2017/06/30 by Raffaella Mulas, Ngoc M. Tran, Ngoc M Tran
Biochemistry, Genetics and Molecular Biology · Computer Science · Engineering · Mathematics · #Cellular Automata and Applications #Characterization (materials science) #Dimension (graph theory) #Embedding #Encoding (memory) #Ferroelectric and Negative Capacitance Devices #Field (mathematics) #Finite field #Receptive field #Topological and Geometric Data Analysis #math.CO #q-bio.NC
paper · pdf · doi:10.2140/astat.2020.11.99
published as Algebraic Statistics 11, 1 (2020) 99-106 · 9 pages, 4 figures
openalex created_date 2017/08/31 · arxiv created 2017/11/28 · openalex publication_date 2020/10/01 · arxiv updated 2020/11/30 · openalex updated_date 2026/08/05
In the past few years, the study of receptive field codes has been of large interest to mathematicians. Here we give a complete characterization of receptive field codes realizable by connected receptive fields and we give the minimal embedding dimensions of these codes. In particular, we show that all connected codes are realizable in dimension at most 3. To our knowledge, this is the first family of receptive field codes for which the exact characterization and minimal embedding dimension is known.