Illustrates the application of mathematical and computational modeling in a variety of disciplines With an emphasis on the interdisciplinary nature of mathematical and computational modeling, Mathematical and Computational Modeling: With Applications in the Natural and Social Sciences, Engineering, and the Arts features chapters written by well-known, international experts in these fields and presents readers with a host of state-of-the-art achievements in the development of mathematical modeling and computational experiment methodology. The book is a valuable guide to the methods, ideas, and tools of applied and computational mathematics as they apply to other disciplines such as the natural and social sciences, engineering, and technology. Mathematical and Computational Modeling: With Applications in the Natural and Social Sciences, Engineering, and the Arts also features: * Rigorous mathematical procedures and applications as the driving force behind mathematical innovation and discovery * Numerous examples from a wide range of disciplines to emphasize the multidisciplinary application and universality of applied mathematics and mathematical modeling * Original results on both fundamental theoretical and applied developments in diverse areas of human knowledge * Discussions that promote interdisciplinary interactions between mathematicians, scientists, and engineers Mathematical and Computational Modeling: With Applications in the Natural and Social Sciences, Engineering, and the Arts is an ideal resource for professionals in various areas of mathematical and statistical sciences, modeling and simulation, physics, computer science, engineering, biology and chemistry, industrial, and computational engineering. The book also serves as an excellent textbook for graduate courses in mathematical modeling, applied mathematics, numerical methods, operations research, and optimization.

Reliability is an essential concept in mathematics, computing, research, and all disciplines of engineering, and reliability as a characteristic is, in fact, a probability. Therefore, in this book, the author uses the statistical approach to reliability modelling along with the MINITAB software package to provide a comprehensive treatment of modelling, from the basics through advanced modelling techniques. The book begins by presenting a thorough grounding in the elements of modelling the lifetime of a single, non-repairable unit. Assuming no prior knowledge of the subject, the author includes a guide to all the fundamentals of probability theory, defines the various measures associated with reliability, then describes and discusses the more common lifetime models: the exponential, Weibull, normal, lognormal and gamma distributions. She concludes the groundwork by looking at ways of choosing and fitting the most appropriate model to a given data set, paying particular attention to two critical points: the effect of censored data and estimating lifetimes in the tail of the distribution. The focus then shifts to topics somewhat more difficult: othe difference in the analysis of lifetimes for repairable versus non-repairable systems and whether repair truly "renews" the system omethods for dealing with system with reliability characteristic specified for more than one component or subsystem othe effect of different types of maintenance strategies othe analysis of life test data The final chapter provides snapshot introductions to a range of advanced models and presents two case studies that illustrate various ideas from throughout the book.

This monograph establishes a theory of classification and translation closedness of time scales, a topic that was first studied by S. Hilger in 1988 to unify continuous and discrete analysis. The authors develop a theory of translation function on time scales that contains (piecewise) almost periodic functions, (piecewise) almost automorphic functions and their related generalization functions (e.g., pseudo almost periodic functions, weighted pseudo almost automorphic functions, and more). Against the background of dynamic equations, these function theories on time scales are applied to study the dynamical behavior of solutions for various types of dynamic equations on hybrid domains, including evolution equations, discontinuous equations and impulsive integro-differential equations. The theory presented allows many useful applications, such as in the Nicholson`s blowfiles model; the Lasota-Wazewska model; the Keynesian-Cross model; in those realistic dynamical models with a more complex hibrid domain, considered under different types of translation closedness of time scales; and in dynamic equations on mathematical models which cover neural networks. This book provides readers with the theoretical background necessary for accurate mathematical modeling in physics, chemical technology, population dynamics, biotechnology and economics, neural networks, and social sciences.

An accessible treatment of the modeling and solution of integer programming problems, featuring modern applications and software

In order to fully comprehend the algorithms associated with integer programming, it is important to understand not only "how" algorithms work, but also "why" they work. "Applied Integer Programming" features a unique emphasis on this point, focusing on problem modeling and solution using commercial software. Taking an application-oriented approach, this book addresses the art and science of mathematical modeling related to the mixed integer programming (MIP) framework and discusses the algorithms and associated practices that enable those models to be solved most efficiently.

