Principles of Copula Theory explores the state of the art on copulas and provides you with the foundation to use copulas in a variety of applications. Throughout the book, historical remarks and further readings highlight active research in the field, including new results, streamlined presentations, and new proofs of old results. After covering the essentials of copula theory, the book addresses the issue of modeling dependence among components of a random vector using copulas. It then presents copulas from the point of view of measure theory, compares methods for the approximation of copulas, and discusses the Markov product for 2-copulas. The authors also examine selected families of copulas that possess appealing features from both theoretical and applied viewpoints. The book concludes with in-depth discussions on two generalizations of copulas: quasi- and semi-copulas. Although copulas are not the solution to all stochastic problems, they are an indispensable tool for understanding several problems about stochastic dependence. This book gives you the solid and formal mathematical background to apply copulas to a range of mathematical areas, such as probability, real analysis, measure theory, and algebraic structures.

• Introduces the dynamics, principles and mathematics behind ten macroeconomic models allowing students to visualise the models and understand the economic intuition behind them. • Provides a step-by-step guide, and the necessary MATLAB codes, to allow readers to simulate and experiment with the models themselves.

This unique textbook presents a course on computational linear algebra. Offers many unique applications. MATLAB is used throughout.

Whether the source is more industry-based or academic research, there certainly appears to be a growing interest in the field of cryptocurrency. The New York Times had a cover story on March 24, 2022, titled "Time to Enter the Crypto Zone?," and they talked about institutional investors pouring billions into digital tokens, salaries being taken in Bitcoins, and even Bitcoin ATMs in grocery stores. Certainly, there have been ups and downs in crypto, but it has a kind of alluring presence that tempts one to include crypto as part of one’s portfolio. Those who are "prime crypto-curious" investors are usually familiar with the tech/pop culture and feel they want to diversify a bit in this fast-moving market. Even universities are beginning to offer more courses and create "Centers on Cryptocurrency." Some universities are even requiring their students who take a crypto course to pay the course tuition via cryptocurrency. In response to the growing interest and fascination about the crypto industry and cryptocurrency in general, Cryptocurrency Concepts, Technology, and Applications brings together many leading worldwide contributors to discuss a broad range of issues associated with cryptocurrency. The book covers a wide array of crypto-related topics, including: Blockchain NFTs Data analytics and AI Crypto crime Crypto industry and regulation Crypto and public choice Consumer confidence Bitcoin and other cryptocurrencies. Presenting various viewpoints on where the crypto industry is heading, this timely book points out both the advantages and limitations of this emerging field. It is an easy-to-read, yet comprehensive, overview of cryptocurrency in the U.S. and international markets.

In 1918, Emmy Noether, in her paper Invariante Variationsprobleme, proved two theorems (and their converses) on variational problems that went on to revolutionise theoretical physics. 100 years later, the mathematics of Noether's theorems continues to be generalised, and the physical applications of her results continue to diversify. This centenary volume brings together world-leading historians, philosophers, physicists, and mathematicians in order to clarify the historical context of this work, its foundational and philosophical consequences, and its myriad physical applications. Suitable for advanced undergraduate and graduate students and professional researchers, this is a go-to resource for those wishing to understand Noether's work on variational problems and the profound applications which it finds in contemporary physics.

An encompassing socio-historical survey of the political and sociological nature of groups, communities and societies. A transdisciplinary study of crowds, masses and groups as historical, sociological, psychological and psychosocial phenomena. A unique combination of sociology, psychoanalysis and group analysis in the study of social formations. An inquiry into the enigma of crowds and mass psychology with the history of group analytic and group relations' advances in England, especially the study of large groups in the research on group processes. A comprehensive presentation of the social unconscious theory in association with the study of large groups and the Incohesion theory as new group analytic tools for understanding contemporary crowds and masses. In today's world, flooded by social conflicts and polarizations and the mass impact of social media, this book enables the reader to map out the field of the unconscious life of crowds illuminating the darkness of twenty-first century collective movements.

Illustrate the usefulness and abuse of statistics in automotive safety arguments that are hidden from public view Show the importance of data and statistics in making safety-related changes that ultimately save or cost lives Discuss the impact of electric vehicles and autonomous vehicles on car safety

Modern ecological and environmental sciences are dominated by observational data. As a result, traditional statistical training often leaves scientists ill-prepared for the data analysis tasks they encounter in their work. Bayesian methods provide a more robust and flexible tool for data analysis, as they enable information from different sources to be brought into the modelling process. Bayesian Applications in Evnironmental and Ecological Studies with R and Stan provides a Bayesian framework for model formulation, parameter estimation, and model evaluation in the context of analyzing environmental and ecological data. Features: An accessible overview of Bayesian methods in environmental and ecological studies Emphasizes the hypothetical deductive process, particularly model formulation Necessary background material on Bayesian inference and Monte Carlo simulation Detailed case studies, covering water quality monitoring and assessment, ecosystem response to urbanization, fisheries ecology, and more Advanced chapter on Bayesian applications, including Bayesian networks and a change point model Complete code for all examples, along with the data used in the book, are available via GitHub The book is primarily aimed at graduate students and researchers in the environmental and ecological sciences, as well as environmental management professionals. This is a group of people representing diverse subject matter fields, who could benefit from the potential power and flexibility of Bayesian methods.

