Mathematical Modeling for Computer Applications

Biswadip Basu Mallik is a senior assistant professor of mathematics in the Department of Basic Sciences and Humanities at the Institute of Engineering and Management, India. He has been involved in teaching and research for more than 21 years and has published several research papers in various scientific journals along with book chapters with various publishers. He has authored five and has five patents to his credit. He is a managing editor of the Journal of Mathematical Sciences & Computational Mathematics and is an editorial board member and reviewer for several scientific journals. M. Niranjanamurthy, PhD, is an assistant professor in the Department of Computer Applications, M S Ramaiah Institute of Technology, Bangalore, Karnataka. He earned his PhD in computer science at JJTU, Rajasthan, India. He has over 11 years of teaching experience and two years of industry experience as a software engineer. He has published several books, and he is working on numerous books for Scrivener Publishing. He has published over 60 papers for scholarly journals and conferences, and he is working as a reviewer in 22 scientific journals. He also has numerous awards to his credit. Sharmistha Ghosh, PhD, is a professor at the Institute of Engineering and Management, India. She received her doctorate in mathematics from the Indian Institute of Technology, India. Her major field of study includes fuzzy and vague databases as well as computational fluid dynamics, and she has published several papers in scientific journals. She is also the editor of several scientific journals and works as reviewer of journals as well as doctoral theses in India as well abroad. Valentina Emilia Balas, PhD, is a full professor in the Department of Automatics and Applied Software at the Faculty of Engineering, "Aurel Vlaicu" University of Arad, Romania. She holds a PhD cum Laude in applied electronics and telecommunications from the Polytechnic University of Timisoara. She is the author of more than 350 research papers and is the editor-in-chief of two esteemed journals and is an editorial board member for several other national and international publications. Krishanu Deyasi is an associate professor in the Department of Basic Sciences and Humanities at the Institute of Engineering and Management, India. He earned his PhD from the Indian Institute of Science Education and Research, and he has postdoctoral experience from The Institute of Mathematical Sciences, India. He has written three books and has published papers in scientific journals. He is also an editor for several scientific journals. Santanu Das is as an assistant professor in the Department of Basic Sciences and Humanities at the Institute of Engineering and Management, India. He completed his undergraduate degree from and is pursuing his doctorate from Jadavpur University.

Preface xxi

1 Fermatean Fuzzy Entropy Measure with Application in Decision Making Using COPRAS Approach 1
Mansi Bhatia, H. D. Arora, Anjali Naithani and Vijay Kumar

1.1 Introduction 2

1.2 Preliminaries 4

1.3 Novel Fermatean Entropy Measure 5

1.4 Application of Entropy Measure Through COPRAS 7

1.5 Comparative Analysis 12

1.6 Conclusion 13

References 13

2 Some Properties of Cartesian and Lexicographic Products of Soft Graphs 17
Jinta Jose, Bobin George and Rajesh K. Thumbakara

2.1 Introduction 17

2.2 Soft Graphs 18

2.3 Some Properties of Cartesian and Restricted Cartesian Products of Soft Graphs 20

2.4 Some Properties of Lexicographic and Restricted Lexicographic Products of Soft Graphs 23

2.5 Conclusion 26

References 26

3 Advancements in Enhancing Car Object Detection in Complex and Adverse Environmental Conditions Through Deep Learning Techniques 29
Rejuwan Shamim, Biswadip Basu Mallik and Trapty Agarwal

3.1 Introduction 30

3.2 Literature Review 33

3.3 Methodology 35

3.4 Result 44

3.5 Discussion 49

3.6 Conclusion 54

References 57

4 Approximation by Durrmeyer Type Operators Using Polya Distribution 61
Prerna Sharma and Diwaker Sharma

4.1 Introduction 61

4.2 Basic Outcomes 63

4.3 Direct Results 65

4.4 Discussion 73

Disclaimer 73

References 73

5 Solution of Pollutant Dispersion in Porous Medium Under Linear Sorption Using Finite Element Method 75
Rashmi Radha, Tapan Paul, Rakesh Kumar Singh, Nav Kumar Mahato and Mritunjay Kumar Singh

5.1 Introduction 76

5.2 Mathematical Formulation 77

5.3 Numerical Derivation of the Proposed Model Problem by FEM Method 79

5.4 Analytical Derivation of the Proposed Model Equation 81

5.5 Results and Discussion 83

5.6 Conclusion 87

References 88

6 A Comparative Analysis of Fuzzy and Neutrosophic Database Models in Handling Imprecise Queries 91
Doyel Sarkar and Sharmistha Ghosh

6.1 Introduction 92

6.2 Basic Definitions 93

6.3 Processing Imprecise Query using Fuzzy and Neutrosophic Sets 94

6.4 Results and Discussion 98

6.5 Concluding Remarks 98

References 99

7 Tweaked Portfolio Estimation Regarding Indian Securities Exchange: An Empirical Study 101
Abhijit Biswas and Meghdoot Ghosh