The book begins with coverage of successful applications, systematic modeling procedures, typical model types, transformation of non-MIP models, combinatorial optimization problem models, and automatic preprocessing to obtain a better formulation. Subsequent chapters present algebraic and geometric basic concepts of linear programming theory and network flows needed for understanding integer programming. Finally, the book concludes with classical and modern solution approaches as well as the key components for building an integrated software system capable of solving large-scale integer programming and combinatorial optimization problems.

Throughout the book, the authors demonstrate essential concepts through numerous examples and figures. Each new concept or algorithm is accompanied by a numerical example, and, where applicable, graphics are used to draw together diverse problems or approaches into a unified whole. In addition, features of solution approaches found in today's commercial software are identified throughout the book.

Thoroughly classroom-tested, "Applied Integer Programming" is an excellent book for integer programming courses at the upper-undergraduate and graduate levels. It also serves as a well-organized reference for professionals, software developers, and analysts who work in the fields of applied mathematics, computer science, operations research, management science, and engineering and use integer-programming techniques to model and solve real-world optimization problems.

Structural equation modeling (SEM) is a general, cross-sectional statistical modeling technique. The chapters in this book propose a Bayesian approach based on SEM; an examination of predictors and outcomes related to school climate using latent class analysis and the testing of specific effects and contrasts in three types of mediation models followed by a discussion on the common types of mediation models and their different types of effects.

This book presents the most recent scientific and technological advances in the fields of engineering mathematics and computational science, to strengthen the links in the scientific community. It is a collection of high-quality, peer-reviewed research papers presented at the First International Conference on Mathematical Modeling and Computational Science (ICMMCS 2020), held in Pattaya, Thailand, during 14-15 August 2020. The topics covered in the book are mathematical logic and foundations, numerical analysis, neural networks, fuzzy set theory, coding theory, higher algebra, number theory, graph theory and combinatory, computation in complex networks, calculus, differential educations and integration, application of soft computing, knowledge engineering, machine learning, artificial intelligence, big data and data analytics, high-performance computing, network and device security, and Internet of things (IoT).

This general introduction to the mathematical techniques needed to understand epidemiology begins with an historical outline of some disease statistics dating from Daniel Bernoulli's smallpox data of 1760. The authors then go on to describe simple deterministic and stochastic models in continuous and discrete time for epidemics taking place in either homogeneous or stratified (nonhomogeneous) populations. They offer a range of methods for constructing and analyzing models, mostly in the context of viral and bacterial diseases of human populations. These models are contrasted with models for rumors and macro-parasitic diseases. Questions of fitting data to models, and the use of models to understand methods for controlling the spread of infection, are discussed. Exercises and complementary results at the end of each chapter extend the scope of the text.

This book focuses on hierarchical organizational structures. Secondly, the authors perform modeling in the context of solving control problems. Next, the conditions of corrupting a major task of control consisting of ensuring sustainable development of modeled hierarchical organizations are reviewed. Here, the authors proceed from the original concept of sustainable management (Ougolnitsky, 2002, 2005, 2010, 2011; Ougolnitsky and Usov, 2010-2014). In contrast to the classical approach of G. Becker and S. Rose-Ackerman (which states that the efficiency of anti-corruption struggle is defined via comparing losses due to corruption and the costs of such measures), the above concept applies certain requirements of sustainable development of a modeled system with proper consideration of economic restrictions. Finally, the empirical base and identification of mathematical models is examined.

