心理网络：触发预期涌现开放性的中心时间
Algorithmic Networks: central time to trigger expected emergent open-endedness
摘要：
本文研究了可以在网络上共享信息的复杂系统的涌现性和复杂性。为此，我们使用的理论方法，从信息论，可计算性理论和复杂网络。研究的一个关键问题是，当一群可计算系统联网时，与孤立时相比，会产生多少紧急复杂性（或信息）。首先，我们定义了一个网络化理论机器的一般模型，我们称之为算法网络。然后，我们缩小我们的范围来研究算法网络，优化节点的平均适应度，在这种情况下，每个节点模仿最适合的邻居和随机生成的人口是由一个随时间变化的图网络。我们表明，有图形拓扑条件，使这些算法网络有足够大的人口的预期紧急开放性的属性。换句话说，当种群规模趋于无穷大时，节点的期望涌现算法复杂度趋于无穷大。给定一个动态网络，我们表明，这些条件意味着存在一个中心时间触发预期的紧急开放。此外，我们表明，与网络大小相比，直径较小的网络满足这些条件。我们还讨论了未来的研究的基础上，我们的研究结果是如何相关的一些问题，在网络科学，信息论，可计算性理论，分布式计算，博弈论，进化生物学，在复杂系统中的协同作用。
英文摘要：
This article investigates emergence and complexity in complex systems that can share information on a network. To this end, we use a theoretical approach from information theory, computability theory, and complex networks. One key studied question is how much emergent complexity (or information) arises when a population of computable systems is networked compared with when this population is isolated. First, we define a general model for networked theoretical machines, which we call algorithmic networks. Then, we narrow our scope to investigate algorithmic networks that optimize the average fitnesses of nodes in a scenario in which each node imitates the fittest neighbor and the randomly generated population is networked by a time-varying graph. We show that there are graph-topological conditions that cause these algorithmic networks to have the property of expected emergent open-endedness for large enough populations. In other words, the expected emergent algorithmic complexity of a node tends to infinity as the population size tends to infinity. Given a dynamic network, we show that these conditions imply the existence of a central time to trigger expected emergent open-endedness. Moreover, we show that networks with small diameter compared to the network size meet these conditions. We also discuss future research based on how our results are related to some problems in network science, information theory, computability theory, distributed computing, game theory, evolutionary biology, and synergy in complex systems.
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