Extremum Seeking through Delays and PDEs, the first book on the topic, expands the scope of applicability of the extremum seeking method, from static and finite-dimensional systems to infinite-dimensional systems. Readers will find: Numerous algorithms for model-free real-time optimization are developed and their convergence guaranteed. Extensions from single-player optimization to noncooperative games, under delays and pdes, are provided. The delays and pdes are compensated in the control designs using the pde backstepping approach, and stability is ensured using infinite-dimensional versions of averaging theory. Accessible and powerful tools for analysis. This book is intended for control engineers in all disciplines (electrical, mechanical, aerospace, chemical), mathematicians, physicists, biologists, and economists. It is appropriate for graduate students, researchers, and industrial users.

Designed for a proof-based course on linear algebra, this rigorous and concise textbook intentionally introduces vector spaces, inner products, and vector and matrix norms before Gaussian elimination and eigenvalues so students can quickly discover the singular value decomposition (SVD)-arguably the most enlightening and useful of all matrix factorizations. Gaussian elimination is then introduced after the SVD and the four fundamental subspaces and is presented in the context of vector spaces rather than as a computational recipe. This allows the authors to use linear independence, spanning sets and bases, and the four fundamental subspaces to explain and exploit Gaussian elimination and the LU factorization, as well as the solution of overdetermined linear systems in the least squares sense and eigenvalues and eigenvectors. This unique textbook also includes examples and problems focused on concepts rather than the mechanics of linear algebra. The problems at the end of each chapter and in an associated website encourage readers to explore how to use the notions introduced in the chapter in a variety of ways. Additional problems, quizzes, and exams will be posted on an accompanying website and updated regularly. The Less Is More Linear Algebra of Vector Spaces and Matrices is for students and researchers interested in learning linear algebra who have the mathematical maturity to appreciate abstract concepts that generalize intuitive ideas. The early introduction of the SVD makes the book particularly useful for those interested in using linear algebra in applications such as scientific computing and data science. It is appropriate for a first proof-based course in linear algebra.

Inverse scattering theory is a major theme in applied mathematics, with applications to such diverse areas as medical imaging, geophysical exploration, and nondestructive testing. The inverse scattering problem is both nonlinear and ill-posed, thus presenting challenges in the development of efficient inversion algorithms. A further complication is that anisotropic materials cannot be uniquely determined from given scattering data. In the first edition of Inverse Scattering Theory and Transmission Eigenvalues, the authors discussed methods for determining the support of inhomogeneous media from measured far field data and the role of transmission eigenvalue problems in the mathematical development of these methods. In this second edition, three new chapters describe recent developments in inverse scattering theory. In particular, the authors explore the use of modified background media in the nondestructive testing of materials and methods for determining the modified transmission eigenvalues that arise in such applications from measured far field data. They also examine nonscattering wave numbers-a subset of transmission eigenvalues-using techniques taken from the theory of free boundary value problems for elliptic partial differential equations and discuss the dualism of scattering poles and transmission eigenvalues that has led to new methods for the numerical computation of scattering poles. This book will be of interest to research mathematicians and engineers and physicists working on problems in target identification. It will also be useful to advanced graduate students in many areas of applied mathematics.

Higher Engineering Mathematics has helped thousands of students to succeed in their exams by developing problem-solving skills, It is supported by over 600 practical engineering examples and applications which relate theory to practice. The extensive and thorough topic coverage makes this a solid text for undergraduate and upper-level vocational courses. Its companion website provides resources for both students and lecturers, including lists of essential formulae, ands full solutions to all 2,000 further questions contained in the 277 practice exercises; and illustrations and answers to revision tests for adopting course instructors.

Dynamic Time Series Models using R-INLA: An Applied Perspective is the outcome of a joint effort to systematically describe the use of R-INLA for analysing time series and showcasing the code and description by several examples. This book introduces the underpinnings of R-INLA and the tools needed for modelling different types of time series using an approximate Bayesian framework. The book is an ideal reference for statisticians and scientists who work with time series data. It provides an excellent resource for teaching a course on Bayesian analysis using state space models for time series. Key Features: Introduction and overview of R-INLA for time series analysis. Gaussian and non-Gaussian state space models for time series. State space models for time series with exogenous predictors. Hierarchical models for a potentially large set of time series. Dynamic modelling of stochastic volatility and spatio-temporal dependence.

