This 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 website

Written in a clear, logical and concise manner, this comprehensive resource provides discussion on essential mathematical tools, required for upgraded system performance. Understanding of basic principles and governing laws is essential to reduce complexity of the system, and this guide offers detailed discussion on analytical and numerical techniques to solve mathematical model equations. Important concepts including nonlinear algebraic equations, initial value ordinary differential equations (ODEs) and boundary value ODEs are discussed in detail. The concepts of optimization methods and sensitivity analysis, which are important from subject point of view, are explained with suitable examples. Numerous problems and MATLAB (R)/Scilab exercises are interspersed throughout the text. Several case studies involving full details of simulation are offered for better understanding. The accompanying website will host additional MATLAB (R)/Scilab problems, model question papers, simulation exercises, tutorials and projects. This book will be useful for students of chemical engineering, mechanical engineering, instrumentation engineering and mathematics.

Computer simulation is an effective and popular universal tool that can be applied to almost all disciplines. Requiring only basic knowledge of programming, mathematics, and probability theory, Computer Simulation: A Foundational Approach Using Python takes a hands-on approach to programming to introduce the fundamentals of computer simulation. The main target of the book is computer science and engineering students who are interested mainly in directly applying the techniques to their research problems. The book will be of great interest to senior undergraduate and starting graduate students in the fields of computer science and engineering and industrial engineering.

Engineering systems operate through actuators, most of which will exhibit phenomena such as saturation or zones of no operation, commonly known as dead zones. These are examples of piecewise-affine characteristics, and they can have a considerable impact on the stability and performance of engineering systems. This book targets controller design for piecewise affine systems, fulfilling both stability and performance requirements. The authors present a unified computational methodology for the analysis and synthesis of piecewise affine controllers, taking an approach that is capable of handling sliding modes, sampled-data, and networked systems. They introduce algorithms that will be applicable to nonlinear systems approximated by piecewise affine systems, and they feature several examples from areas such as switching electronic circuits, autonomous vehicles, neural networks, and aerospace applications. Piecewise Affine Control: Continuous-Time, Sampled-Data, and Networked Systems is intended for graduate students, advanced senior undergraduate students, and researchers in academia and industry. It is also appropriate for engineers working on applications where switched linear and affine models are important.

This book addresses the challenging topic of modeling adaptive networks, which often manifest inherently complex behavior. Networks by themselves can usually be modeled using a neat, declarative, and conceptually transparent Network-Oriented Modeling approach. In contrast, adaptive networks are networks that change their structure; for example, connections in Mental Networks usually change due to learning, while connections in Social Networks change due to various social dynamics. For adaptive networks, separate procedural specifications are often added for the adaptation process. Accordingly, modelers have to deal with a less transparent, hybrid specification, part of which is often more at a programming level than at a modeling level. This book presents an overall Network-Oriented Modeling approach that makes designing adaptive network models much easier, because the adaptation process, too, is modeled in a neat, declarative, and conceptually transparent Network-Oriented Modeling manner, like the network itself. Thanks to this approach, no procedural, algorithmic, or programming skills are needed to design complex adaptive network models. A dedicated software environment is available to run these adaptive network models from their high-level specifications. Moreover, because adaptive networks are described in a network format as well, the approach can simply be applied iteratively, so that higher-order adaptive networks in which network adaptation itself is adaptive (second-order adaptation), too can be modeled just as easily. For example, this can be applied to model metaplasticity in cognitive neuroscience, or second-order adaptation in biological and social contexts. The book illustrates the usefulness of this approach via numerous examples of complex (higher-order) adaptive network models for a wide variety of biological, mental, and social processes. The book is suitable for multidisciplinary Master's and Ph.D. students without assuming much prior knowledge, although also some elementary mathematical analysis is involved. Given the detailed information provided, it can be used as an introduction to Network-Oriented Modeling for adaptive networks. The material is ideally suited for teaching undergraduate and graduate students with multidisciplinary backgrounds or interests. Lecturers will find additional material such as slides, assignments, and software.

