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arXiv · 2106.06565

Neural Codes and Neural ring endomorphisms

Neha Gupta·Suhith K N
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Abstract

We investigate combinatorial, topological and algebraic properties of certain classes of neural codes. We look into a conjecture that states if the minimal \textit{open convex} embedding dimension of a neural code is two then its minimal \textit{convex} embedding dimension is also two. We prove the conjecture for two interesting classes of examples and provide a counterexample for the converse of the conjecture. We introduce a new class of neural codes, \textit{Doublet maximal}. We show that a Doublet maximal code is open convex if and only if it is max-intersection complete. We prove that surjective neural ring homomorphisms preserve max-intersection complete property. We introduce another class of neural codes, \textit{Circulant codes}. We give the count of neural ring endomorphisms for several sub-classes of this class.

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Neha Gupta, Suhith K N. 2023-09-20. Neural Codes and Neural ring endomorphisms. https://arxiv.org/abs/2106.06565

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