solution of related multifaceted problems characterized by nonlinearity, nonregularity, self-similarity and many other properties, frequently encountered in different complex systems.

Motivated by the aforementioned considerations, the content of the chapters along with their novel aspects are outlined as follows.

Chapter 2 entitled Theory of Complexity, Origin and Complex Systems (by Yeliz Karaca) attempts to encompass the possible dimensions of complex systems in different fields focusing on origin-related, historical, evolutionary and epistemological viewpoints of complexity with the goal of providing a global understanding thereof, taking into consideration the various multiple interacting factors of systems. In addition, through the presentation of complex order processes toward modern scientific path, it aims to understand the related conditions and demands for handling complex problems of the 21st century and onwards. It, furthermore, intends to elaborate on accounts of past, present and future in different complex systems, which can help us adopt a deeper understanding and implement the steps along the way. By providing the complex order processes toward modern scientific path, from Darwin and onwards, a conceptual outline is also presented along with the details of complexity and complex systems. Complex systems, complexity thinking and theory, in fact, can broaden the horizon and scope of modern way of thinking, which needs to depend on transition from evolutionary dimension as a revolutionary stage and as a new paradigm for natural sciences and social sciences. Therefore, the characterization, definition, analysis and understanding of complex systems include a powerful relation between variables, sensitivity to initial control as well as strange, nonperiodic and unpredictable time evolution. Overall, this detailed presentation aims to ensure that the foundation for the complex systems' interpretations can be explored in different related areas of complexity.

Chapter 3 named Multi-chaos, Fractal and Multi-fractional AI in Different Complex Systems (by Yeliz Karaca) provides an overview that includes multi-chaos, fractal, fractional and Artificial Intelligence (AI) way of thinking regarding the solution of the complex system problems concerned with natural and social sciences. Moreover, ethical decision-making frameworks and strategies related to big data and AI applications are provided in detail for the purpose of enabling assistance to identify the related problems in different settings and thinking methodically in order that tensions between conflicting aspects can be managed in a systematic way. Data reliability and complexity, chaos thinking and processes and complexity, fractal thinking and processes and complexity, fractional thinking and processes and complexity, finally, AI way of thinking and processes and complexity are among the points elaborated in the chapter. Thus, the chapter is directed toward modern scientific thinking which has to adopt the systemic properties, addressing them by revealing the spontaneous processes pertaining to self-organization in a dynamical system in a state far from the equilibrium point and close to the disequilibrium point with no existence of an external force acting on the system. This way of thinking, naturally, poses a challenge against reductionist way of thinking and the dichotomy between the natural world and social world, by considering the concepts around complexity, evolution and order in detail.

Chapter 4 named High Performance Computing and Computational Intelligence Applications with Multi-chaos Perspective (by Damiano Perri, Marco Simonetti, Osvaldo Gervasi and Sergio Tasso) addresses the experience of the COVID-19 pandemic which has actually accelerated many chaotic processes in modern society besides pronouncing the urge to understand complex processes to achieve common well-being in a very serious and emergent way. The main contribution of the chapter is directed to the set of best practices and case studies, which provide assistance to the researchers while handling computationally complex problems. By analyzing different technologies and applications, complex phenomena are sought to be understood in the environment with ever increasing complexity bearing in mind different elements such as technology, algorithms and changing lifestyles, while striving to achieve maximum efficiency as well as outcomes besides protecting the integrity of individuals' personal data and, above all, respecting the human being as a whole. The chapter considers that all these challenges impose a radical change in many different areas, including ones related to computational resources, which makes it very important to manage complex problems brought about by multi-chaotic situations. One section of the chapter is on computational intelligence, with the description of some of the techniques that enable the acceleration of complex problems' resolution by exploiting the potential provided by machine learning techniques (like Multi-layer Perceptron and Convolutional Neural Network) that can attain dimensions which used to be unimaginable in the past. The chapter also deals with the features of a quantum computer, which can process data at a rate exponentially faster than a classical computer. Taken together, the chapter provides a general sketch of various topics which could be of help to researchers and developers to deal with complex and chaotic situations within the scope of machine learning and the issue of privacy including the recent related regulations.

