Sequence Space Theory With Applications

Authors: Brombin, C., Salmaso, L., Fontanella, L., Ippoliti, L., Fusilli, C.
Explores specific inferential issues arising from the analysis of dynamic shapes with the attempt to solve the problems at hand using probability models and nonparametric testsUses the Expectation Maximization (EM) algorithm to give essential results for a likelihood-based approach to statistical inference in shape analysisCovers the theory of NonParametric Combination (NPC) tests as well as the applications of the methodology to the Face and Gesture Recognition Research Network (FG-NET) data

This book is intended to be both a thorough introduction to contemporary research in optimization theory for elliptic systems with its numerous applications and a textbook at the undergraduate and graduate level for courses in pure or applied mathematics or in continuum mechanics. Various processes of modern technology and production are described by el­ liptic partial differential equations. Optimization of these processes reduces to op­ timization problems for elliptic systems. The numerical solution of such problems is associated with the solution of the following questions. 1. The setting of the optimization problem ensuring the existence of a solution on a set of admissible controls, which is a subset of some infinite-dimensional vector space. 2. Reduction of the infinite-dimensional optimization problem to a sequence of finite-dimensional problems such that the solutions of the finite-dimensional problems converge, in a sense, to the solution of the infinite-dimensional problem.3. Numerical solution of the finite-dimensional problems.

The theory of large deviations deals with the evaluation, for a family of probability measures parameterized by a real valued variable, of the probabilities of events which decay exponentially in the parameter.

Yearly global mean temperature and ocean levels, daily share prices, and the signals transmitted back to Earth by the Voyager space craft are all examples of sequential observations over time known as time series. This book gives you a step-by-step introduction to analysing time series using the open source software R. Each time series model is motivated with practical applications, and is defined in mathematical notation.