Mathematical modelling Books

Book SynopsisSpreadsheet Problem Solving and Programming for Engineers and Scientists provides a comprehensive resource essential to a full understanding of modern spreadsheet skills needed for engineering and scientific computations.Beginning with the basics of spreadsheets and programming, this book builds on the authors' decades of experience teaching spreadsheets and programming to both university students and professional engineers and scientists. Following on from this, it covers engineering economics, key numerical methods, and applied statistics. Finally, this book details the Visual Basic for Applications (VBA) programming system that accompanies Excel.With each chapter including examples and a set of exercises, this book is an ideal companion for all engineering courses and also for self-study. Based on the latest version of Excel (Microsoft Excel for Microsoft 365), it is also compatible with earlier versions of Excel dating back to Version 2013. Including numerTable of ContentsChapter 1 Spreadsheet Basics Chapter 2 Charts and GraphsChapter 3 Engineering and Scientific FormulasChapter 4 Table-based CalculationsChapter 5 Case Studies and TargetingChapter 6 Financial CalculationsChapter 7 Numerical MethodsChapter 8 Applied StatisticsChapter 9 Introduction to VBA and MacrosChapter 10 User-defined FunctionsChapter 11 VBA ProgrammingChapter 12 User InterfacesAppendix A: Matrix Algebra ReviewAppendix B: Shortcut Keys and Key Combinations

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Book SynopsisMechatronics is a mongrel, a crossbreed of classic mechanical engineering, the relatively young pup of computer science, the energetic electrical engineering, the pedigree mathematics and the bloodhound of Control Theory.All too many courses in control theory consist of a diet of Everything you could ever need to know about the Laplace Transform' rather than answering What happens when your servomotor saturates?' Topics in this book have been selected to answer the questions that the mechatronics student is most likely to raise.That does not mean that the mathematical aspects have been left out, far from it. The diet here includes matrices, transforms, eigenvectors, differential equations and even the dreaded z transform. But every effort has been made to relate them to practical experience, to make them digestible. They are there for what they can do, not to support pages of mathematical rigour that defines their origins.The theme running throughout the Table of Contents1. Why Do You Need Control Theory? 2. Modelling Time .3. A Simulation Environment 4. Step Length Considerations. 5. Modelling a Second-Order System .6. The Complication of Motor Drive Limits. 7. Practical Controller Design 8. Adding Dynamics to the Controller 9. Sensors and Actuators. 10. Analogue Simulation. 11. Matrix State Equations. 12. Putting It into Practice. 13. Observers 14. More about the Mathematics 15. Transfer Functions 16. Solving the State Equations 17. Discrete Time and the z Operator. 18. Root locus. 19. More about the Phase Plane. 20. Optimisation and an Experiment. 21. Problem Systems. 22. Final Comments.

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Book SynopsisThe Earth and environmental sciences are becoming progressively more quantitative due to the increased use of mathematical models and new data analysis techniques. This accessible introduction presents an overview of the mathematical methods essential for understanding Earth processes, providing an invaluable resource for students and early career researchers who may have missed (or forgotten) the mathematics they need to succeed as scientists. Topics build gently from basic methods such as calculus to more advanced techniques including linear algebra and differential equations. The practical applications of the mathematical methods to a variety of topics are discussed, ranging from atmospheric science and oceanography to biogeochemistry and geophysics. Including over 530 exercises and end-of-chapter problems, as well as additional computer codes in Python and MATLAB, this book supports readers in applying appropriate analytical or computational methods to solving real research questioTable of ContentsPreface; 1. Estimation and dimensional analysis; 2. Derivatives and integrals; 3. Series and summations; 4. Scalars, vectors, and matrices; 5. Probability; 6. Ordinary differential equations; 7. Vectors and calculus; 8. Special functions; 9. Fourier series and integral transforms; 10. Partial differential equations; 11. Tensors; Appendix A. Units and dimensions; Appendix B. Tables of useful formulae; Appendix C. Complex numbers; Notes; References; Index.

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Book SynopsisThe study of electronic structure of materials is at a momentous stage, with new computational methods and advances in basic theory. Many properties of materials can be determined from the fundamental equations, and electronic structure theory is now an integral part of research in physics, chemistry, materials science and other fields. This book provides a unified exposition of the theory and methods, with emphasis on understanding each essential component. New in the second edition are recent advances in density functional theory, an introduction to Berry phases and topological insulators explained in terms of elementary band theory, and many new examples of applications. Graduate students and research scientists will find careful explanations with references to original papers, pertinent reviews, and accessible books. Each chapter includes a short list of the most relevant works and exercises that reveal salient points and challenge the reader.Trade Review'… this 2nd edition is … very welcome and timely, as it has been significantly expanded to cover the 'new' topics. The core of the book remains unchanged in scope, focusing on 'independent particle methods' such as DFT and Hartree-Fock theory, and their extensions. This is … a worthy … and is strongly recommended for anyone working in the field of electronic structure.' Matt Probert, Contemporary PhysicsTable of ContentsPreface; Acknowledgments; Notation; Part I. Overview and background topics: 1. Introduction; 2. Overview; 3. Theoretical background; 4. Periodic solids and electron bands; 5. Uniform electron gas and sp-bonded metals; Part II. Density functional theory: 6. Density functional theory: foundations; 7. The Kohn–Sham auxiliary system; 8. Functionals for exchange and correlation I; 9. Functionals for exchange and correlation II; Part III. Important preliminaries on atoms: 10. Electronic structure of atoms; 11. Pseudopotentials; Part IV. Determination of electronic structure: the basic methods: 12. Plane waves and grids: basics; 13. Plane waves and real space methods: full calculations; 14. Localized orbitals: tight-binding; 15. Localized orbitals: full calculations; 16. Augmented functions: APW, KKR, MTO; 17. Augmented functions: linear methods; 18. Locality and linear scaling O(N) methods; Part V. From Electronic Structure to Properties of Matter: 19. Quantum molecular dynamics (QMD); 20. Response functions: phonons, magnons, . . .; 21. Excitation spectra and optical properties; 22. Surfaces, interfaces, and lower dimensional systems; 23. Wannier functions; 24. Polarization, localization, and Berry phases; Part VI. Electronic Structure and Topology: 25. Topology of the electronic structure of a crystal: introduction; 26. Two band models: Berry phase, winding and topology; 27. Topological insulators I: Two dimensions; 28. Topological insulators II: Three dimensions; Part VII. APPENDICES: A. Functional equations; B. LSDA and GGA functionals; C. Adiabatic approximation; D. Perturbation Theory, response functions and Green's functions; E. Dielectric functions and optical properties; F. Coulomb interactions in extended systems; G. Stress from electronic structure; H. Energy and stress densities; I. Alternative force expressions; J. Scattering and phase shifts; K. Useful relations and formulas; L. Numerical methods; M. Iterative methods in electronic structure; N. Two-center matrix elements: expressions for arbitrary angular momentum l; O. Dirac equation and spin-orbit interaction; P. Berry phase, curvature and Chern numbers; Q. Quantum Hall effect and edge conductivity; R. Codes for electronic structure calculations for solids; References; Index.

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Book SynopsisLearn to master basic programming tasks from scratch with real-life, scientifically relevant examples and solutions drawn from both science and engineering. Students and researchers at all levels are increasingly turning to the powerful Python programming language as an alternative to commercial packages and this fast-paced introduction moves from the basics to advanced concepts in one complete volume, enabling readers to gain proficiency quickly. Beginning with general programming concepts such as loops and functions within the core Python 3 language, and moving on to the NumPy, SciPy and Matplotlib libraries for numerical programming and data visualization, this textbook also discusses the use of Jupyter Notebooks to build rich-media, shareable documents for scientific analysis. The second edition features a new chapter on data analysis with the pandas library and comprehensive updates, and new exercises and examples. A final chapter introduces more advanced topics such as floating-pTable of ContentsAcknowledgments; 1. Introduction; 2. The core Python language I; 3. Interlude: simple plots and charts; 4. The core Python language II; 5. IPython and Jupyter Notebook; 6. NumPy; 7. Matplotlib; 8. SciPy; 9. Data analysis with pandas; 10. General scientific programming; Appendix A. Solutions; Appendix B. Differences between Python versions 2 and 3; Appendix C. SciPy's odeint ordinary differential equation solver; Glossary; Index.

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Book SynopsisChapter 1: Introduction: The nature and structure of the inventory problem.- Chapter 2: Review of the literature.- Chapter 3: Methodology.- Chapter 4: Analysis of inventory behaviour of OECD countries.- Chapter 5: Stability of macroeconomic variables.- Chapter 6: Inventory developments in individual countries.- Chapter 7: Summary and conclusions.Table of ContentsChapter 1: Introduction: The nature and structure of the inventory problem.- Chapter 2: Review of the literature.- Chapter 3: Methodology.- Chapter 4: Analysis of inventory behaviour of OECD countries.- Chapter 5: Stability of macroeconomic variables.- Chapter 6: Inventory developments in individual countries.- Chapter 7: Summary and conclusions.

