摘要翻译：
利用最近提出的一种优化算法，对任意给定的无标度分布，明确地设计了最优可同步（未加权）网络。我们探索优化过程如何影响度-度相关性，并观察到一个普遍的不协调趋势。然而，我们表明同步性和不协调性之间并不是一一对应的。另一方面，我们研究了最优非同步网络的性质，即拓扑结构使同步状态的稳定范围最小的网络。由此产生的“悲观网络”具有高度协调的弦状结构。我们还导出了控制网络同步性的拉普拉斯特征值比的严格下界，这有助于理解度相关对网络同步性的影响。
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英文标题：
《Network synchronization: Optimal and Pessimal Scale-Free Topologies》
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作者：
Luca Donetti, Pablo I. Hurtado and Miguel A. Munoz
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最新提交年份：
2007
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分类信息：

一级分类：Physics        物理学
二级分类：Disordered Systems and Neural Networks        无序系统与神经网络
分类描述：Glasses and spin glasses; properties of random, aperiodic and quasiperiodic systems; transport in disordered media; localization; phenomena mediated by defects and disorder; neural networks
眼镜和旋转眼镜；随机、非周期和准周期系统的性质；无序介质中的传输；本地化；由缺陷和无序介导的现象；神经网络
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一级分类：Physics        物理学
二级分类：Statistical Mechanics        统计力学
分类描述：Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变，热力学，场论，非平衡现象，重整化群和标度，可积模型，湍流
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英文摘要：
  By employing a recently introduced optimization algorithm we explicitely design optimally synchronizable (unweighted) networks for any given scale-free degree distribution. We explore how the optimization process affects degree-degree correlations and observe a generic tendency towards disassortativity. Still, we show that there is not a one-to-one correspondence between synchronizability and disassortativity. On the other hand, we study the nature of optimally un-synchronizable networks, that is, networks whose topology minimizes the range of stability of the synchronous state. The resulting ``pessimal networks'' turn out to have a highly assortative string-like structure. We also derive a rigorous lower bound for the Laplacian eigenvalue ratio controlling synchronizability, which helps understanding the impact of degree correlations on network synchronizability.
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PDF链接：
https://arxiv.org/pdf/710.4886