论文标题
加权耦合细胞网络中可接受功能的分解
Decomposition of admissible functions in weighted coupled cell networks
论文作者
论文摘要
这项工作使对网络的动力学或网络的其他一阶属性（例如测量功能）进行了明确的自由度。在以前的工作中，通过评估我们所谓的Oracle组件来构建网络中的可接受功能。这些甲骨文组件是通过预期的一些最小属性来定义的。这是一个高级描述，因为尚不清楚如何设计这样的对象。目的是通过将这些物体解开为自由度来获得对这些对象的低级表示。为了实现这一目标，我们引入了两个分解。第一个是更直观的，它允许我们定义耦合顺序的重要概念。第二个分解构建在第一个分解的顶部，对于具有有限耦合顺序的耦合组件有效。尽管有这样的要求，我们表明这仍然是通过限制方法设计带有无限耦合订单的耦合组件的非常有用的工具。
This work makes explicit the degrees of freedom involved in modeling the dynamics of a network, or some other first-order property of a network, such as a measurement function. In previous work, an admissible function in a network was constructed through the evaluation of what we called oracle components. These oracle components are defined through some minimal properties that they are expected to obey. This is a high-level description in the sense that it is not clear how one could design such an object. The goal is to obtain a low-level representation of these objects by unwrapping them into their degrees of freedom. To achieve this, we introduce two decompositions. The first one is the more intuitive one and allows us to define the important concept of coupling order. The second decomposition is built on top of the first one and is valid for the class of coupling components that have finite coupling order. Despite this requirement, we show that this is still a very useful tool for designing coupling components with infinite coupling orders, through a limit approach.
