This book provides a self-study program on how mathematics, computer science and science can be usefully and seamlessly intertwined. Learning to use ideas from mathematics and computation is essential for understanding approaches to cognitive and biological science. As such the book covers calculus on one variable and two variables and works through a number of interesting first-order ODE models. It clearly uses MatLab in computational exercises where the models cannot be solved by hand, and also helps readers to understand that approximations cause errors - a fact that must always be kept in mind.

Focused on recent advances, this book covers theoretical foundations as well as various applications. It presents modern mathematical modeling approaches to the qualitative and numerical analysis of solutions for complex engineering problems in physics, mechanics, biochemistry, geophysics, biology and climatology. Contributions by an international team of respected authors bridge the gap between abstract mathematical approaches, such as applied methods of modern analysis, algebra, fundamental and computational mechanics, nonautonomous and stochastic dynamical systems on the one hand, and practical applications in nonlinear mechanics, optimization, decision making theory and control theory on the other. As such, the book will be of interest to mathematicians and engineers working at the interface of these fields.

This monograph addresses the state of the art of reduced order methods for modeling and computational reduction of complex parametrized systems, governed by ordinary and/or partial differential equations, with a special emphasis on real time computing techniques and applications in computational mechanics, bioengineering and computer graphics.

Several topics are covered, including: design, optimization, and control theory in real-time with applications in engineering; data assimilation, geometry registration, and parameter estimation with special attention to real-time computing in biomedical engineering and computational physics; real-time visualization of physics-based simulations in computer science; the treatment of high-dimensional problems in state space, physical space, or parameter space; the interactions between different model reduction and dimensionality reduction approaches; the development of general error estimation frameworks which take into account both model and discretization effects.

This book is primarily addressed to computational scientists interested in computational reduction techniques for large scale differential problems.

This is the first comprehensive book on information geometry, written by the founder of the field. It begins with an elementary introduction to dualistic geometry and proceeds to a wide range of applications, covering information science, engineering, and neuroscience. It consists of four parts, which on the whole can be read independently. A manifold with a divergence function is first introduced, leading directly to dualistic structure, the heart of information geometry. This part (Part I) can be apprehended without any knowledge of differential geometry. An intuitive explanation of modern differential geometry then follows in Part II, although the book is for the most part understandable without modern differential geometry. Information geometry of statistical inference, including time series analysis and semiparametric estimation (the Neyman-Scott problem), is demonstrated concisely in Part III. Applications addressed in Part IV include hot current topics in machine learning, signal processing, optimization, and neural networks. The book is interdisciplinary, connecting mathematics, information sciences, physics, and neurosciences, inviting readers to a new world of information and geometry. This book is highly recommended to graduate students and researchers who seek new mathematical methods and tools useful in their own fields.

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.

The book integrates theoretical analysis, numerical simulation and modeling approaches for the treatment of singular phenomena. The projects covered focus on actual applied problems, and develop qualitatively new and mathematically challenging methods for various problems from the natural sciences. Ranging from stochastic and geometric analysis over nonlinear analysis and modelling to numerical analysis and scientific computation, the book is divided into the three sections: A) Scaling limits of diffusion processes and singular spaces, B) Multiple scales in mathematical models of materials science and biology and C) Numerics for multiscale models and singular phenomena. Each section addresses the key aspects of multiple scales and model hierarchies, singularities and degeneracies, and scaling laws and self-similarity.

This book offers a self-study program on how mathematics, computer science and science can be profitably and seamlessly intertwined. This book focuses on two variable ODE models, both linear and nonlinear, and highlights theoretical and computational tools using MATLAB to explain their solutions. It also shows how to solve cable models using separation of variables and the Fourier Series.

