Message-passing algorithms for optimal utilization of cognitive radio networks

Cognitive Radio has been proposed as a key technology to significantly improve spectrum usage in wireless networks by enabling unlicensed users to access unused resource. We present new algorithms that are needed for the implementation of opportunistic scheduling policies that maximize the throughput utilization of resources by secondary users, under maximum interference constraints imposed by existing primary users. Our approach is based on the Belief Propagation (BP) algorithm, which is advantageous due to its simplicity and potential for distributed implementation. We examine convergence properties and evaluate the performance of the proposed BP algorithms via simulations and demonstrate that the results compare favorably with a benchmark greedy strategy. © 2013 IEEE.

Convergence and knowledge processing in multi-agent systems

Multi-agent systems are complex systems comprised of multiple intelligent agents that act either independently or in cooperation with one another. Agent-based modelling is a method for studying complex systems like economies, societies, ecologies etc. Due to their complexity, very often mathematical analysis is limited in its ability to analyse such systems. In this case, agent-based modelling offers a practical, constructive method of analysis. The objective of this book is to shed light on some emergent properties of multi-agent systems. The authors focus their investigation on the effect of knowledge exchange on the convergence of complex, multi-agent systems.

Properties of a method of fundamental solutions for the parabolic heat equation

We show that a set of fundamental solutions to the parabolic heat equation, with each element in the set corresponding to a point source located on a given surface with the number of source points being dense on this surface, constitute a linearly independent and dense set with respect to the standard inner product of square integrable functions, both on lateral- and time-boundaries. This result leads naturally to a method of numerically approximating solutions to the parabolic heat equation denoted a method of fundamental solutions (MFS). A discussion around convergence of such an approximation is included.