Persistent cohomology is a powerful technique for discovering topological structure in data. Strategies for its use in neuroscience are still undergoing development. We comprehensively and rigorously assess its performance in simulated neural recordings of the brain’s spatial representation system. Grid, head direction, and conjunctive cell populations each span low-dimensional topological structures embedded in high-dimensional neural activity space. We evaluate the ability for persistent cohomology to discover these structures for different dataset dimensions, variations in spatial tuning, and forms of noise. We quantify its ability to decode simulated animal trajectories contained within these topological structures. We also identify regimes under which mixtures of populations form product topologies that can be detected. Our results reveal how dataset parameters affect the success of topological discovery and suggest principles for applying persistent cohomology, as well as persistent homology, to experimental neural recordings.

中文翻译：

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通过空间表示系统中的持久上同调来评估状态空间发现

持久上同调是发现数据拓扑结构的强大技术。其在神经科学中的应用策略仍在制定中。我们全面而严格地评估其在大脑空间表征系统的模拟神经记录中的性能。网格、头部方向和结细胞群各自跨越嵌入高维神经活动空间中的低维拓扑结构。我们评估持久上同调发现不同数据集维度、空间调谐变化和噪声形式的这些结构的能力。我们量化了它解码这些拓扑结构中包含的模拟动物轨迹的能力。我们还确定了群体混合物形成可检测的产品拓扑的机制。我们的结果揭示了数据集参数如何影响拓扑发现的成功，并提出了将持久上同调以及持久同源应用于实验神经记录的原则。