Using network models to investigate the interconnectivity in modern economic systems allows researchers to better understand and explain some economic phenomena. This volume presents contributions by known experts and active researchers in economic and financial network modeling. Readers are provided with an understanding of the latest advances in network analysis as applied to economics, finance, corporate governance, and investments. Moreover, recent advances in market network analysis that focus on influential techniques for market graph analysis are also examined. Young researchers will find this volume particularly useful in facilitating their introduction to this new and fascinating field. Professionals in economics, financial management, various technologies, and network analysis, will find the network models presented in this book beneficial in analyzing the interconnectivity in modern economic systems.

Exploring complex and intelligent analytical and mathematical methods, this book examines how different approaches can be used to optimize program management in the construction industry. It presents an in-depth study of the different program management methods, ranging from simple decision-making techniques and statistics analysis to the more complex linear programming and demonstrates how knowledge-base systems and genetic algorithms can be used to optimize resources and meet time, budget and quality criteria. It addresses topics including decision-making principles, planning and scheduling, mathematical forecasting models, optimization techniques programming and artificial intelligence techniques. Providing a valuable resource for anyone managing multiple projects in the construction industry, this book is intended for civil and construction engineering students, project managers, construction managers and senior engineers.

This book contributes to better understand how lifestyle modulations can effectively halt the emergence and progression of human diseases. The book will allow the reader to gain a better understanding of the mechanisms by which the environment interferes with the bio-molecular regulatory processes underlying the emergence and progression of complex diseases, such as cancer. Focusing on key and early cellular bio-molecular events giving rise to the emergence of degenerative chronic disease, it builds on previous experience on the development of multi-cellular organisms, to propose a mathematical and computer based framework that allows the reader to analyze the complex interplay between bio-molecular processes and the (micro)-environment from an integrative, mechanistic, quantitative and dynamical perspective. Taking the wealth of empirical evidence that exists it will show how to build and analyze models of core regulatory networks involved in the emergence and progression of chronic degenerative diseases, using a bottom-up approach.

The present volume contains invited talks of 11th biennial conference on "Emerging Mathematical Methods, Models and Algorithms for Science and Technology". The main message of the book is that mathematics has a great potential to analyse and understand the challenging problems of nanotechnology, biotechnology, medical science, oil industry and financial technology. The book highlights all the features and main theme discussed in the conference. All contributing authors are eminent academicians, scientists, researchers and scholars in their respective fields, hailing from around the world.

As in the previous volume on the topic, the authors close the gap between abstract mathematical approaches, such as applied methods of modern algebra and analysis, fundamental and computational mechanics, nonautonomous and stochastic dynamical systems, on the one hand and practical applications in nonlinear mechanics, optimization, decision making theory and control theory on the other. Readers will also benefit from the presentation of modern mathematical modeling methods for the numerical solution of complicated engineering problems in biochemistry, geophysics, biology and climatology. This compilation will be of interest to mathematicians and engineers working at the interface of these fields. It presents selected works of the joint seminar series of Lomonosov Moscow State University and the Institute for Applied System Analysis at National Technical University of Ukraine "Kyiv Polytechnic Institute". The authors come from Brazil, Germany, France, Mexico, Spain, Poland, Russia, Ukraine and the USA.

This book brings together a rich selection of studies in mathematical modeling and computational intelligence, with application in several fields of engineering, like automation, biomedical, chemical, civil, electrical, electronic, geophysical and mechanical engineering, on a multidisciplinary approach. Authors from five countries and 16 different research centers contribute with their expertise in both the fundamentals and real problems applications based upon their strong background on modeling and computational intelligence. The reader will find a wide variety of applications, mathematical and computational tools and original results, all presented with rigorous mathematical procedures. This work is intended for use in graduate courses of engineering, applied mathematics and applied computation where tools as mathematical and computational modeling, numerical methods and computational intelligence are applied to the solution of real problems.

Stokes discusses--and illustrates with output from actual problems--a number of applied econometric techniques, including OLS specification tests, recursive residual analysis, limited dependent variable models, error component models, and others. His book is clearly written and copiously illustrated with equations, with follow-up analysis to show how models are built and some of their limitations. His B34S DEGREESDTM software is available and allows readers to do further research with a large number of datasets distributed with the program. A necessary resource for applied econometrics researchers in economics, finance, and in health, energy, and labor economics.