Features Contains ready-to-use coding recipes allowing fast prototyping and solving of mathematical problems using FEM. Suitable for upper-level undergraduates and graduates in applied mathematics, science, or engineering. Both MATLAB and Python programming codes are provided to give readers more flexibility in the practical framework implementation.

Provides clear guidance on leveraging computational techniques to answer social science questions In disciplines such as political science, sociology, psychology, and media studies, the use of computational analysis is rapidly increasing. Statistical modeling, machine learning, and other computational techniques are revolutionizing the way electoral results are predicted, social sentiment is measured, consumer interest is evaluated, and much more. Computational Analysis of Communication teaches social science students and practitioners how computational methods can be used in a broad range of applications, providing discipline-relevant examples, clear explanations, and practical guidance. Assuming little or no background in data science or computer linguistics, this accessible textbook teaches readers how to use state-of-the art computational methods to perform data-driven analyses of social science issues. A cross-disciplinary team of authors--with expertise in both the social sciences and computer science--explains how to gather and clean data, manage textual, audio-visual, and network data, conduct statistical and quantitative analysis, and interpret, summarize, and visualize the results. Offered in a unique hybrid format that integrates print, ebook, and open-access online viewing, this innovative resource: Covers the essential skills for social sciences courses on big data, data visualization, text analysis, predictive analytics, and others Integrates theory, methods, and tools to provide unified approach to the subject Includes sample code in Python and links to actual research questions and cases from social science and communication studies Discusses ethical and normative issues relevant to privacy, data ownership, and reproducible social science Developed in partnership with the International Communication Association and by the editors of Computational Communication Research Computational Analysis of Communication is an invaluable textbook and reference for students taking computational methods courses in social sciences, and for professional social scientists looking to incorporate computational methods into their work.

-Describes the basic ideas underlying each concept and model. -Includes R, SAS, SPSS and Stata programming codes for all the examples -Features significantly expanded Chapters 4, 5, and 8 (Chapters 4-6, and 9 in the second edition. -Expands discussion for subtle issues in longitudinal and clustered data analysis such as time varying covariates and comparison of generalized linear mixed-effect models with GEE.

Lorentz Geometry is a very important intersection between Mathematics and Physics, being the mathematical language of General Relativity. Learning this type of geometry is the first step in properly understanding questions regarding the structure of the universe, such as: What is the shape of the universe? What is a spacetime? What is the relation between gravity and curvature? Why exactly is time treated in a different manner than other spatial dimensions? Introduction to Lorentz Geometry: Curves and Surfaces intends to provide the reader with the minimum mathematical background needed to pursue these very interesting questions, by presenting the classical theory of curves and surfaces in both Euclidean and Lorentzian ambient spaces simultaneously. Features: Over 300 exercises Suitable for senior undergraduates and graduates studying Mathematics and Physics Written in an accessible style without loss of precision or mathematical rigor Solution manual available on www.routledge.com/9780367468644

What makes mathematics so special? Whether you have anxious memories of the subject from school, or solve quadratic equations for fun, David Acheson's book will make you look at mathematics afresh. Following on from his previous bestsellers, The Calculus Story and The Wonder Book of Geometry, here Acheson highlights the power of algebra, combining it with arithmetic and geometry to capture the spirit of mathematics. This short book encompasses an astonishing array of ideas and concepts, from number tricks and magic squares to infinite series and imaginary numbers. Acheson's enthusiasm is infectious, and, as ever, a sense of quirkiness and fun pervades the book. But it also seeks to crystallize what is special about mathematics: the delight of discovery; the importance of proof; and the joy of contemplating an elegant solution. Using only the simplest of materials, it conjures up the depth and the magic of the subject.

The use of Electronic Health Records (EHR)/Electronic Medical Records (EMR) data is becoming more prevalent for research. However, analysis of this type of data has many unique complications due to how they are collected, processed and types of questions that can be answered. This book covers many important topics related to using EHR/EMR data for research including data extraction, cleaning, processing, analysis, inference, and predictions based on many years of practical experience of the authors. The book carefully evaluates and compares the standard statistical models and approaches with those of machine learning and deep learning methods and reports the unbiased comparison results for these methods in predicting clinical outcomes based on the EHR data. Key Features: Written based on hands-on experience of contributors from multidisciplinary EHR research projects, which include methods and approaches from statistics, computing, informatics, data science and clinical/epidemiological domains. Documents the detailed experience on EHR data extraction, cleaning and preparation Provides a broad view of statistical approaches and machine learning prediction models to deal with the challenges and limitations of EHR data. Considers the complete cycle of EHR data analysis. The use of EHR/EMR analysis requires close collaborations between statisticians, informaticians, data scientists and clinical/epidemiological investigators. This book reflects that multidisciplinary perspective.

