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Analysis of properties of Ising and Kuramoto models that are preserved in networks constructed by visualization algorithms

机译:可视化算法构建的网络中保留的ising和Kuramoto模型的特性分析

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摘要

Recently it has been shown that building networks from time series allows to study complex systems to characterize them when they go through a phase transition. This give us the opportunity to study this systems from a entire new point of view. In the present work we have used the natural and horizontal visualization algorithms to built networks of two popular models, which present phase transitions: the Ising model and the Kuramoto model. By measuring some topological quantities as the average degree, or the clustering coefficient, it was found that the networks retain the capability of detecting the phase transition of the system. From our results it is possible to establish that both visibility algorithms are capable of detecting the critical control parameter, as in every quantity analyzed (the average degree, the average path and the clustering coefficient) there is a minimum or a maximum value. In the case of the natural visualization algorithm, the average path results are much more noisy than in the other quantities in the study. Specially for the Kuramoto Model, which in this case does not allow a detection of the critical point at plain sight as for the other quantities. The horizontal visualization algorithm has proven to be more explicit in every quantity, as every one of them show a clear change of behavior before and after the critical point of the transition.
机译:最近,已经表明,从时间序列的建筑网络允许研究复杂的系统,以在通过相位过渡时表征它们。这让我们有机会从整个新的角度来研究这个系统。在目前的工作中,我们使用了自然和水平可视化算法来构建了两个流行型号的网络,该型号是当前的阶段转换:ising模型和kuramoto模型。通过测量一些拓扑量作为平均程度或聚类系数,发现网络能够检测系统的相位过渡的能力。从我们的结果,可以确定两个可见性算法能够检测到关键控制参数,如在分析的每一个数量(平均度,平均路径和聚类系数)中,存在最小或最大值。在自然可视化算法的情况下,平均路径结果比在研究中的其他数量中噪音得多。特别是Kuramoto模型,在这种情况下,该模型不允许检测普通视野的临界点,如其他数量。横向可视化算法已被证明在每种数量中更明确,因为它们中的每一个都显示出在转换的临界点之前和之后的特殊行为变化。

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