标题： 快速有向$q$-分析脑图 显示英文标题

标题： Fast Directed $q$-Analysis for Brain Graphs

摘要： 最近在重建大规模、全精度、神经元突触尺度的连接组方面的创新，需要后续对图分析方法进行改进，以跟上数据日益增长的复杂性和规模。 其中一个工具是最近引入的有向$q$分析。 我们对该技术进行了许多理论和应用上的改进：在理论上，我们引入了有向$q$分析的关键元素的修改定义，这些定义解决了之前隐藏且未被发现的偏差。 这也带来了与相关计算挑战相关的新的有益视角。 最重要的是，我们提供了一个高速、公开可用的低级实现，在秀丽线虫上实现了几个数量级的速度提升。 此外，速度提升随着所考虑图的大小而增加。 这得益于数学和算法的改进以及精心设计的实现。 这些加速首次使全尺寸连接组的分析成为可能，例如通过最近的重建方法获得的连接组。 此外，速度提升允许对相应的空模型进行比较分析，这些空模型是适当设计的随机结构的人工图，不对应于实际的大脑。 反过来，这使得评估有向$q$分析在研究大脑中的有效性和实用性成为可能。 我们在本文中报告了这些结果。 显示英文摘要

摘要： Recent innovations in reconstructing large scale, full-precision, neuron-synapse-scale connectomes demand subsequent improvements to graph analysis methods to keep up with the growing complexity and size of the data. One such tool is the recently introduced directed $q$-analysis. We present numerous improvements, theoretical and applied, to this technique: on the theoretical side, we introduce modified definitions for key elements of directed $q$-analysis, which remedy a well-hidden and previously undetected bias. This also leads to new, beneficial perspectives to the associated computational challenges. Most importantly, we present a high-speed, publicly available, low-level implementation that provides speed-ups of several orders of magnitude on C. Elegans. Furthermore, the speed gains grow with the size of the considered graph. This is made possible due to the mathematical and algorithmic improvements as well as a carefully crafted implementation. These speed-ups enable, for the first time, the analysis of full-sized connectomes such as those obtained by recent reconstructive methods. Additionally, the speed-ups allow comparative analysis to corresponding null models, appropriately designed randomly structured artificial graphs that do not correspond to actual brains. This, in turn, allows for assessing the efficacy and usefulness of directed $q$-analysis for studying the brain. We report on the results in this paper.