结构趋势-复杂（混沌）系统的适应性进化的影响
Structural tendencies - Effects of adaptive evolution of complex (chaotic) systems
摘要：
我们描述的系统使用考夫曼和类似的网络。它们是由有限个节点和有限个离散状态组成的有向函数网络，在离散时间的同步模式下计算。在本文中，我们介绍了“结构倾向”的概念和现象。一路上，我们扩大考夫曼网络，这是一个同义词的布尔netw orks，两个以上的信号变量，我们发现在网络增长的现象，我们解释为“复杂性阈值”。对于模拟，我们定义了一个简化的算法，它允许我们忽略周期吸引子的问题。我们估计，生活和人类设计的系统是混沌的（在考夫曼意义上），可以命名为-复杂。此类系统在适应性进化中成长。这两个简单的假设导致了一定的统计效应，即经典生物学中观察到的结构趋势，但仍然没有解释，也没有从理论上进行研究。例如，终端修改或终端优势添加，其中终端意味着：接近系统输出。我们引入了两个以上的等概率信号变体，因此我们的网络通常不是布尔网络。它们通过对达尔文淘汰法施加的节点的增加和移除而随机增长。适应度是根据系统的外部输出来定义的。在系统的增长过程中，我们观察到一个相变混沌（阈值的复杂性）的损害蔓延。在这个阈值之上，我们确定了一些不同的网络类型，包括无标度BA网络，我们在模拟研究的结构趋势的机制。
英文摘要：
We describe systems using Kauffman and similar networks. They are directed funct ioning networks consisting of finite number of nodes with finite number of discr ete states evaluated in synchronous mode of discrete time. In this paper we introduce the notion and phenomenon of `structural tendencies'. Along the way we expand Kauffman networks, which were a synonym of Boolean netw orks, to more than two signal variants and we find a phenomenon during network g rowth which we interpret as `complexity threshold'. For simulation we define a simplified algorithm which allows us to omit the problem of periodic attractors. We estimate that living and human designed systems are chaotic (in Kauffman sens e) which can be named - complex. Such systems grow in adaptive evolution. These two simple assumptions lead to certain statistical effects i.e. structural tendencies observed in classic biology but still not explained and not investigated on theoretical way. E.g. terminal modifications or terminal predominance of additions where terminal means: near system outputs. We introduce more than two equally probable variants of signal, therefore our networks generally are not Boolean networks. T hey grow randomly by additions and removals of nodes imposed on Darwinian elimination. Fitness is defined on external outputs of system. During growth of the system we observe a phase transition to chaos (threshold of complexity) in damage spreading. Above this threshold we identify mechanisms of structural tendencies which we investigate in simulation for a few different networks types, including scale-free BA networks.
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