Chapter 5 bears the title of Human Hypercomplexity, Error and Unpredictability in Complex Multi-Chaotic Social Systems (by Piero Dominici), which has the outlook that traditional linear models and deterministic approaches can no longer be capable of the analysis of reality's unstable dynamics. The chapter provides perspectives on the complexity of living energy and living beings; 12 essential planes of awareness; the characteristics of complicated, complex and hypercomplex systems; epistemology of error as well as complex and chaotic characteristics of social systems. The author of the chapter provides insights into the ambivalent nature of complexity, cognitive, subjective, social, ecological and ethical aspects of complexity including linguistics and communication as well as a culture of communication. Given that, hypercomplexity is not an option; but a fact of life. However, the problematics is related to the condition that we have not been trained and educated to recognize it, much less to inhabit it. Thus, it is important to bear in mind that complexity is a structural characteristic of human groups, relations, social systems and the biological world.

Chapter 6 entitled Multifractal Complexity Analysis-Based Dynamic Media Text Categorization Models by Natural Language Processing with BERT (by Yeliz Karaca, Yu-Dong Zhang, Ahu Dereli Dursun and Shui-Hua Wang) addresses the challenges and complexity pertaining to media texts. Due to properties like being unstructured, noisy and nonstandard, accurate conveyance of meaning becomes problematic and against this background, the study aims at ensuring regularity and self-similarity within the digital-based complex media text by multi-fractal methods, which are multifractal Bayesian, multifractal regularization and multifractal wavelet shrinkage. Bidirectional Encoder Representations from Transformers (BERT) as the Natural Language Processing (NLP) method is employed to attain the accurate classification and categorization of the words within texts in the dataset. The related steps of the integrative method proposed in the study includes regularity enhancement by the application of the three aforementioned multifractal methods to the text dataset. By obtaining the significant, self-similar and regular attributes, new datasets were generated with the respective application of the multifractal methods. Subsequently, BERT, as the NLP technique, was employed to the text dataset and the three new datasets were obtained for the classification purposes. In this way, accurate word detection within the text for the category classification was ensured for the analyses. The analysis results for the text dataset and the new datasets were compared by BERT and the most optimal result could be attained by multifractal Bayesian method. The study enunciates the significance of the behavioral patterns of fractal while setting forth the distinctive quality of BERT owing to its capability of classification accuracy and adaptiveness into integrated methodologies.

Chapter 7 (Part I) entitled Mittag-Leffler Functions with Heavy-tailed Distributions' Algorithm based on Different Biology Datasets to be Fit for Optimum Mathematical Models' Strategies (by Dumitru Baleanu and Yeliz Karaca) is motivated by the challenge of integrating fractional calculus in cases of complexity, which requires an effective use of empirical, numerical, experimental and analytical methods to tackle complexity. One of the most noteworthy tools in the fractional calculus context is noted to be the Mittag-Leffler (ML) functions whose distributions have extensive application domains while dealing with irregular and nonhomogeneous environments for the solutions of dynamic problems. The proposed integrated approach in this chapter addresses the Mittag-Leffler (ML) function with two parameters for the purpose of investigating the dynamics of two diseases: cancer cell and diabetes. The following are the steps of the study: ML function with two parameters was applied to the biological datasets, namely the cancer cell dataset and diabetes dataset. It was aimed to obtain new datasets (ml_cancer cell dataset and ml_diabetes dataset) with significant attributes for the diagnosis, prognosis and classification of diseases. Next, heavy-tailed distributions, which are Mittag-Leffler distribution, Pareto distribution, Cauchy distribution and Weibull distribution, were applied to the new datasets obtained. The comparison of them was done relating to the performances by employing the log likelihood value and the Akaike Information Criterion (AIC). Following these steps, the ML functions that represent the cancer cell and diabetes data were identified so that the two parameters which yield the optimum value based on the distributions fit could be found. By finding the most significant attributes with heavy-tailed distributions (The Mittag-Leffler distribution, Pareto distribution, Cauchy distribution and Weibull distribution) based on Mittag-Leffler function with two parameters , the diagnosis, prognosis, and classification of the diseases were ensured in the chapter. The integrative scheme proposed along with the optimal strategical means were for the accurate and robust mathematical models' strategies concerning the diagnosis and progress of the diseases. Accordingly, the results obtained demonstrate that the integrative approach with Mittag-Leffler with heavy-tailed distribution algorithm is applicable, fitting very well to the related data with the robust parameter values observed and estimated in transient chaotic and unpredictable settings.

