With the advent of volumetric EM techniques, large connectomic datasets are being created, providing neuroscience researchers with knowledge about the full connectivity of neural circuits under study. This allows for numerical simulation of detailed, biophysical models of each neuron participating in the circuit. However, these models typically include a large number of parameters, and insight into which of these are essential for circuit function is not readily obtained. Here, we review two mathematical strategies for gaining insight into connectomics data: linear dynamical systems analysis and matrix reordering techniques. Such analytical treatment can allow us to make predictions about time constants of information processing and functional subunits in large networks.

SIGNIFICANCE STATEMENT This viewpoint provides a concise overview on how to extract important insights from Connectomics data by mathematical methods. First, it explains how new dynamics and new time constants can evolve, simply through connectivity between neurons. These new time-constants can be far longer than the intrinsic membrane time-constants of the individual neurons. Second, it summarizes how structural motifs in the circuit can be discovered. Specifically, there are tools to decide whether or not a circuit is strictly feed-forward or whether feed-back connections exist. Only by reordering connectivity matrices can such motifs be made visible.

随着体积电磁技术的出现，大型连接组学数据集正在被创建，为神经科学研究人员提供了有关所研究的神经回路的完整连接性的知识。这允许对参与电路的每个神经元的详细生物物理模型进行数值模拟。然而，这些模型通常包含大量参数，并且很难深入了解其中哪些参数对于电路功能至关重要。在这里，我们回顾了两种深入了解连接组学数据的数学策略：线性动力系统分析和矩阵重排序技术。这种分析处理可以让我们对大型网络中信息处理和功能子单元的时间常数进行预测。

意义陈述该观点提供了如何通过数学方法从连接组学数据中提取重要见解的简明概述。首先，它解释了如何通过神经元之间的连接来进化新的动力学和新的时间常数。这些新的时间常数可能比单个神经元的固有膜时间常数长得多。其次，它总结了如何发现电路中的结构基序。具体来说，有一些工具可以确定电路是否严格前馈或是否存在反馈连接。只有通过重新排序连接矩阵才能使这些图案变得可见。