Mathematical Modeling of Random and Deterministic Phenomena

Name: Mathematical Modeling of Random and Deterministic Phenomena
Brand: Wiley
Price: 139.99 EUR
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Solym Mawaki Manou-Abi Sophie Dabo-Niang Jean-Jacques Salone(Editor)

Wiley (Publisher)

1st Edition

Published on 25. February 2020

308 pages

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978-1-119-70690-8 (ISBN)

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Content

Cover
Half-Title Page
Title Page
Copyright Page
Contents
Preface
Acknowledgments
Introduction
PART 1: Advances in Mathematical Modeling
1. Deviations From the Law of Large Numbers and Extinction of an Endemic Disease
1.1. Introduction
1.2. The three models
1.2.1. The SIS model
1.2.2. The SIRS model
1.2.3. The SIR model with demography
1.3. The stochastic model, LLN, CLT and LD
1.3.1. The stochastic model
1.3.2. Law of large numbers
1.3.3. Central Limit Theorem
1.3.4. Large deviations and extinction of an epidemic
1.4. Moderate deviations
1.4.1. CLT and extinction of an endemic disease
1.4.2. Moderate deviations
1.5. References
2. Nonparametric Prediction for Spatial Dependent Functional Data: Application to Demersal Coastal Fish off Senegal
2.1. Introduction
2.2. Regression model and predictor
2.3. Large sample properties
2.4. Application to demersal coastal fish off Senegal
2.4.1. Procedure of prediction
2.4.2. Demersal coastal fish off Senegal data set
2.4.3. Measuring prediction performance
2.5. Conclusion
2.6. References
3. Space-Time Simulations of Extreme Rainfall: Why and How?
3.1. Why?
3.1.1. Rainfall-induced urban floods
3.1.2. Sample hydraulic simulation of a rainfall-induced urban flood
3.2. How?
3.2.1. Spatial stochastic rainfall generator
3.2.2. Modeling extreme events
3.2.3. Stochastic rainfall generator geared towards extreme events
3.3. Outlook
3.4. References
4. Change-point Detection for Piecewise Deterministic Markov Processes
4.1. A quick introduction to stochastic control and change-point detection
4.2. Model and problem setting
4.2.1. Continuous-time PDMP model
4.2.2. Optimal stopping problem under partial observations
4.2.3. Fully observed optimal stopping problem
4.3. Numerical approximation of the value functions
4.3.1. Quantization
4.3.2. Discretizations
4.3.3. Construction of a stopping strategy
4.4. Simulation study
4.4.1. Linear model
4.4.2. Nonlinear model
4.5. Conclusion
4.6. References
5. Optimal Control of Advection-Diffusion Problems for Cropping Systems with an Unknown Nutrient Service Plant Source
5.1. Introduction
5.2. Statement of the problem
5.2.1. Existence of a solution to the NTB uptake system
5.3. Optimal control for the NTB problem with an unknown source
5.3.1. Existence of a solution to the adjoint problem of NTB uptake system with an unknown source
5.4. Characterization of the low-regret control for the NTB system
5.5. Concluding remarks
5.6. References
6. Existence of an Asymptotically Periodic Solution for a Stochastic Fractional Integro-differential Equation
6.1. Introduction
6.2. Preliminaries
6.2.1. Asymptotically periodic process and periodic limit processes
6.2.2. Sectorial operators
6.3. A stochastic integro-differential equation of fractional order
6.4. An illustrative example
6.5. References
7. Bounded Solutions for Impulsive Semilinear Evolution Equations with Non-local Conditions
7.1. Introduction
7.2. Preliminaries
7.3. Main theorems
7.4. The smoothness of the bounded solution
7.5. Application to the Burgers equation
7.6. References
8. The History of a Mathematical Model and Some of Its Criticisms up to Today: The Diffusion of Heat That Started with a Fourier "Thought Experiment"
8.1. Introduction
8.2. A physical invention is translated into mathematics thanks to the heat flow
8.3. The proper story of proper modes
