This "hands-on" book is for people who are interested in immediately putting Maple to work. The reader is provided with a compact, fast and surveyable guide that introduces them to the extensive capabilities of the software. The book is sufficient for standard use of Maple and will provide techniques for extending Maple for more specialized work. The author discusses the reliability of results systematically and presents ways of testing questionable results. The book allows a reader to become a user almost immediately and helps him/her to grow gradually to a broader and more proficient use. As a consequence, some subjects are dealt with in an introductory way early in the book, with references to a more detailed discussion later on.

This book discusses quantum theory as the theory of random (Brownian) motion of small particles (electrons etc.) under external forces. Implying that the Schroedinger equation is a complex-valued evolution equation and the Schroedinger function is a complex-valued evolution function, important applications are given. Readers will learn about new mathematical methods (theory of stochastic processes) in solving problems of quantum phenomena. Readers will also learn how to handle stochastic processes in analyzing physical phenomena.

This book presents theoretical modeling and numerical simulations applied to drive several applications towards Industrial Revolution 4.0 (IR 4.0). The topics discussed range from theoretical parts to extensive simulations involving many efficient algorithms as well as various statistical techniques. This book is suitable for postgraduate students, researchers as well as other scientists who are working in mathematics, statistics and numerical modeling and simulation.

This book offers a systematic and rigorous treatment of continuous-time Markov decision processes, covering both theory and possible applications to queueing systems, epidemiology, finance, and other fields. Unlike most books on the subject, much attention is paid to problems with functional constraints and the realizability of strategies. Three major methods of investigations are presented, based on dynamic programming, linear programming, and reduction to discrete-time problems. Although the main focus is on models with total (discounted or undiscounted) cost criteria, models with average cost criteria and with impulsive controls are also discussed in depth. The book is self-contained. A separate chapter is devoted to Markov pure jump processes and the appendices collect the requisite background on real analysis and applied probability. All the statements in the main text are proved in detail. Researchers and graduate students in applied probability, operational research, statistics and engineering will find this monograph interesting, useful and valuable.

This book chronicles a 10-year introduction of blended learning into the delivery at a leading technological university, with a longstanding tradition of technology-enabled teaching and learning, and state-of-the-art infrastructure. Hence, both teachers and students were familiar with the idea of online courses. Despite this, the longitudinal experiment did not proceed as expected. Though few technical problems, it required behavioural changes from teachers and learners, thus unearthing a host of socio-technical issues, challenges, and conundrums. With the undercurrent of design ideals such as "tech for good", any industrial sector must examine whether digital platforms are credible substitutes or at best complementary. In this era of Industry 4.0, higher education, like any other industry, should not be about the creative destruction of what we value in universities, but their digital transformation. The book concludes with an agenda for large, repeatable Randomised Controlled Trials (RCTs) to validate digital platforms that could fulfil the aspirations of the key stakeholder groups - students, faculty, and regulators as well as delving into the role of Massive Open Online Courses (MOOCs) as surrogates for "fees-free" higher education and whether the design of such a HiEd 4.0 platform is even a credible proposition. Specifically, the book examines the data-driven evidence within a design-based research methodology to present outcomes of two alternative instructional designs evaluated - traditional lecturing and blended learning. Based on the research findings and statistical analysis, it concludes that the inexorable shift to online delivery of education must be guided by informed educational management and innovation.

Inverse problems such as imaging or parameter identification deal with the recovery of unknown quantities from indirect observations, connected via a model describing the underlying context. While traditionally inverse problems are formulated and investigated in a static setting, we observe a significant increase of interest in time-dependence in a growing number of important applications over the last few years. Here, time-dependence affects a) the unknown function to be recovered and / or b) the observed data and / or c) the underlying process. Challenging applications in the field of imaging and parameter identification are techniques such as photoacoustic tomography, elastography, dynamic computerized or emission tomography, dynamic magnetic resonance imaging, super-resolution in image sequences and videos, health monitoring of elastic structures, optical flow problems or magnetic particle imaging to name only a few. Such problems demand for innovation concerning their mathematical description and analysis as well as computational approaches for their solution.

This book provides a concise point of reference for the most commonly used regression methods. It begins with linear and nonlinear regression for normally distributed data, logistic regression for binomially distributed data, and Poisson regression and negative-binomial regression for count data. It then progresses to these regression models that work with longitudinal and multi-level data structures. The volume is designed to guide the transition from classical to more advanced regression modeling, as well as to contribute to the rapid development of statistics and data science. With data and computing programs available to facilitate readers' learning experience, Statistical Regression Modeling promotes the applications of R in linear, nonlinear, longitudinal and multi-level regression. All included datasets, as well as the associated R program in packages nlme and lme4 for multi-level regression, are detailed in Appendix A. This book will be valuable in graduate courses on applied regression, as well as for practitioners and researchers in the fields of data science, statistical analytics, public health, and related fields.

