This new volume in this groundbreaking series on mathematics and computer science builds on the basic concepts and fundamentals laid out in previous volumes, presenting the reader with more advanced and cutting-edge topics being developed in this exciting field.
is currently working as an Assistant Professor in Department of Basic Science and Humanities at Institute of Engineering & Management, Kolkata. He completed his under graduation and Post-graduation in Mathematics from Jadavpur University and is currently pursuing his PhD from the same University. His field of research work is Cosmology and Dynamical system. He is the Faculty coordinator of Society for Data science IEM student chapter. He is the editor of several books in the domain of Mathematics and computer science .He is also a Development content editor of Journal of Mathematical Sciences & Computational Mathematics (JMSCM), USA.
Table of ContentsPreface
1. Fermatean Fuzzy Entropy Measure with Application in Decision Making Using COPRAS ApproachMansi Bhatia, H. D. Arora, Anjali Naithani and Vijay Kumar
1.1 Introduction
1.2 Preliminaries
1.2.1 Intuitionistic Fuzzy Sets
1.2.2 Pythagorean Fuzzy Sets
1.2.3 Fermatean Fuzzy Sets
1.3 Novel Fermatean Entropy Measure
1.3.1 Entropy
1.4 Application of Entropy Measure Through COPRAS
1.4.1 COPRAS Method
1.4.2 Case Study
1.5 Comparative Analysis
1.6 Conclusion
References
2. Some Properties of Cartesian and Lexicographic Products of Soft GraphsJinta Jose, Bobin George and Rajesh K. Thumbakara
2.1 Introduction
2.2 Soft Graphs
2.3 Some Properties of Cartesian and Restricted Cartesian Products of Soft Graphs
2.4 Some Properties of Lexicographic and Restricted Lexicographic Products of Soft Graphs
2.5 Conclusion
References
3. Advancements in Enhancing Car Object Detection in Complex and Adverse Environmental Conditions Through Deep Learning TechniquesRejuwan Shamim, Biswadip Basu Mallik and Trapty Agarwal
3.1 Introduction
3.1.1 Highlight the Challenging Conditions and Cluttered Backgrounds
3.1.2 Purpose of the Paper
3.2 Literature Review
3.3 Methodology
3.3.1 Selection of Deep Learning Architecture and its Advantages for Handling Complex Visual Patterns
3.3.2 Description of the Dataset
3.3.3 Data Preprocessing Steps
3.3.4 Training and Optimization
3.3.5 Modifications to the Base Architecture
3.3.6 Evaluation Metrics and Benchmark Models
3.4 Result
3.4.1 Comparison of the Performance
3.4.2 Analyze the Results in Terms of Accuracy, Robustness, and Computational Efficiency
3.5 Discussion
3.5.1 Strengths and Weaknesses of the Proposed Approach
3.5.2 Identify Potential Areas for Further Improvement and Future Research
3.6 Conclusion
3.6.1 Reinforce the Significance of the Proposed Deep Learning-Based Approach
3.6.2 Highlight the Impact of the Research on Various Applications
References
4. Approximation by Durrmeyer Type Operators Using Polya DistributionPrerna Sharma and Diwaker Sharma
4.1 Introduction
4.2 Basic Outcomes
4.3 Direct Results
4.4 Discussion
Disclaimer
References
5. Solution of Pollutant Dispersion in Porous Medium Under Linear Sorption Using Finite Element MethodRashmi Radha, Tapan Paul, Rakesh Kumar Singh, Nav Kumar Mahato and Mritunjay Kumar Singh
5.1 Introduction
5.2 Mathematical Formulation
5.3 Numerical Derivation of the Proposed Model Problem by FEM Method
5.4 Analytical Derivation of the Proposed Model Equation
5.5 Results and Discussion
5.6 Conclusion
References
6. A Comparative Analysis of Fuzzy and Neutrosophic Database Models in Handling Imprecise QueriesDoyel Sarkar and Sharmistha Ghosh
6.1 Introduction
6.2 Basic Definitions
6.2.1 Fuzzy Set
6.2.2 Neutrosophic Set
6.2.3 Similarity Measure
6.3 Processing Imprecise Query using Fuzzy and Neutrosophic Sets
