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."

The interaction of the solar and heat radiation with the atmosphere and surface is the subject of the book. It is useful also for wide circle scientists involved in environmental studies. The book contains the description of 17 computer studying programs supporting different topics of courses. It includes only the base ground for comprehension of key topics and provides the accomplishment of practical works with using specially elaborated computer programs. Themes of practical works reflect main sections of mentioned courses of lectures. The packet of computer programs is added for solution of direct and inverse problems. It promotes deep and reliable comprehension of corresponding topics by students. All described approaches and computer programs are valuable resources for solving radiative transfer problems and they could be used by students for courses and diploma studies concerned atmospheric optics.

Written in a clear and lively tone, Statistics Using IBM SPSS provides a data-centric approach to statistics with integrated SPSS (version 22) commands, ensuring that students gain both a deep conceptual understanding of statistics and practical facility with the leading statistical software package. With one hundred worked examples, the textbook guides students through statistical practice using real data and avoids complicated mathematics. Numerous end-of-chapter exercises allow students to apply and test their understanding of chapter topics, with detailed answers available online. The third edition has been updated throughout and includes a new chapter on research design, new topics (including weighted mean, resampling with the bootstrap, the role of the syntax file in workflow management, and regression to the mean) and new examples and exercises. Student learning is supported by a rich suite of online resources, including answers to end-of-chapter exercises, real data sets, PowerPoint slides, and a test bank.

Scientific Computing with MATLAB (R), Second Edition improves students' ability to tackle mathematical problems. It helps students understand the mathematical background and find reliable and accurate solutions to mathematical problems with the use of MATLAB, avoiding the tedious and complex technical details of mathematics. This edition retains the structure of its predecessor while expanding and updating the content of each chapter. The book bridges the gap between problems and solutions through well-grouped topics and clear MATLAB example scripts and reproducible MATLAB-generated plots. Students can effortlessly experiment with the scripts for a deep, hands-on exploration. Each chapter also includes a set of problems to strengthen understanding of the material.

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 Optimization Techniques introduces you to the MATLAB language with practical hands-on instructions and results, allowing you to quickly achieve your goals. It begins by introducing the MATLAB environment and the structure of MATLAB programming before moving on to the mathematics of optimization. The central part of the book is dedicated to MATLAB's Optimization Toolbox, which implements state-of-the-art algorithms for solving multiobjective problems, non-linear minimization with boundary conditions and restrictions, minimax optimization, semi-infinitely constrained minimization and linear and quadratic programming. A wide range of exercises and examples are included, illustrating the most widely used optimization methods.

The second edition of a bestselling textbook, Using R for Introductory Statistics guides students through the basics of R, helping them overcome the sometimes steep learning curve. The author does this by breaking the material down into small, task-oriented steps. The second edition maintains the features that made the first edition so popular, while updating data, examples, and changes to R in line with the current version.

See What’s New in the Second Edition:

Increased emphasis on more idiomatic R provides a grounding in the functionality of base R.

Discussions of the use of RStudio helps new R users avoid as many pitfalls as possible.

Use of knitr package makes code easier to read and therefore easier to reason about.

Additional information on computer-intensive approaches motivates the traditional approach.

Updated examples and data make the information current and topical.

The book has an accompanying package, UsingR, available from CRAN, R’s repository of user-contributed packages. The package contains the data sets mentioned in the text (data(package="UsingR")), answers to selected problems (answers()), a few demonstrations (demo()), the errata (errata()), and sample code from the text.

The topics of this text line up closely with traditional teaching progression; however, the book also highlights computer-intensive approaches to motivate the more traditional approach. The authors emphasize realistic data and examples and rely on visualization techniques to gather insight. They introduce statistics and R seamlessly, giving students the tools they need to use R and the information they need to navigate the sometimes complex world of statistical computing.

Table of Contents

DATA

What Is Data?

