Our daily social and political life is more and more impacted by social networks. The functioning of our living bodies is deeply dependent on biological regulation networks such as neural, genetic, and protein networks. And the physical world in which we evolve, is also structured by systems of interacting particles. Interaction networks can be seen in all spheres of existence that concern us, and yet, our understanding of interaction networks remains severely limited by our present lack of both theoretical and applied insight into their clockworks. In the past, efforts at understanding interaction networks have mostly been directed towards applications. This has happened at the expense of developing understanding of the generic and fundamental aspects of interaction networks. Intrinsic properties of interaction networks (eg the ways in which they transmit information along entities, their ability to produce this or that kind of global dynamical behaviour depending on local interactions) are thus still not well understood. Lack of fundamental knowledge tends to limit the innovating power of applications. Without more theoretical fundamental knowledge, applications cannot evolve deeply and become more impacting. Hence, it is necessary to better apprehend and comprehend the intrinsic properties of interaction networks, notably the relations between their architecture and their dynamics and how they are affected by and set in time. In this chapter, we use the elementary mathematical model of Boolean automata networks as a formal archetype of interaction networks. We survey results concerning the role of feedback cycles and the role of intersections between feedback cycles, in shaping the asymptotic dynamical behaviours of interaction networks.
翻译:我们的日常社会和政治生活越来越受到社会网络的影响。我们的生命体的运作深深地依赖于神经、遗传和蛋白质网络等生物监管网络。我们进化的物理世界也由互动粒子系统组成。互动网络存在于我们关注的所有存在领域,因此仍然不能很好地看到互动网络,然而,我们对于互动网络的理解仍然严重受限制,因为我们目前缺乏对其时钟的理论和应用洞察力。过去,理解互动网络的努力大多针对应用。这牺牲了对互动网络一般和基本方面的理解。互动网络的内在特性(例如它们如何在实体之间传递信息,它们是否有能力产生这种或这种取决于当地互动的全球动态行为)因此仍不为人所熟知。缺乏基本知识往往会限制应用的革新能力。如果没有更多的理论基础知识,应用将无法深入发展,影响更大。因此,有必要更好地了解和理解互动网络的内在特性,特别是其结构与动态关系,以及它们如何在实体之间传递信息,它们制作这种或取决于地方互动的这种全球动态行为的能力。我们使用模型式的网络的模型,在时间结构上的反馈中如何影响。