6.3.1 Membership Value Calculation
6.3.2 Processing Imprecise Query Using Fuzzy Set
6.3.3 Processing Uncertain Query Using Neutrosophic Set
6.4 Results and Discussion
6.5 Concluding Remarks
References
7. Tweaked Portfolio Estimation Regarding Indian Securities Exchange: An Empirical StudyAbhijit Biswas and Meghdoot Ghosh
7.1 Introduction
7.2 Literature Review in Financial Market
7.3 Method
7.3.1 Data and Methodology
7.3.2 Methodology
7.4 Results
7.5 Discussion
References
8. Fixed Point Results Related to Graph TheoryAditya Bhattacharya, Özen Özer, Sonendra Gupta, Ramakant Bhardwaj and Sonam
8.1 Introduction
8.2 Preliminaries
8.2.1 Kannan Mapping
8.2.2 G-Kannan Mapping
8.2.3 G-Connectedness
8.2.4 Reich–Ćirić–Rus Mapping
8.2.5 G-Reich–Ćirić–Rus Mapping
8.3 Main Results
8.3.1 Lemma
8.3.2 Theorem 1
8.3.3 Example
8.3.4 Theorem 2
References
9. Unleashing GPT-3’s Potential in Automatic Text Generation: A Comprehensive Study and AnalysisRejuwan Shamim and Biswadip Basu Mallik
9.1 Introduction
9.2 Literature Review
9.3 Methodology
9.3.1 Description of the Dataset Used for Training and Evaluation
9.3.2 Explanation of the Pre-Processing Steps
9.3.3 GPT-3 Model Architecture and Configuration
9.3.4 Fine-Tuning Process and Hyperparameter Tuning
9.4 Evaluation Metrics
9.4.1 Metrics Used to Assess the Performance of the GPT-3 Model
9.4.2 Discussion of the Criteria for Evaluating Language Fluency, Coherence, and Relevance in the Generated Text
9.4.3 Description of the Human Evaluation Process for Qualitative Assessment
9.5 Experimental Results
9.5.1 Presentation and Analysis of Quantitative Results, Including Language Fluency, Diversity, and Coherence
9.5.2 Comparison of GPT-3’s Performance with Other State-Of-The-Art Text Generation Models
9.5.3 Qualitative Evaluation of Generated Text Samples Through Human Assessment
9.6 Discussion
9.7 Exploration of the Strengths and Weaknesses of GPT-3 for Automatic Text Generation
Conclusion
References
10. Optimization Techniques and Their Applications in Science and EngineeringRavi Kiran Bagadi, Eali Stephen Neal Joshua, T. Pavankumar, S. NagaMallik Raj and Debnath Bhattacharyya
10.1 Introduction
10.1.1 Types of Optimizations
10.1.2 Linear Programming
10.1.3 Nonlinear Programming
10.1.4 Convex Optimization
10.1.5 Mixed-Integer Linear Programming
10.1.6 Nonlinear Mixed-Integer Programming
10.1.6.1 Quadratic Programming
10.1.6.2 Nonlinear Least Squares
10.1.6.3 Global Optimization
10.1.7 Multi-Objective Optimization
10.1.8 Robust Optimization
10.1.8.1 Applications of Optimization in Science and Engineering
10.1.8.2 Aerospace Engineering
10.1.8.3 Chemical Engineering
10.1.8.4 Civil Engineering
10.1.8.5 Electrical Engineering
10.1.8.6 Environmental Engineering
10.1.8.7 Mechanical Engineering
10.1.8.8 Operations Research
10.2 Related Work
10.2.1 Classical Optimization Techniques
10.2.2 Gradient-Based Methods
10.2.3 Newton’s Method
10.2.4 Conjugate Gradient (CG) Method
10.2.5 Quasi-Newton Methods
10.3 Metaheuristic Optimization Techniques
10.3.1 Simulated Annealing
10.3.2 Genetic Algorithms
10.3.3 Particle Swarm Optimization
10.3.4 Ant Colony Optimization
10.4 Multi-Objective Optimization
10.4.1 Pareto Optimization
10.4.2 Multi-Objective Evolutionary Algorithms
10.4.3 Applications of Multi-Objective Optimization in Science and Engineering
10.5 Stochastic Optimization
10.5.1 Markov Chain Monte Carlo
10.5.2 Bayesian Optimization
10.5.3 Applications of Stochastic Optimization in Science and Engineering
10.6 Robust Optimization
10.6.1 Robust Optimization Techniques
10.7 Applications of Robust Optimization in Science and Engineering
10.8 Applications of Optimization Techniques in Science and Engineering
10.8.1 Optimal Control of Dynamical Systems
10.8.2 Structural Optimization
