In response to scientific needs for more diverse and structured explanations of statistical data, researchers have discovered how to model individual data points as belonging to multiple groups. Handbook of Mixed Membership Models and Their Applications shows you how to use these flexible modeling tools to uncover hidden patterns in modern high-dimensional multivariate data. It explores the use of the models in various application settings, including survey data, population genetics, text analysis, image processing and annotation, and molecular biology. Through examples using real data sets, you'll discover how to characterize complex multivariate data in: Studies involving genetic databases Patterns in the progression of diseases and disabilities Combinations of topics covered by text documents Political ideology or electorate voting patterns Heterogeneous relationships in networks, and much more The handbook spans more than 20 years of the editors' and contributors' statistical work in the field. Top researchers compare partial and mixed membership models, explain how to interpret mixed membership, delve into factor analysis, and describe nonparametric mixed membership models. They also present extensions of the mixed membership model for text analysis, sequence and rank data, and network data as well as semi-supervised mixed membership models.

First published in 1967, this book explores the theme of geographical generalization, or model building. It is composed of eight of the chapters from the original Models in Geography, published in 1967. The first chapter broadly outlines geographical generalization and examines the nature and function of generalized statements, ranging from conceptual models to scale models, in a geographical context. The following chapter deals with model theory in a wider scientific framework and the rest of the book discusses models of physical systems and information models. The book considers model-type generalizations that are applied in the three fields of geomorphology, meteorology and climatology, and hydrology before focusing on the transference of information and ideas in geography. This text represents a robustly anti-idiographic statement of modern work in one of the major branches of geography.

In this book Lee Rudolph brings together international contributors who combine psychological and mathematical perspectives to analyse how qualitative mathematics can be used to create models of social and psychological processes. Bridging the gap between the fields with an imaginative and stimulating collection of contributed chapters, the volume updates the current research on the subject, which until now has been rather limited, focussing largely on the use of statistics.

Qualitative Mathematics for the Social Sciences contains a variety of useful illustrative figures, introducing readers from the social sciences to the rich contribution that modern mathematics has made to our knowledge of logic, structures, and dynamic systems. A beguiling array of conceptual systems, topological models and fractals are discussed which transcend the application of statistics, and bring a fresh perspective to the study of social representations.

The wide selection of qualitative mathematical methodologies discussed in this volume will be hugely valuable to higher-level undergraduate and postgraduate students of psychology, sociology and mathematics. It will also be useful for researchers, academics and professionals from the social sciences who want a firmer grasp on the use of qualitative mathematics.

These days, computer-based simulation is considered the quintessential approach to exploring new ideas in the different disciplines of science, engineering and technology (SET). To perform simulations, a physical system needs to be modeled using mathematics; these models are often represented by linear time-invariant (LTI) continuous-time (CT) systems. Oftentimes these systems are subject to additional algebraic constraints, leading to first- or second-order differential-algebraic equations (DAEs), otherwise known as descriptor systems. Such large-scale systems generally lead to massive memory requirements and enormous computational complexity, thus restricting frequent simulations, which are required by many applications. To resolve these complexities, the higher-dimensional system may be approximated by a substantially lower-dimensional one through model order reduction (MOR) techniques. Computational Methods for Approximation of Large-Scale Dynamical Systems discusses computational techniques for the MOR of large-scale sparse LTI CT systems. Although the book puts emphasis on the MOR of descriptor systems, it begins by showing and comparing the various MOR techniques for standard systems. The book also discusses the low-rank alternating direction implicit (LR-ADI) iteration and the issues related to solving the Lyapunov equation of large-scale sparse LTI systems to compute the low-rank Gramian factors, which are important components for implementing the Gramian-based MOR. Although this book is primarly aimed at post-graduate students and researchers of the various SET disciplines, the basic contents of this book can be supplemental to the advanced bachelor's-level students as well. It can also serve as an invaluable reference to researchers working in academics and industries alike. Features: Provides an up-to-date, step-by-step guide for its readers. Each chapter develops theories and provides necessary algorithms, worked examples, numerical experiments and related exercises. With the combination of this book and its supplementary materials, the reader gains a sound understanding of the topic. The MATLAB (R) codes for some selected algorithms are provided in the book. The solutions to the exercise problems, experiment data sets and a digital copy of the software are provided on the book's website; The numerical experiments use real-world data sets obtained from industries and research institutes.

