模块间连接对离散小世界神经网络快速稀疏同步的影响
Effect of Inter-Modular Connection on Fast Sparse Synchronization in Clustered Small-World Neural Networks
摘要：
我们认为一个集群网络的小世界子网络的抑制性快速尖峰interneurons，并调查模块间连接的影响出现快速稀疏同步的节奏，通过改变模块间耦合强度$J_{inter}$和平均数的模块间链接每个interneuron $M_{syn}^{(inter)}$。与非成簇网络的情况相比，发现了两种稀疏同步状态，即模块化和全局同步;对于模块化稀疏同步情况，由于子网络的模块内动力学行为造成了一些不匹配，种群行为表现出模块化结构。另一方面，在全局稀疏同步的情况下，种群行为是全局相同的，独立于集群结构，因为子网络的模块内动力学进行完美匹配。我们引入了一个现实的互相关模块性措施，代表子网络的瞬时子种群尖峰率之间的匹配程度，并检查是否稀疏同步是全球或模块化。此外，我们采用现实的子和整体人口的序参数和螺旋机械措施的模块化和全球稀疏同步的特点。因此，发现$J_{inter}$和$M_{syn}^{(inter)}$的作用如下。对于大的$J_{inter}$，由于强抑制，它起着“破坏”棘波之间起搏的破坏性作用，而对于小的$J_{inter}$，它起着“有利于”棘波之间起搏的建设性作用。相比之下，$M_{syn}^{(inter)}$似乎只是在促进尖峰之间的起搏方面发挥作用。随着$M_{syn}^{(inter)}$的增加，由于尖峰之间的全局通信的有效程度的增加，尖峰之间的起搏程度单调增加。
英文摘要：
We consider a clustered network with small-world sub-networks of inhibitory fast spiking interneurons, and investigate the effect of inter-modular connection on emergence of fast sparsely synchronized rhythms by varying both the inter-modular coupling strength $J_{inter}$ and the average number of inter-modular links per interneuron $M_{syn}^{(inter)}$. In contrast to the case of non-clustered networks, two kinds of sparsely synchronized states such as modular and global synchronization are found. For the case of modular sparse synchronization, the population behavior reveals the modular structure, because the intra-modular dynamics of sub-networks make some mismatching. On the other hand, in the case of global sparse synchronization, the population behavior is globally identical, independently of the cluster structure, because the intra-modular dynamics of sub-networks make perfect matching. We introduce a realistic cross-correlation modularity measure, representing the matching-degree between the instantaneous sub-population spike rates of the sub-networks, and examine whether the sparse synchronization is global or modular. Furthermore, we characterize the modular and global sparse synchronization by employing the realistic sub- and whole-population order parameters and statistical-mechanical measures. The roles of $J_{inter}$ and $M_{syn}^{(inter)}$ are thus found as follows. For large $J_{inter}$, due to strong inhibition it plays a destructive role to "spoil" the pacing between spikes, while for small $J_{inter}$ it plays a constructive role to "favor" the pacing between spikes. In contrast, $M_{syn}^{(inter)}$ seems to play a role just to favor the pacing between spikes. With increasing $M_{syn}^{(inter)}$, the pacing degree between spikes increases monotonically thanks to the increase in the degree of effectiveness of global communication between spikes.
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