Some R Essentials

Accessing Data by Using Indices

Reading in Other Sources of Data

UNIVARIATE DATA

Categorical Data

Numeric Data

Shape of a Distribution

BIVARIATE DATA

Pairs of Categorical Variables

Comparing Independent Samples

Relationships in Numeric Data

Simple Linear Regression

MULTIVARIATE DATA

Viewing Multivariate Data

R Basics: Data Frames and Lists

Using Model Formula with Multivariate Data

Lattice Graphics

Types of Data in R

DESCRIBING POPULATIONS

Populations

Families of Distributions

The Central Limit Theorem

SIMULATION

The Normal Approximation for the Binomial

for loops

Simulations Related to the Central Limit Theorem

Defining a Function

Investigating Distributions

Bootstrap Samples

Alternates to for loops

CONFIDENCE INTERVALS

Confidence Interval Ideas

Confidence Intervals for a Population Proportion, p

Confidence Intervals for the Population Mean, µ

Other Confidence Intervals

Confidence Intervals for Differences

Confidence Intervals for the Median

SIGNIFICANCE TESTS

Significance Test for a Population Proportion

Significance Test for the Mean (t-Tests)

Significance Tests and Confidence Intervals

Significance Tests for the Median

Two-Sample Tests of Proportion

Two-Sample Tests of Center

GOODNESS OF FIT

The Chi-Squared Goodness-of-Fit Test

The Chi-Squared Test of Independence

Goodness-of-Fit Tests for Continuous Distributions

LINEAR REGRESSION

The Simple Linear Regression Model

Statistical Inference for Simple Linear Regression

Multiple Linear Regression

ANALYSIS OF VARIANCE

One-Way ANOVA

Using lm() for ANOVA

ANCOVA

Two-Way ANOVA

TWO EXTENSIONS OF THE LINEAR MODEL

Logistic Regression

Nonlinear Models

APPENDIX A: GETTING, INSTALLING, AND RUNNING R

Installing and Starting R

Extending R Using Additional Packages

APPENDIX B: GRAPHICAL USER INTERFACES AND R

The Windows GUI

The Mac OS X GUI

Rcdmr

APPENDIX C: TEACHING WITH R

APPENDIX D: MORE ON GRAPHICS WITH R

Low- and High-Level Graphic Functions

Creating New Graphics in R

APPENDIX E: PROGRAMMING IN R

Editing Functions

Using Functions

Using Files and a Better Editor

Object-Oriented Programming with R

INDEX

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. This book is designed for use as a scientific/business calculator so that you can get numerical solutions to problems involving a wide array of mathematics using MATLAB. Just look up the function you want in the book and you are ready to use it in MATLAB or use the book to learn about the enormous range of options that MATLAB offers. MATLAB Numerical Calculations focuses on MATLAB capabilities to give you numerical solutions to problems you are likely to encounter in your professional or scholastic life. It introduces you to the MATLAB language with practical hands-on instructions and results, allowing you to quickly achieve your goals. Starting with a look at basic MATLAB functionality with integers, rational numbers and real and complex numbers, and MATLAB's relationship with Maple, you will learn how to solve equations in MATLAB, and how to simplify the results. You will see how MATLAB incorporates vector, matrix and character variables, and functions thereof. MATLAB is a powerful tool used to defined, manipulate and simplify complex algebraic expressions. With MATLAB you can also work with ease in matrix algebra, making use of commands which allow you to find eigenvalues, eigenvectors, determinants, norms and various matrix decompositions, among many other features. Lastly, you will see how you can write scripts and use MATLAB to explore numerical analysis, finding approximations of integrals, derivatives and numerical solutions of differential equations.

A hands-on guide to using Excel in the business context First published in 2012, Using Excel for Business and Financial Modelling contains step-by-step instructions of how to solve common business problems using financial models, including downloadable Excel templates, a list of shortcuts and tons of practical tips and techniques you can apply straight away. Whilst there are many hundreds of tools, features and functions in Excel, this book focuses on the topics most relevant to finance professionals. It covers these features in detail from a practical perspective, but also puts them in context by applying them to practical examples in the real world. Learn to create financial models to help make business decisions whilst applying modelling best practice methodology, tools and techniques. - Provides the perfect mix of practice and theory - Helps you become a DIY Excel modelling specialist - Includes updates for Excel 2019/365 and Excel for Mac - May be used as an accompaniment to the author's online and face-to-face training courses Many people are often overwhelmed by the hundreds of tools in Excel, and this book gives clarity to the ones you need to know in order to perform your job more efficiently. This book also demystifies the technical, design, logic and financial skills you need for business and financial modelling.

Through analysis of the European Union Emissions Trading Scheme (EU ETS) and the Clean Development Mechanism (CDM), this book demonstrates how to use a variety of econometric techniques to analyze the evolving and expanding carbon markets sphere, techniques that can be extrapolated to the worldwide marketplace. It features stylized facts about carbon markets from an economics perspective, as well as covering key aspects of pricing strategies, risk and portfolio management.

