Nearby grid cells have been observed to express a remarkable degree of long-range order, which is often idealized as extending potentially to infinity. Yet their strict periodic firing and ensemble coherence are theoretically possible only in flat environments, much unlike the burrows which rodents usually live in. Are the symmetrical, coherent grid maps inferred in the lab relevant to chart their way in their natural habitat? We consider spheres as simple models of curved environments and waiting for the appropriate experiments to be performed, we use our adaptation model to predict what grid maps would emerge in a network with the same type of recurrent connections, which on the plane produce coherence among the units. We find that on the sphere such connections distort the maps that single grid units would express on their own, and aggregate them into clusters. When remapping to a different spherical environment, units in each cluster maintain only partial coherence, similar to what is observed in disordered materials, such as spin glasses.

中文翻译：

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自组织球形网格中的部分连贯性和挫折。

已经观察到附近的网格单元表现出显着程度的长程有序，这通常被理想化为可能扩展到无穷大。然而，它们严格的周期性发射和整体连贯性在理论上只能在平坦的环境中实现，这与啮齿动物通常居住的洞穴非常不同。实验室中推断出的对称、连贯的网格图是否与它们在自然栖息地中的路线图相关？我们将球体视为弯曲环境的简单模型并等待进行适当的实验，我们使用我们的适应模型来预测具有相同类型的循环连接的网络中会出现哪些网格图，这在平面上产生了单位。我们发现在球体上，这种连接扭曲了单个网格单元自己表达的地图，并将它们聚合成簇。当重新映射到不同的球形环境时，每个簇中的单元仅保持部分相干性，类似于在无序材料（如自旋玻璃）中观察到的情况。