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 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.

MATLAB and Simulink Crash Course for Engineers is a reader-friendly introductory guide to the features, functions, and applications of MATLAB and Simulink. The book provides readers with real-world examples, exercises, and applications, and offers highly illustrated, step-by-step demonstrations of techniques for the modelling and simulation of complex systems. MATLAB coverage includes vectors and matrices, programs and functions, complex numbers, visualization, solving equations, numerical methods, optimization problems, and graphical user interfaces. The Simulink coverage includes commonly used Simulink blocks, control system simulation, electrical circuit analysis, electric power systems, power electronics, and renewable energy technology. This powerful tutorial is a great resource for students, engineers, and other busy technical professionals who need to quickly acquire a solid understanding of MATLAB and Simulink.

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

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.

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 SPSS Survival Manual throws a lifeline to students and researchers grappling with this powerful data analysis software. In her bestselling guide, Julie Pallant takes you through the entire research process, helping you choose the right data analysis technique for your project. This edition has been updated to include up to SPSS version 26. From the formulation of research questions, to the design of the study and analysis of data, to reporting the results, Julie discusses basic and advanced statistical techniques. She outlines each technique clearly, with step-by-step procedures for performing the analysis, a detailed guide to interpreting data output and an example of how to present the results in a report. For both beginners and experienced users in Psychology, Sociology, Health Sciences, Medicine, Education, Business and related disciplines, the SPSS Survival Manual is an essential text. It is illustrated throughout with screen grabs, examples of output and tips, and is also further supported by a website with sample data and guidelines on report writing. This seventh edition is fully revised and updated to accommodate changes to IBM SPSS procedures.

Mathematical Models of Biological Systems provides a practical introduction to basic mathematical modelling methodology and analysis. It covers a variety of biological applications and uses these topics in turn to highlight key components in the art of modelling. Its primary aim is to give students the tools to translate simple, real-world biological problems into rigorous mathematical models. A secondary aim is to teach the reader how to critically assess the modelling components in the primary life science literature.
The book covers deterministic as well as stochastic dynamics, continuous-time as well as discrete-time dynamics, partial differential equations, dimensional analysis, and curve fitting/parameter estimation. It contains numerous case studies, graded from elementary examples to more complicated problems, as well as a general treatment of good modelling practice. Although the book assumes a basic background in mathematics, specifically beginning calculus and elementary statistics, all requisite material is included in a series of appendices.

Mathematical Models of Biological Systems provides a practical introduction to basic mathematical modelling methodology and analysis. It covers a variety of biological applications and uses these topics in turn to highlight key components in the art of modelling. Its primary aim is to give students the tools to translate simple, real-world biological problems into rigorous mathematical models. A secondary aim is to teach the reader how to critically assess the modelling components in the primary life science literature. The book covers deterministic as well as stochastic dynamics, continuous-time as well as discrete-time dynamics, partial differential equations, dimensional analysis, and curve fitting/parameter estimation. It contains numerous case studies, graded from elementary examples to more complicated problems, as well as a general treatment of good modelling practice. Although the book assumes a basic background in mathematics, specifically beginning calculus and elementary statistics, all requisite material is included in a series of appendices.

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.

A comprehensive guide to automated statistical data cleaning The production of clean data is a complex and time-consuming process that requires both technical know-how and statistical expertise. Statistical Data Cleaning brings together a wide range of techniques for cleaning textual, numeric or categorical data. This book examines technical data cleaning methods relating to data representation and data structure. A prominent role is given to statistical data validation, data cleaning based on predefined restrictions, and data cleaning strategy. Key features: Focuses on the automation of data cleaning methods, including both theory and applications written in R. Enables the reader to design data cleaning processes for either one-off analytical purposes or for setting up production systems that clean data on a regular basis. Explores statistical techniques for solving issues such as incompleteness, contradictions and outliers, integration of data cleaning components and quality monitoring. Supported by an accompanying website featuring data and R code. This book enables data scientists and statistical analysts working with data to deepen their understanding of data cleaning as well as to upgrade their practical data cleaning skills. It can also be used as material for a course in data cleaning and analyses.

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.

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).

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.

