* Targests readers with a background in programming, interested in an introduction/refresher in statistical hypothesis testing * Uses Python throughout * Provides the reader with the opportunity of using the book whenever needed rather than following a sequential path.

The main focus of this book is on presenting advances in fuzzy statistics, and on proposing a methodology for testing hypotheses in the fuzzy environment based on the estimation of fuzzy confidence intervals, a context in which not only the data but also the hypotheses are considered to be fuzzy. The proposed method for estimating these intervals is based on the likelihood method and employs the bootstrap technique. A new metric generalizing the signed distance measure is also developed. In turn, the book presents two conceptually diverse applications in which defended intervals play a role: one is a novel methodology for evaluating linguistic questionnaires developed at the global and individual levels; the other is an extension of the multi-ways analysis of variance to the space of fuzzy sets. To illustrate these approaches, the book presents several empirical and simulation-based studies with synthetic and real data sets. In closing, it presents a coherent R package called "FuzzySTs" which covers all the previously mentioned concepts with full documentation and selected use cases. Given its scope, the book will be of interest to all researchers whose work involves advanced fuzzy statistical methods.

This book helps the reader make use of the mathematical models of biological phenomena starting from the basics of programming and computer simulation. Computer simulations based on a mathematical model enable us to find a novel biological mechanism and predict an unknown biological phenomenon. Mathematical biology could further expand the progress of modern life sciences. Although many biologists are interested in mathematical biology, they do not have experience in mathematics and computer science. An educational course that combines biology, mathematics, and computer science is very rare to date. Published books for mathematical biology usually explain the theories of established mathematical models, but they do not provide a practical explanation for how to solve the differential equations included in the models, or to establish such a model that fits with a phenomenon of interest. MATLAB is an ideal programming platform for the beginners of computer science. This book starts from the very basics about how to write a programming code for MATLAB (or Octave), explains how to solve ordinary and partial differential equations, and how to apply mathematical models to various biological phenomena such as diabetes, infectious diseases, and heartbeats. Some of them are original models, newly developed for this book. Because MATLAB codes are embedded and explained throughout the book, it will be easy to catch up with the text. In the final chapter, the book focuses on the mathematical model of the proneural wave, a phenomenon that guarantees the sequential differentiation of neurons in the brain. This model was published as a paper from the author's lab (Sato et al., PNAS 113, E5153, 2016), and was intensively explained in the book chapter "Notch Signaling in Embryology and Cancer", published by Springer in 2020. This book provides the reader who has a biological background with invaluable opportunities to learn and practice mathematical biology.

Contingency tables arise in diverse fields, including life sciences, education, social and political sciences, notably market research and opinion surveys. Their analysis plays an essential role in gaining insight into structures of the quantities under consideration and in supporting decision making. Combining both theory and applications, this book presents models and methods for the analysis of two- and multidimensional-contingency tables. An excellent reference for advanced undergraduates, graduate students, and practitioners in statistics as well as biosciences, social sciences, education, and economics, the work may also be used as a textbook for a course on categorical data analysis. Prerequisites include basic background on statistical inference and knowledge of statistical software packages.

The R Companion to Elementary Applied Statistics includes traditional applications covered in elementary statistics courses as well as some additional methods that address questions that might arise during or after the application of commonly used methods. Beginning with basic tasks and computations with R, readers are then guided through ways to bring data into R, manipulate the data as needed, perform common statistical computations and elementary exploratory data analysis tasks, prepare customized graphics, and take advantage of R for a wide range of methods that find use in many elementary applications of statistics. Features: Requires no familiarity with R or programming to begin using this book. Can be used as a resource for a project-based elementary applied statistics course, or for researchers and professionals who wish to delve more deeply into R. Contains an extensive array of examples that illustrate ideas on various ways to use pre-packaged routines, as well as on developing individualized code. Presents quite a few methods that may be considered non-traditional, or advanced. Includes accompanying carefully documented script files that contain code for all examples presented, and more. R is a powerful and free product that is gaining popularity across the scientific community in both the professional and academic arenas. Statistical methods discussed in this book are used to introduce the fundamentals of using R functions and provide ideas for developing further skills in writing R code. These ideas are illustrated through an extensive collection of examples. About the Author: Christopher Hay-Jahans received his Doctor of Arts in mathematics from Idaho State University in 1999. After spending three years at University of South Dakota, he moved to Juneau, Alaska, in 2002 where he has taught a wide range of undergraduate courses at University of Alaska Southeast.

