Mathematical Methods in Interdisciplinary Sciences (eBook, PDF)

Redaktion: Chakraverty, Snehashish

• Format: PDF

Produktbeschreibung

Brings mathematics to bear on your real-world, scientific problems Mathematical Methods in Interdisciplinary Sciences provides a practical and usable framework for bringing a mathematical approach to modelling real-life scientific and technological problems. The collection of chapters Dr. Snehashish Chakraverty has provided describe in detail how to bring mathematics, statistics, and computational methods to the fore to solve even the most stubborn problems involving the intersection of multiple fields of study. Graduate students, postgraduate students, researchers, and professors will all benefit significantly from the author's clear approach to applied mathematics. The book covers a wide range of interdisciplinary topics in which mathematics can be brought to bear on challenging problems requiring creative solutions. Subjects include: * Structural static and vibration problems * Heat conduction and diffusion problems * Fluid dynamics problems The book also covers topics as diverse as soft computing and machine intelligence. It concludes with examinations of various fields of application, like infectious diseases, autonomous car and monotone inclusion problems.

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Produktdetails

• Verlag: John Wiley & Sons
• Seitenzahl: 464
• Erscheinungstermin: 2. Juni 2020
• Englisch
• ISBN-13: 9781119585619
• Artikelnr.: 59575270

Autorenporträt

PROFESSOR SNEHASHISH CHAKRAVERTY, is working in the Department of Mathematics (Applied Mathematics Group), National Institute of Technology Rourkela, Odisha, India as a Senior (Higher Administrative Grade) Professor. Prior to this he was with CSIR-Central Building Research Institute, Roorkee, India. Prof. Chakraverty received his Ph. D. from University of Roorkee (now IIT Roorkee). There after he did his post-doctoral research at Institute of Sound and Vibration Research (ISVR), University of Southampton, U.K. and at the Faculty of Engineering and Computer Science, Concordia University, Canada. He has authored/co-authored 20 books, published 356 research papers in journals and conferences. Prof. Chakraverty is the Chief Editor of "International Journal of Fuzzy Computation and Modelling" (IJFCM), Inderscience Publisher, Switzerland (http: //www.inderscience.com/ijfcm) and Associate Editor of "Computational Methods in Structural Engineering, Frontiers in Built Environment". He has been the President of the Section of Mathematical sciences (including Statistics) of "Indian Science Congress" (2015-2016) and was the Vice President - "Orissa Mathematical Society" (2011-2013). Prof. Chakraverty is recipient of prestigious awards viz. Indian National Science Academy (INSA) nomination under International Collaboration/Bilateral Exchange Program, Platinum Jubilee ISCA Lecture Award (2014), CSIR Young Scientist (1997), BOYSCAST (DST), UCOST Young Scientist (2007, 2008), Golden Jubilee Director's (CBRI) Award (2001), Roorkee University Gold Medals (1987, 1988) etc. His present research area includes Differential Equations (Ordinary, Partial and Fractional), Numerical Analysis and Computational Methods, Structural Dynamics (FGM, Nano) and Fluid Dynamics, Mathematical Modeling and Uncertainty Modeling, Soft Computing and Machine Intelligence (Artificial Neural Network, Fuzzy, Interval and Affine Computations).

Inhaltsangabe

Notes on Contributors xv

Preface xxv

Acknowledgments xxvii

1 Connectionist Learning Models for Application Problems Involving Differential and Integral Equations 1
Susmita Mall, Sumit Kumar Jeswal, and Snehashish Chakraverty

1.1 Introduction 1

1.1.1 Artificial Neural Network 1

1.1.2 Types of Neural Networks 1

1.1.3 Learning in Neural Network 2

1.1.4 Activation Function 2

1.1.4.1 Sigmoidal Function 3

1.1.5 Advantages of Neural Network 3

1.1.6 Functional Link Artificial Neural Network (FLANN) 3

1.1.7 Differential Equations (DEs) 4

1.1.8 Integral Equation 5

1.1.8.1 Fredholm Integral Equation of First Kind 5

1.1.8.2 Fredholm Integral Equation of Second Kind 5

1.1.8.3 Volterra Integral Equation of First Kind 5

1.1.8.4 Volterra Integral Equation of Second Kind 5

1.1.8.5 Linear Fredholm Integral Equation System of Second Kind 6

1.2 Methodology for Differential Equations 6

1.2.1 FLANN-Based General Formulation of Differential Equations 6

1.2.1.1 Second-Order Initial Value Problem 6

1.2.1.2 Second-Order Boundary Value Problem 7

1.2.2 Proposed Laguerre Neural Network (LgNN) for Differential Equations 7

1.2.2.1 Architecture of Single-Layer LgNN Model 7

1.2.2.2 Training Algorithm of Laguerre Neural Network (LgNN) 8

1.2.2.3 Gradient Computation of LgNN 9

1.3 Methodology for Solving a System of Fredholm Integral Equations of Second Kind 9

1.3.1 Algorithm 10

1.4 Numerical Examples and Discussion 11

1.4.1 Differential Equations and Applications 11

1.4.2 Integral Equations 16

1.5 Conclusion 20

References 20

2 Deep Learning in Population Genetics: Prediction and Explanation of Selection of a Population 23
Romila Ghosh and Satyakama Paul

2.1 Introduction 23

2.2 Literature Review 23

2.3 Dataset Description 25

2.3.1 Selection and Its Importance 25

2.4 Objective 26

2.5 Relevant Theory, Results, and Discussions 27

2.5.1 automl 27

2.5.2 Hypertuning the Best Model 28

2.6 Conclusion 30

References 30

3 A Survey of Classification Techniques in Speech Emotion Recognition 33
Tanmoy Roy, Tshilidzi Marwala, and Snehashish Chakraverty

3.1 Introduction 33

3.2 Emotional Speech Databases 33

3.3 SER Features 34

3.4 Classification Techniques 35

3.4.1 Hidden Markov Model 36

3.4.1.1 Difficulties in Using HMM for SER 37

3.4.2 Gaussian Mixture Model 37

3.4.2.1 Difficulties in Using GMM for SER 38

3.4.3 Support Vector Machine 38

3.4.3.1 Difficulties with SVM 39

3.4.4 Deep Learning 39

3.4.4.1 Drawbacks of Using Deep Learning for SER 41

3.5 Difficulties in SER Studies 41

3.6 Conclusion 41

References 42

4 Mathematical Methods in Deep Learning 49
Srinivasa Manikant Upadhyayula and Kannan Venkataramanan

4.1 Deep Learning Using Neural Networks 49

4.2 Introduction to Neural Networks 49

4.2.1 Artificial Neural Network (ANN) 50

4.2.1.1 Activation Function 52

4.2.1.2 Logistic Sigmoid Activation Function 52

4.2.1.3 tanh or Hyperbolic Tangent Activation Function 53

4.2.1.4 ReLU (Rectified Linear Unit) Activation Function 54

4.3 Other Activation Functions (Variant Forms of ReLU) 55

4.3.1 Smooth ReLU 55

4.3.2 Noisy ReLU 55

4.3.3 Leaky ReLU 55
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