Source:https://arxiv.org/abs/1703.10643
中枢神经系统由许多单独的单元组成 - 从细胞到区域 - 以复杂的链接模式组成功能网络,这些功能网络支持感知,动作和认知。一个自然而简约的想法是用图来表示该系统,其中节点(单元)通过边缘(相互作用)相连。虽然传统的图形方法适用于时空尺度,物种和群体,但是无法解决复杂的时变网络,这种模式对于理解情绪和认知状态,任务切换,适应和发展或老化和疾病蔓延至关重要。在这里我们概述一组应用数学工具,提供了表征动态图形的方法。同时我们也提供可视化、开源的MATLAB工具箱,用于现有或尚未获得的神经影像学数据。我们通过将工具箱应用于以前发布的时变功能图的数据集来举例说明,但请注意,这些工具也可以完全应用于时变结构图或其他类型的关系数据。我们的目标是为神经影像学社群提供一套有用的工具,提供如何使用它的感性认识,以解决准确和创造性解决动态图形方面涌现的新问题。
理解大脑系统需要从还原论和整体论视角的相互补充。还原方法对理解单个单元的结构和功能至关重要;整体论的方法对理解单个单元的在整个系统中的功能至关重要。网络表示是能够满足大脑全局建模要求的数学模型。
功能网络:
- 概念描述:At the neuronal scale, a functional edge might be an estimate of similarity in firing patterns [11], while at the large scale, it might be an estimate of similarity in BOLD time series [12] or ECOG signals [13, 14, 15]. Irrespective of spatial scale, when considering how to build a functional network representation from neural data, one is faced with the natural question of whether a single representation will suffice, or whether an ensemble of representations is required. Early but very important work in this field focused on constructing a single representation [16, 17, 18, 19], in which an edge summarized functional interactions between two neural units over a fixed time period.
- 不足:However, this approach is incompatible with the emerging interests in understanding the network dynamics – and not just its structure – that support cognition. ndeed, querying (i) fluctuations in an animal’s emotional or cognitive state [21, 22, 23], (ii) the manner in which an animal transitions between tasks [24, 25], or (iii) the variations in functional network architecture that are characteristic of perception and processing [26], learning [27, 28], development [29, 30], aging [18, 31], or disease progression [32] all require an assessment of a network’s dynamics.
量化处理时变网络的方法:
- Engineering approaches:independent components analysis, machine learning, and causal inference. (model-free learning: seek to learn a model directly from the data)
- Applied mathematics and specifically graph theory. (model-based learning: assume a formal graph model of the data)
本文主要聚焦于介绍第二类方法,所谓的dynamics graphs, 也称作 temporal networks. 讨论如何可视化、动态图的度量并且展示其在之前神经影像数据中的应用。作者开源了一个matlab工具包,并且阐明该这类工具也能应用在time-varying structural or morphometric graphs问题中。
1)作者描述不同的可视化动态图形的方式,并讨论每个的优缺点。
2)作者讨论如何对动态图进行编码,然后描述几个基本的动态图概念和度量,包括 time-respecting paths, latency, and centrality。
3)作者继续讨论零模型(null models)和其他度量,包括时间小世界和动态模块化结构。
4)作者概述了一些自然场景,其中可以构建动态图来处理关于脑结构和功能以及行为和疾病的神经生理机制的假设。