This work illustrates the use of model specification and diagnostic tests applied to a variety of econometric modeling techniques. For each technique discussed the basic mathematical models are outlined. A sample problem is discussed and estimated using the B34S DEGREESDTM Data Analysis System. The output of the program is displayed in the text and discussed. Where appropriate, output from the RATS DEGREESDTM software is displayed. Follow-up models are estimated and discussed. The examples selected are taken from a variety of sources and reflect actual applied research. Complete data are given in the text to enable the reader to use these problems with other programs and techniques. It is the author's experience that applied econometric techniques are best learned by running actual problems. Since most users experiment with a limited number of techniques, their experience is limited. This book discusses a broad range of techniques and shows how they are interrelated. DEGREESL DEGREESL The techniques discussed include the following: simple, one-equation OLS and GLS models with continuous variables on the left-hand side, which are tested with recursive residual and BLUS residual techniques. Another class of models includes restrictions on the left-hand side variables. Models studied and illustrated with data include probit, logit, multinomial logit, and ordered probit models. Other techniques discussed and illustrated include two-stage least squares, limited information maximum likelihood, three-stage least squares, iterative three-stage least squares, error component models and Markov probability models, which are illustrated with a model of OPEC production dynamics.

ARIMA and transfer function models are shown to be generalizations of the single-equation model, while VAR and VARMA models are shown to be a time series generalization of three-stage least squares and full information maximum likelihood models. VAR models are viewed in the frequency domain for added insight, and extensive nonlinearity tests are developed and applied. More specialized techniques include state space models, optimal control analysis, nonlinear analysis, and the QR approach to computation. An important feature of the book is the emphasis on nonlinear model building. The Hinich nonlinear testing approach is discussed and integrated into the OLS, times series, and nonlinear estimation procedures. The MARS and PISPLINE methods of analysis are illustrated with models that failed linearity tests when estimated with linear methods. The purpose of the monograph is to illustrate the above techniques, using actual research data. To facilitate the calculations, the B34S DEGREESDTM Data Analysis System was developed. Sample output for all procedures discussed in the text has been provided so that the availability of the B34S DEGREESDTM program is DEGREESInot DEGREESR required in order to benefit from this book. While the book is self-contained, interested readers can obtain the B34S DEGREESDTM Data Analysis program and do further research with the datasets discussed in the book which are supplied with the software.

This volume contains a selection of contributions that were presented at the Modeling and Optimization: Theory and Applications Conference (MOPTA) held at Lehigh University in Bethlehem, Pennsylvania, USA on July 30-August 1, 2012. The conference brought together a diverse group of researchers and practitioners, working on both theoretical and practical aspects of continuous or discrete optimization. Topics presented included algorithms for solving convex, network, mixed-integer, nonlinear, and global optimization problems, and addressed the application of optimization techniques in finance, logistics, health, and other important fields. The contributions contained in this volume represent a sample of these topics and applications and illustrate the broad diversity of ideas discussed at the meeting.

The contributions gathered here provide an overview of current research projects and selected software products of the Fraunhofer Institute for Algorithms and Scientific Computing SCAI. They show the wide range of challenges that scientific computing currently faces, the solutions it offers, and its important role in developing applications for industry. Given the exciting field of applied collaborative research and development it discusses, the book will appeal to scientists, practitioners, and students alike. The Fraunhofer Institute for Algorithms and Scientific Computing SCAI combines excellent research and application-oriented development to provide added value for our partners. SCAI develops numerical techniques, parallel algorithms and specialized software tools to support and optimize industrial simulations. Moreover, it implements custom software solutions for production and logistics, and offers calculations on high-performance computers. Its services and products are based on state-of-the-art methods from applied mathematics and information technology.

