This textbook introduces the theories and practical procedures used in planetary spacecraft navigation. Written by a former member of NASA's Jet Propulsion Laboratory (JPL) navigation team, it delves into the mathematics behind modern digital navigation programs, as well as the numerous technological resources used by JPL as a key player in the field. In addition, the text offers an analysis of navigation theory application in recent missions, with the goal of showing students the relationship between navigation theory and the real-world orchestration of mission operations.

Broadly speaking, there are two general approaches to teaching mathematical modeling: 1) the case study approach, and 2) the method based approach (that teaches mathematical techniques with applications to relevant mathematical models). This text emphasizes instead the scientific issues for modeling different phenomena. For the natural or harvested growth of a fish population, we may be interested in the evolution of the population, whether it reaches a steady state (equilibrium or cycle), stable or unstable with respect to a small perturbation from equilibrium, or whether a small change in the environment would cause a catastrophic change, etc. Each scientific issue requires an appropriate model and a different set of mathematical tools to extract information from the model. Models examined are chosen to help explain or justify empirical observations such as cocktail drug treatments are more effective and regenerations after injuries or illness are fast-tracked (compared to original developments).Volume I of this three-volume set limits its scope to phenomena and scientific issues that are modeled by ordinary differential equations (ODE). Scientific issues such as signal and wave propagation, diffusion, and shock formation involving spatial dynamics to be modeled by partial differential equations (PDE) will be treated in Vol. II. Scientific issues involving randomness and uncertainty are examined in Vol. III.

Methods of Statistical Model Estimation examines the most important and popular methods used to estimate parameters for statistical models and provide informative model summary statistics. Designed for R users, the book is also ideal for anyone wanting to better understand the algorithms used for statistical model fitting.

The text presents algorithms for the estimation of a variety of regression procedures using maximum likelihood estimation, iteratively reweighted least squares regression, the EM algorithm, and MCMC sampling. Fully developed, working R code is constructed for each method. The book starts with OLS regression and generalized linear models, building to two-parameter maximum likelihood models for both pooled and panel models. It then covers a random effects model estimated using the EM algorithm and concludes with a Bayesian Poisson model using Metropolis-Hastings sampling.

The book's coverage is innovative in several ways. First, the authors use executable computer code to present and connect the theoretical content. Therefore, code is written for clarity of exposition rather than stability or speed of execution. Second, the book focuses on the performance of statistical estimation and downplays algebraic niceties. In both senses, this book is written for people who wish to fit statistical models and understand them.

See Professor Hilbe discuss the book.

The first comprehensive review of the theory and practice of one of today's most powerful optimization techniques.

The explosive growth of research into and development of interior point algorithms over the past two decades has significantly improved the complexity of linear programming and yielded some of today's most sophisticated computing techniques. This book offers a comprehensive and thorough treatment of the theory, analysis, and implementation of this powerful computational tool.

Interior Point Algorithms provides detailed coverage of all basic and advanced aspects of the subject. Beginning with an overview of fundamental mathematical procedures, Professor Yinyu Ye moves swiftly on to in-depth explorations of numerous computational problems and the algorithms that have been developed to solve them. An indispensable text/reference for students and researchers in applied mathematics, computer science, operations research, management science, and engineering, Interior Point Algorithms:

• Derives various complexity results for linear and convex programming
• Emphasizes interior point geometry and potential theory
• Covers state-of-the-art results for extension, implementation, and other cutting-edge computational techniques
• Explores the hottest new research topics, including nonlinear programming and nonconvex optimization.

This contributed volume offers a collection of papers presented at the 2018 Network Games, Control, and Optimization conference (NETGCOOP), held at the New York University Tandon School of Engineering in New York City, November 14-16, 2018. These papers highlight the increasing importance of network control and optimization in many networking application domains, such as mobile and fixed access networks, computer networks, social networks, transportation networks, and, more recently, electricity grids and biological networks. Covering a wide variety of both theoretical and applied topics in the areas listed above, the authors explore several conceptual and algorithmic tools that are needed for efficient and robust control operation, performance optimization, and better understanding the relationships between entities that may be acting cooperatively or selfishly in uncertain and possibly adversarial environments. As such, this volume will be of interest to applied mathematicians, computer scientists, engineers, and researchers in other related fields.