Engineering mechanics involves the development of mathematical models of the physical world. Statics addresses the forces acting on and in mechanical objects and systems. Statics with MATLAB (R) develops an understanding of the mechanical behavior of complex engineering structures and components using MATLAB (R) to execute numerical calculations and to facilitate analytical calculations. MATLAB (R) is presented and introduced as a highly convenient tool to solve problems for theory and applications in statics. Included are example problems to demonstrate the MATLAB (R) syntax and to also introduce specific functions dealing with statics. These explanations are reinforced through figures generated with MATLAB (R) and the extra material available online which includes the special functions described. This detailed introduction and application of MATLAB (R) to the field of statics makes Statics with MATLAB (R) a useful tool for instruction as well as self study, highlighting the use of symbolic MATLAB (R) for both theory and applications to find analytical and numerical solutions

This book provides anintroduction to multistate event history analysis. It is an extension of survival analysis, in which a single terminal event (endpoint) is considered and the time-to-event is studied. Multistate models focus on life histories or trajectories, conceptualized as sequences of states and sequences of transitions between states. Life histories are modeled as realizations of continuous-time Markov processes. The model parameters, transition rates, are estimated from data on event counts and populations at risk, using the statistical theory of counting processes.

The Comprehensive R Network Archive (CRAN) includes several packages for multistate modeling. This book is about "Biograph." The package is designed to (a) enhance exploratory analysis of life histories and (b) make multistate modeling accessible. The package incorporates utilities that connect to several packages for multistate modeling, including "survival," "eha," "Epi," "mvna," " etm," "mstate," "msm," and "TraMineR" for sequence analysis. The book is a hands-on presentation of "Biograph" and the packages listed. It is written from the perspective of the user. To help the user master the techniques and the software, a single data set is used to illustrate the methods and software. It is the subsample of the German Life History Survey, which was also used by Blossfeld and Rohwer in their popular textbook on event history modeling. Another data set, the Netherlands Family and Fertility Survey, is used to illustrate how "Biograph" can assist in answering questions on life paths of cohorts and individuals.

The book is suitable as a textbook for graduate courses on event history analysis and introductory courses on competing risks and multistate models. It may also be used as a self-study book. The R code used in the book is available online.

Frans Willekens is affiliated with the Max Planck Institute for Demographic Research (MPIDR) in Rostock, Germany. He is Emeritus Professor of Demography at the University of Groningen, a Honorary Fellow of the Netherlands Interdisciplinary Demographic Institute (NIDI) in the Hague, and a Research Associate of the International Institute for Applied Systems Analysis (IIASA), Laxenburg, Austria. He is a member of Royal Netherlands Academy of Arts and Sciences (KNAW). He has contributed to the modeling and simulation of life histories, mainly in the context of population forecasting."

The theme of the meeting was Statistical Methods for the Analysis of Large Data-Sets . In recent years there has been increasing interest in this subject; in fact a huge quantity of information is often available but standard statistical techniques are usually not well suited to managing this kind of data. The conference serves as an important meeting point for European researchers working on this topic and a number of European statistical societies participated in the organization of the event.
The book includes 45 papers from a selection of the 156 papers accepted for presentation and discussed at the conference on Advanced Statistical Methods for the Analysis of Large Data-sets. "

This book collects the proceedings of the 10th Workshop on Model-Oriented Design and Analysis (mODa). A model-oriented view on the design of experiments, which is the unifying theme of all mODa meetings, assumes some knowledge of the form of the data-generating process and naturally leads to the so-called optimum experimental design. Its theory and practice have since become important in many scientific and technological fields, ranging from optimal designs for dynamic models in pharmacological research, to designs for industrial experimentation, to designs for simulation experiments in environmental risk management, to name but a few. The methodology has become even more important in recent years because of the increased speed of scientific developments, the complexity of the systems currently under investigation and the mounting pressure on businesses, industries and scientific researchers to reduce product and process development times. This increased competition requires ever increasing efficiency in experimentation, thus necessitating new statistical designs. This book presents a rich collection of carefully selected contributions ranging from statistical methodology to emerging applications. It primarily aims to provide an overview of recent advances and challenges in the field, especially in the context of new formulations, methods and state-of-the-art algorithms. The topics included in this volume will be of interest to all scientists and engineers and statisticians who conduct experiments.

