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Full-Text Articles in Set Theory
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 …
Computing Homology Of Hypergraphs, Jackson Earl
Computing Homology Of Hypergraphs, Jackson Earl
STAR Program Research Presentations
In the modern age of data science, the necessity for efficient and insightful analytical tools that enable us to interpret large data structures inherently presents itself. With the increasing utility of metrics offered by the mathematics of hypergraph theory and algebraic topology, we are able to explore multi-way relational datasets and actively develop such tools. Throughout this research endeavor, one of the primary goals has been to contribute to the development of computational algorithms pertaining to the homology of hypergraphs. More specifically, coding in python to compute the homology groups of a given hypergraph, as well as their Betti numbers …