Chapter 8 (Part II) has the title Artificial Neural Network Modeling of Systems Biology Datasets Fit Based on Mittag-Leffler Functions with Heavy-tailed Distributions for Diagnostic and Predictive Precision Medicine (by Yeliz Karaca and Dumitru Baleanu), which obtains the generation of optimum model strategies for different biology datasets along with the Mittag-Leffler functions with heavy-tailed distributions. The integrative modeling scheme proposed in the chapter is concerned with the applicability and reliability of the solutions obtained by the two-parametric Mittag-Leffler functions with heavy-tailed distributions. Accordingly, the proposed integrated approach in this chapter investigates the dynamics of diseases related to biological elements. Emerging in the different solutions of varying complex biological systems, the ML function with two parameters was applied to the biological dataset, namely cancer cell and diabetes and the new datasets were generated. The heavy-tailed distributions (The Mittag-Leffler distribution, Pareto distribution, Cauchy distribution and Weibull distribution) were applied to the new datasets obtained with their comparison performed in relation to the performances (by employing the log likelihood value and the Akaike Information Criterion (AIC)). ML functions that represent the cancer cell and diabetes data were identified so that the two parameters yielding the optimum value based on the distributions fit could be found. Subsequently, Multilayer Perceptron (MLP), as one of the ANN algorithms, was applied for the diagnostic and predictive purpose of the disease related to the optimized ML functions that represent the cancer cell and diabetes datasets obtained and the performances of the ML functions with heavy-tailed distributions were compared with ANN training functions (Levenberg-Marquart, Bayes Regularization and BFGS-Quasi-Newton). The results based on mathematical models demonstrate that the integrative approach with Mittag-Leffler and ANN applications is applicable and also fits very well to the related data with the robust parameter values observed and estimated. The integration of ANN with the self-organization and self-learning capability in pattern identification and recognition along with the rational thinking and acting ability while making inferences and decisions based on past experience has also been shown to be critical. Since AI enables the building of precise models to avoid unpredictable risks and identify opportunities in nonlinear complex situations, its integration in precision medicine is also foregrounded in this chapter.

Chapter 9 named Computational Fractional-Order Calculus and Classical Calculus AI for Comparative Differentiability Prediction Analyses of Complex-systems-grounded Paradigm (by Yeliz Karaca and Dumitru Baleanu) aims to provide an intermediary facilitating function both for the physicians and individuals through establishing an accurate and robust model based on the integration of fractional-order calculus and ANN for the diagnostic and differentiability predictive purposes with the diseases which display highly complex properties. The integrative and multi-staged approach proposed in the chapter includes the application of the Caputo fractional derivative with two-parametric Mittag-Leffler function on the stroke dataset and cancer cell dataset. The establishing of new fractional models with varying degrees is performed and the reason why the Mittag-Leffler function has been opted is for its distributions of extensive application domains, which can enable it to handle irregular and heterogeneous environments for the solution of dynamic problems. Subsequently, the new datasets related to cancer cell and stroke were obtained by employing Caputo fractional derivative with the two-parametric Mittag-Leffler function. Furthermore, classical calculus is applied to the raw datasets; and the performance of the new datasets as obtained from the Caputo fractional derivative with the two-parametric Mittag-Leffler function, the datasets obtained from the classical calculus application and the raw datasets is compared by using Feed Forward Back Propagation (FFBP), as one of the algorithms of ANN. As per the accuracy rate results obtained, the FFBP application, the suitability of the Caputo fractional-order derivative model for the diseases has been demonstrated. The experimental results obtained by this chapter also point to the applicability of the complex-systems-grounded paradigm scheme as has been proposed. It should also be noted that modeling many complex systems can be possible by fractional-order derivatives based on fractional calculus so that related syntheses can be realized robustly and effectively. Consequently, computational complexity is shown to provide us with applicable sets of ideas or integrative paradigms to recognize and understand the intricate properties of complex systems.

