Open Access. Powered by Scholars. Published by Universities.®
Discrete Mathematics and Combinatorics Commons™
Open Access. Powered by Scholars. Published by Universities.®
- Discipline
Articles 1 - 2 of 2
Full-Text Articles in Discrete Mathematics and Combinatorics
Foundations Of Memory Capacity In Models Of Neural Cognition, Chandradeep Chowdhury
Foundations Of Memory Capacity In Models Of Neural Cognition, Chandradeep Chowdhury
Master's Theses
A central problem in neuroscience is to understand how memories are formed as a result of the activities of neurons. Valiant’s neuroidal model attempted to address this question by modeling the brain as a random graph and memories as subgraphs within that graph. However the question of memory capacity within that model has not been explored: how many memories can the brain hold? Valiant introduced the concept of interference between memories as the defining factor for capacity; excessive interference signals the model has reached capacity. Since then, exploration of capacity has been limited, but recent investigations have delved into the …
Representations From Group Actions On Words And Matrices, Joel T. Anderson
Representations From Group Actions On Words And Matrices, Joel T. Anderson
Master's Theses
We provide a combinatorial interpretation of the frequency of any irreducible representation of Sn in representations of Sn arising from group actions on words. Recognizing that representations arising from group actions naturally split across orbits yields combinatorial interpretations of the irreducible decompositions of representations from similar group actions. The generalization from group actions on words to group actions on matrices gives rise to representations that prove to be much less transparent. We share the progress made thus far on the open problem of determining the irreducible decomposition of certain representations of Sm × Sn arising from group actions on matrices.