In this monograph some stability properties of linear, time-variant, discrete-time systems are summarized, where some properties are well known, some are little-known facts, and a few may be new. Models for this treatise an the asymp- totical behaviour of solutions of difference equations are the commonly known excellent books of CESARI [3] and CONTI [5]. In the tables of Chapter 1 the definitions and the essen- tial statements an stability of discrete-time systems are summarized, such that Chapter 2 to 5 may be regarded as explaining appendices for these tables. I am grateful to Paul Ludyk, who typed and corrected the manuscript with great skill and patience, and Alois Ludyk, who drew the figures with great artistic skill. Gunter Ludyk Bremen, January 1985 Contents Notations 1 1. Introduction and Summary 4 2. Mathematical Description of Discrete-Time Systems 16 2. 1 State Equations 16 2. 2 Properties of the Transition Matrix 19 2. 3 LAGRANGE-Identity and GREEN's Formula for Difference Equations 20 2. 4 Estimations for the Norm of the Transition Matrix 21 3. Stability of Free Discrete-Time Systems 34 3. 1 LJAPUNOW- and LAGRANGE-Stability 34 3. 2 Short Time Boundedness 40 3. 3 UniformStability 45 3. 4 Asymptotic Stability 63 3. 5 P-stability 70 3. 6 Exponential and Uniform Asymptotic Stability 75 3. 7 Relations between the Stability Glasses 84 4. Stability of Forced Discrete-Time Systems 86 4. 1 Preliminary Results 86 4. 2 Input-State Stability 93 4.

R Markdown: The Definitive Guide is the first official book authored by the core R Markdown developers that provides a comprehensive and accurate reference to the R Markdown ecosystem. With R Markdown, you can easily create reproducible data analysis reports, presentations, dashboards, interactive applications, books, dissertations, websites, and journal articles, while enjoying the simplicity of Markdown and the great power of R and other languages. In this book, you will learn Basics: Syntax of Markdown and R code chunks, how to generate figures and tables, and how to use other computing languages Built-in output formats of R Markdown: PDF/HTML/Word/RTF/Markdown documents and ioslides/Slidy/Beamer/PowerPoint presentations Extensions and applications: Dashboards, Tufte handouts, xaringan/reveal.js presentations, websites, books, journal articles, and interactive tutorials Advanced topics: Parameterized reports, HTML widgets, document templates, custom output formats, and Shiny documents. Yihui Xie is a software engineer at RStudio. He has authored and co-authored several R packages, including knitr, rmarkdown, bookdown, blogdown, shiny, xaringan, and animation. He has published three other books, Dynamic Documents with R and knitr, bookdown: Authoring Books and Technical Documents with R Markdown, and blogdown: Creating Websites with R Markdown. J.J. Allaire is the founder of RStudio and the creator of the RStudio IDE. He is an author of several packages in the R Markdown ecosystem including rmarkdown, flexdashboard, learnr, and radix. Garrett Grolemund is the co-author of R for Data Science and author of Hands-On Programming with R. He wrote the lubridate R package and works for RStudio as an advocate who trains engineers to do data science with R and the Tidyverse.

This third edition of Paul Murrell's classic book on using R for graphics represents a major update, with a complete overhaul in focus and scope. It focuses primarily on the two core graphics packages in R - graphics and grid - and has a new section on integrating graphics. This section includes three new chapters: importing external images in to R; integrating the graphics and grid systems; and advanced SVG graphics. The emphasis in this third edition is on having the ability to produce detailed and customised graphics in a wide variety of formats, on being able to share and reuse those graphics, and on being able to integrate graphics from multiple systems. This book is aimed at all levels of R users. For people who are new to R, this book provides an overview of the graphics facilities, which is useful for understanding what to expect from R's graphics functions and how to modify or add to the output they produce. For intermediate-level R users, this book provides all of the information necessary to perform sophisticated customizations of plots produced in R. For advanced R users, this book contains vital information for producing coherent, reusable, and extensible graphics functions.

