Large Systems and Big Data: Models, Tools, Analysis, and Algorithms

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Understanding the behaviour of complex networked systems as clouds, CRANs, and social networks is critical as their deployments continue to grow rapidly. Another important class of problems is the development of methodologies to understand dependencies between different data sets so that we can obtain better forecasts and understand the temporal flow of information. The proposed research will have applications to weather prediction, financial markets, and medical imaging. The proposed research will consist of model building, the development of analytical tools, and the design of efficient algorithms to achieve the goals. The research addresses challenges related to operating and delivering real-time services on clouds, distributed servers and in 5G systems, and ways of detecting time dependencies in information flow to provide better predictive power. Of interest is the understanding of how to build distributed network architectures to deliver low latency performance and parsimonious prediction models. The research will provide better understanding on the design of load balancing in clouds and information retrieval when systems are in high load and understanding other load balancing strategies such as redundancy type mechanisms in large systems. Drawing on methodologies from stochastic models, randomized algorithms, convex optimization, graph approximation, and high-- dimensional statistics the research will focus on: 1) The development of low latency algorithms for load balancing and information retrieval in large distributed architectures such as clouds or distributed caching systems, 2) Understanding the information dynamics and consensus among a large group of interacting agents with social network applications and problems of the spread of infection, and 3) Understanding the temporal dependence in time series data from different sources with the aim of developing parsimonious representations for prediction algorithms. The first two themes are characterized by scale in the numbers of interacting entities and while the third involves inference of high dimensional statistics from big data. Success in this research will have important scientific and technological contributions. On the scientific side we will obtain new understanding on good latency policies and   extend mean-field techniques to a larger class of models. A better understanding of redundancy models will also be of use in other important applications such as organ exchange networks and hospital surgery scheduling. Understanding the dynamics of information flow in random networks will allow us to design better algorithms for faster information flow that can be critical in both social network and military applications. Finally obtaining better predictive models to deal with time series data is crucial in a wide variety of applications arising in IoT, medical imaging, finance, econometric models, and weather prediction.