10.8.3 Material Design Optimization
10.8.4 Logistics Optimization
10.8.5 Energy Systems Optimization
10.9 Challenges and Future Directions in Optimization
10.9.1 Limitations of Current Optimization Techniques
10.9.2 The Role of Machine Learning in Optimization
10.9.3 Emerging Trends and Future Directions in Optimization
Conclusion
References
11. On Sum 3-Equitable Labeling of Some GraphsSarang Sadawarte and Sweta Srivastav
11.1 Introduction
11.2 Terminology and Notation
11.2.1 Definition - Ternary Vertex Labeling
11.2.2 Definition – 3-Equitable Labeling
11.2.3 Definition – Sum 3-Equitable Labeling
11.2.4 Definition – m-Pan Graph
11.3 Results
11.3.1 Theorem
11.3.2 Illustration
11.3.3 Theorem
11.3.4 Illustration
11.3.5 Theorem
11.3.6 Illustration
11.3.7 Theorem
11.3.8 Illustration
11.4 Conclusions and Perspectives
References
12. An Application of Invariant Point Theory in G-Metric Spaces with Special Emphasis on Alpha-Psi ContractionSamriddhi Ghosh, Sonam, Deb Sarkar, Poulami Halder and Ramakant Bhardwaj
12.1 Introduction
12.1.1 About Nonlinear Functional Analysis
12.1.2 Necessity of Invariant Point Theory
12.1.3 Necessity of Metric Space Theory
12.1.4 Literature Review
12.2 Elementaries
12.2.1 Basics of Invariant Point Theory
12.2.2 Basics of G-MS
12.2.2.1 Definition
12.2.2.2 Corollary
12.2.2.3 Definition
12.2.2.4 Theorem
12.3 Main Result
12.3.1 Definition
12.3.2 Theorem
12.3.3 Example
Acknowledgement
Collision of Interest
References
13. Fixed Point Results for Compatible Mapping of Type (α) in Fuzzy Metric SpacesPoulami Halder, Samriddhi Ghosh, Ramakant Bhardwaj, Sonam and Satyendra Narayan
13.1 Introduction
13.2 Preliminaries
13.2.1 Definition: (Fixed point(FP))
13.2.2 Example
13.2.3 Example
13.2.4 Example
13.2.5 Definition (Common FP)
13.2.6 Definition (Continuous t-norm)
13.2.7 Definition (FMS)
13.2.8 Lemma
13.2.9 Proposition
13.3 Compatible Mappings of Type (α)
13.3.1 Definition
13.3.2 Definition
13.4 Main Results
13.4.1 Theorem
13.4.2 Corollary
Acknowledgement
Conflict of Interest
References
14. Combined Matrices Associated with Soft DigraphsBobin George, Jinta Jose and Rajesh K. Thumbakara
14.1 Introduction
14.2 Soft Digraphs
14.3 Combined Adjacency Matrix of a Soft Digraph
14.4 Combined Incidence Matrix of a Soft Digraph
14.5 Conclusion
References
15. Refining Medical Text Query Responses: Tailoring Hugging Face’s BERT Model for Precise and Swift Medical Question AnsweringRejuwan Shamim, Badria Sulaiman Alfurhood and Biswadip Basu Mallik
15.1 Introduction
15.2 Related Work
15.2.1 Existing Question-Answering Systems in the Medical Domain
15.2.2 Limitations and Gaps in the Current Research
15.3 Methodology
15.3.1 BERT Architecture and Pretraining Process
15.3.2 Description of the Medical Text Dataset
15.3.3 Preprocessing and Data Preparation
15.3.4 Fine-Tuning Process of BERT for Medical Question Answering
15.3.5 Model Evaluation Metrics
15.4 Result
15.4.1 Comparative Analysis
15.5 Strengths and Weaknesses of the Fine-Tuned BERT Model
15.6 Applications
15.7 Conclusion
15.7.1 Future Directions
References
16. Machine Learning Mathematics: A Study on Concepts of Processing KnowledgePrasad Kaviti, Eali Stephen Neal Joshua, N. Venkatram, Dinesh Reddy and Debnath Bhattacharyya
16.1 Introduction
16.2 Mathematical Concepts in Machine Learning
16.2.1 Linear Algebra
16.2.1.1 Matrices and Vectors
16.2.1.2 Matrix Factorization
16.2.1.3 Eigenvalues and Eigenvectors
16.2.1.4 Singular Values and Singular Vectors
16.2.1.5 Linear Transformations
16.2.1.6 Orthogonality
16.2.1.7 Matrix Inversion
16.2.1.8 Distance Metrics
16.2.1.9 Norms
16.2.1.10 Determinants
16.2.2 Calculus
16.2.2.1 Limits and Continuity
16.2.2.2 Derivatives
16.2.2.3 Optimization
16.2.2.4 Integrals
16.2.2.5 Chain Rule