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Book SynopsisThis book focuses on a development of optimal, flexible, and efficient models and algorithms for cell formation in group technology. Its main aim is to provide a reliable tool that can be used by managers and engineers to design manufacturing cells based on their own preferences and constraints imposed by a particular manufacturing system.Trade Review“The book under review is a very good source … continuing the long term passion of Panos Pardalos and his collaborators in exact solution of difficult problems … . It also adds a very valuable contribution to the body of knowledge of the cell formation problem that can be used in both teaching and research including in bioinformatics.” (Boris Mirkin, Optimization Letters, 2015)Table of Contents1. The problem of cell formation.- 2. ​The p-Median problem.- 3. Application of the PMP to cell formation in group technology.- 4. The minimum multicut problem and an exact model for cell formation.- 5. Multiobjective nature of cell formation.- 6. Pattern-based heuristic for the cell formation problem in group technology.- 7. Branch-and-bound algorithm for bi-criterion cell formation problems.- 8. Summary and conclusions.- A. Solutions to the 35 CF instances from [71].- Index.- References.

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Book SynopsisDynamical systems are a principal tool in the modeling, prediction, and control of a wide range of complex phenomena. As the need for improved accuracy leads to larger and more complex dynamical systems, direct simulation often becomes the only available strategy for accurate prediction or control, inevitably creating a considerable burden on computational resources. This is the main context where one considers model reduction, seeking to replace large systems of coupled differential and algebraic equations that constitute high fidelity system models with substantially fewer equations that are crafted to control the loss of fidelity that order reduction may induce in the system response. Interpolatory methods are among the most widely used model reduction techniques, and Interpolatory Methods for Model Reduction is the first comprehensive analysis of this approach available in a single, extensive resource. It introduces state-of-the-art methods reflecting significant developments over the past two decades, covering both classical projection frameworks for model reduction and data-driven, nonintrusive frameworks.This textbook is appropriate for a wide audience of engineers and other scientists working in the general areas of large-scale dynamical systems and data-driven modeling of dynamics.

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Book SynopsisThis self-contained introduction to the fast-growing field of Mathematical Biology is written for students with a mathematical background. It sets the subject in a historical context and guides the reader towards questions of current research interest. A broad range of topics is covered including: Population dynamics, Infectious diseases, Population genetics and evolution, Dispersal, Molecular and cellular biology, Pattern formation, and Cancer modelling. Particular attention is paid to situations where the simple assumptions of homogenity made in early models break down and the process of mathematical modelling is seen in action.Trade ReviewFrom the reviews: It explains its chosen topics clearly and simply, not including extraneous material, and is written at a level that can be understood and appreciated by undergraduate students. Indeed, the level of writing is superb in its clarity and elegance... Just as useful as the writing style are the appendices and hints. Not only does Britton give elementary presentations of some basic mathematical techniques (difference equations, ODEs and PDEs) he also gives extensive hints for the exercises, bordering on complete solutions in some cases. This is a resource that will surely prove extremely useful for all teachers of such a course...there is no denying that Essential Mathematical Biology is superbly designed for the purpose it serves, and will, I am sure, become a popular text book across the world. UK Nonlinear News Britton explains how difference and differential equations have been used to formulate theory and description in biology, but at a level accessible to undergraduate mathematics, physics or engineering majors. His very readable style achieves clear and largely jargon-free explanations with no sacrifice of mathematical rigour.....Clearly intended to be read and used as a course textbook, another attractive feature of this volume is the inclusion of interesting and relevant exercises after each subchapter section, together with an appendix of hints to help students work and understand them. Other appendixes efficiently review the mathematical techniques and concepts that are basic to the applications presented in the chapters....I believe that Essential Mathematical Biology will enrich the personal library of any scholar interested in applied differential equations. The Quarterly Review of Biology, Volume 79, No. 2 "This excellent monograph provides a very readable introduction to the most important aspects of mathematical biology. … The book contains numerous exercises, with hints for the solutions, a guide for further studies, and interesting historical comments. An index helps in finding the many concepts and equations introduced in the monograph. This is a most welcome addition to the literature." (Jean Mawhin, Bulletin of the Belgian Mathematical Society, Vol. 12 (1), 2005) "This book as a textbook covers a diversity of topics from mathematical biology. Its content is best summarized by the title of its eight substantial Chapters. … It poses questions of current research interest, providing a comprehensive overview of the field and a solid foundation for interdisciplinary research in the biological sciences. … includes many exercises as well as detailed solutions for them. … a good introduction for those beginners that are interested in the fast growing field of mathematical biology." (Lan-Sun Chen, Mathematical Reviews, 2003m) "Each chapter of this textbook provides a brief introduction into an important area of mathematical biology. … In addition, there are four appendices, comprising about one fourth of the whole text, which summarize important techniques … . The book is aimed at the undergraduate level … . Many exercises, together with hints for their solution, complement this text which will be useful as a first introduction." (R. Bürger, Monatshefte für Mathematik, Vol. 143 (4), 2004) "In brevity and simplicity lies the great strength of this book. It explains its chosen topics clearly and simply … that can be understood and appreciated by undergraduate students. Indeed, the level of writing is superb … . Just as useful as the writing style are the appendices and the hints. … will surely prove extremely useful for all teachers of such a course. … will, I am sure, become a popular text book across the world." (James Sneyd, UK Nonlinear News, June, 2004) "Britton writes a book that provides for an introductory account of mathematical biology. … Many examples are given … . The figures are clear and precise. All mathematical formulae, equations and models are complete, clear and readable. … The material in the book is clear and concise. The book provides the reader with a wealth of information and is well suited as a textbook for a course in mathematical biology. I highly recommend this book … . It makes a worthwhile addition." (Paul Johnson, New Zealand Mathematical Society Newsletter, Issue 90, April, 2004) "It was a great pleasure reading Essential Mathematical Biology. … the book is very well written without large jumps in the mathematical reasoning, it is also quite concise and covers a large amount of material. … The writing and style are very clear. The mathematical steps are laid out neatly with clear definitions and notation … . The book is a great contribution to students interested in mathematical biology … and a source of important insights for biological scientists." (D. Kault, The Australian Mathematical Society, Vol. 31 (1), 2004) "This book is a self-contained introduction to the fast-growing field of mathematical biology. … it sets the subject in its historical context and then guides the reader towards questions of current research interest, providing a comprehensive overview of the field and a solid foundation for interdisciplinary research in the biological sciences. A broad range of topics is covered … ." (L’Enseignement Mathematique, Vol. 49 (3-4), 2003) "Those of us in mathematical biology like to imagine our field on the verge of achieving critical opalescence … . it is a pleasure and challenge to share the wide spectrum of problems and approaches with eager undergraduates from various backgrounds … . Several textbooks are available, now including Essential Mathematical Biology by Nicholas Britton. The author … exemplifies interdisciplinary approaches … . Essential Mathematical Biology would serve well as a template for an advanced undergraduate or beginning graduate course … ." (Fred Adler, Physics Today, March, 2004) "Each of the eight chapters starts with a brief list of clearly expressed goals, questions or explanations, well motivating the reader to enter the chapter by introducing him into the essential biological problems and their importance. … I can fully recommend to use this ‘undergraduate mathematics textbook’ in any theoretical or practical computer course introducing into Mathematical Biology, but also for other teaching or education purposes within this interdisciplinary filed of growing importance between Mathematics, Scientific Computing, Bioinformatics, Systems Biology, Ecology, Physiology and Biomedicine." (Wolfgang Alt, Mathematical Biosciences, Vol. 208, 2007)Table of Contents1. Single Species Population Dynamics.- 2. Population Dynamics of Interacting Species.- 3. Infectious Diseases.- 4. Population Genetics and Evolution.- 5. Biological Motion.- 6. Molecular and Cellular Biology.- 7. Pattern Formation.- 8. Tumour Modelling.- Further Reading.- A. Some Techniques for Difference Equations.- A.1 First-order Equations.- A.1.1 Graphical Analysis.- A.1.2 Linearisation.- A.2 Bifurcations and Chaos for First-order Equations.- A.2.1 Saddle-node Bifurcations.- A.2.2 Transcritical Bifurcations.- A.2.3 Pitchfork Bifurcations.- A.2.4 Period-doubling or Flip Bifurcations.- A.3 Systems of Linear Equations: Jury Conditions.- A.4 Systems of Nonlinear Difference Equations.- A.4.1 Linearisation of Systems.- A.4.2 Bifurcation for Systems.- B. Some Techniques for Ordinary Differential Equations.- B.1 First-order Ordinary Differential Equations.- B.1.1 Geometric Analysis.- B.1.2 Integration.- B.1.3 Linearisation.- B.2 Second-order Ordinary Differential Equations.- B.2.1 Geometric Analysis (Phase Plane).- B.2.2 Linearisation.- B.2.3 Poincaré-Bendixson Theory.- B.3 Some Results and Techniques for rath Order Systems.- B.3.1 Linearisation.- B.3.2 Lyapunov Functions.- B.3.3 Some Miscellaneous Facts.- B.4 Bifurcation Theory for Ordinary Differential Equations.- B.4.1 Bifurcations with Eigenvalue Zero.- B.4.2 Hopf Bifurcations.- C. Some Techniques for Partial Differential Equations.- C.1 First-order Partial Differential Equations and Characteristics.- C.2 Some Results and Techniques for the Diffusion Equation.- C.2.1 The Fundamental Solution.- C.2.2 Connection with Probabilities.- C.2.3 Other Coordinate Systems.- C.3 Some Spectral Theory for Laplace’s Equation.- C.4 Separation of Variables in Partial Differential Equations.- C.5 Systems of Diffusion Equations with Linear Kinetics.- C.6 Separating the Spatial Variables from Each Other.- D. Non-negative Matrices.- D.1 Perron-Frobenius Theory.- E. Hints for Exercises.