Entitled Pattern Formation Induced by Fractional-order Diffusive Model of COVID-19, Chapter 10 (by Naveed Iqbal and Yeliz Karaca) provides the investigation of the Turing instability produced by fractional diffusion in a COVID-19 model. Considering that differential equations with complex order fractional derivatives enable the regulation of complicated fractional systems, positive equilibrium points have been initially specified and Routh-Hurwitz criteria are used for the assessment of the positive equilibrium point's stability. Local equilibrium points and stability analysis have been employed to find the conditions for Turing instability. The analysis, by looking into the system's dynamical behavior and the bifurcation point centered on the death rate, aims to serve as a leverage for further studies in different disciplines concerning COVID-19 model through the lenses of distinct viewpoints. The results of the analyses reveal the highly complex connection between COVID-19 and fractional order diffusion, the turing bifurcation point, and weakly nonlinear analysis used in the fractional-order dynamics discussed in the chapter. The Turing bifurcation point and weakly nonlinear analysis used throughout the complex fractional-order dynamics handled in the chapter are particularly relevant experimentally and computationally since the related effects can be examined and utilized in numerous mathematical, chemical, and ecological models, along with engineering, computer science, bioengineering, information science, applied sciences and virology as well as other related areas. Within this scale, fractional calculus is known to unfold the fundamental mechanisms and multi-scale dynamic phenomena in biological tissues. The results of the chapter are important in terms of showing that, on a quantitative basis, they can be extended to a variety of statistical, physical, engineering, biological and further related models.

Chapter 11 whose title is Prony's Series in Time and Frequency Domains and Relevant Fractional Models (by Jordan Hristov) addresses Prony's series approximation of monotonical responses in material viscoelastic rheology as well as the possibilities of implementation on such a basis depending on modern fractional operations with nonsingular kernels, namely the Caputo-Fabrizio operator. The chapter also provides the outline of the origins of Prony's series in time and frequency domains along with the relevant approximation and calculation techniques. The results of the study expose the mutual relationships between the operators with singular and nonsingular kernels. The chapter sheds light on what type of operators are applicable in models fitting and modeling their experimental data. In this way, contributions in pure mathematics and experimental aspects are put forth. Consequently, the elaboration and application of Prony's series are said to be extended to modeling problems emerging in mechanical engineering, chemical engineering as well as other related disciplines.

Chapter 12 is entitled A Chain of Kinetic Equations of Bogoliubov-Born-Green-Kirkwood-Yvon and Its Application to Nonequilibrium Complex Systems (by Nicolai (Jr) Bogoliubov, Mukhayo Rasulova, Tohir Akramov and Umarbek Vazov) which is devoted to the study of the Bogoliubov-Born-Green-Kirkwood-Yvon chain of kinetic equations (BBGKYchke) and its applications to modern problems of physics. The chapter focuses on the need of creating a mathematical apparatus which fulfills the existing theory of one-particle systems and systems made up of a huge number of particles. A unique object which satisfies the related conditions is the BBGKYchke as obtained from the Liouville equation for many particles. Two types of BBGKY chains are addressed for both classical and quantum particle systems. And, in contrast with the Liouville equation, the BBGKYchke has collision integrals. The first approximation coincides with the well-known Boltzmann, Vlasov and Landau equations, while the last equations provide the description of the evolution of one or two particles in modern physics. In the chapter, the example of quantum many-particle systems has been provided, which shows how the use of the BBGKYchqke, one-particle problems can be generalized for the case of nonequilibrium systems that consist of interacting particles within a kinetic theory framework. The chapter concerns such nonequilibrium particle systems interacting with the generalized Yukawa potential as well. Overall, the solution of the BBGKYchqke for generalized Yukava potential (gYp) is provided, and solving of the BBGKYchqke with the gYp for systems of many type particles is elaborated on. Finally, the Gross-Pitaevsky equation is derived based on the BBGKYchqke.