Many historical processes are dynamic. Populations grow and decline. Empires expand and collapse. Religions spread and wither. Natural scientists have made great strides in understanding dynamical processes in the physical and biological worlds using a synthetic approach that combines mathematical modeling with statistical analyses. Taking up the problem of territorial dynamics--why some polities at certain times expand and at other times contract--this book shows that a similar research program can advance our understanding of dynamical processes in history. Peter Turchin develops hypotheses from a wide range of social, political, economic, and demographic factors: geopolitics, factors affecting collective solidarity, dynamics of ethnic assimilation/religious conversion, and the interaction between population dynamics and sociopolitical stability. He then translates these into a spectrum of mathematical models, investigates the dynamics predicted by the models, and contrasts model predictions with empirical patterns. Turchin's highly instructive empirical tests demonstrate that certain models predict empirical patterns with a very high degree of accuracy. For instance, one model accounts for the recurrent waves of state breakdown in medieval and early modern Europe. And historical data confirm that ethno-nationalist solidarity produces an aggressively expansive state under certain conditions (such as in locations where imperial frontiers coincide with religious divides). The strength of Turchin's results suggests that the synthetic approach he advocates can significantly improve our understanding of historical dynamics.

The 5th edition of Model Building in Mathematical Programming discusses the general principles of model building in mathematical programming and demonstrates how they can be applied by using several simplified but practical problems from widely different contexts. Suggested formulations and solutions are given together with some computational experience to give the reader a feel for the computational difficulty of solving that particular type of model. Furthermore, this book illustrates the scope and limitations of mathematical programming, and shows how it can be applied to real situations. By emphasizing the importance of the building and interpreting of models rather than the solution process, the author attempts to fill a gap left by the many works which concentrate on the algorithmic side of the subject. In this article, H.P. Williams explains his original motivation and objectives in writing the book, how it has been modified and updated over the years, what is new in this edition and why it has maintained its relevance and popularity over the years: http://www.statisticsviews.com/details/feature/4566481/Model-Building-in-Mathematical-Programming-published-in-fifth-edition.html

Discover the subject of optimization in a new light with this modern and unique treatment. Includes a thorough exposition of applications and algorithms in sufficient detail for practical use, while providing you with all the necessary background in a self-contained manner. Features a deeper consideration of optimal control, global optimization, optimization under uncertainty, multiobjective optimization, mixed-integer programming and model predictive control. Presents a complete coverage of formulations and instances in modelling where optimization can be applied for quantitative decision-making. As a thorough grounding to the subject, covering everything from basic to advanced concepts and addressing real-life problems faced by modern industry, this is a perfect tool for advanced undergraduate and graduate courses in chemical and biochemical engineering.

In this book Lee Rudolph brings together international contributors who combine psychological and mathematical perspectives to analyse how qualitative mathematics can be used to create models of social and psychological processes. Bridging the gap between the fields with an imaginative and stimulating collection of contributed chapters, the volume updates the current research on the subject, which until now has been rather limited, focussing largely on the use of statistics. Qualitative Mathematics for the Social Sciences contains a variety of useful illustrative figures, introducing readers from the social sciences to the rich contribution that modern mathematics has made to our knowledge of logic, structures, and dynamic systems. A beguiling array of conceptual systems, topological models and fractals are discussed which transcend the application of statistics, and bring a fresh perspective to the study of social representations. The wide selection of qualitative mathematical methodologies discussed in this volume will be hugely valuable to higher-level undergraduate and postgraduate students of psychology, sociology and mathematics. It will also be useful for researchers, academics and professionals from the social sciences who want a firmer grasp on the use of qualitative mathematics.

