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End User License Agreement
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Mathematical Methods in Interdisciplinary Sciences
Cover
Notes on Contributors
Preface
Acknowledgments
1 Connectionist Learning Models for Application Problems Involving Differential and Integral Equations
1.1 Introduction
1.2 Methodology for Differential Equations
1.3 Methodology for Solving a System of Fredholm Integral Equations of Second Kind
1.4 Numerical Examples and Discussion
1.5 Conclusion
References
2 Deep Learning in Population Genetics: Prediction and Explanation of Selection of a Population
2.1 Introduction
2.2 Literature Review
2.3 Dataset Description
2.4 Objective
2.5 Relevant Theory, Results, and Discussions
2.6 Conclusion
References
3 A Survey of Classification Techniques in Speech Emotion Recognition
3.1 Introduction
3.2 Emotional Speech Databases
3.3 SER Features
3.4 Classification Techniques
3.5 Difficulties in SER Studies
3.6 Conclusion
References
4 Mathematical Methods in Deep Learning
4.1 Deep Learning Using Neural Networks
4.2 Introduction to Neural Networks
4.3 Other Activation Functions (Variant Forms of ReLU)
4.4 Backpropagation Algorithm
4.5 Performance and Accuracy
4.6 Results and Observation
References
5 Multimodal Data Representation and Processing Based on Algebraic System of Aggregates
5.1 Introduction
5.2 Basic Statements of ASA
5.3 Operations on Aggregates and Multi‐images
5.4 Relations and Digital Intervals
5.5 Data Synchronization
5.6 Fuzzy Synchronization
5.7 Conclusion
References
6 Nonprobabilistic Analysis of Thermal and Chemical Diffusion Problems with Uncertain Bounded Parameters
6.1 Introduction
6.2 Preliminaries
6.3 Finite Element Formulation for Tapered Fin
6.4 Radon Diffusion and Its Mechanism
6.5 Radon Diffusion Mechanism with TFN Parameters
6.6 Conclusion
References
7 Arbitrary Order Differential Equations with Fuzzy Parameters
7.1 Introduction
7.2 Preliminaries
7.3 Arbitrary Order Integral and Derivative for Fuzzy‐Valued Functions
7.4 Generalized Fuzzy Laplace Transform with Respect to Another Function
References
8 Fluid Dynamics Problems in Uncertain Environment
8.1 Introduction
8.2 Preliminaries
8.3 Problem Formulation
8.4 Methodology
8.5 Application of HPM and HPTM
8.6 Results and Discussion
8.7 Conclusion
References
9 Fuzzy Rough Set Theory‐Based Feature Selection: A Review
9.1 Introduction
9.2 Preliminaries
9.3 Fuzzy Rough Set‐Based Attribute Reduction
9.4 Approaches for Semisupervised and Unsupervised Decision Systems
9.5 Decision Systems with Missing Values
9.6 Applications in Classification, Rule Extraction, and Other Application Areas
9.7 Limitations of Fuzzy Rough Set Theory
9.8 Conclusion
References
10 Universal Intervals: Towards a Dependency‐Aware Interval Algebra
10.1 Introduction
10.2 The Need for Interval Computations
10.3 On Some Algebraic and Logical Fundamentals
10.4 Classical Intervals and the Dependency Problem
10.5 Interval Dependency: A Logical Treatment
10.6 Interval Enclosures Under Functional Dependence
10.7 Parametric Intervals: How Far They Can Go
10.8 Universal Intervals: An Interval Algebra with a Dependency Predicate
10.9 The S‐Field Algebra of Universal Intervals
10.10 Guaranteed Bounds or Best Approximation or Both?
Supplementary Materials
Acknowledgments
References
11 Affine‐Contractor Approach to Handle Nonlinear Dynamical Problems in Uncertain Environment
11.1 Introduction
11.2 Classical Interval Arithmetic
11.3 Interval Dependency Problem
11.4 Affine Arithmetic
11.5 Contractor
11.6 Proposed Methodology
11.7 Numerical Examples
11.8 Conclusion
References
12 Dynamic Behavior of Nanobeam Using Strain Gradient Model
12.1 Introduction
12.2 Mathematical Formulation of the Proposed Model
12.3 Review of the Differential Transform Method (DTM)
12.4 Application of DTM on Dynamic Behavior Analysis
12.5 Numerical Results and Discussion
12.6 Conclusion
Acknowledgment
References
13 Structural Static and Vibration Problems
13.1 Introduction
13.2 One‐parameter Groups
13.3 Infinitesimal Transformation
13.4 Canonical Coordinates
13.5 Algorithm for Lie Symmetry Point
13.6 Reduction of the Order of the ODE
13.7 Solution of First‐Order ODE with Lie Symmetry
13.8 Identification
13.9 Vibration of a Microcantilever Beam Subjected to Uniform Electrostatic Field
13.10 Contact Form for the Equation
13.11 Reducing in the Order of the Nonlinear ODE Representing the Vibration of a Microcantilever Beam Under Electrostatic Field
13.12 Nonlinear Pull‐in Voltage
13.13 Nonlinear Analysis of Pull‐in Voltage of Twin Microcantilever Beams
13.14 Nonlinear Analysis of Pull‐in Voltage of Twin Microcantilever Beams of Different Thicknesses
References
14 Generalized Differential and Integral Quadrature: Theory and Applications
14.1 Introduction
14.2 Differential Quadrature
14.3 General View on Differential Quadrature
14.4 Generalized Integral Quadrature
14.5 General View: The Two‐Dimensional Case
References
15 Brain Activity Reconstruction by Finding a Source Parameter in an Inverse Problem
15.1 Introduction
15.2 Methodology
15.3 Implementation
15.4 Numerical Results and Discussion
15.5 Conclusion
References
16 Optimal Resource Allocation in Controlling Infectious Diseases
16.1 Introduction
16.2 Mobility‐Based Resource Distribution
16.3 Connection–Strength Minimization
16.4 Risk Minimization
16.5 Conclusion
References
17 Artificial Intelligence and Autonomous Car
17.1 Introduction
17.2 What Is Artificial Intelligence?
17.3 Natural Language Processing
17.4 Robotics
17.5 Image Processing
17.6 Problem Solving
17.7 Optimization
17.8 Autonomous Systems
17.9 Conclusion
References
18 Different Techniques to Solve Monotone Inclusion Problems
18.1 Introduction
18.2 Preliminaries
18.3 Proximal Point Algorithm
18.4 Splitting Algorithms
18.5 Inertial Methods
18.6 Numerical Experiments
References
Index
End User License Agreement
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