This book presents the theoretical details and computational performances of algorithms used for solving continuous nonlinear optimization applications imbedded in GAMS. Aimed toward scientists and graduate students who utilize optimization methods to model and solve problems in mathematical programming, operations research, business, engineering, and industry, this book enables readers with a background in nonlinear optimization and linear algebra to use GAMS technology to understand and utilize its important capabilities to optimize algorithms for modeling and solving complex, large-scale, continuous nonlinear optimization problems or applications. Beginning with an overview of constrained nonlinear optimization methods, this book moves on to illustrate key aspects of mathematical modeling through modeling technologies based on algebraically oriented modeling languages. Next, the main feature of GAMS, an algebraically oriented language that allows for high-level algebraic representation of mathematical optimization models, is introduced to model and solve continuous nonlinear optimization applications. More than 15 real nonlinear optimization applications in algebraic and GAMS representation are presented which are used to illustrate the performances of the algorithms described in this book. Theoretical and computational results, methods, and techniques effective for solving nonlinear optimization problems, are detailed through the algorithms MINOS, KNITRO, CONOPT, SNOPT and IPOPT which work in GAMS technology.

The volume presents a selection of in-depth studies and state-of-the-art surveys of several challenging topics that are at the forefront of modern applied mathematics, mathematical modeling, and computational science. These three areas represent the foundation upon which the methodology of mathematical modeling and computational experiment is built as a ubiquitous tool in all areas of mathematical applications. This book covers both fundamental and applied research, ranging from studies of elliptic curves over finite fields with their applications to cryptography, to dynamic blocking problems, to random matrix theory with its innovative applications. The book provides the reader with state-of-the-art achievements in the development and application of new theories at the interface of applied mathematics, modeling, and computational science.

This book aims at fostering interdisciplinary collaborations required to meet the modern challenges of applied mathematics, modeling, and computational science. At the same time, the contributions combine rigorous mathematical and computational procedures and examples from applications ranging from engineering to life sciences, providing a rich ground for graduate student projects.

This textbook teaches advanced undergraduate and first-year graduate students in Engineering and Applied Sciences to gather and analyze empirical observations (data) in order to aid in making design decisions. While science is about discovery, the primary paradigm of engineering and "applied science" is design. Scientists are in the discovery business and want, in general, to understand the natural world rather than to alter it. In contrast, engineers and applied scientists design products, processes, and solutions to problems. That said, statistics, as a discipline, is mostly oriented toward the discovery paradigm. Young engineers come out of their degree programs having taken courses such as "Statistics for Engineers and Scientists" without any clear idea as to how they can use statistical methods to help them design products or processes. Many seem to think that statistics is only useful for demonstrating that a device or process actually does what it was designed to do. Statistics courses emphasize creating predictive or classification models - predicting nature or classifying individuals, and statistics is often used to prove or disprove phenomena as opposed to aiding in the design of a product or process. In industry however, Chemical Engineers use designed experiments to optimize petroleum extraction; Manufacturing Engineers use experimental data to optimize machine operation; Industrial Engineers might use data to determine the optimal number of operators required in a manual assembly process. This text teaches engineering and applied science students to incorporate empirical investigation into such design processes. Much of the discussion in this book is about models, not whether the models truly represent reality but whether they adequately represent reality with respect to the problems at hand; many ideas focus on how to gather data in the most efficient way possible to construct adequate models. Includes chapters on subjects not often seen together in a single text (e.g., measurement systems, mixture experiments, logistic regression, Taguchi methods, simulation) Techniques and concepts introduced present a wide variety of design situations familiar to engineers and applied scientists and inspire incorporation of experimentation and empirical investigation into the design process. Software is integrally linked to statistical analyses with fully worked examples in each chapter; fully worked using several packages: SAS, R, JMP, Minitab, and MS Excel - also including discussion questions at the end of each chapter. The fundamental learning objective of this textbook is for the reader to understand how experimental data can be used to make design decisions and to be familiar with the most common types of experimental designs and analysis methods.

