Multi-state bootstrap percolation on digraphs as a framework for neuronal network analysis
Collaborators: Sabrina Streipert (Pitt Mathematics), Gregory Constantine (Pitt Mathematics), Amin Rahimian (Pitt Engineering)
Current trainees involved in the project: Owen Spencer, Cameron Watt (PhD student of Bard Ermentrout), Joe Denham (PhD student of Greg Constantine), Abhiram Kumar
Overarching questions: How does graph structure affect the overall spread of activation through a network? How do the connectivity properties of initially active nodes impact the success and rate of this process?
Some current projects:
(1) Extending the notion of diameter and other measures of information transmission to multi-state percolation processes, especially on Cayley graphs.
(2) Rigorously establishing the critical transition thresholds for multi-state bootstrap percolation on random graphs.
(3) Identifying key properties of initial activation sites that lead to effective multi-state bootstrap percolation, on various graph classes.
Overarching questions: How does graph structure affect the overall spread of activation through a network? How do the connectivity properties of initially active nodes impact the success and rate of this process?
Some current projects:
(1) Extending the notion of diameter and other measures of information transmission to multi-state percolation processes, especially on Cayley graphs.
(2) Rigorously establishing the critical transition thresholds for multi-state bootstrap percolation on random graphs.
(3) Identifying key properties of initial activation sites that lead to effective multi-state bootstrap percolation, on various graph classes.