论文标题
神经代码中的订单
Order-forcing in Neural Codes
论文作者
论文摘要
凸神经代码是布尔晶格的子集，可记录欧几里得空间中凸集的相交模式。近年来，许多工作重点是在代码上查找组合标准，这些代码可用于对代码是否为凸面进行分类。在本文中，我们介绍了订单式 - 一种组合工具，该工具识别何时实现代码中的某些区域必须沿着其他区域之间的线段出现。我们使用订单构建非凸代码的新例子，并扩大现有的示例家庭。我们还构建了一个代码系列，该家族表明，克鲁兹，朱斯蒂，伊斯科夫和克朗霍尔姆的维度结合（称为开放式凸的单调性）在所有维度上都很紧。
Convex neural codes are subsets of the Boolean lattice that record the intersection patterns of convex sets in Euclidean space. Much work in recent years has focused on finding combinatorial criteria on codes that can be used to classify whether or not a code is convex. In this paper we introduce order-forcing, a combinatorial tool which recognizes when certain regions in a realization of a code must appear along a line segment between other regions. We use order-forcing to construct novel examples of non-convex codes, and to expand existing families of examples. We also construct a family of codes which shows that a dimension bound of Cruz, Giusti, Itskov, and Kronholm (referred to as monotonicity of open convexity) is tight in all dimensions.
