Vol. 11, No. 1, 2020

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ISSN (electronic): 2693-3004
ISSN (print): 2693-2997
 
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Minimal embedding dimensions of connected neural codes

Raffaella Mulas and Ngoc M. Tran

Vol. 11 (2020), No. 1, 99–106
Abstract

A receptive field code is a recently proposed deterministic model of neural activity patterns in response to stimuli. The main question is to characterize the set of realizable codes, and their minimal embedding dimensions with respect to a given family of receptive fields. Here we answer both of these questions when the receptive fields are connected. In particular, we show that all connected codes are realizable in dimension at most three. To our knowledge, this is the first family of receptive field codes for which both the exact characterization and minimal embedding dimension are known.

Keywords
none, receptive field code, minimal embedding, realizability
Mathematical Subject Classification 2010
Primary: 92B20, 05C65, 05C10
Milestones
Received: 12 October 2017
Revised: 13 July 2018
Accepted: 18 February 2019
Published: 1 October 2020
Authors
Raffaella Mulas
MPI MiS-Leipzig
Germany
Ngoc M. Tran
University of Texas at Austin
Austin, TX
United States
Hausdorff Center for Mathematics
Bonn
Germany