Mathematical Modeling for Computer Applications The mathematical sciences are part of nearly all aspects of everyday life. The discipline has underpinned such beneficial modern capabilities as internet searches, medical imaging, computer animation, numerical weather predictions, and all types of digital communications. This outstanding new volume in the series, "Mathematics and Computer Science," examines the current state of mathematical science and explores the changes needed for the discipline to be in a strong position and able to maximize its contributions. Besides covering important practical applications for the areas where mathematics and computer science intersect, the editors of this new volume recommend that training for future generations of mathematical scientists should be re-assessed in light of the increasingly cross-disciplinary nature of the mathematical sciences. In addition, because of the valuable interplay between ideas and people from all parts of the mathematical sciences, this group of curated papers emphasizes that universities and governments need to continue to invest in the full spectrum of the mathematical sciences in order for the whole enterprise to continue to flourish long-term. Emphasis on important developments in applied mathematics and modeling, analysis and its applications, applied algebra and its applications, geometry and its applications, algebraic statistics and its applications as well as algebraic topology and its applications are covered. Whether for the veteran engineer, new hire, or student, this is a must-have volume for any library.

Table of Contents:
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