The papers in this volume consider a general area of study known as network routing. The underlying problems are conceptually simple, yet mathematically complex and challenging. How can we best route material or people from one place to another? Or, how can we best design a system (for instance locate facilities) to provide services and goods as efficiently and equitably as possible? The problems encountered in answering these questions often have an underlying combinatorial structure, for example, either we dispatch a vehicle or we do not, or we use one particular route or another. The problems also typically have an underlying network structure (a communication or transportation network). In addition, models for these problems are often very large with hundreds or thousands of constraints and variables. A companion volume in the "Handbook" series, entitled "Network Models", treats basic network models such as minimum cost flows, matching and the travelling salesman problem, as well as, several complex network topics, not directly related to routing, such as network design and network reliability.

This book gives a rigorous yet physics focused introduction to mathematical logic that is geared towards natural science majors. We present the science major with a robust introduction to logic, focusing on the specific knowledge and skills that will unavoidably be needed in calculus topics and natural science topics in general rather than taking a philosophical-math-fundamental oriented approach that is commonly found in mathematical logic textbooks.

The subject of geomathematics focuses on the interpretation and classification of data from geoscientific and satellite sources, reducing information to a comprehensible form and allowing the testing of concepts. Sphere oriented mathematics plays an important part in this study and this book provides the necessary foundation for graduate students and researchers interested in any of the diverse topics of constructive approximation in this area. This book bridges the existing gap between monographs on special functions of mathematical physics and constructive approximation in Euclidean spaces. The primary objective is to provide readers with an understanding of aspects of approximation by spherical harmonics, such as spherical splines and wavelets, as well as indicating future directions of research. Scalar, vectorial, and tensorial methods are each considered in turn. The concentration on spherical splines and wavelets allows a double simplification; not only is the number of independent variables reduced resulting in a lower dimensional problem, but also radial basis function techniques become applicable. When applied to geomathematics this leads to new structures and methods by which sophisticated measurements and observations can be handled more efficiently, thus reducing time and costs.

While the significance of networks in various human behavior and activities has a history as long as human's existence, network awareness is a recent scientific phenomenon. The neologism network science is just one or two decades old. Nevertheless, with this limited time, network thinking has substantially reshaped the recent development in economics, and almost all solutions to real-world problems involve the network element. This book integrates agent-based modeling and network science. It is divided into three parts, namely, foundations, primary dynamics on and of social networks, and applications. The authors begin with the network origin of agent-based models, known as cellular automata, and introduce a number of classic models, such as Schelling's segregation model and Axelrod's spatial game. The essence of the foundation part is the network-based agent-based models in which agents follow network-based decision rules. Under the influence of the substantial progress in network science in late 1990s, these models have been extended from using lattices into using small-world networks, scale-free networks, etc. The text also shows that the modern network science mainly driven by game-theorists and sociophysicists has inspired agent-based social scientists to develop alternative formation algorithms, known as agent-based social networks. It reviews a number of pioneering and representative models in this family. Upon the given foundation, the second part reviews three primary forms of network dynamics, such as diffusions, cascades, and influences. These primary dynamics are further extended and enriched by practical networks in goods-and-service markets, labor markets, and international trade. At the end, the book considers two challenging issues using agent-based models of networks: network risks and economic growth.

This hands-on guide is primarily intended to be used in undergraduate laboratories in the physical sciences and engineering. It assumes no prior knowledge of statistics. It introduces the necessary concepts where needed, with key points illustrated with worked examples and graphic illustrations. In contrast to traditional mathematical treatments it uses a combination of spreadsheet and calculus-based approaches, suitable as a quick and easy on-the-spot reference. The emphasis throughout is on practical strategies to be adopted in the laboratory.
Error analysis is introduced at a level accessible to school leavers, and carried through to research level. Error calculation and propagation is presented though a series of rules-of-thumb, look-up tables and approaches amenable to computer analysis. The general approach uses the chi-square statistic extensively. Particular attention is given to hypothesis testing and extraction of parameters and their uncertainties by fitting mathematical models to experimental data. Routines implemented by most contemporary data analysis packages are analysed and explained. The book finishes with a discussion of advanced fitting strategies and an introduction to Bayesian analysis.

Starting from a clear, concise introduction, the powerful finite element and boundary element methods of engineering are developed for application to quantum mechanics. The reader is led through illustrative examples displaying the strengths of these methods using applications to fundamental quantum mechanical problems and to the design/simulation of quantum nanoscale devices.

