Neural codes, decidability, and a new local obstruction to convexity

@article{Chen2018NeuralCD,
  title={Neural codes, decidability, and a new local obstruction to convexity},
  author={Aaron Chen and Florian Frick and Anne Shiu},
  journal={CoRR},
  year={2018},
  volume={abs/1803.11516}
}
Given an intersection pattern of arbitrary sets in Euclidean space, is there an arrangement of convex open sets in Euclidean space that exhibits the same intersections? This question is combinatorial and topological in nature, but is motivated by neuroscience. Specifically, we are interested in a type of neuron called a place cell, which fires precisely when an organism is in a certain region, usually convex, called a place field. The earlier question, therefore, can be rephrased as follows… CONTINUE READING

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