This book is a short introduction to power system planning and operation using advanced geometrical methods. The approach is based on well-known insights and techniques developed in theoretical physics in the context of Riemannian manifolds. The proof of principle and robustness of this approach is examined in the context of the IEEE 5 bus system. This work addresses applied mathematicians, theoretical physicists and power engineers interested in novel mathematical approaches to power network theory.

This thesis, the result of a literature search conducted at the Naval Postgraduate School, is a collection of different geometrical methods and their applications in respect to network analysis and synthesis in electrical engineering. Part one deals primarily with finding the equivalent of two or more impedances in parallel. The second part is directed towards the application of these methods to the problem of matching two arbitrary impedances in order to obtain maximum power transfer. A comprehensive bibliography is included. (Author).

This thesis, the result of a literature search conducted at the Naval Postgraduate School, is a collection of different geometrical methods and their applications in respect to network analysis and synthesis in electrical engineering. Part one deals primarily with finding the equivalent of two or more impedances in parallel. The second part is directed towards the application of these methods to the problem of matching two arbitrary impedances in order to obtain maximum power transfer. A comprehensive bibliography is included. (Author).

This comprehensive guide offers a new approach for developing and implementing robust computational methodologies that uncover the key geometric and topological information from signals and images. With the help of detailed real-world examples and applications, readers will learn how to solve complex signal and image processing problems in fields ranging from remote sensing to medical imaging, bioinformatics, robotics, security, and defence. With an emphasis on intuitive and application-driven arguments, this text covers not only a range of methods in use today, but also introduces promising new developments for the future, bringing the reader up-to-date with the state of the art in signal and image analysis. Covering basic principles as well as advanced concepts and applications, and with examples and homework exercises, this is an invaluable resource for graduate students, researchers, and industry practitioners in a range of fields including signal and image processing, biomedical engineering, and computer graphics.

This book provides an accessible yet rigorous first reference for readers interested in learning how to model and analyze cellular network performance using stochastic geometry. In addition to the canonical downlink and uplink settings, analyses of heterogeneous cellular networks and dense cellular networks are also included. For each of these settings, the focus is on the calculation of coverage probability, which gives the complementary cumulative distribution function (ccdf) of signal-to-interference-and-noise ratio (SINR) and is the complement of the outage probability. Using this, other key performance metrics, such as the area spectral efficiency, are also derived. These metrics are especially useful in understanding the effect of densification on network performance. In order to make this a truly self-contained reference, all the required background material from stochastic geometry is introduced in a coherent and digestible manner. This Book: Provides an approachable introduction to the analysis of cellular networks and illuminates key system dependencies Features an approach based on stochastic geometry as applied to cellular networks including both downlink and uplink Focuses on the statistical distribution of signal-to-interference-and-noise ratio (SINR) and related metrics

This book presents a unified framework for the tractable analysis of large-scale, multi-antenna wireless networks using stochastic geometry. This mathematical analysis is essential for assessing and understanding the performance of complicated multi-antenna networks, which are one of the foundations of 5G and beyond networks to meet the ever-increasing demands for network capacity. Describing the salient properties of the framework, which makes the analysis of multi-antenna networks comparable to that of their single-antenna counterparts, the book discusses effective design approaches that do not require complex system-level simulations. It also includes various application examples with different multi-antenna network models to illustrate the framework’s effectiveness.