Chapter 13 named Hearing Loss Detection in Complex Setting by Stationary Wavelet Rényi Entropy and Three-segment Biogeography-based Optimization (by Yabei Li and Junding Sun) addresses another health problem which is hearing loss that decreases the life quality of individuals. The main objective of the research is to improve the accuracy and efficiency of detecting images in sensorineural hearing loss through a new solution. The chapter includes the proposal of an improved feature extraction method stationary wavelet Rényi entropy (SWRE) as well as optimization algorithm for model and feature extraction, namely three-segment biogeography-based optimization (3SBBO). It is noted that the current hearing loss detection methods have only a fixed scheme of feature extraction process and optimization mostly for classifiers. The experiments conducted demonstrate high rates of sensitivities, which corroborate the fact that the approach adopted in the research has attained a state-of-the-art performance and can be applied in the diagnosis of hearing loss.

Chapter 14 entitled Shannon Entropy-based Complexity Quantification of Nonlinear Stochastic Process: Diagnostic and Predictive Spatio-temporal Uncertainty of Multiple Sclerosis Subgroups (by Yeliz Karaca and Majaz Moonis) considers the growth of complexity, which in more nonlinear and complicated instances, evolves with increasing information and entropy in a monotonous way. Complex dynamic characteristics of systems based on entropy require a detailed specification and synthesis of the intricate elements as the system gets more and more complex. Thus, the chapter carries the aim of facilitating the accurate classification and course of three subgroups of Multiple Sclerosis (MS), namely Relapsing Remitting (RRMS), Secondary Progressive MS (SPMS), Primary Progressive MS (PPMS), which is a debilitating neurological disease. For this particular aim, an entropy-based feature selection method (Shannon Entropy and Minimum Redundancy Maximum Relevance) as well as linear transformation methods (Principal Component Analysis and Linear Discriminant Analysis) were applied to the MS dataset, from which four new datasets with significant attributes were generated. In addition, each new dataset obtained was addressed as input for the training procedure of k-Nearest Neighbor (k-NN) and decision tree algorithms. Finally, the accuracy rates for the MS subgroups' classification were analyzed comparatively based on the optimized experimental results which demonstrate that Shannon Entropy, as a distinctive entropy method, proved to be higher in terms of accuracy compared to the other feature selection methods. The chapter, therefore, intends to point a new perspective, with a multi-level aspect, for critical decision-making and manageable tracking in medicine and relevant fields, which all need to cope with the complex dynamic systems in which uncertainty and heterogeneity prevail.

Chapter 15 entitled Chest X-ray Image Detection for Pneumonia via Complex Convolutional Neural Network and Biogeography-based Optimization (by Xiang Li, Mengyao Zhai and Junding Sun) proposes a novel chest X-ray image detection for pneumonia, which is stated to be a leading reason for death among children and afflict the elderly worldwide. The detection model proposed by the authors is based on the combination of complex convolutional neural network (CNN) and biogeography-based optimization (BBO). It is proven that the model has higher sensitivity and accuracy in terms of detecting the pneumonia-related chest X-ray images with a detection performance being significantly better than that of advanced approaches within complex medical settings. The utilization of BBO, which