CIF: Medium: Collaborative Research: Tracking low-dimensional information in data streams and dynamical systems

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Many applications of significant societal impact are modeled bycomplex dynamical system behavior, including the (life, physicaland social) sciences, medicine, economics, law, urban development,international politics and global conflict. Fortunately, recentadvances in sensor technology have allowed observation of thesephenomena at an unprecedented scale. Unfortunately, the volume andcomplexity of available data present many challenges to extractingmeaningful information about these systems. Low-dimensional modelsserve as a useful structure for understanding the information inhigh-dimensional signals and systems. However, this informationoften changes over time, and so these models can further beimproved by exploiting temporal dynamics. This project is concernedwith developing new methods for tracking changing low-dimensionalstructure in data streams and dynamical systems, particularly insettings where the observations may be missing, incomplete,corrupted, or compressed.The first research aim in this project is to develop new andsubstantially improve existing techniques for trackinglow-dimensional structure and, in particular, to extend trackingcapabilities far beyond conventional signals to much more generaldata sets with intrinsic low-dimensional structure. A secondresearch aim is to develop new tools for tracking low-dimensionalstructure in systems jointly with estimating the content oftime-varying signals and data sets. A third research aim isconcerned with higher-dimensional and more complex dynamicalsystems, and the goal is to develop improved methods that exploitlow-dimensional structure to perform quantitative and qualitativeanalysis in systems that are too complex and high-dimensional forsystem identification. In a fourth, educational aim, accessibleK-12 outreach materials are being developed for disseminationthrough an online digital library.