This book provides an accessible introduction and practical guidelines to apply asymmetric multidimensional scaling, cluster analysis, and related methods to asymmetric one-mode two-way and three-way asymmetric data. A major objective of this book is to present to applied researchers a set of methods and algorithms for graphical representation and clustering of asymmetric relationships. Data frequently concern measurements of asymmetric relationships between pairs of objects from a given set (e.g., subjects, variables, attributes,...), collected in one or more matrices. Examples abound in many different fields such as psychology, sociology, marketing research, and linguistics and more recently several applications have appeared in technological areas including cybernetics, air traffic control, robotics, and network analysis. The capabilities of the presented algorithms are illustrated by carefully chosen examples and supported by extensive data analyses. A review of the specialized statistical software available for the applications is also provided. This monograph is highly recommended to readers who need a complete and up-to-date reference on methods for asymmetric proximity data analysis.

The nonequilibrium behavior of nanoscopic and biological systems, which are typically strongly fluctuating, is a major focus of current research. Lately, much progress has been made in understanding such systems from a thermodynamic perspective. However, new theoretical challenges emerge when the fluctuating system is additionally subject to time delay, e.g. due to the presence of feedback loops. This thesis advances this young and vibrant research field in several directions. The first main contribution concerns the probabilistic description of time-delayed systems; e.g. by introducing a versatile approximation scheme for nonlinear delay systems. Second, it reveals that delay can induce intriguing thermodynamic properties such as anomalous (reversed) heat flow. More generally, the thesis shows how to treat the thermodynamics of non-Markovian systems by introducing auxiliary variables. It turns out that delayed feedback is inextricably linked to nonreciprocal coupling, information flow, and to net energy input on the fluctuating level.

This book provides a reference for people working in the design, development, and manufacturing of medical devices. ​While there are no statistical methods specifically intended for medical devices, there are methods that are commonly applied to various problems in the design, manufacturing, and quality control of medical devices. The aim of this book is not to turn everyone working in the medical device industries into mathematical statisticians; rather, the goal is to provide some help in thinking statistically, and knowing where to go to answer some fundamental questions, such as justifying a method used to qualify/validate equipment, or what information is necessary to support the choice of sample sizes. While, there are no statistical methods specifically designed for analysis of medical device data, there are some methods that seem to appear regularly in relation to medical devices. For example, the assessment of receiver operating characteristic curves is fundamental to development of diagnostic tests, and accelerated life testing is often critical for assessing the shelf life of medical device products. Another example is sensitivity/specificity computations are necessary for in-vitro diagnostics, and Taguchi methods can be very useful for designing devices. Even notions of equivalence and noninferiority have different interpretations in the medical device field compared to pharmacokinetics. It contains topics such as dynamic modeling, machine learning methods, equivalence testing, and experimental design, for example. This book is for those with no statistical experience, as well as those with statistical knowledgeable—with the hope to provide some insight into what methods are likely to help provide rationale for choices relating to data gathering and analysis activities for medical devices.

This book introduces readers to various signal processing models that have been used in analyzing periodic data, and discusses the statistical and computational methods involved. Signal processing can broadly be considered to be the recovery of information from physical observations. The received signals are usually disturbed by thermal, electrical, atmospheric or intentional interferences, and due to their random nature, statistical techniques play an important role in their analysis. Statistics is also used in the formulation of appropriate models to describe the behavior of systems, the development of appropriate techniques for estimation of model parameters and the assessment of the model performances. Analyzing different real-world data sets to illustrate how different models can be used in practice, and highlighting open problems for future research, the book is a valuable resource for senior undergraduate and graduate students specializing in mathematics or statistics.

