For the last few decades researchers from different fields gather their findings and knowledge trying to give a shape to the new science of complex systems. To address this problem, new tools and methods have to be established. A new, or more precisely an alternative, framework for the characterization of complex system was proposed. In this book we will introduce the applicability of applicability of simplicial complexes in the science of complex systems. After introducing the main definitions and properties of simplicial complexes necessary for representation and analysis of complex systems, we will illustrate the usefulness and versatility of tools and concepts related to the simplicial complexes.

While electric vehicles (EVs) are becoming increasingly popular. Their low oil dependency and low emissions will significantly benefit the environment. However, as demand increases for EVs, their prevalence will also lead to two crucial consequences. First, electric vehicles introduce a heavy load impact onto the power grid by shifting energy demand from gasoline to electricity. The surging load is likely to compromise the grid's reliability and jeopardize its power supply quality. Second, charging stations become indispensable infrastructure to support widescale deployment of EVs. EVs will therefore find themselves competing for both power supply and charging stations. Such competition can degrade quality of service and thus compromise the original intent of advocating electric vehicles. Sustainable Transportation with Electric Vehicles investigates smart electric vehicle charging. It focuses jointly on the quality of service for EV users and the stability and reliability of the power grid. It lays out a solution framework that addresses many of the key problems arising from both the lower and upper levels. The proposed solutions are developed mainly using techniques from the optimization, game theory, algorithmic, and scheduling fields.