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Book SynopsisThis book primarily focuses on rigorous mathematical formulation and treatment of static problems arising in continuum mechanics of solids at large or small strains, as well as their various evolutionary variants, including thermodynamics. As such, the theory of boundary- or initial-boundary-value problems for linear or quasilinear elliptic, parabolic or hyperbolic partial differential equations is the main underlying mathematical tool, along with the calculus of variations. Modern concepts of these disciplines as weak solutions, polyconvexity, quasiconvexity, nonsimple materials, materials with various rheologies or with internal variables are exploited.This book is accompanied by exercises with solutions, and appendices briefly presenting the basic mathematical concepts and results needed. It serves as an advanced resource and introductory scientific monograph for undergraduate or PhD students in programs such as mathematical modeling, applied mathematics, computational continuum physics and engineering, as well as for professionals working in these fields. Trade Review“Advanced mathematical concepts are presented in a logical and clear manner, making the book accessible to graduate students as well as non-mathematicians working on problems in continuum mechanics of solids. … The book is very well organized and well written. The mathematical results are clearly presented.” (Corina- Stefania Drapaca, Mathematical Reviews, November, 2019)Table of ContentsStatic Problems.- Description of Deformable Stressed Bodies.- Elastic Materials.- Polyconvex Materials: Existence Of Energy-Minimizing Deformations.- General Hyperelastic Materials: Existence/Nonexistence Results.- Linearized Elasticity.- Evolution Problems.- Linear Rheological Models at Small Strains.- Nonlinear Materials with Internal Variables at Small Strains.- Thermodynamics of Selected Materials and Processes.- Evolution at finite Strains.

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Book SynopsisThis volume encompasses prototypical, innovative and emerging examples and benchmarks of Differential-Algebraic Equations (DAEs) and their applications, such as electrical networks, chemical reactors, multibody systems, and multiphysics models, to name but a few. Each article begins with an exposition of modelling, explaining whether the model is prototypical and for which applications it is used. This is followed by a mathematical analysis, and if appropriate, a discussion of the numerical aspects including simulation. Additionally, benchmark examples are included throughout the text.Mathematicians, engineers, and other scientists, working in both academia and industry either on differential-algebraic equations and systems or on problems where the tools and insight provided by differential-algebraic equations could be useful, would find this book resourceful. Trade Review“The book can be of special interest to mathematicians, STEM students, and engineers working in multidisciplinary industry settings where the insight provided by differential-algebraic equations can be determinant in decision making.” (Andrzej Sokolowski, MAA Reviews, August 11, 2019)Table of ContentsGeneral Nonlinear Differential Algebraic Equations and Tracking Problems: A Robotics Example.- DAE Aspects in Vehicle Dynamics and Mobile Robotics.- Open-loop Control of Underactuated Mechanical Systems Using Servo-constraints: Analysis and Some Examples.- Systems of Differential Algebraic Equations in Computational Electromagnetics.- Gas Network Benchmark Models.- Topological Index Analysis Applied to Coupled Flow Networks.- Nonsmooth DAEs with Applications in Modeling Phase Changes.- Continuous, Semi-Discrete, and Fully Discretized Navier-Stokes Equations.

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Book SynopsisThe chapters in this contributed volume showcase current theoretical approaches in the modeling of ocular fluid dynamics in health and disease. By including chapters written by experts from a variety of fields, this volume will help foster a genuinely collaborative spirit between clinical and research scientists. It vividly illustrates the advantages of clinical and experimental methods, data-driven modeling, and physically-based modeling, while also detailing the limitations of each approach. Blood, aqueous humor, vitreous humor, tear film, and cerebrospinal fluid each have a section dedicated to their anatomy and physiology, pathological conditions, imaging techniques, and mathematical modeling. Because each fluid receives a thorough analysis from experts in their respective fields, this volume stands out among the existing ophthalmology literature.Ocular Fluid Dynamics is ideal for current and future graduate students in applied mathematics and ophthalmology who wish to explore the field by investigating open questions, experimental technologies, and mathematical models. It will also be a valuable resource for researchers in mathematics, engineering, physics, computer science, chemistry, ophthalmology, and more.Table of ContentsPart I. Introduction.- Mathematical and physical modeling principles of complex biological systems.- Part II. Blood.- Vascular Anatomy and Physiology of the Eye.- Pathological Consequences of Vascular Hemodynamic Alterations in the Eye.- Measurement of geometrical and functional parameters related to ocular blood flow.- Mathematical modeling of blood flow in the eye.- Part III. Aqueous Humor.- Changes in Parameters of Aqueous Humor Dynamics Throughout Life.- Aqueous Humor Dynamics and its Influence on Glaucoma.- Approaches to Aqueous Humor Outflow Imaging.

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Book SynopsisSemi-supervised learning is a learning paradigm concerned with the study of how computers and natural systems such as humans learn in the presence of both labeled and unlabeled data. Traditionally, learning has been studied either in the unsupervised paradigm (e.g., clustering, outlier detection) where all the data are unlabeled, or in the supervised paradigm (e.g., classification, regression) where all the data are labeled. The goal of semi-supervised learning is to understand how combining labeled and unlabeled data may change the learning behavior, and design algorithms that take advantage of such a combination. Semi-supervised learning is of great interest in machine learning and data mining because it can use readily available unlabeled data to improve supervised learning tasks when the labeled data are scarce or expensive. Semi-supervised learning also shows potential as a quantitative tool to understand human category learning, where most of the input is self-evidently unlabeled. In this introductory book, we present some popular semi-supervised learning models, including self-training, mixture models, co-training and multiview learning, graph-based methods, and semi-supervised support vector machines. For each model, we discuss its basic mathematical formulation. The success of semi-supervised learning depends critically on some underlying assumptions. We emphasize the assumptions made by each model and give counterexamples when appropriate to demonstrate the limitations of the different models. In addition, we discuss semi-supervised learning for cognitive psychology. Finally, we give a computational learning theoretic perspective on semi-supervised learning, and we conclude the book with a brief discussion of open questions in the field. Table of Contents: Introduction to Statistical Machine Learning / Overview of Semi-Supervised Learning / Mixture Models and EM / Co-Training / Graph-Based Semi-Supervised Learning / Semi-Supervised Support Vector Machines / Human Semi-Supervised Learning / Theory and OutlookTable of ContentsIntroduction to Statistical Machine Learning.- Overview of Semi-Supervised Learning.- Mixture Models and EM.- Co-Training.- Graph-Based Semi-Supervised Learning.- Semi-Supervised Support Vector Machines.- Human Semi-Supervised Learning.- Theory and Outlook.

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Book SynopsisAnswer Set Programming (ASP) is a declarative problem solving approach, initially tailored to modeling problems in the area of Knowledge Representation and Reasoning (KRR). More recently, its attractive combination of a rich yet simple modeling language with high-performance solving capacities has sparked interest in many other areas even beyond KRR. This book presents a practical introduction to ASP, aiming at using ASP languages and systems for solving application problems. Starting from the essential formal foundations, it introduces ASP's solving technology, modeling language and methodology, while illustrating the overall solving process by practical examples. Table of Contents: List of Figures / List of Tables / Motivation / Introduction / Basic modeling / Grounding / Characterizations / Solving / Systems / Advanced modeling / ConclusionsTable of ContentsList of Figures.- List of Tables.- Motivation.- Introduction.- Basic modeling.- Grounding.- Characterizations.- Solving.- Systems.- Advanced modeling.- Conclusions.

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Book SynopsisSimilarity between objects plays an important role in both human cognitive processes and artificial systems for recognition and categorization. How to appropriately measure such similarities for a given task is crucial to the performance of many machine learning, pattern recognition and data mining methods. This book is devoted to metric learning, a set of techniques to automatically learn similarity and distance functions from data that has attracted a lot of interest in machine learning and related fields in the past ten years. In this book, we provide a thorough review of the metric learning literature that covers algorithms, theory and applications for both numerical and structured data. We first introduce relevant definitions and classic metric functions, as well as examples of their use in machine learning and data mining. We then review a wide range of metric learning algorithms, starting with the simple setting of linear distance and similarity learning. We show how one may scale-up these methods to very large amounts of training data. To go beyond the linear case, we discuss methods that learn nonlinear metrics or multiple linear metrics throughout the feature space, and review methods for more complex settings such as multi-task and semi-supervised learning. Although most of the existing work has focused on numerical data, we cover the literature on metric learning for structured data like strings, trees, graphs and time series. In the more technical part of the book, we present some recent statistical frameworks for analyzing the generalization performance in metric learning and derive results for some of the algorithms presented earlier. Finally, we illustrate the relevance of metric learning in real-world problems through a series of successful applications to computer vision, bioinformatics and information retrieval. Table of Contents: Introduction / Metrics / Properties of Metric Learning Algorithms / Linear Metric Learning / Nonlinear and Local Metric Learning / Metric Learning for Special Settings / Metric Learning for Structured Data / Generalization Guarantees for Metric Learning / Applications / Conclusion / Bibliography / Authors' BiographiesTable of ContentsIntroduction.- Metrics.- Properties of Metric Learning Algorithms.- Linear Metric Learning.- Nonlinear and Local Metric Learning.- Metric Learning for Special Settings.- Metric Learning for Structured Data.- Generalization Guarantees for Metric Learning.- Applications.- Conclusion.- Bibliography.- Authors' Biographies .

