Minimal Embedding Dimensions of Connected Neural Codes

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.