"The old logic put thought in fetters, while the new logic gives it wings." For the past century, philosophers working in the tradition of Bertrand Russell - who promised to revolutionise philosophy by introducing the 'new logic' of Frege and Peano - have employed predicate logic as their formal language of choice. In this book, Dr David Corfield presents a comparable revolution with a newly emerging logic - modal homotopy type theory. Homotopy type theory has recently been developed as a new foundational language for mathematics, with a strong philosophical pedigree. Modal Homotopy Type Theory: The Prospect of a New Logic for Philosophy offers an introduction to this new language and its modal extension, illustrated through innovative applications of the calculus to language, metaphysics, and mathematics. The chapters build up to the full language in stages, right up to the application of modal homotopy type theory to current geometry. From a discussion of the distinction between objects and events, the intrinsic treatment of structure, the conception of modality as a form of general variation to the representation of constructions in modern geometry, we see how varied the applications of this powerful new language can be.

First published in 1967, this book explores the theme of geographical generalization, or model building. It is composed of five of the chapters from the original Models in Geography, published in 1967. The first chapter broadly outlines this theme and examines the nature and function of generalized statements, ranging from conceptual models to scale models, in a geographical context. The following chapters deal with mixed-system model building in geography, wherein data, techniques and concepts in both physical and human geography are integrated. The book contains chapters on organisms and ecosystems as geographical models as well as spatial patterns in human geography. This text represents a robustly anti-idiographic statement of modern work in one of the major branches of geography.

This book introduces readers to a set of powerful and extremely flexible modelling techniques, starting at "square one" and continuing with carefully chosen applications. Some of these applications of methodology include insect oviposition behavior, overwinter survival of birds and fish, avian migration, resource management, conservation biology, agroecology, and human behaviour. This book also explains how to construct, test, and use dynamic state variable models in a wide range of contexts in evolutionary ecology. And its complete and up-to-date coverage allows readers to immediately begin using the described techniques. Dynamic State Variable Models in Ecology is designed for self-instruction or for use in upper division undergraduate or graduate courses. It is ideal for students and scientists interested in behaviour, ecology, anthropology, conservation biology, and related fields.

This book highlights recent advances in the field of districting, territory design, and zone design. Districting problems deal essentially with tactical decisions, and involve mainly dividing a set of geographic units into clusters or territories subject to some planning requirements. This book presents models, theory, algorithms (exact or heuristic), and applications that would bring research on districting systems up-to-date and define the state-of-the-art. Although papers have addressed real-world problems that require districting or territory division decisions, this is the first comprehensive book that directly addresses these problems. The chapters capture the diverse nature of districting applications, as the book is divided into three different areas of research. Part I covers recent up-to-date surveys on important areas of districting such as police districting, health care districting, and districting algorithms based on computational geometry. Part II focuses on recent advances on theory, modeling, and algorithms including mathematical programming and heuristic approaches, and finally, Part III contains successful applications in real-world districting cases.

Examines dynamic models, and how time is fundamental to the structure of the model and data as well as the understanding of how a process unfolds Discusses mathematical modeling with soft computing and the implementations of uncertain mathematical models Examines how uncertain dynamic systems models include uncertain state, uncertain state space and uncertain state's transition functions Assists readers to become familiar with many soft numerical methods to simulate the solution function's behavior

This volume provides recent developments and a state-of-the-art review in various areas of mathematical modeling, computation and optimization. It contains theory, computation as well as the applications of several mathematical models to problems in statistics, games, optimization and economics for decision making. It focuses on exciting areas like models for wireless networks, models of Nash networks, dynamic models of advertising, application of reliability models in economics, support vector machines, optimization, complementarity modeling and games.

Introduction to Mathematical Modeling and Computer Simulations is written as a textbook for readers who want to understand the main principles of Modeling and Simulations in settings that are important for the applications, without using the profound mathematical tools required by most advanced texts. It can be particularly useful for applied mathematicians and engineers who are just beginning their careers. The goal of this book is to outline Mathematical Modeling using simple mathematical descriptions, making it accessible for first- and second-year students. Chapter 1 and the Preface of this book is freely available as a downloadable Open Access PDF under a Creative Commons Attribution-Non Commercial-No Derivatives 4.0 license available at http://www.taylorfrancis.com/books/e/9781315277240

As Ken Wallis (1993) has pOinted out, all macroeconomic forecasters and policy analysts use economic models. That is, they have a way of going from assumptions about macroeconomic policy and the international environment, to a prediction of the likely future state of the economy. Some people do this in their heads. Increasingly though, forecasting and policy analysis is based on a formal, explicit model, represented by a set of mathematical equations and solved by computer. This provides a framework for handling, in a consistent and systematic manner, the ever-increasing amounts of relevant information. Macroeconometric modelling though, is an inexact science. A manageable model must focus only on the major driving forces in a complex economy made up of millions of households and fIrms. International economic agencies such as the IMF and OECD, and most treasuries and central banks in western countries, use macroeconometric models in their forecasting and policy analysis. Models are also used for teaching and research in universities, as well as for commercial forecasting in the private sector.