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Book SynopsisThe purpose of this book is twofold: first, it sets out to equip the reader with a sound understanding of the foundations of probability theory and stochastic processes, offering step-by-step guidance from basic probability theory to advanced topics, such as stochastic differential equations, which typically are presented in textbooks that require a very strong mathematical background. Second, while leading the reader on this journey, it aims to impart the knowledge needed in order to develop algorithms that simulate realistic physical systems. Connections with several fields of pure and applied physics, from quantum mechanics to econophysics, are provided. Furthermore, the inclusion of fully solved exercises will enable the reader to learn quickly and to explore topics not covered in the main text. The book will appeal especially to graduate students wishing to learn how to simulate physical systems and to deepen their knowledge of the mathematical framework, which has very deep connections with modern quantum field theory.Table of Contents1 Review of Probability Theory.- 2 Applications to Mathematical Statistics.- 3 Conditional Probability and Conditional Expectation.- 4 Markov Chains.- 5 Sampling of Random Variables and Simulation.- 6 Brownian Motion.- 7 Introduction to Stochastic Calculus and Ito Integral.- 8 Introduction to Stochastic Differential Equations and Applications.- Bibliography.- Solutions.

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Book SynopsisThe research in this book looks at the likelihood and level of use of implemented technological components with regard to the adoption of different precision agricultural technologies. To identify the variables affecting farmers'' choices to embrace more precise technology, zero-inflated Poisson and negative binomial count data regression models are utilized. Outcomes from the count data analysis of a random sample of various farm operators show that various aspects, including farm dimension, farmer demographics, soil texture, urban impacts, farmer position of liabilities, and position of the farm in a state, were significantly associated with the approval severity and likelihood of precision farming technologies.Technical topics discussed in the book include: Precision agriculture Machine learning Wireless sensor networks IoT Deep learning

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Book SynopsisThis book discusses the importance of knowledge as an intangible asset, separate from physical entities, that can enable us to understand and/or change the world. It provides a thorough treatment of knowledge, one that is free of ideological and philosophical preconceptions, and which relies exclusively on concepts and principles from the theory of computing and logic. It starts with an introduction to knowledge as truthful and useful information, and its development and management by computers and humans. It analyses the relationship between computational processes and physical phenomena, as well as the processes of knowledge production and application by humans and computers. In turn, the book presents autonomous systems that are called upon to replace humans in complex operations as a step toward strong AI, and discusses the risks – real or hypothetical – of the careless use of these systems. It compares human and machine intelligence, attempting to answer the question of whether and to what extent computers, as they stand today, can approach human-level situation awareness and decision-making. Lastly, the book explains the functioning of individual consciousness as an autonomous system that manages short- and long-term objectives on the basis of value criteria and accumulated knowledge. It discusses how individual values are shaped in society and the role of institutions in fostering and maintaining a common set of values for strengthening social cohesion. The book differs from books on the philosophy of science in many respects, e.g. by considering knowledge in its multiple facets and degrees of validity and truthfulness. It follows the dualist tradition of logicians, emphasizing the importance of logic and language and considering an abstract concept of information very different from the one used in the physical sciences. From this perspective, it levels some hopefully well-founded criticism at approaches that consider information and knowledge as nothing more than the emergent properties of physical phenomena. The book strikes a balance between popular books that sidestep fundamental issues and focus on sensationalism, and scientific or philosophical books that are not accessible to non-experts. As such, it is intended for a broad audience interested in the role of knowledge as a driver for change and development, and as a common good whose production and application could shape the future of humanity.Trade Review​In Understanding and Changing the World: From Information to Knowledge and Intelligence, Joseph Sifakis (a 2007 Turing Award recipient) amasses a lifetime of knowledge as a deep thinker and effective practitioner of computer science—indeed, collecting a civilization’s wisdom—to provide a valuable framework that is rooted in the philosophy of science and society."Akash Deshpande, SIAM News, https://sinews.siam.org/Details-Page/intelligence-whence-and-whitherTable of Contents1. Introduction.- Part I For a Gnoseological View of the World.- 2. Fundamental Questions about Knowledge.- 3. Information and Knowledge.- 4. The Development and Application of Knowledge.- Part II Computing, Knowledge and Intelligence.- 5. Physical Phenomena and Computational Processes.- 6. Human vs Artificial Intelligence.- Part III Consciousness and Society.- 7. Consciousness.- 8. Value Systems and Society.- 9. Epilogue.- Index.

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Book SynopsisDarren Bridger is a consultant to designers and marketers, advising on using and analyzing data that tap into consumers' non-conscious thinking and motivations. He was one of the original pioneers of the Consumer Neuroscience industry, helping to pioneer two of the first companies in the field then joining the world's largest agency, Neurofocus (now part of the Nielsen company). He is currently Head of Insights at NeuroStrata. Trade Review"A super, easy-to-read book demystifying the world of neuro design, addressing the balance between the role of human creativity and that of neuroscience in modern design. If you think neuro design is about creating bland designs by deconstructing beauty, you need to read this book. It's not about that at all. Darren Bridger introduces all the major themes, key methods and tools underlying the science in engaging, manageable chunks. Any book that explains the allure of memes has to get five stars from me." * Jamie Croggon, Design Director, SharkNinja *"With solid science as the starting point, Darren Bridger provides an eminently practical guide to designing for your customer's brain. Neuro Design is packed with actionable strategies and techniques, and is a must-read for every marketer and designer." * Roger Dooley, author of Brainfluence *"A topic which should be of great importance to anyone in the business of retailing, advertising and marketing. Darren Bridger deals with complex topics in an engaging and practical manner, covering all aspects of the interplay between brain function and product design. Such an understanding is crucial for ensuring consumers stop and buy, rather than walking on by." * Dr David Lewis, Chairman of Mindlab International & Author of The Brain Sell *Table of Contents Section - 01: What is Neuro Design?; Section - 02: Neuroaesthetics; Section - 03: Processing Fluency; Section - 04: How First Impressions Work; Section - 05: Multisensory and Emotional Design; Section - 06: Visual Saliency Maps; Section - 07: Visual Persuasion and Behavioural Economics; Section - 08: Designing for Screens; Section - 09: Viral Designs; Section - 10: Designing Presentation Slides; Section - 11: Conducting Neuro Design Research; Section - 12: Conclusion;

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Book SynopsisStudies of complexity, singularity, and anomaly using nonlocal continuum models are steadily gaining popularity. This monograph provides an introduction to basic analytical, computational, and modeling issues and to some of the latest developments in these areas.Nonlocal Modeling, Analysis, and Computation includes motivational examples of nonlocal models, basic building blocks of nonlocal vector calculus, elements of theory for well-posedness and nonlocal spaces, connections to and coupling with local models, convergence and compatibility of numerical approximations, and various applications, such as nonlocal dynamics of anomalous diffusion and nonlocal peridynamic models of elasticity and fracture mechanics.A particular focus is on nonlocal systems with a finite range of interaction to illustrate their connection to traditional local systems represented by partial differential equations and fractional PDEs. These models are designed to represent nonlocal interactions explicitly and to remain valid for complex systems involving possible singular solutions and they have the potential to be alternatives to as well as bridges to existing local continuum and discrete models.The author discusses ongoing studies of nonlocal models to encourage the discovery of new mathematical theory for nonlocal continuum models and offer new perspectives on existing discrete models and local continuum models and the connections between them.

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Book SynopsisThis open access book contains review papers authored by thirteen plenary invited speakers to the 9th International Congress on Industrial and Applied Mathematics (Valencia, July 15-19, 2019). Written by top-level scientists recognized worldwide, the scientific contributions cover a wide range of cutting-edge topics of industrial and applied mathematics: mathematical modeling, industrial and environmental mathematics, mathematical biology and medicine, reduced-order modeling and cryptography. The book also includes an introductory chapter summarizing the main features of the congress. This is the first volume of a thematic series dedicated to research results presented at ICIAM 2019-Valencia Congress.Table of Contents1 M. Berger, Asteroid-Generated Tsunamis: A Review.- 2 A. Bermúdez, Some Case Studies in Environmental and Industrial Mathematics.- 3 Z. Cai et al., Hyperbolic Model Reduction for Kinetic Equations.- 4 A. Cohen et al., State Estimation - The Role of Reduced Models.- 5 C. Conca, Modelling Our Sense Of Smell.- 6 L. Edelstein-Keshet, Pattern formation inside living cells.- 7 M. Garzon et al., Efficient Algorithms for Tracking Moving Interfaces.- 8 K. Lauter, Private AI: Machine Learning on Encrypted Data.- 9 C. Le Bris, Mathematical approaches for contemporary materials science: Addressing defects in the microstructure.- 10 H. Leng et al., An iterative thresholding method for topology optimization for the Navier-Stokes flow.- 11 K. Sako, Cryptography and Digital Transformation.- 12 H. Suito et al., Numerical Study for Blood Flows in Thoracic Aorta.- 13 J.A.C. Weideman, Dynamics of Complex Singularities of Nonlinear PDEs: Analysis and Computation.