Bayesian modeling has become an indispensable tool for ecological research because it is uniquely suited to deal with complexity in a statistically coherent way. This textbook provides a comprehensive and accessible introduction to the latest Bayesian methods--in language ecologists can understand. Unlike other books on the subject, this one emphasizes the principles behind the computations, giving ecologists a big-picture understanding of how to implement this powerful statistical approach. Bayesian Models is an essential primer for non-statisticians. It begins with a definition of probability and develops a step-by-step sequence of connected ideas, including basic distribution theory, network diagrams, hierarchical models, Markov chain Monte Carlo, and inference from single and multiple models. This unique book places less emphasis on computer coding, favoring instead a concise presentation of the mathematical statistics needed to understand how and why Bayesian analysis works. It also explains how to write out properly formulated hierarchical Bayesian models and use them in computing, research papers, and proposals. This primer enables ecologists to understand the statistical principles behind Bayesian modeling and apply them to research, teaching, policy, and management. * Presents the mathematical and statistical foundations of Bayesian modeling in language accessible to non-statisticians* Covers basic distribution theory, network diagrams, hierarchical models, Markov chain Monte Carlo, and more* Deemphasizes computer coding in favor of basic principles* Explains how to write out properly factored statistical expressions representing Bayesian models

This 1971 classic on linear models is once again available—as a Wiley Classics Library Edition. It features material that can be understood by any statistician who understands matrix algebra and basic statistical methods.

High temperature, high oil pressure, oil and gas well completion testing have always been a technical challenge and basic theoretical research is one of the key factors needed to ensure a successful completion test. The completion test basic theory includes: a stress analysis of the completion string, completion string buckling behavior, and temperature and pressure distribution prediction. The completion string is the main bearing and power transmission component for oil and gas well operations and production, and it is required to take on a combination of loads, which result in completion string deformation. Because of these complex relationships, completion string stress analysis has become increasingly more complicated. This book discusses the characters of tubular strings in HTHP (High Temperature - High Pressure) oil and gas wells. These characters include the mechanical behavior of tubular strings and the temperature and pressure variation of tubular strings in different conditions. Mathematical models are established for different conditions and solution existence and uniqueness of some models is discussed, providing algorithms corresponding to the different models. Numerical experiments are presented to verify the validity of models and the feasibility of algorithms, and the impact of the parameters of models for oil and gas wells is also discussed. This book is written for production and testing engineers to provide them with the tools to deal more effectively with the numerical decisions they have to take and for researchers and technicians in petroleum and gas testing and production engineering. Finally, it is also intended to serve as a reference book for mathematicians, college teachers and students.

Computational Economics: A concise introduction is a comprehensive textbook designed to help students move from the traditional and comparative static analysis of economic models, to a modern and dynamic computational study. The ability to equate an economic problem, to formulate it into a mathematical model and to solve it computationally is becoming a crucial and distinctive competence for most economists. This vital textbook is organized around static and dynamic models, covering both macro and microeconomic topics, exploring the numerical techniques required to solve those models. A key aim of the book is to enable students to develop the ability to modify the models themselves so that, using the MATLAB/Octave codes provided on the book and on the website, students can demonstrate a complete understanding of computational methods. This textbook is innovative, easy to read and highly focused, providing students of economics with the skills needed to understand the essentials of using numerical methods to solve economic problems. It also provides more technical readers with an easy way to cope with economics through modelling and simulation. Later in the book, more elaborate economic models and advanced numerical methods are introduced which will prove valuable to those in more advanced study. This book is ideal for all students of economics, mathematics, computer science and engineering taking classes on Computational or Numerical Economics.

Use Big Data and technology to uncover real-world insights You don't need a time machine to predict the future. All it takes is a little knowledge and know-how, and Predictive Analytics For Dummies gets you there fast. With the help of this friendly guide, you'll discover the core of predictive analytics and get started putting it to use with readily available tools to collect and analyze data. In no time, you'll learn how to incorporate algorithms through data models, identify similarities and relationships in your data, and predict the future through data classification. Along the way, you'll develop a roadmap by preparing your data, creating goals, processing your data, and building a predictive model that will get you stakeholder buy-in. Big Data has taken the marketplace by storm, and companies are seeking qualified talent to quickly fill positions to analyze the massive amount of data that are being collected each day. If you want to get in on the action and either learn or deepen your understanding of how to use predictive analytics to find real relationships between what you know and what you want to know, everything you need is a page away! * Offers common use cases to help you get started * Covers details on modeling, k-means clustering, and more * Includes information on structuring your data * Provides tips on outlining business goals and approaches The future starts today with the help of Predictive Analytics For Dummies.

