Hierarchical Analysis of the Omega Ontology

Initial delivery for mathematical analysis of the Omega Ontology. We provide an analysis of the hierarchical structure of a version of the Omega Ontology currently in use within the US Government. After providing an initial statistical analysis of the distribution of all link types in the ontology, we then provide a detailed order theoretical analysis of each of the four main hierarchical links present. This order theoretical analysis includes the distribution of components and their properties, their parent/child and multiple inheritance structure, and the distribution of their vertical ranks

Hierarchical Analysis of the Omega Ontology

Initial delivery for mathematical analysis of the Omega Ontology. We provide an analysis of the hierarchical structure of a version of the Omega Ontology currently in use within the US Government. After providing an initial statistical analysis of the distribution of all link types in the ontology, we then provide a detailed order theoretical analysis of each of the four main hierarchical links present. This order theoretical analysis includes the distribution of components and their properties, their parent/child and multiple inheritance structure, and the distribution of their vertical ranks

Graph Approach to Uncertainty Quantification

Traditional analysis of uncertainty of the result of data processing assumes that all measurement errors are independent. In reality, there may be common factor affecting these errors, so these errors may be dependent. In such cases, the independence assumption may lead to underestimation of uncertainty. In such cases, a guaranteed way to be on the safe side is to make no assumption about independence at all. In practice, however, we may have information that a few pairs of measurement errors are indeed independent -- while we still have no information about all other pairs. Alternatively, we may suspect that for a few pairs of measurement errors, there may be correlation -- but for all other pairs, measurement errors are independent. In both cases, unusual pairs can be naturally represented as edges of a graph. In this paper, we show how to estimate the uncertainty of the result of data processing when this graph is small

Hypergraph Analysis of Structure Models

Theoretical discussion on the analysis of hypergraph networks; application of analysis methods to hypergraph networks derived by applying Reconstructability Analysis to health care data (the PhD dissertation work of Teresa Schmidt)