16.2.2.6 Taylor Series
16.2.2.7 Partial Derivatives
16.2.2.8 Convexity
16.2.3 Probability Theory and Statistics
16.2.3.1 Probability Distributions
16.2.3.2 Prior Probability
16.2.3.3 Posterior Probability
16.2.3.4 Baye’s Rule
16.2.3.5 Naive Bayes
16.2.3.6 Bayes’ Theorem
16.2.3.7 Bayesian Nonparametrics
16.2.3.8 Maximum Likelihood
16.2.3.9 Measures of Central Tendency
16.2.4 Information Theory
16.2.4.1 Entropy
16.2.4.2 Mutual Information
16.2.4.3 Maximum Entropy Models
16.2.5 Graph Theory
16.2.5.1 Graph Connectivity
16.2.5.2 Graph Clustering
16.2.5.3 Graph Embedding
16.2.5.4 Graph Algorithms
16.2.6 Optimization
16.2.6.1 Convex Optimization
16.2.6.2 Non-Convex Optimization
16.2.6.3 Linear Programming
16.2.6.4 Quadratic Programming
16.2.6.5 Stochastic Optimization
16.2.6.6 Nonlinear Programming
16.2.6.7 Constrained Optimization
16.2.7 Differential Equations
16.2.7.1 Ordinary Differential Equations (ODEs)
16.2.7.2 Partial Differential Equations (PDEs)
16.2.7.3 Stochastic Differential Equations (SDEs)
16.2.8 Topology
16.2.8.1 Topological Data Analysis (TDA)
16.2.8.2 Computational Topology
16.2.8.3 Topology of Neural Networks
16.2.9 Information Geometry
16.2.9.1 Fisher Information
16.2.9.2 Entropy
16.2.9.3 Divergence
16.2.9.4 Information Geometry of Neural Networks
16.2.10 Spectral Geometry
16.2.10.1 Laplacian Eigenmaps
16.2.10.2 Spectral Clustering
16.2.10.3 Graph Convolutional Networks
16.2.10.4 Graph Fourier Transform
16.2.11 Kernel Methods
16.2.11.1 Support Vector Machines (SVMs)
16.2.11.2 Kernel PCA (Principal Component Analysis)
16.2.11.3 Gaussian Processes (GPs)
16.2.11.4 Kernel Ridge Regression
16.2.12 Mathematical Analysis and Signal Processing
16.2.12.1 Wavelet Transform
16.2.12.2 Discrete Cosine Transformation (DCT)
16.2.12.3 Radon Transformation
16.3 Conclusion
Disclaimer
References
17. Nature-Inspired Algorithms to Optimize the Hyper-Parameters of Deep-Learning Networks for Diagnosing Brain Disorders – A ReviewManoj Kumar Sharma, M. Shamim Kaiser and Kanad Ray
17.1 Introduction
17.2 Literature Review
17.3 Applications
17.4 Challenges and Future Directions
17.5 Conclusions and Perspectives
References
18. YOLOv8 for Anomaly Detection in Surveillance Videos: Advanced Techniques for Identifying and Mitigating Abnormal EventsRejuwan Shamim, Badria Sulaiman Alfurhood, Trapty Agarwal and Biswadip Basu Mallik
18.1 Introduction
18.2 Overview of YOLOv8 and its Advantages in Object Detection
18.3 Related Work
18.3.1 Limitations and Challenges of Previous Methods
18.4 YOLOv8 Architecture
18.4.1 YOLOv8 Architecture and Improvements Over Previous Versions
18.4.2 Adaptation of YOLOv8 for Anomaly Detection
18.5 Dataset Preparation
18.5.1 Description of the Surveillance Video Dataset
18.5.2 Data Preprocessing Techniques
18.5.3 Annotation Process for Labeling Normal and Abnormal Events
18.6 Training YOLOv8 for Anomaly Detection
18.6.1 Transfer Learning from the Pre-Trained YOLOv8 Model
18.6.2 Fine-Tuning the Network on the Anomaly Detection Task
18.6.3 Training Strategies and Hyperparameter Settings
18.7 Evaluation Metrics
18.8 Results and Discussion
18.8.1 Analysis of the Impact of Dataset Size and Training Time
18.8.2 Comparison with Baseline Methods and Other Techniques
18.8.3 Limitations of YOLOv8 for Anomaly Detection
18.9 Conclusion
18.9.1 Contributions and Findings of the Paper
18.9.2 Importance of YOLOv8 for Anomaly Detection
18.9.3 Closing Remarks and Potential Applications of the Proposed Method
References
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 ProblemShilpi Dewangan, A. Narayan and Poonam Duggad
19.1 Introduction
19.2 Equation of Motion
19.3 Position of Triangular Equilibrium Points
19.4 Normalization at Hamiltonian for Stability of First Order