This review volume reports the state-of-the-art in Linear Parameter Varying (LPV) system identification. Written by world renowned researchers, the book contains twelve chapters, focusing on the most recent LPV identification methods for both discrete-time and continuous-time models, using different approaches such as optimization methods for input/output LPV models Identification, set membership methods, optimization methods and subspace methods for state-space LPV models identification and orthonormal basis functions methods. Since there is a strong connection between LPV systems, hybrid switching systems and piecewise affine models, identification of hybrid switching systems and piecewise affine systems will be considered as well.

A ubiquitous tool in mathematical biology and chemical engineering, the chemostat often produces instabilities that pose safety hazards and adversely affect the optimization of bioreactive systems. Singularity theory and bifurcation diagrams together offer a useful framework for addressing these issues. Based on the authors' extensive work in this field, Dynamics of the Chemostat: A Bifurcation Theory Approach explores the use of bifurcation theory to analyze the static and dynamic behavior of the chemostat.

Introduction
The authors first survey the major work that has been carried out on the stability of continuous bioreactors. They next present the modeling approaches used for bioreactive systems, the different kinetic expressions for growth rates, and tools, such as multiplicity, bifurcation, and singularity theory, for analyzing nonlinear systems.

Application
The text moves on to the static and dynamic behavior of the basic unstructured model of the chemostat for constant and variable yield coefficients as well as in the presence of wall attachment. It then covers the dynamics of interacting species, including pure and simple microbial competition, biodegradation of mixed substrates, dynamics of plasmid-bearing and plasmid-free recombinant cultures, and dynamics of predator-prey interactions. The authors also examine dynamics of the chemostat with product formation for various growth models, provide examples of bifurcation theory for studying the operability and dynamics of continuous bioreactor models, and apply elementary concepts of bifurcation theory to analyze the dynamics of a periodically forced bioreactor.

Using singularity theory and bifurcation techniques, this book presents a cohesive mathematical framework for analyzing and modeling the macro- and microscopic interactions occurring in chemostats. The text includes models that describe the intracellular and operating elements of the bioreactive system. It also explains the mathematical theory behind the models.

From the spontaneous rapid firing of cortical neurons to the spatial diffusion of disease epidemics, biological systems exhibit rich dynamic behaviour over a vast range of time and space scales. Unifying many of these diverse phenomena, Dynamics of Biological Systems provides the computational and mathematical platform from which to understand the underlying processes of the phenomena. Through an extensive tour of various biological systems, the text introduces computational methods for simulating spatial diffusion processes in excitable media, such as the human heart, as well as mathematical tools for dealing with systems of nonlinear ordinary and partial differential equations, such as neuronal activation and disease diffusion. The mathematical models and computer simulations offer insight into the dynamics of temporal and spatial biological systems, including cardiac pacemakers, artificial electrical defibrillation, pandemics, pattern formation, flocking behaviour, the interaction of autonomous agents, and hierarchical and structured network topologies. Tools from complex systems and complex networks are also presented for dealing with real phenomenological systems. With exercises and projects in each chapter, this classroom-tested text shows students how to apply a variety of mathematical and computational techniques to model and analyze the temporal and spatial phenomena of biological systems. MATLAB (R) implementations of algorithms and case studies are available on the author's website.

This textbook presents basic numerical methods and applies them to a large variety of physical models in multiple computer experiments. Classical algorithms and more recent methods are explained. Partial differential equations are treated generally comparing important methods, and equations of motion are solved by a large number of simple as well as more sophisticated methods. Several modern algorithms for quantum wavepacket motion are compared. The first part of the book discusses the basic numerical methods, while the second part simulates classical and quantum systems. Simple but non-trivial examples from a broad range of physical topics offer readers insights into the numerical treatment but also the simulated problems. Rotational motion is studied in detail, as are simple quantum systems. A two-level system in an external field demonstrates elementary principles from quantum optics and simulation of a quantum bit. Principles of molecular dynamics are shown. Modern boundary element methods are presented in addition to standard methods, and waves and diffusion processes are simulated comparing the stability and efficiency of different methods. A large number of computer experiments is provided, which can be tried out even by readers with no programming skills. Exercises in the applets complete the pedagogical treatment in the book. In the third edition Monte Carlo methods and random number generation have been updated taking recent developments into account. Krylov-space methods for eigenvalue problems are discussed in much more detail. Short time Fourier transformation and wavelet transformation have been included as tools for time-frequency analysis. Lastly, elementary quantum many-body problems demonstrate the application of variational and Monte-Carlo methods.