This book is an entertaining, easy to read introduction to advanced numerical modeling. The aim of the book is to lead the reader on a journey towards the 'holy grail' of numerical simulation, namely one without the requirement of mesh generation, that takes data directly from CAD programs. On this journey readers will discover the beauty of Non-uniform Rational B-Splines or NURBS and see how well they are suited for describing geometry, discover how CAD programs work and how their data can be used for simulation. The implementation of NURBS-based simulation is discussed using Finite Element and Boundary Element technology. This is a hands-on book with emphasis on implementation and examples of programming in a higher level language are given. It has been written for users of simulation software, so they can understand the benefits of this new technology and demand progress from a somewhat conservative industry, for software developers, so they can see that this is a technology with a big future and for researchers, in the hope that it will attract more people to work in this exciting new field.

This book is about the statistical principles behind the design of effective experiments and focuses on the practical needs of applied statisticians and experimenters engaged in design, implementation and analysis. Emphasising the logical principles of statistical design, rather than mathematical calculation, the authors demonstrate how all available information can be used to extract the clearest answers to many questions. The principles are illustrated with a wide range of examples drawn from real experiments in medicine, industry, agriculture and many experimental disciplines. Numerous exercises are given to help the reader practise techniques and to appreciate the difference that good design can make to an experimental research project. Based on Roger Mead's excellent Design of Experiments, this new edition is thoroughly revised and updated to include modern methods relevant to applications in industry, engineering and modern biology. It also contains seven new chapters on contemporary topics, including restricted randomisation and fractional replication.

This book demonstrates how to conduct latent variable modeling (LVM) in R by highlighting the features of each model, their specialized uses, examples, sample code and output, and an interpretation of the results. Each chapter features a detailed example including the analysis of the data using R, the relevant theory, the assumptions underlying the model, and other statistical details to help readers better understand the models and interpret the results. Every R command necessary for conducting the analyses is described along with the resulting output which provides readers with a template to follow when they apply the methods to their own data. The basic information pertinent to each model, the newest developments in these areas, and the relevant R code to use them are reviewed. Each chapter also features an introduction, summary, and suggested readings. A glossary of the text's boldfaced key terms and key R commands serve as helpful resources. The book is accompanied by a website with exercises, an answer key, and the in-text example data sets. Latent Variable Modeling with R: -Provides some examples that use messy data providing a more realistic situation readers will encounter with their own data. -Reviews a wide range of LVMs including factor analysis, structural equation modeling, item response theory, and mixture models and advanced topics such as fitting nonlinear structural equation models, nonparametric item response theory models, and mixture regression models. -Demonstrates how data simulation can help researchers better understand statistical methods and assist in selecting the necessary sample size prior to collecting data. -www.routledge.com/9780415832458 provides exercises that apply the models along with annotated R output answer keys and the data that corresponds to the in-text examples so readers can replicate the results and check their work. The book opens with basic instructions in how to use R to read data, download functions, and conduct basic analyses. From there, each chapter is dedicated to a different latent variable model including exploratory and confirmatory factor analysis (CFA), structural equation modeling (SEM), multiple groups CFA/SEM, least squares estimation, growth curve models, mixture models, item response theory (both dichotomous and polytomous items), differential item functioning (DIF), and correspondance analysis. The book concludes with a discussion of how data simulation can be used to better understand the workings of a statistical method and assist researchers in deciding on the necessary sample size prior to collecting data. A mixture of independently developed R code along with available libraries for simulating latent models in R are provided so readers can use these simulations to analyze data using the methods introduced in the previous chapters. Intended for use in graduate or advanced undergraduate courses in latent variable modeling, factor analysis, structural equation modeling, item response theory, measurement, or multivariate statistics taught in psychology, education, human development, and social and health sciences, researchers in these fields also appreciate this book's practical approach. The book provides sufficient conceptual background information to serve as a standalone text. Familiarity with basic statistical concepts is assumed but basic knowledge of R is not.

