2021/06/11 by Neha Gupta, Gupta, Neha, K N Suhith +1
Biochemistry, Genetics and Molecular Biology · Computer Science · Neuroscience · #16W20 #52A37 #54H99 #92B20 #Combinatorics (math.CO) #FOS: Mathematics #Geometric Topology (math.GT) #Neuroinflammation and Neurodegeneration Mechanisms #Receptor Mechanisms and Signaling #Rings and Algebras (math.RA) #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2106.06565
openalex publication_date 2021/06/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We investigate combinatorial, topological and algebraic properties of certain classes of neural codes. We look into a conjecture that states if the minimal open convex embedding dimension of a neural code is two then its minimal 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, 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, Circulant codes. We give the count of neural ring endomorphisms for several sub-classes of this class.