This new book focuses on nanomaterial development as well as investigations of combustion and explosion processes. It presents valuable information on the modeling of processes and on quantum chemical calculations and leading-edge research from around the world in this dynamic field, focusing on concepts above formal experimental techniques and theoretical methods of chemical physics for micro- and nanotechnologies. Also presented are non-linear kinetic appearances and their possible applications.

This international, comprehensive guide to modeling and simulation studies in activated sludge systems leads the reader through the entire modeling process - from building a mechanistic model to applying the model in practice. Mathematical Modelling and Computer Simulation of Activated Sludge Systems will: Enhance the readers' understanding of different model concepts for several (most essential) biochemical processes in the advanced activated sludge systems Provide extensive and up-to-date coverage of experimental methodologies of a complete model parameter estimation (longitudinal dispersion coefficient, influent wastewater fractions, kinetic and stoichiometric coefficients, settling velocity, etc.) Summarize and critically review the ranges of model parameters reported in literature Compare the existing protocols aiming at a systematic organization of the simulation study Outline the capabilities of the existing commercial simulators Present documented, successful case studies of practical model applications as a guide while planning a simulation study. The book is organized to provide a general background and some basic definitions, then theoretical aspects of modeling and finally, the issues important for practical model applications. Mathematical Modelling and Computer Simulation of Activated Sludge Systems can be used as supplementary material for a graduate level wastewater engineering courses and is useful to a wide audience of researchers and practitioners. Experienced model users such as consultants, trained plant management staff may find the book useful as a reference and as a resource for self-guided study. Visit the IWA WaterWiki to read and share material related to this title: http://www.iwawaterwiki.org/xwiki/bin/view/Articles/MathmematicalModellingandActivatedSludgeSystems

Mathematics for the Environment shows how to employ simple mathematical tools, such as arithmetic, to uncover fundamental conflicts between the logic of human civilization and the logic of Nature. These tools can then be used to understand and effectively deal with economic, environmental, and social issues. With elementary mathematics, the book seeks answers to a host of real-life questions, including: * How safe is our food and will it be affordable in the future? * What are the simple lessons to be learned from the economic meltdown of 2008-2009? * Is global climate change happening? * Were some humans really doing serious mathematical thinking 50,000 years ago? * What does the second law of thermodynamics have to do with economics? * How can identity theft be prevented? * What does a mathematical proof prove? A truly interdisciplinary, concrete study of mathematics, this classroom-tested text discusses the importance of certain mathematical principles and concepts, such as fuzzy logic, feedback, deductive systems, fractions, and logarithms, in various areas other than pure mathematics. It teaches students how to make informed choices using fundamental mathematical tools, encouraging them to find solutions to critical real-world problems.

Everything you need to make the most of building information modeling If you're looking to get involved in the world of BIM, but don't quite know where to start, Building Information Modeling For Dummies is your one-stop guide to collaborative building using one coherent system of computer models rather than as separate sets of drawings. Inside, you'll find an easy-to-follow introduction to BIM and hands-on guidance for understanding drivers for change, the benefits of BIM, requirements you need to get started, and where BIM is headed. The future of BIM is bright it provides the industry with an increased understanding of predictability, improved efficiency, integration and coordination, less waste, and better value and quality. Additionally, the use of BIM goes beyond the planning and design phase of the project, extending throughout the building life cycle and supporting processes, including cost management, construction management, project management, and facility operation. Now heavily adopted in the U.S., Hong Kong, India, Singapore, France, Canada, and countless other countries, BIM is set to become a mandatory practice in building work in the UK, and this friendly guide gives you everything you need to make sense of it fast. * Demonstrates how BIM saves time and waste on site * Shows you how the information generated from BIM leads to fewer errors on site * Explains how BIM is based on data sets that describe objects virtually, mimicking the way they'll be handled physically in the real world * Helps you grasp how the integration of BIM allows every stage of the life cycle to work together without data or process conflict Written by a team of well-known experts, this friendly, hands-on guide gets you up and running with BIM fast.

