Joint Centrality Distinguishes Optimal Leaders in Noisy Networks

We study the performance of a network of agents tasked with tracking an external unknown signal in the presence of stochastic disturbances and under the condition that only a limited subset of agents, known as leaders, can measure the signal directly. We investigate the optimal leader selection problem for a prescribed maximum number of leaders, where the optimal leader set minimizes total system error defined as steady-state variance about the external signal. In contrast to previously established greedy algorithms for optimal leader selection, our results rely on an expression of total system error in terms of properties of the underlying network graph. We demonstrate that the performance of any given set of leaders depends on their influence as determined by a new graph measure of centrality of a set. We define the $joint \; centrality$ of a set of nodes in a network graph such that a leader set with maximal joint centrality is an optimal leader set. In the case of a single leader, we prove that the optimal leader is the node with maximal information centrality. In the case of multiple leaders, we show that the nodes in the optimal leader set balance high information centrality with a coverage of the graph. For special cases of graphs, we solve explicitly for optimal leader sets. We illustrate with examples.Comment: Conditionally accepted to IEEE TCN

Research in progress in applied mathematics, numerical analysis, fluid mechanics, and computer science

This report summarizes research conducted at the Institute for Computer Applications in Science and Engineering in applied mathematics, fluid mechanics, and computer science during the period October 1, 1993 through March 31, 1994. The major categories of the current ICASE research program are: (1) applied and numerical mathematics, including numerical analysis and algorithm development; (2) theoretical and computational research in fluid mechanics in selected areas of interest to LaRC, including acoustics and combustion; (3) experimental research in transition and turbulence and aerodynamics involving LaRC facilities and scientists; and (4) computer science

A Study Into The Feasibility of Local Renewable Energy Systems With Storage, Using Security and Sustainability Metrics for Optimisation and Evaluation

The aim of this thesis was to develop tools for evaluating the potential sustainability and security of renewable energy systems in the UK, with a long-term view of maximising the potential renewable energy penetration of wind and solar by deployment of electrical energy storage. Using computer modelled renewable energy systems, a number of system variables are considered such as system size, energy sources (solar and/or wind), type of demand load, and capacity and type of storage technology. The results allow for a broad comparison of different types of renewable energy systems, and their optimisation. The optimisation methodology is also critically evaluated with consideration of its robustness and applicability, using two alternative metrics to measure system energy security and two different measurements of energy return on investment (EROI) to measure sustainability. When comparing renewable energy systems, results found that large systems that predominately got their power from wind sources were the most sustainable and secure, using optimisation methods that penalised both their overproduction and underproduction. Nearly all systems benefit from the use of electrical energy storage, without impacting too much on sustainability levels, but larger wind systems used less storage, suffering lower energy security as a result. System performance can best be improved by developing solar power technologies with lower embodied energy costs, followed by a reduction in embodied energy of storage technology. The former will enable more effective use of storage methods, while the latter allows for larger storage capacities with less environmental impact. Sustainability and energy security were given equal priority in the optimisation, however it was found that more sustainable generation technologies were preferable to more secure technologies, as there is more scope to improve energy return on investment than security. Therefore there is a limit, generally around 45-85\% (depending on size of system and choice of technology) to the proportion of time that renewable energy systems using variable energy sources can be autonomous, meaning that energy backup from the grid and/or dispatchable sources is still required

Handbook of Mathematical Geosciences

This Open Access handbook published at the IAMG's 50th anniversary, presents a compilation of invited path-breaking research contributions by award-winning geoscientists who have been instrumental in shaping the IAMG. It contains 45 chapters that are categorized broadly into five parts (i) theory, (ii) general applications, (iii) exploration and resource estimation, (iv) reviews, and (v) reminiscences covering related topics like mathematical geosciences, mathematical morphology, geostatistics, fractals and multifractals, spatial statistics, multipoint geostatistics, compositional data analysis, informatics, geocomputation, numerical methods, and chaos theory in the geosciences