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Book SynopsisSimulating the behavior of a human heart, predicting tomorrow's weather, optimizing the aerodynamics of a sailboat, finding the ideal cooking time for a hamburger: to solve these problems, cardiologists, meteorologists, sportsmen, and engineers can count on math help. This book will lead you to the discovery of a magical world, made up of equations, in which a huge variety of important problems for our life can find useful answers.Trade Review“By providing tools and current examples on modeling issues ... the book makes a contribution answering the becoming more and more prevalent presence of Mathematics in our daily lives. The examples come essentially from the physical and natural sciences, but the book can be relied on in other areas, including the humanities, aside seminal works on mathematical modeling ... . The journey consists in eight rigorous and enjoying chapters.” (Lisa Morhaim, zbMATH 1519.00001, 2023)Table of Contents1 The model, aka the magic box.- 2 Weather Forecast Models.- 3 Epidemics: the Mathematics of Contagion.- 4 Mathematical Hearth.- 5 Mathematics in the Wind.- 6 Flying on Sun Power.- 7 The taste for Mathematics.- 8 Conclusions.

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Book SynopsisThis contributed volume convenes a rich selection of works with a focus on innovative mathematical methods with applications in real-world, industrial problems. Studies included in this book are all motivated by a relevant industrial challenge, and demonstrate that mathematics for industry can be extremely rewarding, leading to new mathematical methods and sometimes even to entirely new fields within mathematics.The book is organized into two parts: Computational Sciences and Engineering, and Data Analysis and Finance. In every chapter, readers will find a brief description of why such work fits into this volume; an explanation on which industrial challenges have been instrumental for their inspiration; and which methods have been developed as a result. All these contribute to a greater unity of the text, benefiting not only practitioners and professionals seeking information on novel techniques but also graduate students in applied mathematics, engineering, and related fields.Table of ContentsPart I: Computational Science and Engineering.- Multirate Schemes — An Answer of Numerical Analysis to a Demand from Applications.- Electronic Circuit Simulation and the Development of New Krylov-Subspace Methods.- Modular time integration of coupled problems in system dynamics.- Differential-Algebraic Equations and Beyond: From Smooth to Nonsmooth Constrained Dynamical Systems.- Fast Numerical Methods to Compute Periodic Solutions of Electromagnetic Models.- Challenges in the Simulation of Radio Frequency Circuits.- An integrated data-driven computational pipeline with model order reduction for industrial and applied mathematics.- From rotating fluid masses and Ziegler’s paradox to Pontryagin- and Krein spaces and bifurcation theory.- Part II: Data Analysis and finance.- Topological Data Analysis.- Prediction Models with Functional Data for Variables related with Energy Production.- Quantization Methods for Stochastic Differential Equations.

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Book SynopsisThis hands-on introduction to numerical geodynamic modelling provides a solid grounding in the necessary mathematical theory and techniques, including continuum mechanics and partial differential equations, before introducing key numerical modelling methods and applications. Fully updated, this second edition includes four completely new chapters covering the most recent advances in modelling inertial processes, seismic cycles and fluid-solid interactions, and the development of adaptive mesh refinement algorithms. Many well-documented, state-of-the-art visco-elasto-plastic 2D models are presented, which allow robust modelling of key geodynamic processes. Requiring only minimal prerequisite mathematical training, and featuring over sixty practical exercises and ninety MATLAB examples, this user-friendly resource encourages experimentation with geodynamic models. It is an ideal introduction for advanced courses and can be used as a self-study aid for graduates seeking to master geodynamic modelling for their own research projects.Trade Review'A great introduction to computational geodynamics with vivid examples, hands-on exercises and step-by-step derivations of formulas. Even better than the first edition.' Sascha Brune, Das Helmholtz-Zentrum Potsdam – Deutsches GeoForschungsZentrum'This book is so much more than an introduction to geodynamic modelling. Taras Gerya opens the world of geodynamic experiments by taking the reader through a carefully designed set of hands-on programming exercises that will convince you that modelling is not terribly complicated, but a process to logically follow through. Go ahead and get started!' Susanne Buiter, Geological Survey of Norway'This comprehensive textbook challenges all solid Earth scientists to give geodynamic modelling a try in a hands-on, empowering style. The new edition covers even more ground, including cutting-edge topics. A great achievement, and the community will be the better for it.' Thorsten Becker, University of Texas, AustinPraise for the first edition: '… the book provides excellent value for those wanting an introduction to the field. Anyone who works carefully through this book and completes all the exercises should be well prepared for further work in geodynamic modelling.' GeoscientistPraise for the first edition: 'The book is written in a light and engaging style such that it deserves a place on the recommended reading list of any undergraduate or Masters course that includes geodynamics. Additionally, it will be a valuable resource for any geoscientist who wants to include geodynamic modelling within their research activities.' Geological MagazineTable of Contents1. The continuity equation; 2. Density and gravity; 3. Numerical solutions of partial differential equations; 4. Stress and strain; 5. The momentum equation; 6. Viscous rheology of rocks; 7. Numerical solutions of the momentum and continuity equations; 8. The advection equation and marker-in-cell method; 9. The heat conservation equation; 10. Numerical solution of the heat conservation equation; 11. 2D thermomechanical code structure; 12. Elasticity and plasticity; 13. 2D implementation of visco-elasto-plasticity; 14. 2D thermomechanical modelling of inertial processes; 15. Seismo-thermomechanical modelling; 16. Hydro-thermomechanical modelling; 17. Adaptive mesh refinement; 18. The multigrid method; 19. Programming of 3D problems; 20. Numerical benchmarks; 21. Design of 2D numerical geodynamic models; Epilogue: outlook; Appendix: MATLAB® program examples; References; Index.