With the critical role of statistics in the design, conduct, analysis and reporting of clinical trials or observational studies intended for regulatory purposes, numerous guidelines have been issued by regulatory authorities around the world focusing on statistical issues related to drug development. However, the available literature on this important topic is sporadic, and often not readily accessible to drug developers or regulatory personnel. This book provides a systematic exposition of the interplay between the two disciplines, including emerging themes pertaining to the acceleration of the development of pharmaceutical medicines to serve patients with unmet needs. Features: Regulatory and statistical interactions throughout the drug development continuum The critical role of the statistician in relation to the changing regulatory and healthcare landscapes Statistical issues that commonly arise in the course of drug development and regulatory interactions Trending topics in drug development, with emphasis on current regulatory thinking and the associated challenges and opportunities The book is designed to be accessible to readers with an intermediate knowledge of statistics, and can be a useful resource to statisticians, medical researchers, and regulatory personnel in drug development, as well as graduate students in the health sciences. The authors' decades of experience in the pharmaceutical industry and academia, and extensive regulatory experience, comes through in the many examples throughout the book.

Provides a thorough coverage and comparison of a wide array of time series models and methods: Exponential Smoothing, Holt Winters, ARMA and ARIMA, deep learning models including RNNs, LSTMs, GRUs, and ensemble models composed of combinations of these models. Introduces the factor table representation of ARMA and ARIMA models. This representation is not available in any other book at this level and is extremely useful in both practice and pedagogy. Uses real world examples that can be readily found via web links from sources such as the US Bureau of Statistics, Department of Transportation and the World Bank. There is an accompanying R package that is easy to use and requires little or no previous R experience. The package implements the wide variety of models and methods presented in the book and has tremendous pedagogical use.

One of the most popular introductory texts in its field, Statistics for Technology: A Course in Applied Studies presents the range of statistical methods commonly used in science, social science, and engineering.
The mathematics are simple and straightforward; statistical concepts are explained carefully; and real-life (rather than contrived) examples are used throughout the chapters.
Divided into three parts, the Introduction describes some simple methods of summarizing data. Theory examines the basic concepts and theory of statistics. Applications covers the planning and procedures of experiments, quality control, and life testing.
Revised throughout, this Third Edition places a higher priority on the role of computers in analysis, and many new references have been incorporated. A new appendix describes general methods of tackling statistical problems, including guidance on literature searching and report writing.

Despite major advances in healthcare over the past century, the successful treatment of cancer has remained a significant challenge, and cancers are the second leading cause of death worldwide behind cardiovascular disease. Early detection and survival are important issues to control cancer. The development of quantitative methods and computer technology has facilitated the formation of new models in medical and biological sciences. The application of mathematical modelling in solving many real-world problems in medicine and biology has yielded fruitful results. In spite of advancements in instrumentations technology and biomedical equipment, it is not always possible to perform experiments in medicine and biology for various reasons. Thus, mathematical modelling and simulation are viewed as viable alternatives in such situations, and are discussed in this book. The conventional diagnostic techniques of cancer are not always effective as they rely on the physical and morphological appearance of the tumour. Early stage prediction and diagnosis is very difficult with conventional techniques. It is well known that cancers are involved in genome level changes. As of now, the prognosis of various types of cancer depends upon findings related to the data generated through different experiments. Several machine learning techniques exist in analysing the data of expressed genes; however, the recent results related with deep learning algorithms are more accurate and accommodative, as they are effective in selecting and classifying informative genes. This book explores the probabilistic computational deep learning model for cancer classification and prediction.

This book takes a deep dive into several key linear algebra subjects as they apply to data analytics and data mining. The book offers a case study approach where each case will be grounded in a real-world application. This text is meant to be used for a second course in applications of Linear Algebra to Data Analytics, with a supplemental chapter on Decision Trees and their applications in regression analysis. The text can be considered in two different but overlapping general data analytics categories, clustering and interpolation. Knowledge of mathematical techniques related to data analytics, and exposure to interpretation of results within a data analytics context, are particularly valuable for students studying undergraduate mathematics. Each chapter of this text takes the reader through several relevant and case studies using real world data. All data sets, as well as Python and R syntax are provided to the reader through links to Github documentation. Following each chapter is a short exercise set in which students are encouraged to use technology to apply their expanding knowledge of linear algebra as it is applied to data analytics. A basic knowledge of the concepts in a first Linear Algebra course are assumed; however, an overview of key concepts are presented in the Introduction and as needed throughout the text.