Muir Dylan R, Mrsic-Flogel Thomas
Biozentrum, University of Basel, 4056 Basel, Switzerland.
Phys Rev E Stat Nonlin Soft Matter Phys. 2015 Apr;91(4):042808. doi: 10.1103/PhysRevE.91.042808. Epub 2015 Apr 24.
The eigenvalue spectrum of the matrix of directed weights defining a neural network model is informative of several stability and dynamical properties of network activity. Existing results for eigenspectra of sparse asymmetric random matrices neglect spatial or other constraints in determining entries in these matrices, and so are of partial applicability to cortical-like architectures. Here we examine a parameterized class of networks that are defined by sparse connectivity, with connection weighting modulated by physical proximity (i.e., asymmetric Euclidean random matrices), modular network partitioning, and functional specificity within the excitatory population. We present a set of analytical constraints that apply to the eigenvalue spectra of associated weight matrices, highlighting the relationship between connectivity rules and classes of network dynamics.
定义神经网络模型的有向权重矩阵的特征值谱能够反映网络活动的多种稳定性和动力学特性。稀疏非对称随机矩阵特征值谱的现有结果在确定这些矩阵的元素时忽略了空间或其他约束条件，因此仅部分适用于类皮质结构。在此，我们研究一类参数化网络，这类网络由稀疏连接定义，连接权重受物理距离调制（即非对称欧几里得随机矩阵）、模块化网络划分以及兴奋性群体内的功能特异性影响。我们提出了一组适用于相关权重矩阵特征值谱的解析约束条件，突出了连接规则与网络动力学类别之间的关系。
