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Full-Text Articles in Physical Sciences and Mathematics
Monoidal Supercategories And Superadjunction, Dene Lepine
Monoidal Supercategories And Superadjunction, Dene Lepine
Rose-Hulman Undergraduate Mathematics Journal
We define the notion of superadjunction in the context of supercategories. In particular, we give definitions in terms of counit-unit superadjunctions and hom-space superadjunctions, and prove that these two definitions are equivalent. These results generalize well-known statements in the non-super setting. In the super setting, they formalize some notions that have recently appeared in the literature. We conclude with a brief discussion of superadjunction in the language of string diagrams.
Strengthening Relationships Between Neural Ideals And Receptive Fields, Angelique Morvant
Strengthening Relationships Between Neural Ideals And Receptive Fields, Angelique Morvant
Rose-Hulman Undergraduate Mathematics Journal
Neural codes are collections of binary vectors that represent the firing patterns of neurons. The information given by a neural code C can be represented by its neural ideal JC. In turn, the polynomials in JC can be used to determine the relationships among the receptive fields of the neurons. In a paper by Curto et al., three such relationships, known as the Type 1-3 relations, were linked to the neural ideal by three if-and-only-if statements. Later, Garcia et al. discovered the Type 4-6 relations. These new relations differed from the first three in that they were …