8.3.1. Mathematical position of the lamina problem
8.3.2. Simple modes are naturally involved
8.3.3. A remarkable switch to proper modes
8.4. The numerical example of the periodic step function gives way to a physical interpretation
8.4.1. A calculation that a priori imposes an extension to the function f at the base of the lamina
8.4.2. A crazy calculation
8.4.3. Fourier is happily confronted with the task of finding an explanation for the simplicity of the result about coefficients
8.4.4. Criticisms of the modeling
8.5. To invoke arbitrary functions leads to an interpretation of orthogonality relations
8.5.1. Function is a leitmotiv in Fourier's intellectual career
8.6. The modeling of the temperature of the Earth and the greenhouse effect
8.7. Axiomatic shaping by Hilbert spaces provides a good account for another dictionary part in Fourier's theory, and also to its limits, so that his representation finally had to be modified to achieve efficient numerical purposes
8.7.1. Another dictionary: the Fourier transform for tempered distributions
8.7.2. Heisenberg inequalities may just be deduced from the existence of a scalar product
8.7.3. Orthogonality and a quick look to wavelets
8.8. Conclusion
8.9. References
PART 2: Some Topics on Mayotte and Its Region
9. Towards a Methodology for Interdisciplinary Modeling of Complex Systems Using Hypergraphs
9.1. Introduction
9.1.1. The ARESMA project
9.1.2. Towards a methodology of interdisciplinary modeling
9.2. Systemic and lexicometric analyses of questionnaires
9.2.1. Complex systems
9.2.2. Methodology
9.2.3. Results
9.2.4. Conclusion of the section
9.3. Hypergraphic analyses of diagrams
9.3.1. Hypergraphs and modeling of a complex system
9.3.2. Methodology
9.3.3. Results
9.3.4. Conclusion of the section
9.4. Discussion and perspectives
9.5. Appendix
9.5.1. Other properties of a connected hypergraph
9.5.2. Metric over an FHT
9.6. References
10. Modeling of Post-forestry Transitions in Madagascar and the Indian Ocean: Setting Up a Dialogue Between Mathematics, Computer Science and Environmental Sciences
10.1. Introduction
10.2. Interdisciplinary exploration of agrarian transitions
10.2.1. Exploration of post-forestry transitions in rainforests of Madagascar
10.2.2. Applications to dry forests in southwestern Madagascar
10.2.3. Viability
10.3. Community management of resources, looking for consensus
10.3.1. Degradation, violation, sanction
10.3.2. Local farmers' maps and conceptual graphs
10.4. Discussion and conclusion
10.5. References
11. Structural and Predictive Analysis of the Birth Curve in Mayotte from 2011 to 2017
11.1. Introduction
11.1.1. Motivation
11.1.2. Context
11.1.3. About the literature on the birth curve in Mayotte
11.1.4. Objective of ARS OI
11.2. Origin of the data
11.3. Methodologies and results
11.3.1. Methodological approach
11.3.2. Annual trend
11.3.3. Monthly trend
11.3.4. Characterization of the explosion risk of the number of births
11.3.5. Autocorrelation
11.3.6. Modeling by an ARIMA process (p, d, q)
11.3.7. Predictions for the year 2018
11.4. Discussion
11.5. Conclusion
11.6. References
12. Reflections Upon the Mathematization of Mayotte's Economy
12.1. Introduction
12.2. Justifying the mathematization of economics
12.2.1. The ontological and linguistic arguments
12.2.2. Towards a naturalization of modeling in economics
12.2.3. A number of caveats
12.3. For a reasonable mathematization of economics: the case of Mayotte
12.3.1. The trend towards the mathematization of the economics of Mayotte
12.3.2. From Mayotte's formal economy to its informal one
12.3.3. When the formal economy interacts with the informal one: some issues for the modelization of complex systems
12.4. Concluding remark
12.5. References
List of Authors
Index
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