Mathematical Modeling for Complex Fluids and Flows provides researchers and engineering practitioners encountering fluid flows with state-of-the-art knowledge in continuum concepts and associated fluid dynamics. In doing so it supplies the means to design mathematical models of these flows that adequately express the engineering physics involved. It exploits the implicit link between the turbulent flow of classical Newtonian fluids and the laminar and turbulent flow of non-Newtonian fluids such as those required in food processing and polymeric flows.

The book develops a descriptive mathematical model articulated through continuum mechanics concepts for these non-Newtonian, viscoelastic fluids and turbulent flows. Each complex fluid and flow is examined in this continuum context as well as in combination with the turbulent flow of viscoelastic fluids. Some details are also explored via kinetic theory, especially viscoelastic fluids and their treatment with the Boltzmann equation. Both solution and modeling strategies for turbulent flows are laid out using continuum concepts, including a description of constructing polynomial representations and accounting for non-inertial and curvature effects.

Ranging from fundamental concepts to practical methodology, and including discussion of emerging technologies, this book is ideal for those requiring a single-source assessment of current practice in this intricate yet vital field.

This book contains the most recent progress in data assimilation in meteorology, oceanography and hydrology including land surface. It spans both theoretical and applicative aspects with various methodologies such as variational, Kalman filter, ensemble, Monte Carlo and artificial intelligence methods. Besides data assimilation, other important topics are also covered including targeting observation, sensitivity analysis, and parameter estimation. The book will be useful to individual researchers as well as graduate students for a reference in the field of data assimilation.

Combining control theory and modeling, this textbook introduces and builds on methods for simulating and tackling concrete problems in a variety of applied sciences. Emphasizing "learning by doing," the authors focus on examples and applications to real-world problems. An elementary presentation of advanced concepts, proofs to introduce new ideas, and carefully presented MATLAB(r) programs help foster an understanding of the basics, but also lead the way to new, independent research.

With minimal prerequisites and exercises in each chapter, this work serves as an excellent textbook and referencefor graduate and advanced undergraduatestudents, researchers, and practitioners in mathematics, physics, engineering, computer science, as well as biology, biotechnology, economics, and finance."

This thesis demonstrates techniques that provide faster and more accurate solutions to a variety of problems in machine learning and signal processing. The author proposes a "greedy" algorithm, deriving sparse solutions with guarantees of optimality. The use of this algorithm removes many of the inaccuracies that occurred with the use of previous models.

The subject of fractional calculus and its applications (that is, convolution-type pseudo-differential operators including integrals and derivatives of any arbitrary real or complex order) has gained considerable popularity and importance during the past three decades or so, mainly due to its applications in diverse fields of science and engineering. These operators have been used to model problems with anomalous dynamics, however, they also are an effective tool as filters and controllers, and they can be applied to write complicated functions in terms of fractional integrals or derivatives of elementary functions, and so on.This book will give readers the possibility of finding very important mathematical tools for working with fractional models and solving fractional differential equations, such as a generalization of Stirling numbers in the framework of fractional calculus and a set of efficient numerical methods. Moreover, we will introduce some applied topics, in particular fractional variational methods which are used in physics, engineering or economics. We will also discuss the relationship between semi-Markov continuous-time random walks and the space-time fractional diffusion equation, which generalizes the usual theory relating random walks to the diffusion equation. These methods can be applied in finance, to model tick-by-tick (log)-price fluctuations, in insurance theory, to study ruin, as well as in macroeconomics as prototypical growth models.All these topics are complementary to what is dealt with in existing books on fractional calculus and its applications. This book was written with a trade-off in mind between full mathematical rigor and the needs of readers coming from different applied areas of science and engineering. In particular, the numerical methods listed in the book are presented in a readily accessible way that immediately allows the readers to implement them on a computer in a programming language of their choice. Numerical code is also provided.