Whalen Andrew J, Brennan Sean N, Sauer Timothy D, Schiff Steven J
Center for Neural Engineering, Penn State University, University Park, PA 16802.
Department of Mechanical Engineering, Penn State University, University Park, PA 16802.
Proc Conf Inf Sci Syst. 2012 Mar;2012. doi: 10.1109/CISS.2012.6310923.
We quantify observability in small (3 node) neuronal networks as a function of 1) the connection topology and symmetry, 2) the measured nodes, and 3) the nodal dynamics (linear and nonlinear). We find that typical observability metrics for 3 neuron motifs range over several orders of magnitude, depending upon topology, and for motifs containing symmetry the network observability decreases when observing from particularly confounded nodes. Nonlinearities in the nodal equations generally decrease the average network observability and full network information becomes available only in limited regions of the system phase space. Our findings demonstrate that such networks are partially observable, and suggest their potential efficacy in reconstructing network dynamics from limited measurement data. How well such strategies can be used to reconstruct and control network dynamics in experimental settings is a subject for future experimental work.
我们将小型（3节点）神经元网络中的可观测性量化为以下因素的函数：1）连接拓扑结构和对称性；2）被测量节点；3）节点动力学（线性和非线性）。我们发现，3神经元基序的典型可观测性指标范围跨越几个数量级，这取决于拓扑结构，并且对于包含对称性的基序，当从特别混淆的节点进行观测时，网络可观测性会降低。节点方程中的非线性通常会降低平均网络可观测性，并且只有在系统相空间的有限区域中才能获得完整的网络信息。我们的研究结果表明，此类网络是部分可观测的，并暗示了它们在从有限测量数据重建网络动力学方面的潜在功效。在实验环境中，这些策略在多大程度上能够用于重建和控制网络动力学，是未来实验工作的一个主题。
