论文标题
具有三个最大代码字的神经代码：凸度和最小嵌入维度
Neural Codes With Three Maximal Codewords: Convexity and Minimal Embedding Dimension
论文作者
论文摘要
神经代码（表示为二元字符串的集合称为编码字），用于编码神经活动。如果将其代码字表示为欧几里得空间中的凸开放集的布置，则称为凸面。以前的工作重点是解决以下问题：我们如何判断神经代码何时为凸？朱斯蒂（Giusti）和斯科夫（Iskov）确定了局部障碍，并证明凸神经法规没有局部障碍。相反的是最多四个神经元的代码，但通常是错误的。然而，我们证明了这种相反的代码最多具有三个最大代码字，而且此类代码的最小嵌入尺寸最多是两个。
Neural codes, represented as collections of binary strings called codewords, are used to encode neural activity. A code is called convex if its codewords are represented as an arrangement of convex open sets in Euclidean space. Previous work has focused on addressing the question: how can we tell when a neural code is convex? Giusti and Itskov identified a local obstruction and proved that convex neural codes have no local obstructions. The converse is true for codes on up to four neurons, but false in general. Nevertheless, we prove this converse holds for codes with up to three maximal codewords, and moreover the minimal embedding dimension of such codes is at most two.