7.1 Introduction 102

7.2 Literature Review in Financial Market 102

7.3 Method 103

7.4 Results 107

7.5 Discussion 116

References 116

8 Fixed Point Results Related to Graph Theory 117
Aditya Bhattacharya, Özen Özer, Sonendra Gupta, Ramakant Bhardwaj and Sonam

8.1 Introduction 117

8.2 Preliminaries 118

8.3 Main Results 119

References 128

9 Unleashing GPT-3’s Potential in Automatic Text Generation: A Comprehensive Study and Analysis 131
Rejuwan Shamim and Biswadip Basu Mallik

9.1 Introduction 132

9.2 Literature Review 133

9.3 Methodology 135

9.4 Evaluation Metrics 140

9.5 Experimental Results 143

9.6 Discussion 147

9.7 Exploration of the Strengths and Weaknesses of GPT-3 for Automatic Text Generation 148

Conclusion 150

References 151

10 Optimization Techniques and Their Applications in Science and Engineering 153
Ravi Kiran Bagadi, Eali Stephen Neal Joshua, T. Pavankumar, S. NagaMallik Raj and Debnath Bhattacharyya

10.1 Introduction 154

10.2 Related Work 159

10.3 Metaheuristic Optimization Techniques 167

10.4 Multi-Objective Optimization 172

10.5 Stochastic Optimization 176

10.6 Robust Optimization 180

10.7 Applications of Robust Optimization in Science and Engineering 182

10.8 Applications of Optimization Techniques in Science and Engineering 183

10.9 Challenges and Future Directions in Optimization 189

Conclusion 194

References 195

11 On Sum 3-Equitable Labeling of Some Graphs 197
Sarang Sadawarte and Sweta Srivastav

11.1 Introduction 197

11.2 Terminology and Notation 198

11.3 Results 199

11.4 Conclusions and Perspectives 205

References 205

12 An Application of Invariant Point Theory in G-Metric Spaces with Special Emphasis on Alpha-Psi Contraction 207
Samriddhi Ghosh, Sonam, Deb Sarkar, Poulami Halder and Ramakant Bhardwaj

12.1 Introduction 207

12.2 Elementaries 210

12.3 Main Result 211

Acknowledgement 216

Collision of Interest 216

References 217

13 Fixed Point Results for Compatible Mapping of Type (α) in Fuzzy Metric Spaces 219
Poulami Halder, Samriddhi Ghosh, Ramakant Bhardwaj, Sonam and Satyendra Narayan

13.1 Introduction 219

13.2 Preliminaries 220

13.3 Compatible Mappings of Type (α) 222

13.4 Main Results 223

Acknowledgement 229

Conflict of Interest 229

References 229

14 Combined Matrices Associated with Soft Digraphs 231
Bobin George, Jinta Jose and Rajesh K. Thumbakara

14.1 Introduction 231

14.2 Soft Digraphs 232

14.3 Combined Adjacency Matrix of a Soft Digraph 234

14.4 Combined Incidence Matrix of a Soft Digraph 236

14.5 Conclusion 238

References 238

15 Refining Medical Text Query Responses: Tailoring Hugging Face’s BERT Model for Precise and Swift Medical Question Answering 241
Rejuwan Shamim, Badria Sulaiman Alfurhood and Biswadip Basu Mallik

15.1 Introduction 242

15.2 Related Work 244

15.3 Methodology 248

15.4 Result 253

15.5 Strengths and Weaknesses of the Fine-Tuned BERT Model 255

15.6 Applications 257

15.7 Conclusion 258

References 260

16 Machine Learning Mathematics: A Study on Concepts of Processing Knowledge 263
Prasad Kaviti, Eali Stephen Neal Joshua, N. Venkatram, Dinesh Reddy and Debnath Bhattacharyya

16.1 Introduction 264

16.2 Mathematical Concepts in Machine Learning 264

16.3 Conclusion 299

Disclaimer 299

References 299

17 Nature-Inspired Algorithms to Optimize the Hyper-Parameters of Deep-Learning Networks for Diagnosing Brain Disorders – A Review 301
Manoj Kumar Sharma, M. Shamim Kaiser and Kanad Ray

17.1 Introduction 302

17.2 Literature Review 303

17.3 Applications 307

17.4 Challenges and Future Directions 309

17.5 Conclusions and Perspectives 312

References 312

18 YOLOv8 for Anomaly Detection in Surveillance Videos: Advanced Techniques for Identifying and Mitigating Abnormal Events 317
Rejuwan Shamim, Badria Sulaiman Alfurhood, Trapty Agarwal and Biswadip Basu Mallik