Beginning with a review of the important areas of mathematics, this book then covers many of the underlying theoretical and practical aspects of NMR and MRI spectroscopy from a maths point of view. Competence in algebra and introductory calculus is needed but all other maths concepts are covered. It will bridge a gap between high level and introductory titles used in NMR or MRI spectroscopy. Uniquely, it takes a very careful and pedagogical approach to the mathematics behind NMR and MRI. It leaves out very few steps, which distinguishes it from other books in the field. The author is an NMR laboratory manager and is sympathetic to the frustrations of trying to understand where some of the fundamental equations come from hence his desire to either explicitly derive all equations for the reader or direct them to derivations. This is an essential text aimed at graduate students who are beginning their careers in NMR or MRI spectroscopy and laboratory managers if they need an understanding of the theoretical foundations of the technique.

This volume collects numerous recent advances in the study of stratified fluids. It includes analytical and experimental work from a wide range of fields, including meteorology, limnology, oceanography, and the study of estuarine processes. It also includes fundamental research on stratified and rotating fluid dynamics. A compendium of current work, the book is an ideal starting point for future research.

An introduction to statistical data mining, Data Analysis and Data Mining is both textbook and professional resource. Assuming only a basic knowledge of statistical reasoning, it presents core concepts in data mining and exploratory statistical models to students and professional statisticians-both those working in communications and those working in a technological or scientific capacity-who have a limited knowledge of data mining. This book presents key statistical concepts by way of case studies, giving readers the benefit of learning from real problems and real data. Aided by a diverse range of statistical methods and techniques, readers will move from simple problems to complex problems. Through these case studies, authors Adelchi Azzalini and Bruno Scarpa explain exactly how statistical methods work; rather than relying on the "push the button" philosophy, they demonstrate how to use statistical tools to find the best solution to any given problem. Case studies feature current topics highly relevant to data mining, such web page traffic; the segmentation of customers; selection of customers for direct mail commercial campaigns; fraud detection; and measurements of customer satisfaction. Appropriate for both advanced undergraduate and graduate students, this much-needed book will fill a gap between higher level books, which emphasize technical explanations, and lower level books, which assume no prior knowledge and do not explain the methodology behind the statistical operations.

This second book on Unity Root Matrix Theory extends its original three-dimensional formulation, as given in the first book, to an arbitrary number of higher dimensions. Unity Root Matrix Theory is formulated with strong adherence to concepts in mathematical physics and it is thought it may provide a discrete formulation of physical phenomena at the Planck level and upward. Consequently, it is essential that the theory incorporates the geometric dimensionality present in established physical theories. In particular, it must naturally embody the four-dimensional spacetime of Special Relativity, the five dimensions of Kaluza-Klein theory, and the eleven or more dimensions of Grand Unified Theories such as String Theory. Not only has an n-dimensional extension of Unity Root Matrix Theory successfully been achieved, whilst retaining all the three-dimensional mathematical and physical properties detailed in the first book, but a complete n-dimensional solution has been obtained which exhibits the geometric property of compactification, or dimensional reduction. This solution shows that dimensional shrinkage of higher dimensions may occur over long evolutionary timescales. The emergence of compactification and other physical phenomena gives further confidence that n-dimensional Unity Root Matrix Theory may, indeed, offer a discrete formulation of Physics starting at its most elemental level.

As the operations of the world become more and more dependent on highly interconnected, massively complex, networked systems of computational devices, the need to develop a mathematical understanding of their properties and behaviours is increasingly pressing. Our approach, described in this monograph, is to combine the compositionality of formal specification -- using techniques from algebra, computation theory, logic, and probability theory -- with the control of level of abstraction afforded by the classical mathematical modelling method.

Developed on surprisingly simple but fundamental concepts, it provides a rich mathematical and physical structure, justifying it as a subject to be studied in its own right by physicists and mathematicians alike. Ultimately, it is thought that unity root matrix theory may provide an alternative reformulation of some fundamental concepts in physics and an integer-based escape from the current, unification impasse.

Stochastic processes have a wide range of applications ranging from image processing, neuroscience, bioinformatics, financial management, and statistics. Mathematical, physical, and engineering systems use stochastic processes for modeling and reasoning phenomena. While comparing AI-stochastic systems with other counterpart systems, we are able to understand their significance, thereby applying new techniques to obtain new real-time results and solutions. Stochastic Processes and Their Applications in Artificial Intelligence opens doors for artificial intelligence experts to use stochastic processes as an effective tool in real-world problems in computational biology, speech recognition, natural language processing, and reinforcement learning. Covering key topics such as social media, big data, and artificial intelligence models, this reference work is ideal for mathematicians, industry professionals, researchers, scholars, academicians, practitioners, instructors, and students.

Written by a team of experts, Advances in Flowmeter Technology surveys the full range of modern flowmeters for product managers, strategic planners, engineers, distributors, and students. The origins, principles of operation,controls and instrumentation, and the relative advantages of each major flowmeter type are thoroughly explained. Extensive coverage of new types that employ cutting-edge technologies - such as coriolis, magnetic, ultrasonic, vortex, thermal flowmeters - is provided. The text includes comparative examples, placing these new types of meters in the context of more traditional ones, such as differential pressure, turbine, and positive displacement flowmeters.

