Topological data analyses are widely used for describing and conceptualizing large volumes of neurobiological data, e.g., for quantifying spiking outputs of large neuronal ensembles and thus understanding the functions of the corresponding networks. Below we discuss an approach in which convergent topological analyses produce insights into how information may be processed in mammalian hippocampus—a brain part that plays a key role in learning and memory. The resulting functional model provides a unifying framework for integrating spiking data at different timescales and following the course of spatial learning at different levels of spatiotemporal granularity. This approach allows accounting for contributions from various physiological phenomena into spatial cognition—the neuronal spiking statistics, the effects of spiking synchronization by different brain waves, the roles played by synaptic efficacies and so forth. In particular, it is possible to demonstrate that networks with plastic and transient synaptic architectures can encode stable cognitive maps, revealing the characteristic timescales of memory processing.

中文翻译：

---

从拓扑分析到功能建模：以海马为例

拓扑数据分析广泛用于描述和概念化大量神经生物学数据，例如，用于量化大型神经元集合的尖峰输出，从而了解相应网络的功能。下面我们将讨论一种方法，在该方法中，收敛拓扑分析可以深入了解哺乳动物海马体（一个在学习和记忆中起关键作用的大脑部分）中如何处理信息。由此产生的功能模型提供了一个统一的框架，用于集成不同时间尺度的尖峰数据，并遵循不同时空粒度级别的空间学习过程。这种方法可以解释各种生理现象对空间认知的贡献——神经元尖峰统计，不同脑电波刺激同步的影响，突触效应所起的作用等。特别是，可以证明具有可塑性和瞬态突触结构的网络可以编码稳定的认知图，揭示记忆处理的特征时间尺度。