Introduction to Modeling and Simulation with MATLAB and Python is intended for students and professionals in science, social science, and engineering that wish to learn the principles of computer modeling, as well as basic programming skills. The book content focuses on meeting a set of basic modeling and simulation competencies that were developed as part of several National Science Foundation grants. Even though computer science students are much more expert programmers, they are not often given the opportunity to see how those skills are being applied to solve complex science and engineering problems and may also not be aware of the libraries used by scientists to create those models. The book interleaves chapters on modeling concepts and related exercises with programming concepts and exercises. The authors start with an introduction to modeling and its importance to current practices in the sciences and engineering. They introduce each of the programming environments and the syntax used to represent variables and compute mathematical equations and functions. As students gain more programming expertise, the authors return to modeling concepts, providing starting code for a variety of exercises where students add additional code to solve the problem and provide an analysis of the outcomes. In this way, the book builds both modeling and programming expertise with a "just-in-time" approach so that by the end of the book, students can take on relatively simple modeling example on their own. Each chapter is supplemented with references to additional reading, tutorials, and exercises that guide students to additional help and allows them to practice both their programming and analytical modeling skills. In addition, each of the programming related chapters is divided into two parts - one for MATLAB and one for Python. In these chapters, the authors also refer to additional online tutorials that students can use if they are having difficulty with any of the topics. The book culminates with a set of final project exercise suggestions that incorporate both the modeling and programming skills provided in the rest of the volume. Those projects could be undertaken by individuals or small groups of students. The companion website at http://www.intromodeling.com provides updates to instructions when there are substantial changes in software versions, as well as electronic copies of exercises and the related code. The website also offers a space where people can suggest additional projects they are willing to share as well as comments on the existing projects and exercises throughout the book. Solutions and lecture notes will also be available for qualifying instructors.

Originally published in 1987. This collection of original papers deals with various issues of specification in the context of the linear statistical model. The volume honours the early econometric work of Donald Cochrane, late Dean of Economics and Politics at Monash University in Australia. The chapters focus on problems associated with autocorrelation of the error term in the linear regression model and include appraisals of early work on this topic by Cochrane and Orcutt. The book includes an extensive survey of autocorrelation tests; some exact finite-sample tests; and some issues in preliminary test estimation. A wide range of other specification issues is discussed, including the implications of random regressors for Bayesian prediction; modelling with joint conditional probability functions; and results from duality theory. There is a major survey chapter dealing with specification tests for non-nested models, and some of the applications discussed by the contributors deal with the British National Accounts and with Australian financial and housing markets.

Filling a gap in the existing literature, this book presents a integrated treatment of latent trait, multilevel, and repeated measurement models in a unified framework that demonstrates the similarities between these models. The author emphasizes and accommodates incomplete data and data of lower measurement levels. He suggests a new estimation strategy along with a comprehensive treatment of methods for obtaining scores on latent traits and random coefficients for individual units, both appearing here for the first time. The text demonstrates the versatility of the methods presented with four extensively worked examples from different disciplines.

This book publishes select papers presented at the 4th International Conference on Frontiers in Industrial and Applied Mathematics (FIAM-2021), held at the Sant Longowal Institute of Engineering and Technology, Longowal, Punjab, India, from 21-22 December 2021. Most of the papers deal with mathematical theory embedded with its applications to engineering and sciences. This book illustrates numerical simulation of scientific problems and the state-of-the-art research in industrial and applied mathematics, including various computational and modeling techniques with case studies and concrete examples. Graduate students and researchers, who are interested in real applications of mathematics in the areas of computational and theoretical fluid dynamics, solid mechanics, optimization and operations research, numerical analysis, bio-mathematics, fuzzy, control and systems theory, dynamical systems and nonlinear analysis, algebra and approximation theory, will find the book useful.

This book provides easy access to the basic principles and methods for solving constrained and unconstrained convex optimization problems. Included are sections that cover: basic methods for solving constrained and unconstrained optimization problems with differentiable objective functions; convex sets and their properties; convex functions and their properties and generalizations; and basic principles of sub-differential calculus and convex programming problems. Convex Optimization provides detailed proofs for most of the results presented in the book and also includes many figures and exercises for a better understanding of the material. Exercises are given at the end of each chapter, with solutions and hints to selected exercises given at the end of the book. Undergraduate and graduate students, researchers in different disciplines, as well as practitioners will all benefit from this accessible approach to convex optimization methods.

The book comprises contributions by some of the most respected scientists in the field of mathematical modeling and numerical simulation of the human cardiocirculatory system. It covers a wide range of topics, from the assimilation of clinical data to the development of mathematical and computational models, including with parameters, as well as their efficient numerical solution, and both in-vivo and in-vitro validation. It also considers applications of relevant clinical interest. This book is intended for graduate students and researchers in the field of bioengineering, applied mathematics, computer, computational and data science, and medicine wishing to become involved in the highly fascinating task of modeling the cardiovascular system.