This book constitutes the refereed proceedings of the 19th International Conference on Distributed and Computer and Communication Networks, DCCN 2016, held in Moscow, Russia, in November 2016. The 50 revised full papers and the 6 revised short papers presented were carefully reviewed and selected from 141 submissions. The papers cover the following topics: computer and communication networks architecture optimization; control in computer and communication networks; performance and QoS/QoE evaluation in wireless networks; analytical modeling and simulation of next-generation communications systems; queuing theory and reliability theory applications in computer networks; wireless 4G/5G networks, cm- and mm-wave radio technologies; RFID technology and its application in intellectual transportation networks; internet of things, wearables, and applications of distributed information systems; probabilistic and statistical models in information systems; mathematical modeling of high-tech systems; mathematical modeling and control problems; distributed and cloud computing systems, big data analytics.

The purpose of this handbook is to allow users to learn and master the mathematics software package MATLAB (R), as well as to serve as a quick reference to some of the most used instructions in the package. A unique feature of this handbook is that it can be used by the novice and by experienced users alike. For experienced users, it has four chapters with examples and applications in engineering, finance, physics, and optimization. Exercises are included, along with solutions available for the interested reader on the book's web page. These exercises are a complement for the interested reader who wishes to get a deeper understanding of MATLAB. Features Covers both MATLAB and introduction to Simulink Covers the use of GUIs in MATLAB and Simulink Offers downloadable examples and programs from the handbook's website Provides an introduction to object oriented programming using MATLAB Includes applications from many areas Includes the realization of executable files for MATLAB programs and Simulink models

This book discusses the problem of model choice when the statistical models are separate, also called nonnested. Chapter 1 provides an introduction, motivating examples and a general overview of the problem. Chapter 2 presents the classical or frequentist approach to the problem as well as several alternative procedures and their properties. Chapter 3 explores the Bayesian approach, the limitations of the classical Bayes factors and the proposed alternative Bayes factors to overcome these limitations. It also discusses a significance Bayesian procedure. Lastly, Chapter 4 examines the pure likelihood approach. Various real-data examples and computer simulations are provided throughout the text.

Among the various multi-level formulations of mathematical models in decision making processes, this book focuses on the bi-level model. Being the most frequently used, the bi-level model addresses conflicts which exist in multi-level decision making processes. From the perspective of bi-level structure and uncertainty, this book takes real-life problems as the background, focuses on the so-called random-like uncertainty, and develops the general framework of random-like bi-level decision making problems. The random-like uncertainty considered in this book includes random phenomenon, random-overlapped random (Ra-Ra) phenomenon and fuzzy-overlapped random (Ra-Fu) phenomenon. Basic theory, models, algorithms and practical applications for different types of random-like bi-level decision making problems are also presented in this book.

This volume provides essential guidance for transforming mathematics learning in schools through the use of innovative technology, pedagogy, and curriculum. It presents clear, rigorous evidence of the impact technology can have in improving students learning of important yet complex mathematical concepts -- and goes beyond a focus on technology alone to clearly explain how teacher professional development, pedagogy, curriculum, and student participation and identity each play an essential role in transforming mathematics classrooms with technology. Further, evidence of effectiveness is complemented by insightful case studies of how key factors lead to enhancing learning, including the contributions of design research, classroom discourse, and meaningful assessment. The volume organizes over 15 years of sustained research by multiple investigators in different states and countries who together developed an approach called "SimCalc" that radically transforms how Algebra and Calculus are taught. The SimCalc program engages students around simulated motions, such as races on a soccer field, and builds understanding using visual representations such as graphs, and familiar representations such as stories to help students to develop meaning for more abstract mathematical symbols. Further, the SimCalc program leverages classroom wireless networks to increase participation by all students in doing, talking about, and reflecting on mathematics. Unlike many technology programs, SimCalc research shows the benefits of balanced attention to curriculum, pedagogy, teacher professional development, assessment and technology -- and has proven effectiveness results at the scale of hundreds of schools and classrooms. Combining the findings of multiple investigators in one accessible volume reveals the depth and breadth of the research program, and engages readers interested in: * Engaging students in deeply learning the important concepts in mathematics * Designing innovative curriculum, software, and professional development * Effective uses of technology to improve mathematics education * Creating integrated systems of teaching that transform mathematics classrooms * Scaling up new pedagogies to hundreds of schools and classrooms * Conducting research that really matters for the future of mathematics learning * Engaging students in deeply learning the important concepts in mathematics * Designing innovative curriculum, software, and professional development * Effective uses of technology to improve mathematics education * Creating integrated systems of teaching that transform mathematics classrooms * Scaling up new pedagogies to hundreds of schools and classrooms * Conducting research that really matters for the future of mathematics learning

This volume contains pioneering contributions to both the theory and practice of optimal experimental design. Topics include the optimality of designs in linear and nonlinear models, as well as designs for correlated observations and for sequential experimentation. There is an emphasis on applications to medicine, in particular, to the design of clinical trials. Scientists from Europe, the US, Asia, Australia and Africa contributed to this volume of papers from the 11th Workshop on Model Oriented Design and Analysis.