Collecting a set of classical and emerging methods that otherwise would not be available in a single treatment, Foundations of Computational Imaging: A Model-Based Approach is the first book to define a common foundation for the mathematical and statistical methods used in computational imaging. The book is designed to bring together an eclectic group of researchers with a wide variety of applications and disciplines including applied math, physics, chemistry, optics, and signal processing, to address a collection of problems that can benefit from a common set of methods. Inside, readers will find: Basic techniques of model-based image processing. A comprehensive treatment of Bayesian and regularized image reconstruction methods. An integrated treatment of advanced reconstruction techniques such as majorization, constrained optimization, ADMM, and Plug-and-Play methods for model integration. Foundations of Computational Imaging can be used in courses on Model-Based or Computational Imaging, Advanced Numerical Analysis, Special Topics on Numerical Analysis, Topics on Data Science, Topics on Numerical Optimization, and Topics on Approximation Theory. It is also for researchers or practitioners in medical imaging, scientific imaging, commercial imaging, or industrial imaging.

This book highlights the practical aspects of computer modelling and simulation of complex dynamical systems for students. Mechanical systems are considered in the book as representative examples of dynamical systems. Wolfram SystemModeler, in combination with Learning Management System Sakai, is used as an instrument for studying features of various physical and technical phenomena and processes. Each of the presented virtual labs may be considered a stand-alone mini project to enable students to go through all the steps of mathematical modelling and computer simulation-from the problem statement to mathematical and physical analysis of the obtained result. The book is useful for teachers to organize the educational process, allowing gradual monitoring of the learning process and assessment of students' competencies. It also allows tutors to design individual educational trajectories for students to achieve educational properties. The subject of the book is an extension of activity started by the international team of authors within the InMotion project of the European programme ERASMUS+.

Offering a fresh take on laser engineering, Laser Modeling: A Numerical Approach with Algebra and Calculus presents algebraic models and traditional calculus-based methods in tandem to make concepts easier to digest and apply in the real world. Each technique is introduced alongside a practical, solved example based on a commercial laser. Assuming some knowledge of the nature of light, emission of radiation, and basic atomic physics, the text: Explains how to formulate an accurate gain threshold equation as well as determine small-signal gain Discusses gain saturation and introduces a novel pass-by-pass model for rapid implementation of "what if?" scenarios Outlines the calculus-based Rigrod approach in a simplified manner to aid in comprehension Considers thermal effects on solid-state lasers and other lasers with new and efficient quasi-three-level materials Demonstrates how the convolution method is used to predict the effect of temperature drift on a DPSS system Describes the technique and technology of Q-switching and provides a simple model for predicting output power Addresses non-linear optics and supplies a simple model for calculating optimal crystal length Examines common laser systems, answering basic design questions and summarizing parameters Includes downloadable Microsoft (R) Excel (TM) spreadsheets, allowing models to be customized for specific lasers Don't let the mathematical rigor of solutions get in the way of understanding the concepts. Laser Modeling: A Numerical Approach with Algebra and Calculus covers laser theory in an accessible way that can be applied immediately, and numerically, to real laser systems.

Beginning Algorithms

A good understanding of algorithms, and the knowledge of when to apply them, is crucial to producing software that not only works correctly, but also performs efficiently. This is the only book to impart all this essential information--from the basics of algorithms, data structures, and performance characteristics to the specific algorithms used in development and programming tasks.

Packed with detailed explanations and instructive examples, the book begins by offering you some fundamental data structures and then goes on to explain various sorting algorithms. You'll then learn efficient practices for storing and searching by way of hashing, trees, sets, and maps. The authors also share tips on optimization techniques and ways to avoid common performance pitfalls. In the end, you'll be prepared to build the algorithms and data structures most commonly encountered in day-to-day software development.