This textbook presents an introduction to generalized linear models, complete with real-world data sets and practice problems, making it applicable for both beginning and advanced students of applied statistics. Generalized linear models (GLMs) are powerful tools in applied statistics that extend the ideas of multiple linear regression and analysis of variance to include response variables that are not normally distributed. As such, GLMs can model a wide variety of data types including counts, proportions, and binary outcomes or positive quantities. The book is designed with the student in mind, making it suitable for self-study or a structured course. Beginning with an introduction to linear regression, the book also devotes time to advanced topics not typically included in introductory textbooks. It features chapter introductions and summaries, clear examples, and many practice problems, all carefully designed to balance theory and practice. The text also provides a working knowledge of applied statistical practice through the extensive use of R, which is integrated into the text. Other features include: * Advanced topics such as power variance functions, saddlepoint approximations, likelihood score tests, modified profile likelihood, small-dispersion asymptotics, and randomized quantile residuals * Nearly 100 data sets in the companion R package GLMsData * Examples that are cross-referenced to the companion data set, allowing readers to load the data and follow the analysis in their own R session

Complex systems that bridge the traditional disciplines of physics, chemistry, biology, and materials science can be studied at an unprecedented level of detail using increasingly sophisticated theoretical methodology and high-speed computers. The aim of this book is to prepare burgeoning users and developers to become active participants in this exciting and rapidly advancing research area by uniting for the first time, in one monograph, the basic concepts of equilibrium and time-dependent statistical mechanics with the modern techniques used to solve the complex problems that arise in real-world applications. The book contains a detailed review of classical and quantum mechanics, in-depth discussions of the most commonly used ensembles simultaneously with modern computational techniques such as molecular dynamics and Monte Carlo, and important topics including free-energy calculations, linear-response theory, harmonic baths and the generalized Langevin equation, critical phenomena, and advanced conformational sampling methods. Burgeoning users and developers are thus provided firm grounding to become active participants in this exciting and rapidly advancing research area, while experienced practitioners will find the book to be a useful reference tool for the field.

Praise for the First Edition "The main strength of this book is that it provides a unified framework of graphical tools for data analysis, especially for univariate and low-dimensional multivariate data. In addition, it is clearly written in plain language and the inclusion of R code is particularly useful to assist readers' understanding of the graphical techniques discussed in the book. ... It not only summarises graphical techniques, but it also serves as a practical reference for researchers and graduate students with an interest in data display." -Han Lin Shang, Journal of Applied Statistics Graphics for Statistics and Data Analysis with R, Second Edition, presents the basic principles of graphical design and applies these principles to engaging examples using the graphics and lattice packages in R. It offers a wide array of modern graphical displays for data visualization and representation. Added in the second edition are coverage of the ggplot2 graphics package, material on human visualization and color rendering in R, on screen, and in print. Features Emphasizes the fundamentals of statistical graphics and best practice guidelines for producing and choosing among graphical displays in R Presents technical details on topics such as: the estimation of quantiles, nonparametric and parametric density estimation; diagnostic plots for the simple linear regression model; polynomial regression, splines, and locally weighted polynomial regression for producing a smooth curve; Trellis graphics for multivariate data Provides downloadable R code and data for figures at www.graphicsforstatistics.com Kevin J. Keen is a Professor of Mathematics and Statistics at the University of Northern British Columbia (Prince George, Canada) and an Accredited Professional StatisticianTM by the Statistical Society of Canada and the American Statistical Association.

Pour Ie cinquieme congres de la serie, COMPSTAT 82 reunit environ 500 participants d'origines scientifiques et geographiques tres variees, prouvant a l'evidence l'interet persis tant de la communaute scientifique pour tous les problemes de calculs statistiques. Le Comite de Programme charge de l'organisation scientifique du Congres etait com pose de: o S. Apelt (Republique democratique d'Allemagne) - A. Bj6rck (Suede) - H. Caussinus (France), President - Y. Escoufier (France) - A. de Falguerolles (France), Secretaire - J. W. Frane (U. S. A. ) - J. Gordesch (Republique Federale d'Allemagne) - Th. Havranek (Tchechoslovaquie) - N. Lauro (Italie) - C. Millier (France) - R. J. Mokken (pays-Bas)- R. Tomassone (France) - D. Wishart (Royaume Uni) Ce Comite a decide d'augmenter Ie nombre des conferenciers invites, cherchant de la sorte une representation des diverses ecoles ainsi que l'introduction de nouveaux themes. La tache la plus difficile a ensuite ete de selectionner une soixantaine de contributions parmi 250 soumissions. La encore Ie Comite de Programme s'est efforce de favoriser des voies qui semblaient les plus nouvelles et a essaye de maintenir une bonne repartition scientifique et geographique. Cependant, comme dans les precedents congres COMPSTAT, il a donne la preference aux propositions clairement marquees simultanement du double aspect Statistique et Calcul. Dans bien des cas, ces deux aspects sont tres lies rendant en particulier difficile et peu pertinente toute classification fine des contributions."

