Improvements on the Study of Clumping Particulates and Pollutants
Leverage probabilistic dependency theory to better predict clumping in particulates
Improve sensor design and interpretation of data
In many different applications, objects such as particles, atoms, and even large bodies distributed at random have a tendency to "clump" or overlap. In many cases, we wish to know if such clumps are formed by chance or by interaction. One obvious use case is in the sampling of water or air seeking a pollutant count. Errors can be made if two overlapping particles are counted as one, and can lead to a bias.
There has been much research done in the area of random clumping, but much of it tends to assume independence among distributions or of particles. While particle interactions and other forces render this assumption incorrect, there lacks sufficient mathematical framework for improving the models. This project will leverage The Math Citadel's developed dependency theory in order to provide improved models for studying particle clumping.
In specialized manufacturing, such as electronics, pharmaceuticals, or other sensitive processes, improved methods of pollutant counting would help ensure more stringent standards for industrial hygiene
Manufacturing Quality Control
Fast-moving industrial processes rely on sensors or cameras to count objects moving by speedily. This research can help improve quality issues when clumping occurs.
Medicine and Epidemiology
Bacterial or other contaminant counting needs to be accurate. This body of research can help improve potential sampling bias issues, which can have large consequences in the study of contaminants in liquids, solids, or air.
One large bird or multiple birds? Flight requires the quick identification of objects or clumps of objects that may spread out and cause damage at the approach of an airplane.