Marchiori Massimo, Possamai Lino
Department of Mathematics, University of Padua, Padua, Italy; Atomium Culture, Brussels, Belgium.
Department of Mathematics, University of Padua, Padua, Italy.
PLoS One. 2015 Jan 30;10(1):e0116670. doi: 10.1371/journal.pone.0116670. eCollection 2015.
Complex systems have attracted considerable interest because of their wide range of applications, and are often studied via a "classic" approach: study a specific system, find a complex network behind it, and analyze the corresponding properties. This simple methodology has produced a great deal of interesting results, but relies on an often implicit underlying assumption: the level of detail on which the system is observed. However, in many situations, physical or abstract, the level of detail can be one out of many, and might also depend on intrinsic limitations in viewing the data with a different level of abstraction or precision. So, a fundamental question arises: do properties of a network depend on its level of observability, or are they invariant? If there is a dependence, then an apparently correct network modeling could in fact just be a bad approximation of the true behavior of a complex system. In order to answer this question, we propose a novel micro-macro analysis of complex systems that quantitatively describes how the structure of complex networks varies as a function of the detail level. To this extent, we have developed a new telescopic algorithm that abstracts from the local properties of a system and reconstructs the original structure according to a fuzziness level. This way we can study what happens when passing from a fine level of detail ("micro") to a different scale level ("macro"), and analyze the corresponding behavior in this transition, obtaining a deeper spectrum analysis. The obtained results show that many important properties are not universally invariant with respect to the level of detail, but instead strongly depend on the specific level on which a network is observed. Therefore, caution should be taken in every situation where a complex network is considered, if its context allows for different levels of observability.
复杂系统因其广泛的应用而备受关注，并且通常通过一种“经典”方法进行研究：研究一个特定系统，找到其背后的复杂网络，并分析相应的属性。这种简单的方法已经产生了大量有趣的结果，但依赖于一个通常隐含的基本假设：观察系统的细节程度。然而，在许多物理或抽象的情况下，细节程度可能是众多情况之一，并且还可能取决于以不同抽象或精度级别查看数据时的内在限制。因此，出现了一个基本问题：网络的属性是否取决于其可观察性水平，还是它们是不变的？如果存在依赖性，那么一个看似正确的网络建模实际上可能只是对复杂系统真实行为的一个糟糕近似。为了回答这个问题，我们提出了一种新颖的复杂系统微观 - 宏观分析方法，该方法定量描述了复杂网络的结构如何随细节级别而变化。在这个范围内，我们开发了一种新的伸缩算法，该算法从系统的局部属性中抽象出来，并根据模糊度级别重建原始结构。通过这种方式，我们可以研究从精细的细节级别（“微观”）过渡到不同的尺度级别（“宏观”）时会发生什么，并分析这种过渡中的相应行为，从而获得更深入的频谱分析。所得结果表明，许多重要属性并非相对于细节级别普遍不变，而是强烈依赖于观察网络的特定级别。因此，如果复杂网络的上下文允许不同的可观察性级别，那么在考虑任何涉及复杂网络的情况时都应谨慎。
