Technical Report No. 2014-2 : Sheaf Invariants for Information Systems (AU-CAS-MathStats)

The primary objective of this project was to construct, classify, and exploit invariants for discriminating information systems that are based on abstracted structural descriptions. This main objective was split into three smaller objectives: (1) Construct invariants for information systems that exploit coarse and multiscale structural specifications about their underlying network or communication topology, (2) Classify the semantic and dynamic features of the systems that these in- variants consider, and (3) Exploit the classification results to provide actionable design and analysis rules that can be incorporated into experimental and simulation workflows. All of these objectives were met. Several interesting (and potentially important) discoveries were made as a result of the project. These discoveries have been reported to the scientifi c community, and they are being written as articles for archival journals. In addition, the Principal Investigator (PI), Prof. Michael Robinson, completed a draft of a manuscript entitled Topological Signal Processing that can be used to teach the techniques discovered on this project to beginning graduate student researchers. Finally, Prof. Robinson's research group grew from one student at the start of the project to ve students (partially funded by this project), partially as a means to apply the new algorithmic techniques discovered on this program.