This book shows how information theory, probability, statistics, mathematics and personal computers can be applied to the exploration of numbers and proportions in music. It brings the methods of scientific and quantitative thinking to questions like: What are the ways of encoding a message in music and how can we be sure of the correct decoding? How do claims of names hidden in the notes of a score stand up to scientific analysis? How many ways are there of obtaining proportions and are they due to chance? After thoroughly exploring the ways of encoding information in music, the ambiguities of numerical alphabets and the words to be found "hidden" in a score, the book presents a novel way of exploring the proportions in a composition with a purpose-built computer program and gives example results from the application of the techniques. These include information theory, combinatorics, probability, hypothesis testing, Monte Carlo simulation and Bayesian networks, presented in an easily understandable form including their development from ancient history through the life and times of J. S. Bach, making connections between science, philosophy, art, architecture, particle physics, calculating machines and artificial intelligence. For the practitioner the book points out the pitfalls of various psychological fallacies and biases and includes succinct points of guidance for anyone involved in this type of research. This book will be useful to anyone who intends to use a scientific approach to the humanities, particularly music, and will appeal to anyone who is interested in the intersection between the arts and science.With a foreword by Ruth Tatlow (Uppsala University), award winning author of Bach's Numbers: Compositional Proportion and Significance and Bach and the Riddle of the Number Alphabet."With this study Alan Shepherd opens a much-needed examination of the wide range of mathematical claims that have been made about J. S. Bach's music, offering both tools and methodological cautions with the potential to help clarify old problems." Daniel R. Melamed, Professor of Music in Musicology, Indiana University

An Introduction to Stata for Health Researchers, Fifth Edition updates this classic book that has become a standard reference for health researchers. As with previous editions, readers will learn to work effectively in Stata to perform data management, compute descriptive statistics, create meaningful graphs, fit regression models, and perform survival analysis. The fifth edition adds examples of performing power, precision, and sample-size analysis; working with Unicode characters; managing data with ICD-9 and ICD-10 codes; and creating customized tables. With many worked examples and downloadable datasets, this text is the ideal resource for hands-on learning, whether for students in a statistics course or for researchers in fields such as epidemiology, biostatistics, and public health who are learning to use Stata's tools for health research.

This thesis presents a revolutionary technique for modelling the dynamics of a quantum system that is strongly coupled to its immediate environment. This is a challenging but timely problem. In particular it is relevant for modelling decoherence in devices such as quantum information processors, and how quantum information moves between spatially separated parts of a quantum system. The key feature of this work is a novel way to represent the dynamics of general open quantum systems as tensor networks, a result which has connections with the Feynman operator calculus and process tensor approaches to quantum mechanics. The tensor network methodology developed here has proven to be extremely powerful: For many situations it may be the most efficient way of calculating open quantum dynamics. This work is abounds with new ideas and invention, and is likely to have a very significant impact on future generations of physicists.

This book gathers a selection of invited and contributed lectures from the European Conference on Numerical Mathematics and Advanced Applications (ENUMATH) held in Lausanne, Switzerland, August 26-30, 2013. It provides an overview of recent developments in numerical analysis, computational mathematics and applications from leading experts in the field. New results on finite element methods, multiscale methods, numerical linear algebra and discretization techniques for fluid mechanics and optics are presented. As such, the book offers a valuable resource for a wide range of readers looking for a state-of-the-art overview of advanced techniques, algorithms and results in numerical mathematics and scientific computing.

A Tour of Data Science: Learn R and Python in Parallel covers the fundamentals of data science, including programming, statistics, optimization, and machine learning in a single short book. It does not cover everything, but rather, teaches the key concepts and topics in Data Science. It also covers two of the most popular programming languages used in Data Science, R and Python, in one source. Key features: Allows you to learn R and Python in parallel Cover statistics, programming, optimization and predictive modelling, and the popular data manipulation tools - data.table and pandas Provides a concise and accessible presentation Includes machine learning algorithms implemented from scratch, linear regression, lasso, ridge, logistic regression, gradient boosting trees, etc. Appealing to data scientists, statisticians, quantitative analysts, and others who want to learn programming with R and Python from a data science perspective.

The book "Analysis and Design of Control Systems using MATLAB", is designed as a supplement to an introductory course in feedback control systems for undergraduate or graduate engineering students of all disciplines. Feedback control systems engineering is a multidisciplinary subject and presents a control engineering methodology based on mathematical fundamentals and stresses physical system modeling.This book includes the coverage of classical methods of control systems engineering: introduction to control systems, matrix analysis, Laplace transforms, mathematical modeling of dynamic systems, control system representation, performance and stability of feedback systems, analysis and design of feedback control systems, state space analysis and design, and MATLAB basics and MATLAB tutorial. The numerous worked examples offer detailed explanations, and guide the students through each set of problems to enable them to save a great deal of time and effort in arriving at an understanding of problems in this subject. Extensive references to guide the students to further sources of information on control systems and MATLAB is provided. In addition to students, practising engineers will also find this book immensely useful.

This book highlights recent advances in natural computing, including biology and its theory, bio-inspired computing, computational aesthetics, computational models and theories, computing with natural media, philosophy of natural computing and educational technology. It presents extended versions of the best papers selected from the symposium "7th International Workshop on Natural Computing" (IWNC7), held in Tokyo, Japan, in 2013. The target audience is not limited to researchers working in natural computing but also those active in biological engineering, fine/media art design, aesthetics and philosophy.