The damages and hardships caused by floods and flooding remain an issue and are continuously increasing in the Chi River Basin, Thailand. It is difficult to make an accurate assessment of the costs and consequences associated with floods. However, flood hazards can also be seen as an opportunity, a chance to correct possible flaws and ambiguities in the flood management. The Chi River system cannot handle the regularly occurring floods, consequently, flooding of the low-lying areas occurs on a regular basis. Therefore, an integrated flood management framework needs to be developed to minimize the negative effects of floods of different magnitude. In response, a hydrological model (SWAT) and a hydraulic (1D/2D SOBEK) model were integrated to simulate floods in detailed way and to analyse the current system. A reliable simulation of the river flows and inundated areas is an essential component of a holistic flood management plan. The developed modelling framework enabled to analyse the impact of different structural measures such as river normalisation, green river (bypass), and retention basin. In addition, non-structural measures including reservoir operation and spatial land use planning were assessed in their capability to protect people and valuable infrastructure. For each measure, several possible scenarios were tested and evaluated based on economic and technical efficiency criteria to determine the most promising and efficient scenario. However, effective interventions may involve a judicious combination of flood mitigation approaches, rather than reliance on a stand-alone solution. A truly optimum combination of aforesaid measures was then chosen since it could considerably reduce flood extent and its damage. Finally, the study illustrates the effects of land use changes on floods, which indicated little or no significant potential impact on flood regime at river basin level, but rather at sub-basin scale. This finding is important for a better understanding of the scale and direction of impacts of developments in the future. Integrated land use planning was shown to be an essential component of a comprehensive flood management framework.

Probability theory has diverse applications in a plethora of fields, including physics, engineering, computer science, chemistry, biology and economics. This book will familiarize students with various applications of probability theory, stochastic modeling and random processes, using examples from all these disciplines and more. The reader learns via case studies and begins to recognize the sort of problems that are best tackled probabilistically. The emphasis is on conceptual understanding, the development of intuition and gaining insight, keeping technicalities to a minimum. Nevertheless, a glimpse into the depth of the topics is provided, preparing students for more specialized texts while assuming only an undergraduate-level background in mathematics. The wide range of areas covered - never before discussed together in a unified fashion - includes Markov processes and random walks, Langevin and Fokker-Planck equations, noise, generalized central limit theorem and extreme values statistics, random matrix theory and percolation theory.

Complex Analysis with Applications to Flows and Fields presents the theory of functions of a complex variable, from the complex plane to the calculus of residues to power series to conformal mapping. The book explores numerous physical and engineering applications concerning potential flows, the gravity field, electro- and magnetostatics, steady heat conduction, and other problems. It provides the mathematical results to sufficiently justify the solution of these problems, eliminating the need to consult external references. The book is conveniently divided into four parts. In each part, the mathematical theory appears in odd-numbered chapters while the physical and engineering applications can be found in even-numbered chapters. Each chapter begins with an introduction or summary and concludes with related topics. The last chapter in each section offers a collection of many detailed examples. This self-contained book gives the necessary mathematical background and physical principles to build models for technological and scientific purposes. It shows how to formulate problems, justify the solutions, and interpret the results.

Integrated assessment modelling is an active and rapidly developing field, triggered by the debate on climate change and the move towards the goal of sustainable development. This book provides an integrated approach to modelling, using a transdisciplinary approach. The author summarizes the main issues involved in the changing global system, and gives an overview of the emerging field of integrated assessment. He then presents a general discussion of the methodological principles of a multidisciplinary integrated modelling approach. Existing tools are examined and new methodological approaches are applied to various aspects of the problem of global change. The case studies focus on optimizing climate change mitigating policies, the allocation of emission rights and the the adaptive behaviour of social and biological agents. Special attention is given to the role of uncertainty, especially the subjective interpretation of uncertainties (world views), and the role of adaptive multi-agent modelling. The book concludes with a discussion on future uses of integrated assessment modelling in the global environment. Modelling Global Change will be vital to economists and scientists who have an interest in integrated assessment modelling, global modelling and decision support, environmental and ecological economists and those interested in sustainable development.

