2015/01/01 by Yuri I. Manin, Manin, Yuri I.
Computer Science · Mathematics · #94A08 #FOS: Biological sciences #FOS: Mathematics #History and Overview (math.HO) #Image Retrieval and Classification Techniques #Morphological variations and asymmetry #Neural Networks and Applications #Neurons and Cognition (q-bio.NC)
paper · pdf · doi:10.48550/arxiv.1501.00897
openalex publication_date 2015/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This note is a brief survey of some results of the recent collaboration of neurobiologists and mathematicians dedicated to stimulus reconstruction from neuronal spiking activity. This collaboration, in particular, led to the consideration of binary codes used by brain for encoding a stimuli domain such as a rodent's territory through the combinatorics of its covering by local neighborhoods. The survey is addressed to mathematicians (cf. [DeSch01]) and focuses on the idea that stimuli spaces are represented by the relevant neural codes as simplicial sets and thus encode say, the homotopy type of space if local neighborhoods are convex (see [CuIt08], [CuItVCYo13], [Yo14], [SiGh07]).