基于分布Zeta函数的系统性能测量
Systemic Performance Measures from Distributional Zeta-Function
摘要：
我们建议使用分布Zeta函数（DZF）构建一套新的系统性能指标（SPM）。SPM已经被提出来研究网络合成问题，如线性共识网络的增长。DZF的采用已经显示出在通常的复制方法中仍然未澄清的有趣的物理后果，即，无序模型中自发对称性破缺机制与副本空间结构之间的联系。我们将网络的拓扑结构与DZF中的配分函数联系起来，利用系统的谱结构和哈密顿结构。研究对象是场网络的广义配分函数、DZF、副本配分函数的期望值和猝灭自由能。我们表明，这些对象，我们需要很少的操作，以增加网络的性能增强的百分比。此外，我们评估的位置的最佳添加的链接，为每个新的SPM和计算的性能改善的新网络的每个新的SPM通过频谱zeta函数，$\mathcal{H}_{2}$ -范数，和节点之间的可通信性。我们提出了这一新的SPM在网络合成中的优势，我们提出了其他方法使用DZF探索一些问题，如无序，临界现象，有限温度，和有限大小的影响网络。结果的相关性进行了讨论。
英文摘要：
We propose the use of the Distributional Zeta-Function (DZF) for constructing a new set of Systemic Performance Measures (SPM). SPM have been proposed to investigate network synthesis problems such as the growing of linear consensus networks. The adoption of the DZF has shown interesting physical consequences that in the usual replica method are still unclarified, i.e., the connection between the spontaneous symmetry breaking mechanism and the structure of the replica space in the disordered model. We relate topology of the network and the partition function present in the DZF by using the spectral and the Hamiltonian structure of the system. The studied objects are the generalized partition funcion, the DZF, the Expected value of the replica partition function, and the quenched free energy of a field network. We show that with these objects we need few operations to increase the percentage of performance enhancement of a network. Furthermore, we evalue the location of the optimal added links for each new SPM and calculate the performance improvement of the new network for each new SPM via the spectral zeta function, $\mathcal{H}_{2}$-norm, and the communicability between nodes. We present the advantages of this new set of SPM in the network synthesis and we propose other methods for using the DZF to explore some issues such as disorder, critical phenomena, finite-temperature, and finite-size effects on networks. Relevance of the results are discussed.
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