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.

This book presents the reader with comprehensive insight into various kinds of mathematical modeling and numerical computation for problems arising in several branches of engineering, such as mechanical engineering, computer science engineering, electrical engineering, electronics and communication engineering, and civil engineering. The book: * Discusses topics related to clean and green energy production and storage * Bridges the gap between core theory and costly industrial experiments * Covers advanced biomechanics and nanodrug delivery topics * Explores diversified applications of mathematical techniques to solve practical engineering problems The text in this book emphasizes mathematical treatment of soft computing, image and signal processing, fluid flows in various geometries, biomechanics, biological modeling, a mathematical description of the solar cell, analytical and numerical treatment of problems in fracture mechanics, and antenna design modeling. It also discusses the numerical computations of biomechanics problems and problems arising in cryptography. The text further covers optimization techniques that are useful for real-world problems. This material is primarily written for graduate students and academic researchers in a number of engineering fields, including electrical, electronics and communication, industrial, manufacturing, mechanical, computer science, and mathematics.

This book presents a detailed study of the Lanczos potential in general relativity by using tetrad formalisms. It demonstrates that these formalisms offer some simplifications over the tensorial methods, and investigates a general approach to finding the Lanczos potential for algebraic space-time by translating all the tensorial relations concerning the Lanczos potential into the language of tetrad formalisms and using the Newman-Penrose and Geroch-Held-Penrose formalisms. In addition, the book obtains the Lanczos potential for perfect fluid space-time, and applies the results to cosmological models of the universe. In closing, it highlights other methods, apart from tetrad formalisms, for finding the Lanczos potential, as well as further applications of the Newman-Penrose formalism. Given its scope, the book will be of interest to pure mathematicians, theoretical physicists and cosmologists, and will provide common ground for communication among these scientific communities.

This Element presents a unified computational fluid dynamics framework from rarefied to continuum regimes. The framework is based on the direct modelling of flow physics in a discretized space. The mesh size and time step are used as modelling scales in the construction of discretized governing equations. With the variation-of-cell Knudsen number, continuous modelling equations in different regimes have been obtained, and the Boltzmann and Navier-Stokes equations become two limiting equations in the kinetic and hydrodynamic scales. The unified algorithms include the discrete velocity method (DVM)-based unified gas-kinetic scheme (UGKS), the particlebased unified gas-kinetic particle method (UGKP), and the wave and particle-based unified gas-kinetic wave-particle method (UGKWP). The UGKWP is a multi-scale method with the particle for non-equilibrium transport and wave for equilibrium evolution. The particle dynamics in the rarefied regime and the hydrodynamic flow solver in the continuum regime have been unified according to the cell's Knudsen number.

Over the past 25 years, Harold and Darren Franck have investigated hundreds of accidents involving vehicles of almost every shape, size, and type imaginable. In Mathematical Methods for Accident Reconstruction: A Forensic Engineering Perspective, these seasoned experts demonstrate the application of mathematics to modeling accident reconstructions involving a range of moving vehicles, including automobiles, small and large trucks, bicycles, motorcycles, all-terrain vehicles, and construction equipment such as hoists and cranes.

The book is anchored on basic principles of physics that may be applied to any of the above-named vehicles or equipment. Topics covered include the foundations of measurement, the various energy methods used in reconstruction, momentum methods, vehicle specifications, failure analysis, geometrical characteristics of highways, and softer scientific issues such as visibility, perception, and reaction.

The authors examine the fundamental characteristics of different vehicles, discuss the retrieval of data from crash data recorders, and review low speed impacts with an analysis of staged collisions. Finally, the book details standards and protocols for accident reconstruction.