Numerical Methods with MATLAB provides a highly-practical reference work to assist anyone working with numerical methods. A wide range of techniques are introduced, their merits discussed and fully working MATLAB code samples supplied to demonstrate how they can be coded and applied. Numerical methods have wide applicability across many scientific, mathematical, and engineering disciplines and are most often employed in situations where working out an exact answer to the problem by another method is impractical. Numerical Methods with MATLAB presents each topic in a concise and readable format to help you learn fast and effectively. It is not intended to be a reference work to the conceptual theory that underpins the numerical methods themselves. A wide range of reference works are readily available to supply this information. If, however, you want assistance in applying numerical methods then this is the book for you.

Learn how to develop powerful data analytics applications quickly for SQL Server database administrators and developers. Organizations will be able to sift data and derive the business intelligence needed to drive business decisions and profit. The addition of R to SQL Server 2016 places a powerful analytical processor into an environment most developers are already comfortable with - Visual Studio. This book walks even the newest of users through the creation process of a powerful R-language tool set for use in analyzing and reporting on your data. As a SQL Server database administrator or developer, it is sometimes difficult to stay on the bleeding edge of technology. Microsoft's addition of R to SQL Server 2016 is sure to be a game-changer, and the language will certainly become an integral part of future releases. R is in fact widely used today in statistical and related applications, and its use is only growing. Beginning SQL Server R Services helps you jump on board this important trend by providing good examples with detailed explanations of the WHY and not just the HOW. Walks you through setup and installation of SQL Server R Services. Explains the basics of working with R Tools for Visual Studio. Provides a road map to successfully creating custom R code. What You Will Learn Discover R's role in the SQL Server 2016 hierarchy. Manage the components needed to run SQL Server R Services code. Run R-language analytics and queries inside the database. Create analytic solutions that run across multiple datasets. Gain in-depth knowledge of the R language itself. Implement custom SQL Server R Services solutions. Who This Book Is For Any level of database administrator or developer, but specifically it's for those developers with the need to develop powerful data analytics applications quickly. Seasoned R developers will appreciate the book for its robust learning pattern, using visual aids in combination with properties explanations and scenarios. Beginning SQL Server R Services is the perfect "new hire" gift for new database developers in any organization.

Dynamical system theory has developed rapidly over the past fifty years. It is a subject upon which the theory of limit cycles has a significant impact for both theoretical advances and practical solutions to problems. Hopf bifurcation from a center or a focus is integral to the theory of bifurcation of limit cycles, for which normal form theory is a central tool. Although Hopf bifurcation has been studied for more than half a century, and normal form theory for over 100 years, efficient computation in this area is still a challenge with implications for Hilbert's 16th problem.

This book introduces the most recent developments in this field and provides major advances in fundamental theory of limit cycles. Split into two parts, the first focuses on the study of limit cycles bifurcating from Hopf singularity using normal form theory with later application to Hilbert's 16th problem, while the second considers near Hamiltonian systems using Melnikov function as the main mathematical tool.

Classic topics with new results are presented in a clear and concise manner and are accompanied by the liberal use of illustrations throughout. Containing a wealth of examples and structured algorithms that are treated in detail, a good balance between theoretical and applied topics is demonstrated. By including complete Maple programs within the text, this book also enables the reader to reconstruct the majority of formulas provided, facilitating the use of concrete models for study.

Through the adoption of an elementary and practical approach, this book will be of use to graduate mathematics students wishing to study the theory of limit cycles as well as scientists, across a number of disciplines, with an interest in the applications of periodic behavior."

This book teaches how to use Mathematica to solve a wide variety of problems in mathematics and physics. It is based on the lecture notes of a course taught at the University of Illinois at Chicago to advanced undergrad and graduate students. The book is illustrated with many detailed examples that require the student to construct meticulous, step-by-step, easy to read Mathematica programs. The first part, in which the reader learns how to use a variety of Mathematica commands, contains examples, not long explanations; the second part contains attractive applications.

