标题： 轮子：神经代码非凸性的新标准 显示英文标题

标题： Wheels: A New Criterion for Non-convexity of Neural Codes

摘要： 我们引入了新的几何和组合准则，这些准则排除了神经代码成为凸的可能，并利用它们来解决六个神经元的代码分类问题。 在此过程中，我们给出了第一个非凸的代码示例，该代码没有局部障碍，并且其单纯复形的维度为二。 我们还对单纯复形为低维或高维纯复形的神经代码的凸性进行了表征。 显示英文摘要

摘要： We introduce new geometric and combinatorial criteria that preclude a neural code from being convex, and use them to tackle the classification problem for codes on six neurons. Along the way, we give the first example of a code that is non-convex, has no local obstructions, and has simplicial complex of dimension two. We also characterize convexity for neural codes for which the simplicial complex is pure of low or high dimension.