19.5 Resonance Cases
19.6 Conclusion
References
20. Magnetic Nanofluid Flow with Micro‑Organisms and Viscous DissipationShweta Mishra, Sharmistha Ghosh and Hiranmoy Mondal
Nomenclature
20.1 Introduction
20.2 Mathematical Exploration
20.3 Similarity Transformation
20.4 Heat-Mass Transferal
20.5 Discussion of Results
20.6 Conclusion
References
21. The Application of Deep Learning to the Localization of Brain TumorsCharanarur Panem, Srinivasa Rao Gundu, J. Vijaylaxmi and Biswadip Basu Mallik
21.1 Introduction
21.2 Proposed Method
21.2.1 Experimental Analysis
21.3 Conclusion
Acknowledgement
References
22. Contextual Information Retrieval using Root Word Stemming in Indian LanguagesChandamita Nath and Bhairab Sarma
22.1 Introduction
22.2 Literature Review
22.3 Problem Statement
22.4 Experimental Work
22.4.1 Choice of Methodology
22.4.2 Development Methodology
22.4.3 Result Analysis
22.5 Conclusion and Future Work
Disclaimer
References
23. Recent Advances in Object Detection Based on YOLO-V4 and Faster RCNN: A Review Anwesa Das, Atanu Nandi and Ishani Deb
23.1 Introduction
23.2 Literature Review
23.3 Proposed Methodology
23.4 Result and Discussion
23.5 Conclusion
References
24. Detection of Leukemia Using Transfer LearningBiplab Kanti Das, Chanchal Ghosh, Joydeb Sheet and Himadri Sekhar Dutta
24.1 Introduction
24.2 Literature Survey
24.3 Dataset
24.4 Proposed Methodology
24.5 Pre-Processing of Image
24.6 Deep Learning Model Generation
24.6.1 CNN Model Structure
24.6.2 Transfer Learning
24.6.3 Model Selection
24.7 Classification
24.8 Results and Analysis
24.9 Conclusion and Future Direction
References
25. IoMT – An ML-Based Patient Monitoring System with Prediction of Health ConditionKakali Das, Sagnik Ghosh and Himadri Sekhar Dutta
25.1 Introduction
25.2 System Architecture
25.2.1 Hardware Design
25.2.2 Software Design
25.3 Machine Learning Algorithm
25.3.1 Algorithm
25.4 Results and Discussion
25.5 Conclusion
References
26. Eulerian Soft GraphsJinta Jose, Bobin George and Rajesh K. Thumbakara
26.1 Introduction
26.2 Soft Graphs
26.3 Eulerian Soft Graphs
26.4 Conclusion
References
27. An Algorithm to Solve an Exponential Diophantine EquationSubramani K. and Srinivasa Prasanna
27.1 Introduction
27.2 Example
27.2.1 Algorithm
27.2.2 Verification
27.3 Conclusion
Acknowledgements
References
28. Optimal Number of Emergency Facility and Its Positioning Using Nature-Based Algorithm: A Case of Mumbai CityK.V. Ajaygopal and Rakesh Verma
28.1 Introduction
28.2 Literature Review
28.2.1 Facility Location Problems
28.2.2 Genetic Algorithm
28.2.3 Improved Genetic Algorithm
28.3 Real-Life Application
28.3.1 Problem Description
28.3.2 Methodology
28.3.3 Mathematical Model
28.4 Results and Discussion
28.5 Conclusion
References
Appendix
29. Chicken Swarm Optimization Algorithm-Based Propagation Delay Estimation in Transmission Path of UWASNA. Kannappan and R.M. Bommi
29.1 Introduction
29.2 General Biology Behavior of Chicken Swarm
29.3 Chicken Swarm Pseudocode
29.4 Results and Discussion
29.5 Conclusion
References
30. Frequency Analysis of Coreference ResolutionMridusmita Das and Apurbalal Senapati
30.1 Introduction
30.1.1 Theoretical Consideration
30.1.2 Frequency Analysis in NLP/Coreference Resolution
30.2 Existing Literature
30.3 Resource Building for the English and Assamese Languages
30.4 Description of the Data Sets
30.4.1 Pre-Processing Tools for Tagging
30.5 Frequency Analysis of Coreference Relations
30.6 Experiment and Result
30.7 Conclusion
References
31. Hate Neologism in Election Context in IndiaSujit Das and Apurbalal Senapati
31.1 Introduction
31.2 Related Work
31.3 Corpus Creation
31.4 Methodology
31.5 Result
31.6 Conclusion
References
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