A Sheaf Theoretical Approach to Uncertainty Quantification of Heterogeneous Geolocation Information.

Integration of multiple, heterogeneous sensors is a challenging problem across a range of applications. Prominent among these are multi-target tracking, where one must combine observations from different sensor types in a meaningful and efficient way to track multiple targets. Because different sensors have differing error models, we seek a theoretically justified quantification of the agreement among ensembles of sensors, both overall for a sensor collection, and also at a fine-grained level specifying pairwise and multi-way interactions among sensors.

The gene ontology categorizer.

The Gene Ontology Categorizer, developed jointly by the Los Alamos National Laboratory and Procter & Gamble Corp., provides a capability for the categorization task in the Gene Ontology (GO): given a list of genes of interest, what are the best nodes of the GO to summarize or categorize that list? The motivating question is from a drug discovery process, where after some gene expression analysis experiment, we wish to understand the overall effect of some cell treatment or condition by identifying 'where' in the GO the differentially expressed genes fall: 'clustered' together in one place? in two places? uniformly spread throughout the GO? 'high', or 'low'? In order to address this need, we view bio-ontologies more as combinatorially structured databases than facilities for logical inference, and draw on the discrete mathematics of finite partially ordered sets (posets) to develop data representation and algorithms appropriate for the GO. In doing so, we have laid the foundations for a general set of methods to address not just the categorization task, but also other tasks (e.