18.1 Introduction 318

18.2 Overview of YOLOv8 and its Advantages in Object Detection 319

18.3 Related Work 321

18.4 YOLOv8 Architecture 324

18.5 Dataset Preparation 327

18.6 Training YOLOv8 for Anomaly Detection 330

18.7 Evaluation Metrics 332

18.8 Results and Discussion 334

18.9 Conclusion 343

References 346

19 Linear Stability and Resonance of Oblate Infinitesimal in the Nearby Region of Triangular Equilibrium Points for Triaxial Primaries in the Elliptic Restricted Three Body Problem 351
Shilpi Dewangan, A. Narayan and Poonam Duggad

19.1 Introduction 352

19.2 Equation of Motion 353

19.3 Position of Triangular Equilibrium Points 355

19.4 Normalization at Hamiltonian for Stability of First Order 356

19.5 Resonance Cases 366

19.6 Conclusion 368

References 370

20 Magnetic Nanofluid Flow with Micro‐Organisms and Viscous Dissipation 373
Shweta Mishra, Sharmistha Ghosh and Hiranmoy Mondal

Nomenclature 374

20.1 Introduction 375

20.2 Mathematical Exploration 376

20.3 Similarity Transformation 378

20.4 Heat-Mass Transferal 379

20.5 Discussion of Results 380

20.6 Conclusion 384

References 384

21 The Application of Deep Learning to the Localization of Brain Tumors 387
Charanarur Panem, Srinivasa Rao Gundu, J. Vijaylaxmi and Biswadip Basu Mallik

21.1 Introduction 388

21.2 Proposed Method 389

21.3 Conclusion 395

Acknowledgement 395

References 395

22 Contextual Information Retrieval using Root Word Stemming in Indian Languages 397
Chandamita Nath and Bhairab Sarma

22.1 Introduction 397

22.2 Literature Review 399

22.3 Problem Statement 399

22.4 Experimental Work 400

22.5 Conclusion and Future Work 402

Disclaimer 403

References 404

23 Recent Advances in Object Detection Based on YOLO-V 4 and Faster RCNN: A Review 405
Anwesa Das, Atanu Nandi and Ishani Deb

23.1 Introduction 406

23.2 Literature Review 407

23.3 Proposed Methodology 409

23.4 Result and Discussion 413

23.5 Conclusion 416

References 417

24 Detection of Leukemia Using Transfer Learning 419
Biplab Kanti Das, Chanchal Ghosh, Joydeb Sheet and Himadri Sekhar Dutta

24.1 Introduction 420

24.2 Literature Survey 421

24.3 Dataset 423

24.4 Proposed Methodology 424

24.5 Pre-Processing of Image 425

24.6 Deep Learning Model Generation 426

24.7 Classification 430

24.8 Results and Analysis 430

24.9 Conclusion and Future Direction 434

References 434

25 IoMT – An ML-Based Patient Monitoring System with Prediction of Health Condition 437
Kakali Das, Sagnik Ghosh and Himadri Sekhar Dutta

25.1 Introduction 438

25.2 System Architecture 440

25.3 Machine Learning Algorithm 443

25.4 Results and Discussion 444

25.5 Conclusion 449

References 449

26 Eulerian Soft Graphs 453
Jinta Jose, Bobin George and Rajesh K. Thumbakara

26.1 Introduction 453

26.2 Soft Graphs 454

26.3 Eulerian Soft Graphs 454

26.4 Conclusion 460

References 461

27 An Algorithm to Solve an Exponential Diophantine Equation 463
Subramani K. and Srinivasa Prasanna

27.1 Introduction 464

27.2 Example 466

27.3 Conclusion 475

Acknowledgements 475

References 475

28 Optimal Number of Emergency Facility and Its Positioning Using Nature-Based Algorithm: A Case of Mumbai City 477
K.V. Ajaygopal and Rakesh Verma

28.1 Introduction 478

28.2 Literature Review 479

28.3 Real-Life Application 484

28.4 Results and Discussion 487

28.5 Conclusion 489

References 490

Appendix 492

29 Chicken Swarm Optimization Algorithm-Based Propagation Delay Estimation in Transmission Path of UWASN 501
A. Kannappan and R.M. Bommi

29.1 Introduction 502

29.2 General Biology Behavior of Chicken Swarm 503

29.3 Chicken Swarm Pseudocode 506

29.4 Results and Discussion 507

29.5 Conclusion 508

References 509

30 Frequency Analysis of Coreference Resolution 513
Mridusmita Das and Apurbalal Senapati

30.1 Introduction 514

30.2 Existing Literature 515

30.3 Resource Building for the English and Assamese Languages 517

30.4 Description of the Data Sets 517

30.5 Frequency Analysis of Coreference Relations 518

30.6 Experiment and Result 520

30.7 Conclusion 520

References 520

31 Hate Neologism in Election Context in India 523
Sujit Das and Apurbalal Senapati

31.1 Introduction 524

31.2 Related Work 525

31.3 Corpus Creation 526

31.4 Methodology 528

31.5 Result 529

31.6 Conclusion 530

References 530

Index 533