Goal is to contribute to understanding of localized spatial and spatio-temporal structures far from thermodynamic equilibrium. Here we report on our progress in the study of three classes of systems. (1) We have studied cellular flame structures arising in a circular burner. Using numerical computations we have found a number of traveling-wave structures in which different cells undergo different motion. Most strikingly, we have found a localized wave traveling through the array of steady cells. Results are interpreted using various asymptotic approaches. They are in qualitative agreement with recent experiments. (2) We have continued our investigation of localized waves in binary-mixture convection. Starting from the extended Ginzburg-Landau equations introduced earlier, we have derived equations of motion for interacting fronts connecting the conductive and the convective state. These equations reveal a repulsive interaction between the fronts which implies a new localization mechanism for waves. It is solely due to the long-wavelength mode specific to the extended Ginzburg-Landau equations. The stability properties of the resulting localized waves are in qualitative agreement with very recent experiments. (3) We have extended our investigation of domain structures to include their temporal evolution.

The world is becoming increasingly complex, with larger quantities of data available to be analyzed. It so happens that much of these "big data" that are available are spatio-temporal in nature, meaning that they can be indexed by their spatial locations and time stamps. Spatio-Temporal Statistics with R provides an accessible introduction to statistical analysis of spatio-temporal data, with hands-on applications of the statistical methods using R Labs found at the end of each chapter. The book: Gives a step-by-step approach to analyzing spatio-temporal data, starting with visualization, then statistical modelling, with an emphasis on hierarchical statistical models and basis function expansions, and finishing with model evaluation Provides a gradual entry to the methodological aspects of spatio-temporal statistics Provides broad coverage of using R as well as "R Tips" throughout. Features detailed examples and applications in end-of-chapter Labs Features "Technical Notes" throughout to provide additional technical detail where relevant Supplemented by a website featuring the associated R package, data, reviews, errata, a discussion forum, and more The book fills a void in the literature and available software, providing a bridge for students and researchers alike who wish to learn the basics of spatio-temporal statistics. It is written in an informal style and functions as a down-to-earth introduction to the subject. Any reader familiar with calculus-based probability and statistics, and who is comfortable with basic matrix-algebra representations of statistical models, would find this book easy to follow. The goal is to give as many people as possible the tools and confidence to analyze spatio-temporal data.