Data science unifies statistics, data analysis and machine learning to achieve a better understanding of the masses of data which are produced today, and to improve prediction. Special kinds of data (symbolic, network, complex, compositional) are increasingly frequent in data science. These data require specific methodologies, but there is a lack of reference work in this field. Advances in Data Science fills this gap. It presents a collection of up-to-date contributions by eminent scholars following two international workshops held in Beijing and Paris. The 10 chapters are organized into four parts: Symbolic Data, Complex Data, Network Data and Clustering. They include fundamental contributions, as well as applications to several domains, including business and the social sciences.

This book introduces econometric analysis of cross section, time series and panel data with the application of statistical software. It serves as a basic text for those who wish to learn and apply econometric analysis in empirical research. The level of presentation is as simple as possible to make it useful for undergraduates as well as graduate students. It contains several examples with real data and Stata programmes and interpretation of the results. While discussing the statistical tools needed to understand empirical economic research, the book attempts to provide a balance between theory and applied research. Various concepts and techniques of econometric analysis are supported by carefully developed examples with the use of statistical software package, Stata 15.1, and assumes that the reader is somewhat familiar with the Strata software. The topics covered in this book are divided into four parts. Part I discusses introductory econometric methods for data analysis that economists and other social scientists use to estimate the economic and social relationships, and to test hypotheses about them, using real-world data. There are five chapters in this part covering the data management issues, details of linear regression models, the related problems due to violation of the classical assumptions. Part II discusses some advanced topics used frequently in empirical research with cross section data. In its three chapters, this part includes some specific problems of regression analysis. Part III deals with time series econometric analysis. It covers intensively both the univariate and multivariate time series econometric models and their applications with software programming in six chapters. Part IV takes care of panel data analysis in four chapters. Different aspects of fixed effects and random effects are discussed here. Panel data analysis has been extended by taking dynamic panel data models which are most suitable for macroeconomic research. The book is invaluable for students and researchers of social sciences, business, management, operations research, engineering, and applied mathematics.

Highlighting the new aspects of MATLAB (R) 7.10 and expanding on many existing features, MATLAB (R) Primer, Eighth Edition shows you how to solve problems in science, engineering, and mathematics. Now in its eighth edition, this popular primer continues to offer a hands-on, step-by-step introduction to using the powerful tools of MATLAB. New to the Eighth Edition A new chapter on object-oriented programming Discussion of the MATLAB File Exchange window, which provides direct access to over 10,000 submissions by MATLAB users Major changes to the MATLAB Editor, such as code folding and the integration of the Code Analyzer (M-Lint) into the Editor Explanation of more powerful Help tools, such as quick help popups for functions via the Function Browser The new bsxfun function A synopsis of each of the MATLAB Top 500 most frequently used functions, operators, and special characters The addition of several useful features, including sets, logical indexing, isequal, repmat, reshape, varargin, and varargout The book takes you through a series of simple examples that become progressively more complex. Starting with the core components of the MATLAB desktop, it demonstrates how to handle basic matrix operations and expressions in MATLAB. The text then introduces commonly used functions and explains how to write your own functions, before covering advanced features, such as object-oriented programming, calling other languages from MATLAB, and MATLAB graphics. It also presents an in-depth look at the Symbolic Toolbox, which solves problems analytically rather than numerically.

