After the pioneering work of Schur, little progress was made for half a century on projective representations, despite considerable activity on the related topic of linear representations. However, in the last twenty years, important new advances have spurred further research. This book develops both the early theory of Schur and then describes the key advances that the subject has seen since then. In particular, the theory of Q-functions and skew Q-functions is extensively covered which is central to the development of the subject.

Distributed SystemsThe next part presents a process algebra (mCRL2) that targets distributed applications, looks at how to turn prose descriptions into unambiguous specifications, extends pi-calculus to create a service-oriented mobility abstract machine, and introduces the Channel Ambient Machine for mobile applications.

Embedded SystemsThe final section combines state-based Z with the event-based process algebra CSP in a formal methodology called Circus. It also develops a pair of process algebras (PARS) to address the problem of scheduling in real-time embedded systems and emphasizes the reuse of concurrent artifacts across different hardware platforms.

Highlighting recent research work, this volume addresses multicore programming problems and the evolution of the growing body of concurrency-enabled languages. It proposes solutions to the problems of designing and implementing today’s concurrency-constrained multicore processor and cloud architectures.

These topics are important in many applications of stabilization theory. We hope that this monograph may illustrate the way in which mathematical theories do influence advanced technol­ ogy. This book is not intended to be a text book nor a guide for control-designers. In engineering practice, control-design is a very complex task in which stability is only one of the re­ quirements and many aspects and facets of the problem have to be taken into consideration. Even if we restrict ourselves to stabilization, the book does not provide just recipes, but it fo­ cuses more on the ideas lying behind the recipes. In short, this is not a book on control, but on some mathematics of control.

By the end of this course, advanced undergraduate and beginning graduate students should be able to read a word problem or a corporate report, realize the uncertainty involved in the described situation, select a suitable probability model, estimate and test its parameters based on real data, compute probabilities of interesting events and other vital characteristics, and make appropriate conclusions and forecasts.

The text begins with some basics of object-oriented languages, followed by a “boot-camp” on the use of C++ and R. The authors then discuss code development for the solution of specific computational problems that are relevant to statistics including optimization, numerical linear algebra, and random number generation. Later chapters introduce abstract data structures (ADTs) and parallel computing concepts. The appendices cover R and UNIX Shell programming.

Features

• Includes numerous student exercises ranging from elementary to challenging
• Integrates both C++ and R for the solution of statistical computing problems
• Uses C++ code in R and R functions in C++ programs
• Provides downloadable programs, available from the authors’ website

The translation of a mathematical problem into its computational analog (or analogs) is a skill that must be learned, like any other, by actively solving relevant problems. The text reveals the basic principles of algorithmic thinking essential to the modern statistician as well as the fundamental skill of communicating with a computer through the use of the computer languages C++ and R. The book lays the foundation for original code development in a research environment.

The author provides complete arguments for nearly every result. An extensive list of references and bibliographic notes provide a clear picture of the applicability of geometric methods in functional analysis, and the open questions presented throughout the text highlight interesting new research opportunities.

Daniel Beltitâ is a Principal Researcher at the Institute of Mathematics “Simion Stoilow” of the Romanian Academy, Bucharest, Romania.