Einstein institute of Mathematics, The Hebrew University, Jerusalem, 9190401, Israel.
School of Computing, University of Leeds, Woodhouse Lane, Leeds, LS9 2JT, UK.
Sci Rep. 2021 Oct 25;11(1):20957. doi: 10.1038/s41598-021-00281-y.
A common approach to interpreting spiking activity is based on identifying the firing fields-regions in physical or configuration spaces that elicit responses of neurons. Common examples include hippocampal place cells that fire at preferred locations in the navigated environment, head direction cells that fire at preferred orientations of the animal's head, view cells that respond to preferred spots in the visual field, etc. In all these cases, firing fields were discovered empirically, by trial and error. We argue that the existence and a number of properties of the firing fields can be established theoretically, through topological analyses of the neuronal spiking activity. In particular, we use Leray criterion powered by persistent homology theory, Eckhoff conditions and Region Connection Calculus to verify consistency of neuronal responses with a single coherent representation of space.
一种常见的尖峰活动解释方法是基于识别发放区域——在物理或配置空间中，神经元会对这些区域做出反应。常见的例子包括在导航环境中对首选位置放电的海马体位置细胞、对动物头部首选方向放电的头方向细胞、对视野中首选点作出反应的视图细胞等。在所有这些情况下，发放区域都是通过反复试验经验性地发现的。我们认为，通过对神经元尖峰活动的拓扑分析，可以从理论上确定发放区域的存在和一些性质。具体来说，我们使用持久同调理论驱动的 Leray 准则、Eckhoff 条件和区域连接演算来验证神经元反应与单一连贯的空间表示的一致性。
