This book provides a generalised approach to fractal dimension theory from the standpoint of asymmetric topology by employing the concept of a fractal structure. The fractal dimension is the main invariant of a fractal set, and provides useful information regarding the irregularities it presents when examined at a suitable level of detail. New theoretical models for calculating the fractal dimension of any subset with respect to a fractal structure are posed to generalise both the Hausdorff and box-counting dimensions. Some specific results for self-similar sets are also proved. Unlike classical fractal dimensions, these new models can be used with empirical applications of fractal dimension including non-Euclidean contexts. In addition, the book applies these fractal dimensions to explore long-memory in financial markets. In particular, novel results linking both fractal dimension and the Hurst exponent are provided. As such, the book provides a number of algorithms for properly calculating the self-similarity exponent of a wide range of processes, including (fractional) Brownian motion and Levy stable processes. The algorithms also make it possible to analyse long-memory in real stocks and international indexes. This book is addressed to those researchers interested in fractal geometry, self-similarity patterns, and computational applications involving fractal dimension and Hurst exponent.

This book presents cutting-edge perspectives and research results in smart energy spanning multiple disciplines across four main topics: smart metering, smart grid modeling, control and optimization, and smart grid communications and networking. Chapters from an international panel of experts in the field cover: privacy-preserving data aggregation in smart metering systems; smart price-based scheduling of flexible residential appliances; smart tariffs for demand response from smart metering platforms; decentralized models for real-time renewable integration in future grid; distributed and decentralized control in future power systems; multiobjective optimization for smart grid system design; frequency regulation of smart grid via dynamic demand control and battery energy storage systems; distributed frequency control and demand-side management; game theory approaches for demand side management in the smart grid; energy storage systems and grid integration; overview of research in the ADVANTAGE project; big data analysis of power grid from random matrix theory; a model-driven evaluation of demand response communication protocols for smart grid; energy efficient smart grid communications; and cyber security of smart grid state estimation.