Incorporating new topics and original material, Introduction to Finite and Spectral Element Methods Using MATLAB (R), Second Edition enables readers to quickly understand the theoretical foundation and practical implementation of the finite element method and its companion spectral element method. Readers gain hands-on computational experience by using the free online FSELIB library of MATLAB (R) functions and codes. With the book as a user guide, readers can immediately run the codes and graphically display solutions to a variety of elementary and advanced problems. New to the Second Edition Two new chapters with updated material Updated detailed proofs and original derivations New schematic illustrations and graphs Additional solved problems Updated MATLAB software, including improved and new computer functions as well as complete finite element codes incorporating domain discretization modules in three dimensions Suitable for self-study or as a textbook in various science and engineering courses, this self-contained book introduces the fundamentals on a need-to-know basis and emphasizes the development of algorithms and the computer implementation of essential procedures. The text first explains basic concepts and develops the algorithms before addressing problems in solid mechanics, fluid mechanics, and structural mechanics.

This book discusses advanced topics such as R core programing, object oriented R programing, parallel computing with R, and spatial data types. The author leads readers to merge mature and effective methdologies in traditional programing to R programing. It shows how to interface R with C, Java, and other popular programing laguages and platforms.

SPSS is the international standard software package for data analysis in the social sciences. This book is the only SPSS guide designed specifically for students in the fields of sport, exercise and kinesiology. It Includes sport specific cases and data throughout.

"This book is remarkable in its accessible treatment of interaction effects. Although this concept can be challenging for students (even those with some background in statistics), this book presents the material in a very accessible manner, with plenty of examples to help the reader understand how to interpret their results." -Nicole Kalaf-Hughes, Bowling Green State University Offering a clear set of workable examples with data and explanations, Interaction Effects in Linear and Generalized Linear Models is a comprehensive and accessible text that provides a unified approach to interpreting interaction effects. The book develops the statistical basis for the general principles of interpretive tools and applies them to a variety of examples, introduces the ICALC Toolkit for Stata, and offers a series of start-to-finish application examples to show students how to interpret interaction effects for a variety of different techniques of analysis, beginning with OLS regression. The author's website provides a downloadable toolkit of Stata (R) routines to produce the calculations, tables, and graphics for each interpretive tool discussed. Also available are the Stata (R) dataset files to run the examples in the book.

To date, statistics has tended to be neatly divided into two theoretical approaches or frameworks: frequentist (or classical) and Bayesian. Scientists typically choose the statistical framework to analyse their data depending on the nature and complexity of the problem, and based on their personal views and prior training on probability and uncertainty. Although textbooks and courses should reflect and anticipate this dual reality, they rarely do so. This accessible textbook explains, discusses, and applies both the frequentist and Bayesian theoretical frameworks to fit the different types of statistical models that allow an analysis of the types of data most commonly gathered by life scientists. It presents the material in an informal, approachable, and progressive manner suitable for readers with only a basic knowledge of calculus and statistics. Statistical Modeling with R is aimed at senior undergraduate and graduate students, professional researchers, and practitioners throughout the life sciences, seeking to strengthen their understanding of quantitative methods and to apply them successfully to real world scenarios, whether in the fields of ecology, evolution, environmental studies, or computational biology.

This book is intended for someone learning functions of a complex variable and who enjoys using MATLAB. It will enhance the exprience of learning complex variable theory and will strengthen the knowledge of someone already trained in ths branch of advanced calculus. ABET, the accrediting board for engineering programs, makes it clear that engineering graduates must be skilled in the art of programming in a language such as MATLAB (R). Supplying students with a bridge between the functions of complex variable theory and MATLAB, this supplemental text enables instructors to easily add a MATLAB component to their complex variables courses. A MATLAB (R) Companion to Complex Variables provides readers with a clear understanding of the utility of MATLAB in complex variable calculus. An ideal adjunct to standard texts on the functions of complex variables, the book allows professors to quickly find and assign MATLAB programming problems that will strengthen students' knowledge of the language and concepts of complex variable theory. The book shows students how MATLAB can be a powerful learning aid in such staples of complex variable theory as conformal mapping, infinite series, contour integration, and Laplace and Fourier transforms. In addition to MATLAB programming problems, the text includes many examples in each chapter along with MATLAB code. Fractals, the most recent interesting topic involving complex variables, demands to be treated with a language such as MATLAB. This book concludes with a Coda, which is devoted entirely to this visually intriguing subject. MATLAB is not without constraints, limitations, irritations, and quirks, and there are subtleties involved in performing the calculus of complex variable theory with this language. Without knowledge of these subtleties, engineers or scientists attempting to use MATLAB for solutions of practical problems in complex variable theory suffer the risk of making major mistakes. This book serves as an early warning system about these pitfalls.

