@phdthesis{oai:oist.repo.nii.ac.jp:02000022,
 author = {Thomas Francis Burns},
 month = {2023-09-27, 2023-09-27},
 note = {Geometry and topology offer rich mathematical worlds and perspectives with which to study and improve our understanding of cognitive function. Here I present the following examples: (1) a functional role for inhibitory diversity in associative memories with graph- ical relationships; (2) improved memory capacity in an associative memory model with setwise connectivity, with implications for glial and dendritic function; (3) safe and effi- cient group navigation among conspecifics using purely local geometric information; and　(4) enhancing geometric and topological methods to probe the relations between neural activity and behaviour. In each work, tools and insights from geometry and topology are used in essential ways to gain improved insights or performance. This thesis contributes to our knowledge of the potential computational affordances of biological mechanisms (such as inhibition and setwise connectivity), while also demonstrating new geometric and topological methods and perspectives with which to deepen our understanding of cognitive tasks and their neural representations.},
 school = {Okinawa Institute of Science and Technology Graduate University},
 title = {記憶と探索におけるジオメトリとトポロジ},
 year = {}
}