This Bayesian modeling book provides a self-contained entry to computational Bayesian statistics. Focusing on the most standard statistical models and backed up by real datasets and an all-inclusive R (CRAN) package called bayess, the book provides an operational methodology for conducting Bayesian inference, rather than focusing on its theoretical and philosophical justifications. Readers are empowered to participate in the real-life data analysis situations depicted here from the beginning. Special attention is paid to the derivation of prior distributions in each case and specific reference solutions are given for each of the models. Similarly, computational details are worked out to lead the reader towards an effective programming of the methods given in the book. In particular, all R codes are discussed with enough detail to make them readily understandable and expandable. Bayesian Essentials with R can be used as a textbook at both undergraduate and graduate levels. It is particularly useful with students in professional degree programs and scientists to analyze data the Bayesian way. The text will also enhance introductory courses on Bayesian statistics. Prerequisites for the book are an undergraduate background in probability and statistics, if not in Bayesian statistics.

Intended for anyone needing to apply statistical analysis to a large variety of science and engineering problems, this book shows how to use SPSS, MATLAB, STATISTICA and R for data description, statistical inference, classification and regression, factor analysis, survival data and directional statistics. The 2nd edition includes the R language, a new section on bootstrap estimation methods and an improved treatment of tree classifiers, plus additional examples and exercises.

A state-of-the-art research monograph providing consistent treatment of supervisory control, by one of the world's leading groups in the area of Bayesian identification, control, and decision making.

The emphasis of the book is given in how to construct different types of solutions (exact, approximate analytical, numerical, graphical) of numerous nonlinear PDEs correctly, easily, and quickly. The reader can learn a wide variety of techniques and solve numerous nonlinear PDEs included and many other differential equations, simplifying and transforming the equations and solutions, arbitrary functions and parameters, presented in the book). Numerous comparisons and relationships between various types of solutions, different methods and approaches are provided, the results obtained in Maple and Mathematica, facilitates a deeper understanding of the subject. Among a big number of CAS, we choose the two systems, Maple and Mathematica, that are used worldwide by students, research mathematicians, scientists, and engineers. As in the our previous books, we propose the idea to use in parallel both systems, Maple and Mathematica, since in many research problems frequently it is required to compare independent results obtained by using different computer algebra systems, Maple and/or Mathematica, at all stages of the solution process. One of the main points (related to CAS) is based on the implementation of a whole solution method (e.g. starting from an analytical derivation of exact governing equations, constructing discretizations and analytical formulas of a numerical method, performing numerical procedure, obtaining various visualizations, and comparing the numerical solution obtained with other types of solutions considered in the book, e.g. with asymptotic solution).

This book provides insight and enhanced appreciation of analysis, modeling and control of dynamic systems. The reader is assumed to be familiar with calculus, physics and some programming skills. It might develop the reader's ability to interpret physical significance of mathematical results in system analysis. The book also prepares the reader for more advanced treatment of subsequent knowledge in the automatic control field. Learning objectives are performance-oriented, using for this purpose interactive MATLAB and SIMULINK software tools. It presents realistic problems in order to analyze, design and develop automatic control systems. Learning with computing tools can aid theory and help students to think, analyze and reason in meaningful ways. The book is also complemented with classroom slides and MATLAB and SIMULINK exercise files to aid students to focus on fundamental concepts treated.

Many interesting behaviors of real physical, biological, economical, and chemical systems can be described by ordinary differential equations (ODEs). Scientific Computing with Mathematica provides a general framework useful for the applications on the conceptual aspects of the theory of ODEs, as well as a sophisticated use of Mathematica software for the solutions of problems related to ODEs. In particular, a chapter is devoted to the use of ODEs and Mathematica in the dynamics of rigid bodies.

Mathematical methods and scientific computation are dealt with jointly to supply a unified presentation. The main problems of ODEs such as phase portrait, approximate solutions, periodic orbits, stability, bifurcation, and boundary problems are covered in an integrated fashion with numerous worked examples and computer program demonstrations using Mathematica.

Topics and Features:

* Explanation of how to use the Mathematica package ODE.m to support qualitative and quantitative problem solving

* End-of-chapter exercise sets incorporating the use of Mathematica programs

* Detailed description of the mathematical procedures underlying the twenty-eight programs written in Mathematica

* Appendix describing the use of ten notebooks to guide the reader through all the exercises.

This book is an essential text/reference for students, graduates and practitioners in engineering and applied mathematics interested in problems of ODEs in both the qualitative and quantitative description of solutions with the Mathematica program. It is also suitable as a self-study resource for professionals and others seeking an understanding of how to use ODEs in modeling physical, biological, and economic phenomena.

