Natural computation in the mesoscale dynamics of the brain

自然计算。从树木复杂的分枝生长到DNA的处理，许多自然过程和现象都可以通过计算的透镜来模拟和理解。 这个研究项目背后的主要驱动力是在计算方面自然系统的动力学框架。一旦以这种方式构建，我们就可以利用计算数学来建模和理解自然过程。与此同时，自然系统建模的挑战通过迫使新概念和技术的发展来扩展已知数学的边界。 在这个广泛的研究计划中，我建议研究人类大脑中大规模网络的动态。我们将收集神经成像数据，粗略地量化大脑空间受限区域的“神经活动”。如果我们将每个区域分配给一个节点，并且如果两个区域具有相似的活动模式，则在两个节点之间画一条线，我们定义了一个基于大脑活动的图。如果我们不是建立一个单一的图，而是建立一系列的图--随着神经关系的发展--我们现在就有了一个动态的图。拟议研究的“前端”是开发从神经成像数据推断这种动态图的最佳方法。 一旦生成了动态图形，我们就可以开始寻找图形随时间变化的模式。模式可以转化为（概率）规则，组成一个正式的计算系统，然后可以使用理论计算机科学的工具进行分析。 该计划的预期成果是开发新的自然计算模型，并将这些模型应用于理解人类大脑的动力学。

Nature computes. From the complex branching growth of a tree to the processing of DNA, many natural processes and phenomena can be modelled, and understood, through the lens of computation. The primary drive behind this research program is the framing of the dynamics of natural systems in terms of computation. Once framed this way, we can bring to bear the mathematics of computation to model and understand natural processes. At the same time, the challenge of modelling natural systems extends the boundaries of known mathematics by forcing the development of new concepts and techniques. Within this broad research program, I propose to study the dynamics of large-scale networks in the human brain. We will collect neuroimaging data which, roughly, quantifies "neural activity" in spatially constrained regions of the brain. If we assign each region to a node, and draw a line between two nodes if the two regions have similar patterns of activity, we define a brain activity based graph. If, instead of a single graph, we build a series of graphs -- as neural relationships evolve in time -- we now have a dynamic graph. The "front end" of the proposed research is to develop optimal methods for inferring such dynamic graphs from neuroimaging data. Once the dynamic graphs have been generated, we can begin to look for patterns in how the graphs change over time. Patterns can be turned into (probabilistic) rules which compose a formal computing system which can then be analyzed using the tools of theoretical computer science. The anticipated outcomes of this program are the development of new models of natural computing and the application of these models to understanding the dynamics of the human brain.