Research Statement

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Dr. Abubakar Muhammad has done fundamental research at the interface of computational geometry, distributed algorithms, communication networks and control theory, concerning three prominent yet overlapping areas of research. He is investigating complex networked systems that will enable the future deployment of very large-scale and ubiquitous instances of sensor networks, robotic swarms and mobile networking. Second, he studies massive highdimensional data sets in various settings for rapid information discovery.He is also exploring quantum information theory and quantum control to understand better the physics of information. His approach in all three directions shares an emphasis on global topological methods, modes of information propagation and the role of feedback.

Connections & Complexity: Large-Scale Distributed Networks and their Dynamics

Perhaps the best word that summarizes summarizes the behavior of today’s global society is connectivity [1]. The pervasive influence of networks in allaspects of life - biological, physical, and social - has led researchers on the quest todiscover fundamental principles underpinning complex networked systems.Network phenomena manifest themselves in all aspects of biological diversities, from biochemical reactions and neural networks to insect swarms and complex ecological systems [2]. These effects are also visible in fundamental physics, for example in lattices ensembles of particles in statistical physics and spin networks inmost variants of quantum gravity. They are also found in such diverse engineered systems as power grids, communications networks, irrigation networks and transportation infrastructures.
Connectivity is also visible in all sorts of human social interactions such as collaboration, coordination and exchange of information, thus enabling the necessities and conveniences of modern life. All such network phenomena share a common principle — the emergence of global behavior from local interactions via adaptation and cooperation. Thus systematic studies of these remarkably diverse and pervasive examples hold great promises for solving numerous engineering and scientific problems. Research on networked sensing & control systems has already enabled the design, analysis and deployment of new types of networks, from sensory to robotic and from wireless to adhoc.

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