All the Essentials to Start Using Adaptive Designs in No Time Compared to traditional clinical trial designs, adaptive designs often lead to increased success rates in drug development at reduced costs and time. Introductory Adaptive Trial Designs: A Practical Guide with R motivates newcomers to quickly and easily grasp the essence of adaptive designs as well as the foundations of adaptive design methods. The book reduces the mathematics to a minimum and makes the material as practical as possible. Instead of providing general, black-box commercial software packages, the author includes open-source R functions that enable readers to better understand the algorithms and customize the designs to meet their needs. Readers can run the simulations for all the examples and change the input parameters to see how each input parameter affects the simulation outcomes or design operating characteristics. Taking a learning-by-doing approach, this tutorial-style book guides readers on planning and executing various types of adaptive designs. It helps them develop the skills to begin using the designs immediately.

Commissioned by the Statistical Society of Canada (SSC), Statistics in Action: A Canadian Outlook helps both general readers and users of statistics better appreciate the scope and importance of statistics. It presents the ways in which statistics is used while highlighting key contributions that Canadian statisticians are making to science, technology, business, government, and other areas. The book emphasizes the role and impact of computing in statistical modeling and analysis, including the issues involved with the huge amounts of data being generated by automated processes. The first two chapters review the development of statistics as a discipline in Canada and describe some major contributions to survey methodology made by Statistics Canada, one of the world's premier official statistics agencies. The book next discusses how statistical methodologies, such as functional data analysis and the Metropolis algorithm, are applied in a wide variety of fields, including risk management and genetics. It then focuses on the application of statistical methods in medicine and public health as well as finance and e-commerce. The remainder of the book addresses how statistics is used to study critical scientific areas, including difficult-to-access populations, endangered species, climate change, and agricultural forecasts. About the SSCFounded in Montreal in 1972, the SSC is the main professional organization for statisticians and related professionals in Canada. Its mission is to promote the use and development of statistics and probability. The SSC publishes the bilingual quarterly newsletter SSC Liaison and the peer-reviewed scientific journal The Canadian Journal of Statistics. More information can be found at www.ssc.ca.

Review of the First Edition: The authors strive to reduce theory to a minimum, which makes it a self-learning text that is comprehensible for biologists, physicians, etc. who lack an advanced mathematics background. Unlike in many other textbooks, R is not introduced with meaningless toy examples; instead the reader is taken by the hand and shown around some analyses, graphics, and simulations directly relating to meta-analysis... A useful hands-on guide for practitioners who want to familiarize themselves with the fundamentals of meta-analysis and get started without having to plough through theorems and proofs. -Journal of Applied Statistics Statistical Meta-Analysis with R and Stata, Second Edition provides a thorough presentation of statistical meta-analyses (MA) with step-by-step implementations using R/Stata. The authors develop analysis step by step using appropriate R/Stata functions, which enables readers to gain an understanding of meta-analysis methods and R/Stata implementation so that they can use these two popular software packages to analyze their own meta-data. Each chapter gives examples of real studies compiled from the literature. After presenting the data and necessary background for understanding the applications, various methods for analyzing meta-data are introduced. The authors then develop analysis code using the appropriate R/Stata packages and functions. What's New in the Second Edition: Adds Stata programs along with the R programs for meta-analysis Updates all the statistical meta-analyses with R/Stata programs Covers fixed-effects and random-effects MA, meta-regression, MA with rare-event, and MA-IPD vs MA-SS Adds five new chapters on multivariate MA, publication bias, missing data in MA, MA in evaluating diagnostic accuracy, and network MA Suitable as a graduate-level text for a meta-data analysis course, the book is also a valuable reference for practitioners and biostatisticians (even those with little or no experience in using R or Stata) in public health, medical research, governmental agencies, and the pharmaceutical industry.

