Fagerholm Erik D, Foulkes W M C, Gallero-Salas Yasir, Helmchen Fritjof, Friston Karl J, Leech Robert, Moran Rosalyn J
Department of Neuroimaging, King's College London, London, United Kingdom.
Department of Physics, Imperial College London, London, United Kingdom.
Front Comput Neurosci. 2021 Apr 21;15:643148. doi: 10.3389/fncom.2021.643148. eCollection 2021.
We derive a theoretical construct that allows for the characterisation of both scalable and scale free systems within the dynamic causal modelling (DCM) framework. We define a dynamical system to be "scalable" if the same equation of motion continues to apply as the system changes in size. As an example of such a system, we simulate planetary orbits varying in size and show that our proposed methodology can be used to recover Kepler's third law from the timeseries. In contrast, a "scale free" system is one in which there is no characteristic length scale, meaning that images of such a system are statistically unchanged at different levels of magnification. As an example of such a system, we use calcium imaging collected in murine cortex and show that the dynamical critical exponent, as defined in renormalization group theory, can be estimated in an empirical biological setting. We find that a task-relevant region of the cortex is associated with higher dynamical critical exponents in task vs. spontaneous states and vice versa for a task-irrelevant region.
我们推导了一种理论结构，该结构能够在动态因果模型（DCM）框架内对可扩展和无标度系统进行表征。如果运动方程在系统大小发生变化时仍然适用，我们就将一个动态系统定义为“可扩展的”。作为此类系统的一个例子，我们模拟了大小不同的行星轨道，并表明我们提出的方法可用于从时间序列中恢复开普勒第三定律。相比之下，“无标度”系统是指不存在特征长度尺度的系统，这意味着该系统的图像在不同放大倍数下在统计上是不变的。作为此类系统的一个例子，我们使用在小鼠皮层中收集的钙成像，并表明在经验性生物学环境中可以估计重整化群理论中定义的动态临界指数。我们发现，与任务相关的皮层区域在任务状态与自发状态下与更高的动态临界指数相关，而与任务无关的区域则相反。