In Spectral Properties of Certain Operators on a Free Hilbert Space and the Semicircular Law, the authors consider the so-called free Hilbert spaces, which are the Hilbert spaces induced by the usual l2 Hilbert spaces and operators acting on them. The construction of these operators itself is interesting and provides new types of Hilbert-space operators. Also, by considering spectral-theoretic properties of these operators, the authors illustrate how “free-Hilbert-space” Operator Theory is different from the classical Operator Theory. More interestingly, the authors demonstrate how such operators affect the semicircular law induced by the ONB-vectors of a fixed free Hilbert space. Different from the usual approaches, this book shows how “inside” actions of operator algebra deform the free-probabilistic information—in particular, the semicircular law.

Reachable Sets of Dynamic Systems: Uncertainty, Sensitivity, and Complex Dynamics introduces differential inclusions, providing an overview as well as multiple examples of its interdisciplinary applications. The design of dynamic systems of any type is an important issue as is the influence of uncertainty in model parameters and model sensitivity. The possibility of calculating the reachable sets may be a powerful additional tool in such tasks. This book can help graduate students, researchers, and engineers working in the field of computer simulation and model building, in the calculation of reachable sets of dynamic models.

Theoretical advances and new foundations have been reported at the Conference for more than 40 years which has helped expand the range of applications as well as the type of materials in response to industrial and professional requirements. Since the conference started it has attracted high quality papers that report further advances in techniques that reduce or eliminate the type of meshes associated with finite elements or finite differences, for instance. As design, analysis and manufacture become more integrated, the chances are that the users will be less aware of the capabilities of the analytical techniques that are at the core of the process. This reinforces the need to retain expertise in certain specialised areas of numerical methods, such as BEM/MRM, to ensure that all new tools perform satisfactorily in the integrated process. The maturity of BEM since 1978 has resulted in a substantial number of industrial applications, which demonstrate the accuracy, robustness and easy use of the technique. Their range still needs to be widened, taking into account the potentialities of the Mesh Reduction techniques in general. The included papers originate from the 46th conference on Boundary Elements and other Mesh Reduction Methods (BEM/MRM) which acts as a forum to discuss new ideas and critically compare results before the solution and tools are released to the end users.

The subject of information geometry blends several areas of statistics, computer science, physics, and mathematics. The subject evolved from the groundbreaking article published by legendary statistician C.R. Rao in 1945. His works led to the creation of Cramer-Rao bounds, Rao distance, and Rao-Blackawellization. Fisher-Rao metrics and Rao distances play a very important role in geodesics, econometric analysis to modern-day business analytics. The chapters of the book are written by experts in the field who have been promoting the field of information geometry and its applications.

The Boolean functions may be iterated either asynchronously, when their coordinates are computed independently of each other, or synchronously, when their coordinates are computed at the same time. In Boolean Systems: Topics in Asynchronicity, a book addressed to mathematicians and computer scientists interested in Boolean systems and their use in modelling, author Serban E. Vlad presents a consistent and original mathematical theory of the discrete-time Boolean asynchronous systems. The purpose of the book is to set forth the concepts of such a theory, resulting from the synchronous Boolean system theory and mostly from the synchronous real system theory, by analogy, and to indicate the way in which known synchronous deterministic concepts generate new asynchronous nondeterministic concepts. The reader will be introduced to the dependence on the initial conditions, periodicity, path-connectedness, topological transitivity, and chaos. A property of major importance is invariance, which is present in five versions. In relation to it, the reader will study the maximal invariant subsets, the minimal invariant supersets, the minimal invariant subsets, connectedness, separation, the basins of attraction, and attractors. The stability of the systems and their time-reversal symmetry end the topics that refer to the systems without input. The rest of the book is concerned with input systems. The most consistent chapters of this part of the book refer to the fundamental operating mode and to the combinational systems (systems without feedback). The chapter Wires, Gates, and Flip-Flops presents a variety of applications. The first appendix addresses the issue of continuous time, and the second one sketches the important theory of Daizhan Cheng, which is put in relation to asynchronicity. The third appendix is a bridge between asynchronicity and the symbolic dynamics of Douglas Lind and Brian Marcus.

Introduction to Chemical Engineering Analysis Using Mathematica, Second Edition reviews the processes and designs used to manufacture, use, and dispose of chemical products using Mathematica, one of the most powerful mathematical software tools available for symbolic, numerical, and graphical computing. Analysis and computation are explained simultaneously. The book covers the core concepts of chemical engineering, ranging from the conservation of mass and energy to chemical kinetics. The text also shows how to use the latest version of Mathematica, from the basics of writing a few lines of code through developing entire analysis programs. This second edition has been fully revised and updated, and includes analyses of the conservation of energy, whereas the first edition focused on the conservation of mass and ordinary differential equations.