Sharpening Your Advanced SAS (R) Skills presents sophisticated SAS programming techniques, procedures, and tools, such as Proc SQL, hash tables, and SAS Macro programming, for any industry. Drawing on his more than 20 years' experience of SAS programming in the pharmaceutical industry, the author provides a unique approach that empowers both advanced programmers who need a quick refresher and programmers interested in learning new techniques. The book helps you easily search for key points by summarizing and differentiating the syntax between similar SAS statements and options. Each chapter begins with an overview so you can quickly locate the detailed examples and syntax. The basic syntax, expected data, and descriptions are organized in summary tables to facilitate better memory recall. General rules list common points about similar statements or options. Real-world examples of SAS programs and code statements are line numbered with references, such as SAS papers and websites, for more detailed explanations. The text also includes end-of-chapter questions to reinforce your knowledge of the topics and prepare you for the advanced SAS certification exam. In addition, the author's website offers mindmaps and process flowcharts that connect concepts and relationships.

CUDA is now the dominant language used for programming GPUs, one of the most exciting hardware developments of recent decades. With CUDA, you can use a desktop PC for work that would have previously required a large cluster of PCs or access to a HPC facility. As a result, CUDA is increasingly important in scientific and technical computing across the whole STEM community, from medical physics and financial modelling to big data applications and beyond. This unique book on CUDA draws on the author's passion for and long experience of developing and using computers to acquire and analyse scientific data. The result is an innovative text featuring a much richer set of examples than found in any other comparable book on GPU computing. Much attention has been paid to the C++ coding style, which is compact, elegant and efficient. A code base of examples and supporting material is available online, which readers can build on for their own projects.

Bootstrapping is a conceptually simple statistical technique to increase the quality of estimates, conduct robustness checks and compute standard errors for virtually any statistic. This book provides an intelligible and compact introduction for students, scientists and practitioners. It not only gives a clear explanation of the underlying concepts but also demonstrates the application of bootstrapping using Python and Stata.

Big Data: A Tutorial-Based Approach explores the tools and techniques used to bring about the marriage of structured and unstructured data. It focuses on Hadoop Distributed Storage and MapReduce Processing by implementing (i) Tools and Techniques of Hadoop Eco System, (ii) Hadoop Distributed File System Infrastructure, and (iii) efficient MapReduce processing. The book includes Use Cases and Tutorials to provide an integrated approach that answers the 'What', 'How', and 'Why' of Big Data. Features Identifies the primary drivers of Big Data Walks readers through the theory, methods and technology of Big Data Explains how to handle the 4 V's of Big Data in order to extract value for better business decision making Shows how and why data connectors are critical and necessary for Agile text analytics Includes in-depth tutorials to perform necessary set-ups, installation, configuration and execution of important tasks Explains the command line as well as GUI interface to a powerful data exchange tool between Hadoop and legacy r-dbms databases

The updated guide to the newest graphing calculator from Texas Instruments

The TI-Nspire graphing calculator is popular among high school and college students as a valuable tool for calculus, AP calculus, and college-level algebra courses. Its use is allowed on the major college entrance exams. This book is a nuts-and-bolts guide to working with the TI-Nspire, providing everything you need to get up and running and helping you get the most out of this high-powered math tool.Texas Instruments' TI-Nspire graphing calculator is perfect for high school and college students in advanced algebra and calculus classes as well as students taking the SAT, PSAT, and ACT examsThis fully updated guide covers all enhancements to the TI-Nspire, including the touchpad and the updated software that can be purchased along with the deviceShows how to get maximum value from this versatile math tool

With updated screenshots and examples, "TI-Nspire For Dummies" provides practical, hands-on instruction to help students make the most of this revolutionary graphing calculator.

"Industrial Statistics with MINITAB" demonstrates the use of MINITAB as a tool for performing statistical analysis in an industrial context. This book covers introductory industrial statistics, exploring the most commonly used techniques alongside those that serve to give an overview of more complex issues. A plethora of examples in MINITAB are featured along with case studies for each of the statistical techniques presented.

"Industrial Statistics with MINITAB" Provides comprehensive coverage of user-friendly practical guidance to the essential statistical methods applied in industry.Explores statistical techniques and how they can be used effectively with the help of MINITAB 16.Contains extensive illustrative examples and case studies throughout and assumes no previous statistical knowledge.Emphasises data graphics and visualization, and the most used industrial statistical tools, such as Statistical Process Control and Design of Experiments. Is supported by an accompanying website featuring case studies and the corresponding datasets.

Six Sigma Green Belts and Black Belts will find explanations and examples of the most relevant techniques in DMAIC projects. The book can also be used as quick reference enabling the reader to be confident enough to explore other MINITAB capabilities.