This book provides insights into important new developments in the area of statistical quality control and critically discusses methods used in on-line and off-line statistical quality control. The book is divided into three parts: Part I covers statistical process control, Part II deals with design of experiments, while Part III focuses on fields such as reliability theory and data quality. The 12th International Workshop on Intelligent Statistical Quality Control (Hamburg, Germany, August 16 - 19, 2016) was jointly organized by Professors Sven Knoth and Wolfgang Schmid. The contributions presented in this volume were carefully selected and reviewed by the conference's scientific program committee. Taken together, they bridge the gap between theory and practice, making the book of interest to both practitioners and researchers in the field of quality control.

A "how to" guide for applying statistical methods to biomarker data analysis Presenting a solid foundation for the statistical methods that are used to analyze biomarker data, Analysis of Biomarker Data: A Practical Guide features preferred techniques for biomarker validation. The authors provide descriptions of select elementary statistical methods that are traditionally used to analyze biomarker data with a focus on the proper application of each method, including necessary assumptions, software recommendations, and proper interpretation of computer output. In addition, the book discusses frequently encountered challenges in analyzing biomarker data and how to deal with them, methods for the quality assessment of biomarkers, and biomarker study designs. Covering a broad range of statistical methods that have been used to analyze biomarker data in published research studies, Analysis of Biomarker Data: A Practical Guide also features: A greater emphasis on the application of methods as opposed to the underlying statistical and mathematical theory The use of SAS(R), R, and other software throughout to illustrate the presented calculations for each example Numerous exercises based on real-world data as well as solutions to the problems to aid in reader comprehension The principles of good research study design and the methods for assessing the quality of a newly proposed biomarker A companion website that includes a software appendix with multiple types of software and complete data sets from the book's examples Analysis of Biomarker Data: A Practical Guide is an ideal upper-undergraduate and graduate-level textbook for courses in the biological or environmental sciences. An excellent reference for statisticians who routinely analyze and interpret biomarker data, the book is also useful for researchers who wish to perform their own analyses of biomarker data, such as toxicologists, pharmacologists, epidemiologists, environmental and clinical laboratory scientists, and other professionals in the health and environmental sciences.

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.

This book is published open access under a CC BY 4.0 license. This book presents computer programming as a key method for solving mathematical problems. This second edition of the well-received book has been extensively revised: All code is now written in Python version 3.6 (no longer version 2.7). In addition, the two first chapters of the previous edition have been extended and split up into five new chapters, thus expanding the introduction to programming from 50 to 150 pages. Throughout the book, the explanations provided are now more detailed, previous examples have been modified, and new sections, examples and exercises have been added. Also, a number of small errors have been corrected. The book was inspired by the Springer book TCSE 6: A Primer on Scientific Programming with Python (by Langtangen), but the style employed is more accessible and concise, in keeping with the needs of engineering students. The book outlines the shortest possible path from no previous experience with programming to a set of skills that allows students to write simple programs for solving common mathematical problems with numerical methods in the context of engineering and science courses. The emphasis is on generic algorithms, clean program design, the use of functions, and automatic tests for verification.

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.

- includes MATLABr fundamentals, matrices, arrays, general graphics and specialized plots in quality assurance problems, script files, ordinary and partial differential equations - gives calculation of six sigma, total quality management, time series forecasting, reliability, process improvement, metrology, quality control and assurance, measurement and testing techniques - provides tools for graphical presentation, basic and special statistics and testing, ordinary and partial differential solvers, and fitting tools - includes comprehensive command information in tables Many books are available on MATLABr programming for engineers in general or in some specific area, but none in the highly topical field of quality assurance (QA). MATLABr in quality assurance sciences fills this gap as a compact guide for students, engineers, and scientists in this field. It concentrates on MATLABr fundamentals with examples of application to a wide range of current problems from general, nano and bio-technology, and statistical control, to medicine and industrial management. Examples cover both the school and advanced level; comprising calculations of total quality management, six sigma, time series, process improvement, metrology, quality control, human factors in quality assurance, measurement and testing techniques, quality project and function management, and customer satisfaction. The book covers key topics, including: the basics of software with examples; graphics and representations; numerical computation, scripts and functions for QA calculations; ODE and PDEPE solvers applied to QA problems; curve fitting and time series tool interfaces in calculations of quality; and statistics calculations applied to quality testing.