Exploring a broad range of accident scenarios and also acknowledging the limits of applicability of the various physical methods employed, the breadth and depth of the book s coverage makes it a critical reference for engineers and scientists who perform vehicular accident reconstructions.

Understand multiphase flows using multidisciplinary knowledge in physical principles, modelling theories, and engineering practices. This essential text methodically introduces the important concepts, governing mechanisms, and state-of-the-art theories, using numerous real-world applications, examples, and problems. Covers all major types of multiphase flows, including gas-solid, gas-liquid (sprays or bubbling), liquid-solid, and gas-solid-liquid flows. Introduces the volume-time-averaged transport theorems and associated Lagrangian-trajectory modelling and Eulerian-Eulerian multi-fluid modelling. Explains typical computational techniques, measurement methods and four representative subjects of multiphase flow systems. Suitable as a reference for engineering students, researchers, and practitioners, this text explores and applies fundamental theories to the analysis of system performance using a case-based approach.

This book presents the state-of-the-art in supercomputer simulation. It includes the latest findings from leading researchers using systems from the High Performance Computing Center Stuttgart (HLRS) in 2021. The reports cover all fields of computational science and engineering ranging from CFD to computational physics and from chemistry to computer science with a special emphasis on industrially relevant applications. Presenting findings of one of Europe's leading systems, this volume covers a wide variety of applications that deliver a high level of sustained performance. The book covers the main methods in high-performance computing. Its outstanding results in achieving the best performance for production codes are of particular interest for both scientists and engineers. The book comes with a wealth of color illustrations and tables of results.

The wave equation, a classical partial differential equation, has been studied and applied since the eighteenth century. Solving it in the presence of an obstacle, the scatterer, can be achieved using a variety of techniques and has a multitude of applications. This book explains clearly the fundamental ideas of time-domain scattering, including in-depth discussions of separation of variables and integral equations. The author covers both theoretical and computational aspects, and describes applications coming from acoustics (sound waves), elastodynamics (waves in solids), electromagnetics (Maxwell's equations) and hydrodynamics (water waves). The detailed bibliography of papers and books from the last 100 years cement the position of this work as an essential reference on the topic for applied mathematicians, physicists and engineers.

The food industry is on the verge of making some serious advances in the food processing sector. If successful, tomorrow's consumers will have unhindered access to safe, nutritious, and high-quality products via novel food processing technologies. Food Processing Operations Modeling: Design and Analysis, Second Edition demonstrates how to effectively use numerical modeling to predict the effects of food processing on targeted components. This non-destructive testing method virtually eliminates the health risks of under-processed food and maintains high nutritional values that are often lost in overcooked food. Using a task-oriented approach, this second edition discusses basic and advanced modeling tools that allow researchers to predict and prevent worse-case scenarios, perform comprehensive analyses, and optimize system design and efficiency. Contains Selected Applications of Thermal and Non-Thermal Processing Operations NEW TO THIS EDITION: Six new chapters on radio frequency heating, high-pressure processing, pulsed electric field treatment, fouling model on heat exchangers, ozone treatment, and UV radiation Expanded scope to address innovative and up-to-date food processing technologies Numerous real-world case studies Updated information on infrared heating of biological materials and modeling electrical resistance heating of foods Electromagnetic treatments (RF, Infrared, and UV) and fundamentals relative to heat and mass transfer, fluid flow, and stochastic processes Synergistic effect of combined food processing techniques and its numerical simulation Food processing methods are constantly improving in an effort to maintain safe, high-quality, and fresh-tasting products. Providing the theoretical basis for these cutting-edge techniques, this tried-and-tested reference provides indispensable insight into food systems modeling, while exploring applications for further research.