This book introduces the method of lower and upper solutions for ordinary differential equations. This method is known to be both easy and powerful to solve second order boundary value problems. Besides an extensive introduction to the method, the first half of the book describes some recent and more involved results on this subject. These concern the combined use of the method with degree theory, with variational methods and positive operators. The second half of the book concerns applications. This part exemplifies the method and provides the reader with a fairly large introduction to the problematic of boundary value problems. Although the book concerns mainly ordinary differential equations, some attention is given to other settings such as partial differential equations or functional differential equations. A detailed history of the problem is described in the introduction.
- Presents the fundamental features of the method
- Construction of lower and upper solutions in problems
- Working applications and illustrated theorems by examples
- Description of the history of the method and Bibliographical notes

The book provides an introduction to deterministic (and some stochastic) modeling of spatiotemporal phenomena in ecology, epidemiology, and neural systems. A survey of the classical models in the fields with up to date applications is given. The book begins with detailed description of how spatial dynamics/diffusive processes influence the dynamics of biological populations. These processes play a key role in understanding the outbreak and spread of pandemics which help us in designing the control strategies from the public health perspective. A brief discussion on the functional mechanism of the brain (single neuron models and network level) with classical models of neuronal dynamics in space and time is given. Relevant phenomena and existing modeling approaches in ecology, epidemiology and neuroscience are introduced, which provide examples of pattern formation in these models. The analysis of patterns enables us to study the dynamics of macroscopic and microscopic behaviour of underlying systems and travelling wave type patterns observed in dispersive systems. Moving on to virus dynamics, authors present a detailed analysis of different types models of infectious diseases including two models for influenza, five models for Ebola virus and seven models for Zika virus with diffusion and time delay. A Chapter is devoted for the study of Brain Dynamics (Neural systems in space and time). Significant advances made in modeling the reaction-diffusion systems are presented and spatiotemporal patterning in the systems is reviewed. Development of appropriate mathematical models and detailed analysis (such as linear stability, weakly nonlinear analysis, bifurcation analysis, control theory, numerical simulation) are presented. Key Features Covers the fundamental concepts and mathematical skills required to analyse reaction-diffusion models for biological populations. Concepts are introduced in such a way that readers with a basic knowledge of differential equations and numerical methods can understand the analysis. The results are also illustrated with figures. Focuses on mathematical modeling and numerical simulations using basic conceptual and classic models of population dynamics, Virus and Brain dynamics. Covers wide range of models using spatial and non-spatial approaches. Covers single, two and multispecies reaction-diffusion models from ecology and models from bio-chemistry. Models are analysed for stability of equilibrium points, Turing instability, Hopf bifurcation and pattern formations. Uses Mathematica for problem solving and MATLAB for pattern formations. Contains solved Examples and Problems in Exercises. The Book is suitable for advanced undergraduate, graduate and research students. For those who are working in the above areas, it provides information from most of the recent works. The text presents all the fundamental concepts and mathematical skills needed to build models and perform analyses.

This book will serve as a reference guide, and state-of-the-art review, for the wide spectrum of numerical models and computational techniques available to solve some of the most challenging problems in coastal engineering. The topics covered in this book, are explained fundamentally from a numerical perspective and also include practical examples applications. Important classic themes such as wave generation, propagation and breaking, turbulence modelling and sediment transport are complemented by hot topics such as fluid and structure interaction or multi-body interaction to provide an integral overview on numerical techniques for coastal engineering. Through the vision of 10 high impact authors, each an expert in one or more of the fields included in this work, the chapters offer a broad perspective providing several different approaches, which the readers can compare critically to select the most suitable for their needs. Advanced Numerical Modelling of Wave Structure Interaction will be useful for a wide audience, including PhD students, research scientists, numerical model developers and coastal engineering consultants alike.

This book Algebraic Modeling Systems - Modeling and Solving Real World Optimization Problems - deals with the aspects of modeling and solving real-world optimization problems in a unique combination. It treats systematically the major algebraic modeling languages (AMLs) and modeling systems (AMLs) used to solve mathematical optimization problems. AMLs helped significantly to increase the usage of mathematical optimization in industry. Therefore it is logical consequence that the GOR (Gesellschaft fur Operations Research) Working Group Mathematical Optimization in Real Life had a second meeting devoted to AMLs, which, after 7 years, followed the original 71st Meeting of the GOR (Gesellschaft fur Operations Research) Working Group Mathematical Optimization in Real Life which was held under the title Modeling Languages in Mathematical Optimization during April 23-25, 2003 in the German Physics Society Conference Building in Bad Honnef, Germany. While the first meeting resulted in the book Modeling Languages in Mathematical Optimization, this book is an offspring of the 86th Meeting of the GOR working group which was again held in Bad Honnef under the title Modeling Languages in Mathematical Optimization.