This book is intended for use as the textbook in a second course in applied statistics that covers topics in multiple regression and analysis of variance at an intermediate level. Generally, students enrolled in such courses are p- marily graduate majors or advanced undergraduate students from a variety of disciplines. These students typically have taken an introductory-level s- tistical methods course that requires the use a software system such as SAS for performing statistical analysis. Thus students are expected to have an - derstanding of basic concepts of statistical inference such as estimation and hypothesis testing. Understandably, adequate time is not available in a ?rst course in stat- tical methods to cover the use of a software system adequately in the amount of time available for instruction. The aim of this book is to teach how to use the SAS system for data analysis. The SAS language is introduced at a level of sophistication not found in most introductory SAS books. Important features such as SAS data step programming, pointers, and line-hold spe- ?ers are described in detail. The powerful graphics support available in SAS is emphasized throughout, and many worked SAS program examples contain graphic components.

MATLAB is a high-level language and environment for numerical computation, visualization, and programming. Using MATLAB, you can analyze data, develop algorithms, and create models and applications. The language, tools, and built-in math functions enable you to explore multiple approaches and reach a solution faster than with spreadsheets or traditional programming languages, such as C/C++ or Java. Programming MATLAB for Numerical Analysis introduces you to the MATLAB language with practical hands-on instructions and results, allowing you to quickly achieve your goals. You will first become familiar with the MATLAB environment, and then you will begin to harness the power of MATLAB. You will learn the MATLAB language, starting with an introduction to variables, and how to manipulate numbers, vectors, matrices, arrays and character strings. You will learn about MATLAB's high-precision capabilities, and how you can use MATLAB to solve problems, making use of arithmetic, relational and logical operators in combination with the common functions and operations of real and complex analysis and linear algebra. You will learn to implement various numerical methods for optimization, interpolation and solving non-linear equations. You will discover how MATLAB can solve problems in differential and integral calculus, both numerically and symbolically, including techniques for solving ordinary and partial differential equations, and how to graph the solutions in brilliant high resolution. You will then expand your knowledge of the MATLAB language by learning how to use commands which enable you to investigate the convergence of sequences and series, and explore continuity and other analytical features of functions in one and several variables.

MATLAB Mathematical Analysis is a reference book that presents the techniques of mathematical analysis through examples and exercises resolved with MATLAB software. The purpose is to give you examples of the mathematical analysis functions offered by MATLAB so that you can use them in your daily work regardless of the application. The book supposes proper training in the mathematics and so presents the basic knowledge required to be able to use MATLAB for calculational or symbolic solutions to your problems for a vast amount of MATLAB functions. The book begins by introducing the reader to the use of numbers, operators, variables and functions in the MATLAB environment. Then it delves into working with complex variables. A large section is devoted to working with and developing graphical representations of curves, surfaces and volumes. MATLAB functions allow working with two-dimensional and three-dimensional graphics, statistical graphs, curves and surfaces in explicit, implicit, parametric and polar coordinates. Additional work implements twisted curves, surfaces, meshes, contours, volumes and graphical interpolation. The following part covers limits, functions, continuity and numerical and power series. Then differentiation is addressed in one and several variables including differential theorems for vector fields. Thereafter the topic of integration is handled including improper integrals, definite and indefinite integration, integration in multiple variables and multiple integrals and their applications. Differential equations are exemplified in detail, Laplace transforms, Tayor series, and the Runga-Kutta method and partial differential equations.

MATLAB is a high-level language and environment for numerical computation, visualization, and programming. Using MATLAB, you can analyze data, develop algorithms, and create models and applications. The language, tools, and built-in math functions enable you to explore multiple approaches and reach a solution faster than with spreadsheets or traditional programming languages, such as C/C++ or Java. MATLAB Differential and Integral Calculus introduces you to the MATLAB language with practical hands-on instructions and results, allowing you to quickly achieve your goals. In addition to giving a short introduction to the MATLAB environment and MATLAB programming, this book provides all the material needed to work with ease in differential and integral calculus in one and several variables. Among other core topics of calculus, you will use MATLAB to investigate convergence, find limits of sequences and series and, for the purpose of exploring continuity, limits of functions. Various kinds of local approximations of functions are introduced, including Taylor and Laurent series. Symbolic and numerical techniques of differentiation and integration are covered with numerous examples, including applications to finding maxima and minima, areas, arc lengths, surface areas and volumes. You will also see how MATLAB can be used to solve problems in vector calculus and how to solve differential and difference equations.