What you will learn from this book The basics of algorithms, such as iteration and recursion Elementary data structures such as lists, stacks, and queues Basic and advanced sorting algorithms including insertion sort, quicksort, and shell sort Advanced data structures such as binary trees, ternary trees, and heaps Algorithms for string searching, string matching, hashing, and computational geometry How to use test-driven development techniques to ensure your code works as intended How to dramatically improve the performance of your code with hands-on techniques for profiling and optimization

Who this book is for

This book is for anyone who develops applications, or is just beginning to do so, and is looking to understand algorithms and data structures. Anunderstanding of computer programming is beneficial.

Wrox Beginning guides are crafted to make learning programming languages and technologies easier than you think, providing a structured, tutorial format that will guide you through all the techniques involved.

This book contains a selection of research articles written by prominent researchers participating in The 27th World Congress on Engineering (WCE 2019) which was held in London, UK, July 3-5, 2019. Topics covered include engineering mathematics, electrical engineering, communications systems, computer science, chemical engineering, systems engineering, manufacturing engineering, and industrial applications. With contributions carefully chosen to represent the most cutting-edge research presented during the conference, the book contains some of the state of the art in engineering technologies and the physical sciences and their applications and serves as a useful reference for researchers and graduate students working in these fields.

In contrast to mainstream economics, complexity theory conceives the economy as a complex system of heterogeneous interacting agents characterised by limited information and bounded rationality. Agent Based Models (ABMs) are the analytical and computational tools developed by the proponents of this emerging methodology. Aimed at students and scholars of contemporary economics, this book includes a comprehensive toolkit for agent-based computational economics, now quickly becoming the new way to study evolving economic systems. Leading scholars in the field explain how ABMs can be applied fruitfully to many real-world economic examples and represent a great advancement over mainstream approaches. The essays discuss the methodological bases of agent-based approaches and demonstrate step-by-step how to build, simulate and analyse ABMs and how to validate their outputs empirically using the data. They also present a wide set of applications of these models to key economic topics, including the business cycle, labour markets, and economic growth.

This book presents the best papers from the 2nd International Conference on Mathematical Research for Blockchain Economy (MARBLE) 2020, held in Vilamoura, Portugal. While most blockchain conferences and forums are dedicated to business applications, product development or Initial Coin Offering (ICO) launches, this conference focused on the mathematics behind blockchain to bridge the gap between practice and theory. Blockchain Technology has been considered as the most fundamental and revolutionising invention since the Internet. Every year, thousands of blockchain projects are launched and circulated in the market, and there is a tremendous wealth of blockchain applications, from finance to healthcare, education, media, logistics and more. However, due to theoretical and technical barriers, most of these applications are impractical for use in a real-world business context. The papers in this book reveal the challenges and limitations, such as scalability, latency, privacy and security, and showcase solutions and developments to overcome them.

This book presents various computational and cognitive modeling approaches in the areas of health, education, finance, theenvironment, engineering, commerce and industry. Gathering selected conference papers presented atthe International Conference on Trends in Computational and Cognitive Engineering (TCCE), it sharescutting-edge insights and ideas from mathematicians, engineers, scientists and researchers anddiscusses fresh perspectives on problem solving in a range of research areas.

Is college worth the cost? Should I worry about arsenic in my rice? Can we recycle pollution? Real questions of personal finance, public health, and social policy require sober, data-driven analyses. This unique text provides students with the tools of quantitative reasoning to answer such questions. The text models how to clarify the question, recognize and avoid bias, isolate relevant factors, gather data, and construct numerical analyses for interpretation. Themes and techniques are repeated across chapters, with a progression in mathematical sophistication over the course of the book, which helps the student get comfortable with the process of thinking in numbers. This textbook includes references to source materials and suggested further reading, making it user-friendly for motivated undergraduate students. The many detailed problems and worked solutions in the text and extensive appendices help the reader learn mathematical areas such as algebra, functions, graphs, and probability. End-of-chapter problem material provides practice for students, and suggested projects are provided with each chapter. A solutions manual is available online for instructors.