Computational biology, mathematical biology, biology and biomedicine are currently undergoing spectacular progresses due to a synergy between technological advances and inputs from physics, chemistry, mathematics, statistics and computer science. The goal of this book is to evidence this synergy by describing selected developments in the following fields: bioinformatics, biomedicine and neurosc…
This brief monograph is an in-depth study of the infinite divisibility and self-decomposability properties of central and noncentral Student’s distributions, represented as variance and mean-variance mixtures of multivariate Gaussian distributions with the reciprocal gamma mixing distribution. These results allow us to define and analyse Student-Lévy processes as Thorin subordinated Gaussian…
Poisson manifolds play a fundamental role in Hamiltonian dynamics, where they serve as phase spaces. They also arise naturally in other mathematical problems, and form a bridge from the "commutative world" to the "noncommutative world". The aim of this book is twofold: On the one hand, it gives a quick, self-contained introduction to Poisson geometry and related subjects, including singular fol…
The subject of space-filling curves has fascinated mathematicians for over a century and has intrigued many generations of students of mathematics. Working in this area is like skating on the edge of reason. Unfortunately, no comprehensive treatment has ever been attempted other than the gallant effort by W. Sierpiriski in 1912. At that time, the subject was still in its infancy and the most in…
This newly-translated book takes the reader from the basic principles and conservation laws of hydrodynamics to the description of general atmospheric circulation. Among the topics covered are the Kelvin, Ertel and Rossby-Obukhov invariants, quasi-geostrophic equation, thermal wind, singular Helmholtz vortices, derivation of the Navier-Stokes equation, Kolmogorov's flow, hydrodynamic stability,…
This volume, as Andrew M. Odlzyko writes in the foreword, “commemorates and celebrates the life and achievements of an extraordinary person.” Originally conceived as an 80th birthday tribute to Herbert Wilf, the well-known combinatorialist, the book has evolved beyond the proceeds of the W80 tribute. Professor Wilf was an award-winning teacher, who was supportive of women mathematicians,…
This study shows that the Caspian Sea level time series possess long range dependence even after removing linear trends, based on analyses of the Hurst statistic, the sample autocorrelation functions, and the periodogram of the series. Forecasting performance of ARMA, ARIMA, ARFIMA and Trend Line-ARFIMA (TL-ARFIMA) combination models are investigated. The forecast confidence bands and the forec…
This book presents the state of the art in high-performance computing and simulation on modern supercomputer architectures. It covers trends in hardware and software development in general and specifically the future of high-performance systems and heterogeneous architectures. The application contributions cover computational fluid dynamics, material science, medical applications and climate re…
The book addresses the topic of on-line implementation of structural and mechanical design criteria as an explicit part of optimal control schemes. The intention of the present research monograph is to reflect recent developments within this area. Examples of application of relevant control algorithms are included to illustrate their practical implementation. These examples are mainly taken fro…
The book collects over 120 exercises on different subjects of Mathematical Finance, including Option Pricing, Risk Theory, and Interest Rate Models. Many of the exercises are solved, while others are only proposed. Every chapter contains an introductory section illustrating the main theoretical results necessary to solve the exercises. The book is intended as an exercise textbook to accompany g…