Linear mixed-effects models (LMMs) are an important class of statistical models that can be used to analyze correlated data. Such data are encountered in a variety of fields including biostatistics, public health, psychometrics, educational measurement, and sociology. This book aims to support a wide range of uses for the models by applied researchers in those and other fields by providing state-of-the-art descriptions of the implementation of LMMs in R. To help readers to get familiar with the features of the models and the details of carrying them out in R, the book includes a review of the most important theoretical concepts of the models. The presentation connects theory, software and applications. It is built up incrementally, starting with a summary of the concepts underlying simpler classes of linear models like the classical regression model, and carrying them forward to LMMs. A similar step-by-step approach is used to describe the R tools for LMMs. All the classes of linear models presented in the book are illustrated using real-life data. The book also introduces several novel R tools for LMMs, including new class of variance-covariance structure for random-effects, methods for influence diagnostics and for power calculations. They are included into an R package that should assist the readers in applying these and other methods presented in this text.

This small book addresses different kinds of datafiles, as commonly encountered in clinical research, and their data-analysis on SPSS Software. Some 15 years ago serious statistical analyses were conducted by specialist statisticians using ma- frame computers. Nowadays, there is ready access to statistical computing using personal computers or laptops, and this practice has changed boundaries between basic statistical methods that can be conveniently carried out on a pocket calculator and more advanced statistical methods that can only be executed on a computer. Clinical researchers currently perform basic statistics without professional help from a statistician, including t-tests and chi-square tests. With help of user-friendly software the step from such basic tests to more complex tests has become smaller, and more easy to take. It is our experience as masters' and doctorate class teachers of the European College of Pharmaceutical Medicine (EC Socrates Project Lyon France) that s- dents are eager to master adequate command of statistical software for that purpose. However, doing so, albeit easy, still takes 20-50 steps from logging in to the final result, and all of these steps have to be learned in order for the procedures to be successful.

Python Algorithms, Second Edition explains the Python approach to algorithm analysis and design. Written by Magnus Lie Hetland, author of Beginning Python, this book is sharply focused on classical algorithms, but it also gives a solid understanding of fundamental algorithmic problem-solving techniques. The book deals with some of the most important and challenging areas of programming and computer science in a highly readable manner. It covers both algorithmic theory and programming practice, demonstrating how theory is reflected in real Python programs. Well-known algorithms and data structures that are built into the Python language are explained, and the user is shown how to implement and evaluate others.

This volume presents theoretical developments, applications and computational methods for the analysis and modeling in behavioral and social sciences where data are usually complex to explore and investigate. The challenging proposals provide a connection between statistical methodology and the social domain with particular attention to computational issues in order to effectively address complicated data analysis problems.
The papers in this volume stem from contributions initially presented at the joint international meeting JCS-CLADAG held in Anacapri (Italy) where the Japanese Classification Society and the Classification and Data Analysis Group of the Italian Statistical Society had a stimulating scientific discussion and exchange.

Nonlinear physics continues to be an area of dynamic modern research, with applications to physics, engineering, chemistry, mathematics, computer science, biology, medicine and economics. In this text extensive use is made of the Mathematica computer algebra system. No prior knowledge of Mathematica or programming is assumed. This book includes 33 experimental activities that are designed to deepen and broaden the reader's understanding of nonlinear physics. These activities are correlated with Part I, the theoretical framework of the text.

Post-Optimal Analysis in Linear Semi-Infinite Optimization examines the following topics in regards to linear semi-infinite optimization: modeling uncertainty, qualitative stability analysis, quantitative stability analysis and sensitivity analysis. Linear semi-infinite optimization (LSIO) deals with linear optimization problems where the dimension of the decision space or the number of constraints is infinite. The authors compare the post-optimal analysis with alternative approaches to uncertain LSIO problems and provide readers with criteria to choose the best way to model a given uncertain LSIO problem depending on the nature and quality of the data along with the available software. This work also contains open problems which readers will find intriguing a challenging. Post-Optimal Analysis in Linear Semi-Infinite Optimization is aimed toward researchers, graduate and post-graduate students of mathematics interested in optimization, parametric optimization and related topics.