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Book SynopsisThis book provides a user-friendly, hands-on introduction to the Nonlinear Mixed Effects Modeling (NONMEM) system, the most powerful tool for pharmacokinetic / pharmacodynamic analysis. Introduces requisite background to using Nonlinear Mixed Effects Modeling (NONMEM), covering data requirements, model building and evaluation, and quality control aspects Provides examples of nonlinear modeling concepts and estimation basics with discussion on the model building process and applications of empirical Bayesian estimates in the drug development environment Includes detailed chapters on data set structure, developing control streams for modeling and simulation, model applications, interpretation of NONMEM output and results, and quality control Has datasets, programming code, and practice exercises with solutions, available on a supplementary websiteTrade Review“This book may make the “User Guide V experience” a story from the good old times for the next generation of pharmacometricians.” (CPT: Pharmacometrics & Systems Pharmacology, 22 December 2014)Table of ContentsPreface xiii CHAPTER 1 The Practice of Pharmacometrics 1 1.1 Introduction 1 1.2 Applications of Sparse Data Analysis 2 1.3 Impact of Pharmacometrics 4 1.4 Clinical Example 5 CHAPTER 2 Population Model Concepts and Terminology 9 2.1 Introduction 9 2.2 Model Elements 10 2.3 Individual Subject Models 11 2.4 Population Models 12 2.4.1 Fixed-Effect Parameters 13 2.4.2 Random-Effect Parameters 14 2.5 Models of Random Between-Subject Variability (L1) 17 2.5.1 Additive Variation 17 2.5.2 Constant Coefficient of Variation 18 2.5.3 Exponential Variation 18 2.5.4 Modeling Sources of Between-Subject Variation 19 2.6 Models of Random Variability in Observations (L2) 19 2.6.1 Additive Variation 20 2.6.2 Constant Coefficient of Variation 21 2.6.3 Additive Plus CCV Model 22 2.6.4 Log-Error Model 24 2.6.5 Relationship Between RV Expressions and Predicted Concentrations 24 2.6.6 Significance of the Magnitude of RV 25 2.7 Estimation Methods 26 2.8 Objective Function 26 2.9 Bayesian Estimation 27 CHAPTER 3 NONMEM Overview and Writing an NM-TRAN Control Stream 28 3.1 Introduction 28 3.2 Components of the NONMEM System 28 3.3 General Rules 30 3.4 Required Control Stream Components 31 3.4.1 $PROBLEM Record 31 3.4.2 The $DATA Record 32 3.4.3 The $INPUT Record 35 3.5 Specifying the Model in NM-TRAN 35 3.5.1 Calling PREDPP Subroutines for Specific PK Models 35 3.5.2 Specifying the Model in the $PK Block 38 3.5.3 Specifying Residual Variability in the $ERROR Block 45 3.5.4 Specifying Models Using the $PRED Block 49 3.6 Specifying Initial Estimates with $THETA, $OMEGA, and $SIGMA 50 3.7 Requesting Estimation and Related Options 56 3.8 Requesting Estimates of the Precision of Parameter Estimates 62 3.9 Controlling the Output 63 CHAPTER 4 Datasets 66 4.1 Introduction 66 4.2 Arrangement of the Dataset 68 4.3 Variables of the Dataset 71 4.3.1 TIME 71 4.3.2 DATE 71 4.3.3 ID 72 4.3.4 DV 74 4.3.5 MDV 74 4.3.6 CMT 74 4.3.7 EVID 75 4.3.8 AMT 76 4.3.9 RATE 77 4.3.10 ADDL 78 4.3.11 II 79 4.3.12 SS 80 4.4 Constructing Datasets with Flexibility to Apply Alternate Models 80 4.5 Examples of Event Records 81 4.5.1 Alternatives for Specifying Time 81 4.5.2 Infusions and Zero-Order Input 81 4.5.3 Using ADDL 82 4.5.4 Steady-State Approach 83 4.5.5 Samples Before and After Achieving Steady State 83 4.5.6 Unscheduled Doses in a Steady-State Regimen 84 4.5.7 Steady-State Dosing with an Irregular Dosing Interval 84 4.5.8 Multiple Routes of Administration 85 4.5.9 Modeling Multiple Dependent Variable Data Types 86 4.5.10 Dataset for $PRED 86 4.6 Beyond Doses and Observations 87 4.6.1 Other Data Items 87 4.6.2 Covariate Changes over Time 88 4.6.3 Inclusion of a Header Row 89 CHAPTER 5 Model Building: Typical Process 90 5.1 Introduction 90 5.2 Analysis Planning 90 5.3 Analysis Dataset Creation 92 5.4 Dataset Quality Control 93 5.5 Exploratory Data Analysis 94 5.5.1 EDA: Population Description 95 5.5.2 EDA: Dose-Related Data 99 5.5.3 EDA: Concentration-Related Data 99 5.5.4 EDA: Considerations with Large Datasets 111 5.5.5 EDA: Summary 115 5.6 Base Model Development 116 5.6.1 Standard Model Diagnostic Plots and Interpretation 116 5.6.2 Estimation of Random Effects 130 5.6.3 Precision of Parameter Estimates (Based on $COV Step) 137 5.7 Covariate Evaluation 138 5.7.1 Covariate Evaluation Methodologies 140 5.7.2 Statistical Basis for Covariate Selection 141 5.7.3 Diagnostic Plots to Illustrate Parameter-Covariate Relationships 143 5.7.4 Typical Functional Forms for Covariate-Parameter Relationships 148 5.7.5 Centering Covariate Effects 156 5.7.6 Forward Selection Process 160 5.7.7 Evaluation of the Full Multivariable Model 167 5.7.8 Backward Elimination Process 169 5.7.9 Other Covariate Evaluation Approaches 171 5.8 Model Refinement 172 CHAPTER 6 Interpreting the NONMEM Output 178 6.1 Introduction 178 6.2 Description of the Output Files 178 6.3 The NONMEM Report File 179 6.3.1 NONMEM-Related Output 179 6.3.2 PREDPP-Related Output 180 6.3.3 Output from Monitoring of the Search 180 6.3.4 Minimum Value of the Objective Function and Final Parameter Estimates 182 6.3.5 Covariance Step Output 186 6.3.6 Additional Output 187 6.4 Error Messages: Interpretation and Resolution 188 6.4.1 NM-TRAN Errors 188 6.4.2 $ESTIMATION Step Failures 189 6.4.3 $COVARIANCE Step Failures 190 6.4.4 PREDPP Errors 191 6.4.5 Other Types of NONMEM Errors 192 6.4.6 FORTRAN Compiler or Other Run-Time Errors 193 6.5 General Suggestions for Diagnosing Problems 193 CHAPTER 7 App lications Using Parameter Estimates from the Individual 198 7.1 Introduction 198 7.2 Bayes Theorem and Individual Parameter Estimates 200 7.3 Obtaining Individual Parameter Estimates 202 7.4 Applications of Individual Parameter Estimates 204 7.4.1 Generating Subject-Specific Exposure Estimates 204 7.4.2 Individual Exposure Estimates for Group Comparisons 210 CHAPTER 8 Introduction to Model Evaluation 212 8.1 Introduction 212 8.2 Internal Validation 212 8.3 External Validation 213 8.4 Predictive Performance Assessment 214 8.5 Objective Function Mapping 217 8.6 Leverage Analysis 220 8.7 Bootstrap Procedures 222 8.8 Visual and Numerical Predictive Check Procedures 223 8.8.1 The VPC Procedure 223 8.8.2 Presentation of VPC Results 225 8.8.3 The Numerical Predictive Check (NPC) Procedure 229 8.9 Posterior Predictive Check Procedures 229 CHAPTER 9 User-Written Models 232 9.1 Introduction 232 9.2 $MODEL 235 9.3 $SUBROUTINES 236 9.3.1 General Linear Models (ADVAN5 and ADVAN7) 236 9.3.2 General Nonlinear Models (ADVAN6, ADVAN8, ADVAN9, and ADVAN13) 238 9.3.3 $DES 238 9.4 A Series of Examples 240 9.4.1 Defined Fractions Absorbed by Zero- and First-Order Processes 240 9.4.2 Sequential Absorption with First-Order Rates, without Defined Fractions 242 9.4.3 Parallel Zero-Order and First-Order Absorption, without Defined Fractions 243 9.4.4 Parallel First-Order Absorption Processes, without Defined Fractions 245 9.4.5 Zero-Order Input into the Depot Compartment 246 9.4.6 Parent and Metabolite Model: Differential Equations 247 CHAPTER 10 PK/PD Models 250 10.1 Introduction 250 10.2 Implementation of PD Models in NONMEM 251 10.3 $PRED 252 10.3.1 Direct-Effect PK/PD Examples: PK Concentrations in the Dataset 253 10.3.2 Direct-Effect PK/PD Example: PK from Computed Concentrations 255 10.4 $PK 256 10.4.1 Specific ADVANs (ADVAN1–ADVAN4 and ADVAN10–ADVAN12) 256 10.4.2 General ADVANs (ADVAN5–ADVAN9 and ADVAN13) 257 10.4.3 PREDPP: Effect Compartment Link Model Example (PD in $ERROR) 257 10.4.4 PREDPP: Indirect Response Model Example: PD in $DES 259 10.5 Odd-Type Data: Analysis of Noncontinuous Data 261 10.6 PD Model Complexity 262 10.7 Communication of Results 263 CHAPTER 11 Simulation Basics 265 11.1 Introduction 265 11.2 The Simulation Plan 265 11.2.1 Simulation Components 266 11.2.2 The Input–Output Model 266 11.2.3 The Covariate Distribution Model 270 11.2.4 The Trial Execution Model 273 11.2.5 Replication of the Study 274 11.2.6 Analysis of the Simulated Data 275 11.2.7 Decision Making Using Simulations 275 11.3 Miscellaneous Other Simulation-Related Considerations 276 11.3.1 The Seed Value 276 11.3.2 Consideration of Parameter Uncertainty 277 11.3.3 Constraining Random Effects or Responses 278 CHAPTER 12 Quality Control 285 12.1 Introduction 285 12.2 QC of the Data Analysis Plan 285 12.3 Analysis Dataset Creation 286 12.3.1 Exploratory Data Analysis and Its Role in Dataset QC 287 12.3.2 QC in Data Collection 287 12.4 QC of Model Development 288 12.4.1 QC of NM-TRAN Control Streams 289 12.4.2 Model Diagnostic Plots and Model Evaluation Steps as QC 290 12.5 Documentation of QC Efforts 290 12.6 Summary 291 References 292 Index 293

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Book SynopsisControl theory, an interdisciplinary topic within the study of dynamical systems, is an important but often overlooked part of a physicist's education. This is the first broad and complete treatment of the subject specifically tailored for physicists, spanning the basics to the most recent advances.Trade Review'Exceptionally well written, organized and presented, Control Theory for Physicists is an ideal and comprehensive volume that is unreservedly recommended as a curriculum textbook. While a core addition to college and university library Mathematical Physics & Calculus collections, it should be noted for students, academia, physicists, and non-specialist general readers with an interest in the subject …' Midwest Book Review'… will enhance appreciation of the limits of practical applications of physics, especially those associated with thermodynamics and information theory … Highly recommended.' E. Kincanon, Choice Connect'This is a rare example of a textbook that is concise yet clear, math dense yet very accessible, and rigorous yet beautifully written. The treatment throughout prioritizes first-principles descriptions, with an emphasis on not only when control works but also when it fails. It includes well-contextualized examples and well-formulated problems. It is ready for classroom use, with additional resources for instructors-such as a solution manual and associated Mathematica notebooks-available from the publisher. A 100-page supplement on background mathematics is also available on the publisher's website, which provides a comprehensive review of key mathematical topics. As already noted by Hugo Touchette in his back cover endorsement, this book may indeed lead more departments to include control theory in their curriculum.' Adilson E. Motter, Professor of Physics and Astronomy at Northwestern University, Illinois, IEEE Control Systems'… Together with information theory, control theory is the area of engineering that has the most fundamental lessons to teach physicists, and John Bechhoefer's recent textbook, Control Theory for Physicists, is an excellent place to start learning them … the pedagogical presentation of the material in the book perfectly complements its engaging subject matter.' Michael Hinczewski, The BiophysicistTable of ContentsPart I. Core Material: 1. Historical introduction; 2. Dynamical systems; 3. Frequency-domain control; 4. Time-domain control; 5. Discrete-time systems; 6. System identification; Part II. Advanced Ideas: 7. Optimal control; 8. Stochastic systems; 9. Robust control; 10. Adaptive control; 11. Nonlinear control; Part III. Special Topics: 12. Discrete-state systems; 13. Quantum control; 14. Networks and complex systems; 15. Limits to control.

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a huge range and FREE tracked UK delivery on ALL orders.

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a huge range and FREE tracked UK delivery on ALL orders.