This book presents the textile-, mathematical and mechanical background for the modelling of fiber based structures such as yarns, braided and knitted textiles. The hierarchical scales of these textiles and the structural elements at the different levels are analysed and the methods for their modelling are presented. The author reports about problems, methods and algorithms and possible solutions from his twenty year experience in the modelling and software development of CAD for textiles.

The mystique of biologically inspired (or bioinspired) paradigms is their ability to describe and solve complex relationships from intrinsically very simple initial conditions and with little or no knowledge of the search space. Edited by two prominent, well-respected researchers, the Handbook of Bioinspired Algorithms and Applications reveals the connections between bioinspired techniques and the development of solutions to problems that arise in diverse problem domains. A repository of the theory and fundamentals as well as a manual for practical implementation, this authoritative handbook provides broad coverage in a single source along with numerous references to the available literature for more in-depth information. The book's two sections serve to balance coverage of theory and practical applications. The first section explains the fundamentals of techniques, such as evolutionary algorithms, swarm intelligence, cellular automata, and others. Detailed examples and case studies in the second section illustrate how to apply the theory in actually developing solutions to a particular problem based on a bioinspired technique. Emphasizing the importance of understanding and harnessing the robust capabilities of bioinspired techniques for solving computationally intractable optimizations and decision-making applications, the Handbook of Bioinspired Algorithms and Applications is an absolute must-read for anyone who is serious about advancing the next generation of computing.

This insightful reference/text describes the application of viable mathematical models in data analysis to increase crop growth and yields-highlighting effective, analytical functions that have been found useful for the comparison of alternative management techniques to maximize water and nutrient resources. Features solutions to various differential equations and considers different characteristics of the functions related to the phenomenological growth model. Mathematical Models of Crop Growth and Yield examines the response of seasonal dry matter to applied nutrients considers the accumulation of dry matter and plant nutrients explores sensitivity analysis and dimensionless plots assesses the transfer of nitrogen from a legume to a grass analyzes the linkage of animal production with forage production discusses water availability evaluates coupling among applied, soil, and plant components presents numerical procedures for regression analysis supplies extensive exercises for further study Enhanced by the inclusion of more than 1300 literature citations, display equations, tables, and figures, Mathematical Models of Crop Growth and Yield will prove an invaluable reference for plant pathologists; agriculturists; toxicologists; ecologists; botanists; agronomists; horticulturists; biochemists; foresters; plant culturists; biotechnologists; plant and crop physiologists; plant, crop, soil, and environmental scientists; agricultural, biological, and environmental engineers; crop managers; and crop modeling specialists; and an essential text for upper-level undergraduate and graduate students in these disciplines. Return to Top Table of Contents Introduction Seasonal Response Models Growth Response Models Mathematical Characteristics of Models Pasture Systems Nonlinear Regression for Mathematical Models Index Return to Top

Many methods for analyzing clustered data exist, all with advantages and limitations in particular applications. Compiled from the contributions of leading specialists in the field, Topics in Modelling of Clustered Data describes the tools and techniques for modelling the clustered data often encountered in medical, biological, environmental, and social science studies. It focuses on providing a comprehensive treatment of marginal, conditional, and random effects models using, among others, likelihood, pseudo-likelihood, and generalized estimating equations methods. The authors motivate and illustrate all aspects of these models in a variety of real applications. They discuss several variations and extensions, including individual-level covariates and combined continuous and discrete outcomes. Flexible modelling with fractional and local polynomials, omnibus lack-of-fit tests, robustification against misspecification, exact, and bootstrap inferential procedures all receive extensive treatment. The applications discussed center primarily, but not exclusively, on developmental toxicity, which leads naturally to discussion of other methodologies, including risk assessment and dose-response modelling. Clearly written, Topics in Modelling of Clustered Data offers a practical, easily accessible survey of important modelling issues. Overview models give structure to a multitude of approaches, figures help readers visualize model characteristics, and a generous use of examples illustrates all aspects of the modelling process.