For courses on SPSS. SPSS is, essentially, a visually-driven program, but most texts rely primarily on a verbal approach to describe its use. A Visual Approach to SPSS for Windows is the first text of its kind to employ what the author refers to as "visual sequencing" to teach students how to use SPSS.

This book covers all the topics found in introductory descriptive statistics courses, including simple linear regression and time series analysis, the fundamentals of inferential statistics (probability theory, random sampling and estimation theory), and inferential statistics itself (confidence intervals, testing). Each chapter starts with the necessary theoretical background, which is followed by a variety of examples. The core examples are based on the content of the respective chapter, while the advanced examples, designed to deepen students' knowledge, also draw on information and material from previous chapters. The enhanced online version helps students grasp the complexity and the practical relevance of statistical analysis through interactive examples and is suitable for undergraduate and graduate students taking their first statistics courses, as well as for undergraduate students in non-mathematical fields, e.g. economics, the social sciences etc.

Understanding Regression Analysis unifies diverse regression applications including the classical model, ANOVA models, generalized models including Poisson, Negative binomial, logistic, and survival, neural networks, and decision trees under a common umbrella -- namely, the conditional distribution model. It explains why the conditional distribution model is the correct model, and it also explains (proves) why the assumptions of the classical regression model are wrong. Unlike other regression books, this one from the outset takes a realistic approach that all models are just approximations. Hence, the emphasis is to model Nature's processes realistically, rather than to assume (incorrectly) that Nature works in particular, constrained ways. Key features of the book include: Numerous worked examples using the R software Key points and self-study questions displayed "just-in-time" within chapters Simple mathematical explanations ("baby proofs") of key concepts Clear explanations and applications of statistical significance (p-values), incorporating the American Statistical Association guidelines Use of "data-generating process" terminology rather than "population" Random-X framework is assumed throughout (the fixed-X case is presented as a special case of the random-X case) Clear explanations of probabilistic modelling, including likelihood-based methods Use of simulations throughout to explain concepts and to perform data analyses This book has a strong orientation towards science in general, as well as chapter-review and self-study questions, so it can be used as a textbook for research-oriented students in the social, biological and medical, and physical and engineering sciences. As well, its mathematical emphasis makes it ideal for a text in mathematics and statistics courses. With its numerous worked examples, it is also ideally suited to be a reference book for all scientists.

A MATLAB (R) Primer for Technical Programming for Materials Science and Engineering draws on examples from the field, providing the latest information on this programming tool that is targeted towards materials science. The book enables non-programmers to master MATLAB (R) in order to solve problems in materials science, assuming only a modest mathematical background. In addition, the book introduces programming and technical concepts in a logical manner to help students use MATLAB (R) for subsequent projects. This title offers materials scientists who are non-programming specialists with a coherent and focused introduction to MATLAB (R).

Bayes Factors for Forensic Decision Analyses with R provides a self-contained introduction to computational Bayesian statistics using R. With its primary focus on Bayes factors supported by data sets, this book features an operational perspective, practical relevance, and applicability-keeping theoretical and philosophical justifications limited. It offers a balanced approach to three naturally interrelated topics: Probabilistic Inference - Relies on the core concept of Bayesian inferential statistics, to help practicing forensic scientists in the logical and balanced evaluation of the weight of evidence. Decision Making - Features how Bayes factors are interpreted in practical applications to help address questions of decision analysis involving the use of forensic science in the law. Operational Relevance - Combines inference and decision, backed up with practical examples and complete sample code in R, including sensitivity analyses and discussion on how to interpret results in context. Over the past decades, probabilistic methods have established a firm position as a reference approach for the management of uncertainty in virtually all areas of science, including forensic science, with Bayes' theorem providing the fundamental logical tenet for assessing how new information-scientific evidence-ought to be weighed. Central to this approach is the Bayes factor, which clarifies the evidential meaning of new information, by providing a measure of the change in the odds in favor of a proposition of interest, when going from the prior to the posterior distribution. Bayes factors should guide the scientist's thinking about the value of scientific evidence and form the basis of logical and balanced reporting practices, thus representing essential foundations for rational decision making under uncertainty. This book would be relevant to students, practitioners, and applied statisticians interested in inference and decision analyses in the critical field of forensic science. It could be used to support practical courses on Bayesian statistics and decision theory at both undergraduate and graduate levels, and will be of equal interest to forensic scientists and practitioners of Bayesian statistics for driving their evaluations and the use of R for their purposes. This book is Open Access.