This proposed text appears to be a good introduction to evolutionary computation for use in applied statistics research. The authors draw from a vast base of knowledge about the current literature in both the design of evolutionary algorithms and statistical techniques. Modern statistical research is on the threshold of solving increasingly complex problems in high dimensions, and the generalization of its methodology to parameters whose estimators do not follow mathematically simple distributions is underway. Many of these challenges involve optimizing functions for which analytic solutions are infeasible. Evolutionary algorithms represent a powerful and easily understood means of approximating the optimum value in a variety of settings. The proposed text seeks to guide readers through the crucial issues of optimization problems in statistical settings and the implementation of tailored methods (including both stand-alone evolutionary algorithms and hybrid crosses of these procedures with standard statistical algorithms like Metropolis-Hastings) in a variety of applications. This book would serve as an excellent reference work for statistical researchers at an advanced graduate level or beyond, particularly those with a strong background in computer science.

This book presents methods for computing correlation equations. All the topics treated hefe are eluci dated in terms of concrete examples, which have been chosen, for the most part, from the Held of analysis of the mechanical properties of steel, wood, and other materials. A necessary prerequisite for any study of correlation equations is so me knowledge of the moments of random variables. In the Appendix, there is provided a brief treatment of moments, as well as a discussion of the simplest methods of computing them. We have paid particular attention in this book to the techniques of computing correlation equations, and to the use of tables for alleviating the computationalload. The mathematical bases of the methods used in setting up correlation equations are expounded in the books cited at the end of this volume. A. M. December 1965 PIe ase note that the abbreviation 19 is used in this book to designate the logarithm to base ten, Note further that the comma has been retained as the decimal point in tabular material."

Sampling consists of selection, acquisition, and quantification of a part of the population. While selection and acquisition apply to physical sampling units of the population, quantification pertains only to the variable of interest, which is a particular characteristic of the sampling units. A sampling procedure is expected to provide a sample that is representative with respect to some specified criteria. Composite sampling, under idealized conditions, incurs no loss of information for estimating the population means. But an important limitation to the method has been the loss of information on individual sample values, such as, the extremely large value. In many of the situations where individual sample values are of interest or concern, composite sampling methods can be suitably modified to retrieve the information on individual sample values that may be lost due to compositing. This book presents statistical solutions to issues that arise in the context of applications of composite sampling.

Containing a summary of several recent results on Markov-based input modeling in a coherent notation, this book introduces and compares algorithms for parameter fitting and gives an overview of available software tools in the area. Due to progress made in recent years with respect to new algorithms to generate PH distributions and Markovian arrival processes from measured data, the models outlined are useful alternatives to other distributions or stochastic processes used for input modeling. Graduate students and researchers in applied probability, operations research and computer science along with practitioners using simulation or analytical models for performance analysis and capacity planning will find the unified notation and up-to-date results presented useful. Input modeling is the key step in model based system analysis to adequately describe the load of a system using stochastic models.

The goal of input modeling is to find a stochastic model to describe a sequence ofmeasurements from a real system to model for example the inter-arrival times of packets in a computer network or failure times of components in a manufacturing plant. Typical application areas are performance and dependability analysis of computer systems, communication networks, logistics or manufacturing systems but also the analysis of biological or chemical reaction networks and similar problems. Often the measured values have a high variability and are correlated. It s been known for a long time that Markov based models like phase type distributions or Markovian arrival processes are very general and allow one to capture even complex behaviors. However, the parameterization of these models results often in a complex and non-linear optimization problem. Only recently, several new results about the modeling capabilities of Markov based models and algorithms to fit the parameters of those models have been published.

"

Learn how to write R code with fewer bugs. The problem with programming is that you are always one typo away from writing something silly. Likewise with data analysis, a small mistake in your model can lead to a big mistake in your results. Combining the two disciplines means that it is all too easy for a missed minus sign to generate a false prediction that you don't spot until it's too late. Testing is the only way to be sure that your code, and your results, are correct. Testing R Code teaches you how to perform development-time testing using the testthat package, allowing you to ensure that your code works as intended. The book also teaches run-time testing using the assertive package; enabling your users to correctly run your code. After beginning with an introduction to testing in R, the book explores more advanced cases such as integrating tests into R packages; testing code that accesses databases; testing C++ code with Rcpp; and testing graphics. Each topic is explained with real-world examples, and has accompanying exercises for readers to practise their skills - only a small amount of experience with R is needed to get started!

Separation of signal from noise is the most fundamental problem in data analysis, arising in such fields as: signal processing, econometrics, actuarial science, and geostatistics. This book introduces the local regression method in univariate and multivariate settings, with extensions to local likelihood and density estimation. Practical information is also included on how to implement these methods in the programs S-PLUS and LOCFIT.