Mathematical Modeling: Branching Beyond Calculus reveals the versatility of mathematical modeling. The authors present the subject in an attractive manner and flexibley manner. Students will discover that the topic not only focuses on math, but biology, engineering, and both social and physical sciences. The book is written in a way to meet the needs of any modeling course. Each chapter includes examples, exercises, and projects offering opportunities for more in-depth investigations into the world of mathematical models. The authors encourage students to approach the models from various angles while creating a more complete understanding. The assortment of disciplines covered within the book and its flexible structure produce an intriguing and promising foundation for any mathematical modeling course or for self-study. Key Features: Chapter projects guide more thorough investigations of the models The text aims to expand a student's communication skills and perspectives WThe widespread applications are incorporated, even includinge biology and social sciences Its structure allows it to serve as either primary or supplemental text Uses Mathematica and MATLAB are used to develop models and computations

Statisticians rely heavily on making models of 'causal situations' in order to fully explain and predict events. Modelling therefore plays a vital part in all applications of statistics and is a component of most undergraduate programmes. 'An Introduction to Statistical Modelling' provides a single reference with an applied slant that caters for all three years of a degree course. The book concentrates on core issues and only the most essential mathematical justifications are given in detail. Attention is firmly focused on the statistical aspects of the techniques, in this lively, practical approach.

Mankind now faces even more challenging environment- and health-related problems than ever before. Readily available transportation systems facilitate the swift spread of diseases as large populations migrate from one part of the world to another. Studies on the spread of the communicable diseases are very important. This book, Mathematical Population Dynamics and Epidemiology in Temporal and Spatio-Temporal Domains, provides a useful experimental tool for making practical predictions, building and testing theories, answering specific questions, determining sensitivities of the parameters, forming control strategies, and much more. This volume focuses on the study of population dynamics with special emphasis on the migration of populations and the spreading of epidemics among human and animal populations. It also provides the background needed to interpret, construct, and analyze a wide variety of mathematical models. Most of the techniques presented in the book can be readily applied to model other phenomena, in biology as well as in other disciplines.

This book on multivariate models, statistical inference, and data analysis contains deep coverage of multivariate non-normal distributions for modeling of binary, count, ordinal, and extreme value response data. It is virtually self-contained, and includes many exercises and unsolved problems.

Business Process Modeling, Simulation and Design, Third Edition provides students with a comprehensive coverage of a range of analytical tools used to model, analyze, understand, and ultimately design business processes. The new edition of this very successful textbook includes a wide range of approaches such as graphical flowcharting tools, cycle time and capacity analyses, queuing models, discrete-event simulation, simulation-optimization, and data mining for process analytics. While most textbooks on business process management either focus on the intricacies of computer simulation or managerial aspects of business processes, this textbook does both. It presents the tools to design business processes and management techniques on operating them efficiently. The book focuses on the use of discrete event simulation as the main tool for analyzing, modeling, and designing effective business processes. The integration of graphic user-friendly simulation software enables a systematic approach to create optimal designs.

Wavelet-based procedures are key in many areas of statistics, applied mathematics, engineering, and science. This book presents wavelets in functional data analysis, offering a glimpse of problems in which they can be applied, including tumor analysis, functional magnetic resonance and meteorological data. Starting with the Haar wavelet, the authors explore myriad families of wavelets and how they can be used. High-dimensional data visualization (using Andrews' plots), wavelet shrinkage (a simple, yet powerful, procedure for nonparametric models) and a selection of estimation and testing techniques (including a discussion on Stein's Paradox) make this a highly valuable resource for graduate students and experienced researchers alike.

Just 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 policymakers working in the field.

Model theory begins with an audacious idea: to consider statements about mathematical structures as mathematical objects of study in their own right. While inherently important as a tool of mathematical logic, it also enjoys connections to and applications in diverse branches of mathematics, including algebra, number theory and analysis. Despite this, traditional introductions to model theory assume a graduate-level background of the reader. In this innovative textbook, Jonathan Kirby brings model theory to an undergraduate audience. The highlights of basic model theory are illustrated through examples from specific structures familiar from undergraduate mathematics, paying particular attention to definable sets throughout. With numerous exercises of varying difficulty, this is an accessible introduction to model theory and its place in mathematics.

Do 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 software packages, this is essential reading.

During the last two decades, structural equation modelling (SEM) has emerged as a powerful multivariate data analysis tool in social science research settings, especially in the fields of sociology, psychology, and education. Social science researchers and students benefit greatly from acquiring knowledge and skills in SEM, since the methods can provide a bridge between the theoretical and empirical aspects of behavioural research. Ramlall explains in a rigorous, concise, and practical manner all the vital components embedded in structural equation modelling (SEM). Focusing on R and Stata to implement and perform various structural equation models, Ramlall examines the types, benefits, and drawbacks of SEM, delving into model specifications and identifications, fit evaluations, and path diagrams.