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Book SynopsisThis book provides thorough and comprehensive coverage of most of the new and important quantitative methods of data analysis for graduate students and practitioners. In recent years, data analysis methods have exploded alongside advanced computing power, and it is critical to understand such methods to get the most out of data, and to extract signal from noise. The book excels in explaining difficult concepts through simple explanations and detailed explanatory illustrations. Most unique is the focus on confidence limits for power spectra and their proper interpretation, something rare or completely missing in other books. Likewise, there is a thorough discussion of how to assess uncertainty via use of Expectancy, and the easy to apply and understand Bootstrap method. The book is written so that descriptions of each method are as self-contained as possible. Many examples are presented to clarify interpretations, as are user tips in highlighted boxes.Trade Review'This text is suitable for undergraduates and graduates, as well as seasoned scientists and engineers seeking to broaden their statistical skills. It will have lasting value as it is comprehensive, containing detailed explanations of a wide range of statistical methods. The book is clearly written by a meticulous scientist who is an expert in the field and an award winning teacher.' James Hays, Columbia University, New York'At last: a guide for getting the most out of your data analysis while avoiding the many pitfalls, hazards and common mistakes. This book is an invaluable and inspired opus on the fundamentals of quantitative data analysis. It is both comprehensive and illuminating, with many a nugget of enlightened wisdom, as well as succinctly summarized 'take-home' points in each and every section. A very accessible must-have guide for exploring data in the most informed way, and a gem of a textbook for students, teachers and practitioners alike.' Sharon Stammerjohn, University of Colorado, Boulder'Coherent book-length treatments are so valuable in the Data Age: the internet is full of algorithms - but described flatly, and in myriad notations and nomenclatures. This long-time teacher's lucid text expresses the spirit and strategy of data analysis, as well as the details. Boxes set off optional advanced derivations, appendices survey matrix algebra and uncertainty analysis, and the chapters aim for standalone readability, making this a valuable reference as well as a flexible textbook (with questions). Spectral estimation is especially well covered.' Brian Mapes, University of Miami'This is a competent development of many data analysis methods … Overall, the book is the outgrowth of teaching the subject for 30 years, which shows in the well-developed, clear narrative descriptions accompanying the theory.' D. A. Vaccari, ChoiceTable of ContentsPart I. Fundamentals: 1. The nature of data and analysis; 2. Probability theory; 3. Statistics; Part II. Fitting Curves to Data; 4. Interpolation; 5. Smoothed curve fitting; 6. Special curve fitting; Part III. Sequential Data Fundamentals: 7. Serial products; 8. Fourier series; 9. Fourier transform; 10. Fourier sampling theory; 11. Spectral analysis; 12. Cross spectral analysis; 13. Filtering and deconvolution; 14. Linear parametric models; 15. Empirical orthogonal function (EOF) analysis; A1. Overview of matrix algebra; A2. Uncertainty analysis; References; Index.

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Book SynopsisDo you want to deepen your understanding of complex systems and design integrated circuits more quickly? Learn how with this step-by-step guide that shows, from first principles, how to employ estimation techniques to analyze and solve complex problems in IC design using a simplified modeling approach. Applications are richly illustrated using real-world examples from across IC design, from simple circuit theory, to the electromagnetic effects and high frequency design, and systems such as data converters and phase-locked loops. Basic concepts like inductance and capacitance are related to one other and other RF phenomena inside a modern chip, enhancing understanding without the need for simulators. Use the easy-to-follow models presented to start designing your own products, from inductors and amplifiers to more complex systems. Whether you are an early-career professional or researcher, graduate student, or established IC engineer looking to reduce your reliance on commercial softwarTrade Review'The estimation analysis techniques in this book open up a new and unique approach to gaining a deeper understanding of circuits, thus accelerating the optimization and design of a broad range of circuits, which is a critical skill in the fast paced IC design world where time to market is crucial to success.' Joel King, Skyworks Solutions, Inc.'Developing engineering solutions benefits greatly from the proverbial back of the envelope analysis. This book does an excellent job of not only providing a great reference to a number of estimating techniques (limitations clearly identified) for a number of key topics. It also resurrects the concept of engineering estimation, to quickly evaluate ideas and drive to useful conclusions without losing context. This art form is dwindling as today's engineers continue to depend on (very capable) computer simulators, slowing the development of intuition and hence innovation.' Claudio Anzil, Innophase Inc.Table of Contents1. General guidelines in estimation analysis in integrated circuits; 2. Basic amplifier stages; 3. Higher level amplifier stages; 4. Electromagnetism – fundamentals; 5. Electromagnetism – circuit applications; 6. Electromagnetic field simulators; 7. System aspects; Appendix A: basic transistor and technology model; Appendix B: useful mathematical relationships; Index.

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Book SynopsisJust like humans, animals and plants suffer from infectious diseases, which can critically threaten biodiversity. This book describes key studies that have driven our understanding of the ecology and evolution of wildlife diseases. Each chapter introduces the host and disease, and explains how that system has aided our general understanding of the evolution and spread of wildlife diseases, through the development and testing of important epidemiological and evolutionary theories. Questions addressed include: How do hosts and parasites co-evolve? What determines how fast a disease spreads through a population? How do co-infecting parasites interact? Why do hosts vary in parasite burden? Which factors determine parasite virulence and host resistance? How do parasites influence the spread of invasive species? How do we control infectious diseases in wildlife? This book will provide a valuable introduction to students new to the topic, and novel insights to researchers, professionals and pTrade Review'Overall, this is a fascinating collection of studies that showcases why wildlife diseases are worthy of study and how combining field observations, experiments, mathematical models and the latest in genomic and molecular research provides not only research insight, but also contributes to effective conservation and management efforts.' Rob Robinson, British Trust for Ornithology'Advances in modeling, epidemiologic techniques, and genetics have been crucial in some examples treated by contributors, and the importance of long-term field studies, essential for understanding dynamic systems, is emphasized throughout the volume. Some studies are observational, some experimental, and some largely theoretical. All contributions are extensively referenced and effectively illustrated.' M. Gochfeld, Choice'Overall, this well-written book is, in my opinion, a valuable contribution that will encourage further collecting and analysing long-term data in the study of wildlife diseases. It also gives hope. The advances in our understanding of wildlife disease dynamics enable better planning of conservation and management efforts, as shown in the case of wild and farmed salmon or the bighorn sheep pneumonia. As such, it is undoubtedly of high value for researchers and managers working in the field of wildlife disease ecology, but also for advanced undergraduate students or academic lecturers who would like to broaden their knowledge. The book was a great company during the coronavirus lockdown and a fascinating journey through the realm of wildlife diseases. I highly recommend it!' Agata Mrugala, Basic and Applied Ecology'This book comes to fill an important niche in disease ecology: synthesizing the state of knowledge about wildlife disease ecology while integrating theoretical models with a wide variety empirical case studies … this book presents an invaluable synthesis of our knowledge of disease ecology in wildlife hosts.' Miguel A. Acevedo, The Quarterly Review of BiologyTable of ContentsPreface: wildlife disease ecology; Glossary of terms; Part I. Understanding Within-Host Processes: 1. Pollinator diseases: the Bombus-Crithidia system; 2. Genetic diversity and disease spread: epidemiological models and empirical studies of a snail-trematode system; 3. Wild rodents as a natural model to study within-host parasite interactions; 4. From population to individual host scale and back again: testing theories of infection and defence in the Soay sheep of St Kilda; 5. The causes and consequences of parasite interactions: African buffalo as a case study; 6. Effects of host lifespan on the evolution of age-specific resistance: a case study of anther-smut disease on wild carnations; 7. Sexually transmitted infections in natural populations: what have we learnt from beetles and beyond?; Part II. Understanding Between-Host Processes: 8. Using insect baculoviruses to understand how population structure affects disease spread; 9. Infection and invasion: study cases from aquatic communities; 10. Parasite mediated selection in red grouse – consequences for population dynamics and mate choice; 11. Emergence, transmission and evolution of an uncommon enemy: Tasmanian devil facial tumour disease; 12. Bovine tuberculosis in badgers: sociality, infection and demography in a social mammal; 13. Mycoplasma ovipneumoniae in bighorn sheep: from exploration to action; 14. Manipulating parasites in an Arctic herbivore: gastrointestinal nematodes and the population regulation of Svalbard reindeer; Part III. Understanding Wildlife Disease Ecology at the Community and Landscape Level: 15. The ecological and evolutionary trajectory of oak powdery mildew in Europe; 16. Healthy herds or predator spreaders? Insights from the plankton into how predators suppress and spread disease; 17. Multi-trophic interactions and migration behaviour determine the ecology and evolution of parasite infection in monarch butterflies; 18. When chytrid fungus invades: integrating theory and data to understand disease- induced amphibian declines; 19. Ecology of a marine ectoparasite in farmed and wild salmon; 20. Mycoplasmal conjunctivitis in house finches: the study of an emerging disease; 21. Heterogeneities in infection and transmission in a parasite-rabbit system: key issues for understanding disease dynamics and persistence; 22. Sylvatic plague in Central Asia: a case study of abundance thresholds.

