Rethinking the Data-driven Discovery of Rare Phenomena. This project will investigate novel technologies for the data-driven discovery of rare phenomena. Scientific disciplines are increasingly able to generate large amounts of data relevant to key discoveries such as novel photovoltaic materials or explanations of brain seizures. However, these discoveries typically correspond to extremely rare phenomena in high dimensional spaces, which current data science methods are unable to detect. The pr ....Rethinking the Data-driven Discovery of Rare Phenomena. This project will investigate novel technologies for the data-driven discovery of rare phenomena. Scientific disciplines are increasingly able to generate large amounts of data relevant to key discoveries such as novel photovoltaic materials or explanations of brain seizures. However, these discoveries typically correspond to extremely rare phenomena in high dimensional spaces, which current data science methods are unable to detect. The project will fill this void and yield novel methods, publications, and open source software for the data-driven discovery or rare phenomena. Thus, it will expand the capabilities of data science, providing better use of the massive data collections accumulating across science, government, and industry.Read moreRead less
Computational methods for population-size-dependent branching processes. Branching processes are the primary mathematical tool used to model populations that evolve randomly in time. Most key results in the theory are derived under the simplifying assumption that individuals reproduce and die independently of each other. However, this assumption fails in most real-life situations, in particular when the environment has limited resources or when the habitat has a restricted capacity. This project ....Computational methods for population-size-dependent branching processes. Branching processes are the primary mathematical tool used to model populations that evolve randomly in time. Most key results in the theory are derived under the simplifying assumption that individuals reproduce and die independently of each other. However, this assumption fails in most real-life situations, in particular when the environment has limited resources or when the habitat has a restricted capacity. This project aims to develop novel and effective algorithmic techniques and statistical methods for a class of branching processes with dependences. We will use these results to study significant problems in the conservation of endangered island bird populations in Oceania, and to help inform their conservation management.Read moreRead less