如何运用网络的力量简化复杂系统？

什么是标度非线性？

如何控制复杂系统？

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专题：含时网络理论及应用

（Modern temporal network theory: a colloquium）

Eur. Phys. J. B (2015) 88: 234 April 16, 7:24 PMApril 15, 10:34 PM

BY Petter Holme

(Translated by -)

任何网络方法的力量在于简化复杂系统的能力，通过这种简化，我们可以更好地理解其作为一个整体的功能。然而，有时更多的信息是比只有点和边的简单图更有益的。添加关于相互作用时间信息可以使预测和机制理解更准确。然而，对应的缺点是没有太多可用的方法，部分是因为含时网络是相对年轻的领域，部分是因为相比于静态网络，发展这样的方法更加困难。在本次专题上，我们回顾了在过去三年间的分析和建模含时网络和及与之相关的各种过程的方法。这些研究包括传染病、观点、谣言在社交网络中的传播；计算机网络中的信息包；生物学中各种类型的信号。我们还讨论了该领域未来的发展方向。

The power of any kind of network approach lies in the ability to simplify a complex system so that one can better understand its function as a whole. Sometimes it is beneficial, however, to include more information than in a simple graph of only nodes and links. Adding information about times of interactions can make predictions and mechanistic understanding more accurate. The drawback, however, is that there are not so many methods available, partly because temporal networks is a relatively young field, partly because it is more difficult to develop such methods compared to for static networks. In this colloquium, we review the methods to analyze and model temporal networks and processes taking place on them, focusing mainly on the last three years. This includes the spreading of infectious disease, opinions, rumors, in social networks; information packets in computer networks; various types of signaling in biology, and more. We also discuss future directions.

原文链接：http://link.springer.com/article/10.1140%2Fepjb%2Fe2015-60657-4

标度非线性？

（Is this scaling nonlinear? ）

arXiv:1604.02872 physics.soc-ph April 16, 9:20 PM

BY J. C. Leitao, J.M. Miotto, M. Gerlach, E. G. Altmann

(Translated by – 刘清晴)

近10年来复杂系统研究领域中最著名的发现之一是：不同的指标y（如专利数）随着城市人口x非线性变化，呈现出某些规律，如 y～x^β, β≠1。最近，在一些使用了新的数据库并用不同的方法定义城市边界的研究中，这个发现的普适性受到了质疑。在本文中，我们用一种概率论的框架研究了非线性标度的存在性，在研究中，我们可以将涨落明确地描述出来。特别地，我们发现这种方法不仅允许（a）估计β和置信区间，还允许（b）量化支持β≠1的证据，并且（c）检验观察数据符合非线性标度的假设。我们使用这种研究思路来比较了为15个不同的数据库建模的5个不同的模型，我们发现，数据的涨落、建模方法和城市规模为重尾分布的事实对（a）~（c）的结果是至关重要的。

One of the most celebrated findings in complex systems in the last decade is that different indexes y (e.g., patents) scale nonlinearly with the population-x of the cities in which they appear, i.e., y～x^β, β≠1. More recently, the generality of this finding has been questioned in studies using new databases and different definitions of city boundaries. In this paper we investigate the existence of nonlinear scaling using a probabilistic framework in which fluctuations are accounted explicitly. In particular, we show that this allows not only to (a) estimate β and confidence intervals, but also to (b) quantify the evidence in favor of β≠1 and (c) test the hypothesis that the observations are compatible with the nonlinear scaling. We employ this framework to compare 5 different models to 15 different datasets and we find that the answers to points (a)-(c) crucially depend on the fluctuations contained in the data, on how they are modeled, and on the fact that the city sizes are heavy-tailed distributed.

原文链接： http://journals.plos.org/plosbiology/article?id=10.1371/journal.pbio.1002433

复杂网络的控制需要结构和动态

（Control of complex networks requires both structure and dynamics）

Scientific Reports 6, Article number: 24456 (2016) April 19, 11:50 PM

BY Alexander J. Gates & Luis M. Rocha

(Translated by -女周瑜)

对网络结构的研究揭示了复杂系统组织的鲜明特征。然而，我们还需要去理解如何控制复杂系统，例如确认将病变细胞恢复到健康状态或是将成熟细胞变成多能状态的策略。两个最近的研究方法表明，复杂系统的可控性仅仅通过变量间相互作用的拓扑、而不考虑它们的动力学就能被预测，即结构可控性和最小支配集。我们证明了这种只关注结构的方法在动力学被引入时很难描绘出系统的可控性特征。我们研究了网络基序的布尔网络集合以及生物化学调控的三种模型，即黑腹果蝇的体节极性网络、酿酒酵母的细胞周期和拟南芥中花器官的排列。我们论证了只关注结构的方法要么低估要么高估了关键变量的数量和哪组关键变量最好地控制了这些模型的动力学，从而突出了实际动力学在系统控制中的重要性。我们的分析进一步显示了自动机转换功能的逻辑（即它们是如何被引导的）在结构预测动态的程度中发挥着重要的作用。

The study of network structure has uncovered signatures of the organization of complex systems. However, there is also a need to understand how to control them; for example, identifying strategies to revert a diseased cell to a healthy state, or a mature cell to a pluripotent state. Two recent methodologies suggest that the controllability of complex systems can be predicted solely from the graph of interactions between variables, without considering their dynamics: structural controllability and minimum dominating sets. We demonstrate that such structure-only methods fail to characterize controllability when dynamics are introduced. We study Boolean network ensembles of network motifs as well as three models of biochemical regulation: the segment polarity network in Drosophila melanogaster, the cell cycle of budding yeast Saccharomyces cerevisiae, and the floral organ arrangement in Arabidopsis thaliana. We demonstrate that structure-only methods both undershoot and overshoot the number and which sets of critical variables best control the dynamics of these models, highlighting the importance of the actual system dynamics in determining control. Our analysis further shows that the logic of automata transition functions, namely how canalizing they are, plays an important role in the extent to which structure predicts dynamics.

原文链接：http://www.nature.com/articles/srep24456

有重尾的符号分布频率的相似点

（Similarity of Symbol Frequency Distributions with Heavy Tails）

Phys. Rev. X 6, 021009 April 21, 9:45 PM

BY Martin Gerlach, Francesc Font-Clos, and Eduardo G. Altmann

(Translated by -王与剑)

用一种数学手段对比大量的符号集合，结果表明使用频率较少的单词对于过去两个世纪的英语语言的演变起了主要作用。

A mathematical technique for comparing large symbol sets suggests that less frequently used words are mainly responsible for the evolution of the English language over the past two centuries.