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Book SynopsisThese books are intended for undergraduate, graduate researchers and practitioners in computational sciences, and as reference books for an advanced computational methods course. We have included new results for iterative procedures in abstract spaces general enough for handling inverse problems in various situations related to real life problems through mathematical modeling. These books contain a plethora of updated bibliography and provide comparison between various investigations made in recent years in the field of computational mathematics in the wide sense. Iterative processes are the tools used to generate sequences approximating solutions of equations describing the real life problems stated above and others originating from biosciences, engineering, mathematical economics, mathematical biology, mathematical chemistry, mathematical physics medicine, mathematical programming, and other disciplines. These books also provide, recent advancements on the study of iterative procedures, and can be used as a source from which one can obtain the proper method to use in order to solve a problem. The books require a fundamental background in mathematical statistics, linear algebra and numerical analysis. It may be used as a self-study reference or as a supplementary text for an advanced course in biosciences, engineering and computational sciences.Table of ContentsFor more information, please visit our website at:https://novapublishers.com/shop/mathematical-modeling-for-the-solution-of-equations-and-systems-of-equations-with-applications-volume-iii/

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Book SynopsisPresents mathematical ideas and models that can be used to facilitate rational environmental policy making. Describes classical models for biological community performance, ecological system stability, and population dynamics, presents air pollution models and methods for solving emission problems, and highlights major results of the application of

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Book SynopsisThis book presents translations of selected Russian papers on the theoretical aspects of differential equations and applications of mathematical methods to modelling. These papers have been selected for their high scientific standards, innovative approaches, and topical interests.

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Book SynopsisLinear algebra has become the subject to know for people in quantitative disciplines of all kinds. No longer the exclusive domain of mathematicians and engineers, it is now used everywhere there is data and everybody who works with data needs to know more. This new book from Professor Gilbert Strang, author of the acclaimed Introduction to Linear Algebra, now in its fifth edition, makes linear algebra accessible to everybody, not just those with a strong background in mathematics. It takes a more active start, beginning by finding independent columns of small matrices, leading to the key concepts of linear combinations and rank and column space. From there it passes on to the classical topics of solving linear equations, orthogonality, linear transformations and subspaces, all clearly explained with many examples and exercises. The last major topics are eigenvalues and the important singular value decomposition, illustrated with applications to differential equations and image compression. A final optional chapter explores the ideas behind deep learning.

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Book SynopsisThe book covers structural, torsion, vibration, heat transfer, and fluid flow problems. It explains equations of equilibrium, stress-strain relations, interpolation functions, element design, symmetry, and FEM applications. Each chapter includes a question bank for self-study.

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Book SynopsisThe idea of modelling systems using graph theory has its origin in several scientific areas: in statistical physics (the study of large particle systems), in genetics (studying inheritable properties of natural species), and in interactions in contingency tables. The use of graphical models in statistics has increased considerably over recent years and the theory has been greatly developed and extended. This book provides the first comprehensive and authoritative account of the theory of graphical models and is written by a leading expert in the field. It contains the fundamental graph theory required and a thorough study of Markov properties associated with various type of graphs. The statistical theory of log-linear and graphical models for contingency tables, covariance selection models, and graphical models with mixed discrete-continous variables in developed detail. Special topics, such as the application of graphical models to probabilistic expert systems, are described briefly, Trade Review...this is an excellent reference book for those who are interested in studying the mathematical theory for graphical models. * Short Book Reviews, vol. 18, no. 1, April 1998 *Table of ContentsIntroduction ; 1. Graphs and Hypergraphs ; 2. Conditional Independence and Markov Properties ; 3. Contingency Tables ; 4. Multivariate Normal Models ; 5. Models for Mixed Data ; 6. Further topics ; A Various Prerequisites ; B Linear Algebra and Random Vectors ; C The Multivariate Distribution ; D Exponential Models

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Book SynopsisFinancial Asset Pricing Theory offers a comprehensive overview of the classic and the current research in theoretical asset pricing. Asset pricing is developed around the concept of a state-price deflator which relates the price of any asset to its future (risky) dividends and thus incorporates how to adjust for both time and risk in asset valuation. The willingness of any utility-maximizing investor to shift consumption over time defines a state-price deflator which provides a link between optimal consumption and asset prices that leads to the Consumption-based Capital Asset Pricing Model (CCAPM). A simple version of the CCAPM cannot explain various stylized asset pricing facts, but these asset pricing ''puzzles'' can be resolved by a number of recent extensions involving habit formation, recursive utility, multiple consumption goods, and long-run consumption risks. Other valuation techniques and modelling approaches (such as factor models, term structure models, risk-neutral valuation, and option pricing models) are explained and related to state-price deflators. The book will serve as a textbook for an advanced course in theoretical financial economics in a PhD or a quantitative Master of Science program. It will also be a useful reference book for researchers and finance professionals. The presentation in the book balances formal mathematical modelling and economic intuition and understanding. Both discrete-time and continuous-time models are covered. The necessary concepts and techniques concerning stochastic processes are carefully explained in a separate chapter so that only limited previous exposure to dynamic finance models is required.Trade ReviewThis monograph provides a consistent and comprehensive presentation of the classical asset pricing paradigm, from the basics of the theory to the latest developments in the field. The reader's task is simplified by the consistent notation and the integrated conceptual framework that is employed; his technical facility improved by the extensive proofs of the main results that are offered; and his curiosity piqued by the extensive references to the empirical literature. The expert will find it a convenient reference and the student will find it an invaluable guide. * Michael J. Brennan, Professor of Finance at Anderson School, University of California Los Angeles, at Manchester Business School, and at King Abdulaziz University, Jeddah *Munk takes a completely fresh and well organized approach to communicating the key concepts and techniques of modern asset pricing theory. His treatment is clear, accessible, rigorously unified around the notion of state pricing, and encompasses the latest model specifications. He has set the new standard for doctoral-level courses on this subject. * Darrell Duffie, Dean Witter Distinguished Professor of Finance, at the Graduate School of Business, Stanford University *Financial Asset Pricing Theory is a rigorous, yet eminently accessible, textbook at the frontier of modern asset pricing theory with applications in portfolio management, the term structure of interest rates, and derivatives, and a nice selection of problem sets. Claus Munk's textbook is my top choice as a comprehensive and intuitive textbook for an introductory or advanced PhD course on asset pricing theory. * George M. Constantinides, Leo Melamed Professor of Finance, The University of Chicago, Booth School of Business *Table of ContentsPreface ; 1. Introduction and Overview ; 2. Uncertainty, Information, and Stochastic Processes ; 3. Portfolios, Arbitrage, and Market Completeness ; 4. State Prices ; 5. Preferences ; 6. Individual Optimality ; 7. Market Equilibrium ; 8. Basic Consumption-Based Asset Pricing ; 9. Advanced Consumption-Based Asset Pricing ; 10. Factor Models ; 11. The Economics of the Term Structure of Interest Rates ; 12. Risk-Adjusted Probabilities ; 13. Derivatives ; Appendix A. A Review of Basic Probability Concepts ; Appendix B. Results on the Lognormal Distribution ; Appendix C. Results from Linear Algebra

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Book SynopsisPublished in 2002, the first edition of Geostatistical Reservoir Modeling brought the practice of petroleum geostatistics into a coherent framework, focusing on tools, techniques, examples, and guidance. It emphasized the interaction between geophysicists, geologists, and engineers, and was received well by professionals, academics, and both graduate and undergraduate students.In this revised second edition, Deutsch collaborates with co-author Michael Pyrcz to provide a full update on the latest tools, methods, practice, and research in the field of petroleum Geostatistics. Key geostatistical concepts such as integration of production data, scale-up, and cosimulation receive greater attention, and new topics like model checking, multiple point simulation, and production data integration are included in detail. Geostatistical methods are extensively illustrated through enhanced schematics, work flows and examples. A greater number of examples also are included, such as the integration oTable of Contents1. Introduction ; 2. Modeling Principles ; 3. Modeling Prerequisites ; 4. Modeling Methods ; 5. Model Applications ; 6. Special Topics ; Glossary and Notation ; Bibliography ; Index

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Book SynopsisThis book provides an introduction to MIP modeling and to planning systems, a unique collection of reformulation results, and an easy to use problem-solving library. This approach is demonstrated through a series of real life case studies, exercises and detailed illustrations.Trade ReviewFrom the reviews: "The book provides a complete overview of different models existing in the literature as well as in practice. … The authors also analyze MIP (mixed integer programming) based algorithms … . Practitioners who are interested in using MIP … can use the book to identify the most efficient way to formulate the problems and to choose the most efficient solution method. … it also can serve as a good reference for students and researchers. Overall, this is an excellent book." (Panos M. Pardalos, Mathematical Reviews, Issue 2006 k) "Recently published Production Planning by Mixed Integer Programming by Yves Pochet and Laurence Wolsey has raised considerable expectations. Firstly, problems of production planning are among the most interesting in Operations Research. … Secondly, both authors are renowned experts in the field. … There is no doubt that this volume offers the present best introduction to integer programming formulations of lot-sizing problems, encountered in production planning." (Jakub Marecek, The Computer Journal, September, 2007)Table of ContentsProduction Planning and MIP.- The Modeling and Optimization Approach.- Production Planning Models and Systems.- Mixed Integer Programming Algorithms.- Classification and Reformulation.- Reformulations in Practice.- Basic Polyhedral Combinatorics for Production Planning and MIP.- Mixed Integer Programming Algorithms and Decomposition Approaches.- Single-Item Uncapacitated Lot-Sizing.- Basic MIP and Fixed Cost Flow Models.- Single-Item Lot-Sizing.- Lot-Sizing with Capacities.- Backlogging and Start-Ups.- Single-Item Variants.- Multi-Item Lot-Sizing.- Multi-Item Single-Level Problems.- Multi-Level Lot-Sizing Problems.- Problem Solving.- Test Problems.

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