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The goal of this internship is to create a venue for students to apply mathematical tools from more abstract fields such as algebraic topology or graph theory to engineering and scientific problems in space networking.
This opportunity is a continuation of several group efforts by students working together. Their contributions are integrated into the project, and typically we try to get some publications out based on the work.
In the past, we have explored applications towards such areas as machine learning, star tracking, route-planning, and network dynamics. For the summer of 2022, we are focusing on the list of topics below, which expands upon our ongoing research.
• Applications of sheaves to communications networks in space
o Continue development of sheaf-based networking theory and temporal graph theory
o Implement networking ideas in software (e.g. using PySheaf or NetworkX)
o Construct simulated networks and incorporate software with simulated network data
o Determine and test models for network data management using sheaves
o Draw inspiration using papers from past internships such as:
A Mathematical Analysis of an Example Delay Tolerant Network Using Sheaves
Towards Sheaf Theoretic Analyses for Delay Tolerant Networking
Dude Where’s My Stars: A Novel Topologically Justified Approach to Star Tracking
Path Optimization Sheaves
• Applications of tropical geometry to space networking
o Continue development of parametric graph optimization strategy
o Construct parametric graph models of simulated networks
o Create simulations to verify operation of tropical implementations
o Draw inspiration from papers such as:
Parametric shortest-path algorithms via tropical geometry
Modeling and control of switching max-plus-linear systems with random and deterministic switching
Desired Qualifications: A background in mathematics or computer science with an interest in networking and applications.
Computer/Software Skills: C/C++/Python/Sage/Maple/R
NASA’s Space Communications and Navigation (SCaN) Program Office, a division of the Human Exploration and Operations Mission Directorate at NASA Headquarters in Washington, provides programmatic oversight of NASA’s networks, advanced communication technologies, and other space communication requirements. These capabilities form the backbone of all NASA missions, providing critical connectivity from spacecraft to ground. SCaN provides the strategic guidance necessary to ensure NASA’s space communication resources continue to meet the needs of their customers and the agency for years to come. SCaN is actively engaged in the wider international community dedicated to interoperability and compatibility for space communications and navigation.