Modelling large-scale wave fields and their interaction with coastal and offshore structures has become much more feasible over the last two decades with increases in computer speeds. Wave modelling can be viewed as an extension of wave theory, a mature and widely published field, applied to practical engineering through the use of computer tools. Information about the various wave models which have been developed is often widely scattered in the literature, and consequently this is one of the first books devoted to wave models and their applications. At the core of the book is an introduction to various types of wave models. For each model, the theoretical assumptions, the application range, and the advantages and limitations are elaborated. The combined use of different wave models from large-scale to local-scale is highlighted with a detailed discussion of the application and matching of boundary conditions. At the same time the book provides a grounding in hydrodynamics, wave theory, and numerical methods which underlie wave modelling. It presents the theoretical background and also shows how to use these models for achieving different engineering tasks, illustrated and reinforced with case study examples.

Numerical relativity has emerged as the key tool to model gravitational waves - recently detected for the first time - that are emitted when black holes or neutron stars collide. This book provides a pedagogical, accessible, and concise introduction to the subject. Relying heavily on analogies with Newtonian gravity, scalar fields and electromagnetic fields, it introduces key concepts of numerical relativity in a context familiar to readers without prior expertise in general relativity. Readers can explore these concepts by working through numerous exercises, and can see them 'in action' by experimenting with the accompanying Python sample codes, and so develop familiarity with many techniques commonly employed by publicly available numerical relativity codes. This is an attractive, student-friendly resource for short courses on numerical relativity, as well as providing supplementary reading for courses on general relativity and computational physics.

This new edition of Six Simple Twists: The Pleat Pattern Approach to Origami Tessellation Design introduces an innovative pleat pattern technique for origami designs that is easily accessible to anyone who enjoys the geometry of paper. The book begins with six basic forms meant to ease the reader into the style, and then systematically scaffolds the instructions to build a strong understanding of the techniques, leading to instructions on a limitless number of patterns. It then describes a process of designing additional building blocks. At the end, what emerges is a fascinating artform that will enrich folders for many years. Unlike standard, project-based origami books, Six Simple Twists focuses on how to design, rather than construct. In this thoroughly updated second edition, the book explores new techniques and example tessellations, with full-page images, and mathematical analysis of the patterns. A reader will, through practice, gain the ability to create still more complex and fascinating designs. Key Features Introduces the reader to origami tessellations and demonstrates their place in the origami community New layout and instructional approach restructure the book from the ground up Addresses common tessellation questions, such as what types of paper are best to use, and how this artform rose in popularity Teaches the reader how to grid a sheet of paper and the importance of the pre-creases Gives the reader the ability to create and understand tessellations through scaffolded instruction Includes exercises to test understanding Introduces a new notation system for precisely describing pleat intersections Analyzes pleat intersections mathematically using geometrically-focused models, including information about Brocard points

This book reviews the state of the art in deep learning approaches to high-performance robust disease detection, robust and accurate organ segmentation in medical image computing (radiological and pathological imaging modalities), and the construction and mining of large-scale radiology databases. It particularly focuses on the application of convolutional neural networks, and on recurrent neural networks like LSTM, using numerous practical examples to complement the theory. The book's chief features are as follows: It highlights how deep neural networks can be used to address new questions and protocols, and to tackle current challenges in medical image computing; presents a comprehensive review of the latest research and literature; and describes a range of different methods that employ deep learning for object or landmark detection tasks in 2D and 3D medical imaging. In addition, the book examines a broad selection of techniques for semantic segmentation using deep learning principles in medical imaging; introduces a novel approach to text and image deep embedding for a large-scale chest x-ray image database; and discusses how deep learning relational graphs can be used to organize a sizable collection of radiology findings from real clinical practice, allowing semantic similarity-based retrieval.The intended reader of this edited book is a professional engineer, scientist or a graduate student who is able to comprehend general concepts of image processing, computer vision and medical image analysis. They can apply computer science and mathematical principles into problem solving practices. It may be necessary to have a certain level of familiarity with a number of more advanced subjects: image formation and enhancement, image understanding, visual recognition in medical applications, statistical learning, deep neural networks, structured prediction and image segmentation.