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首页> 外文期刊>Frontiers in Applied Mathematics and Statistics >Mimicking Directed Binary Networks for Exploring Systemic Sensitivity: Is NCAA FBS a Fragile Competition System?
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Mimicking Directed Binary Networks for Exploring Systemic Sensitivity: Is NCAA FBS a Fragile Competition System?

机译：模仿定向二进制网络探索系统敏感性：NCAA FBS是脆弱的竞争系统吗？

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Can a popular real-world competition system indeed be fragile? To address this question, we represent such a system by a directed binary network. Upon observed network data, typically in a form of win-and-loss matrix, our computational developments begin with collectively extracting network's information flows. And then we compute and discover network's macrostate. This computable macrostate is further shown to contain deterministic structures embedded with randomness mechanisms. Such coupled deterministic and stochastic components becomes the basis for generating the microstate ensemble. Specifically a network mimicking algorithm is proposed to generate a microstate ensemble by subject to the statistical mechanics principle: All generated microscopic states have to conform to its macrostate of the target system. We demonstrate that such a microstate ensemble is an effective platform for exploring systemic sensitivity. Throughout our computational developments, we employ the NCAA Football Bowl Subdivision (FBS) as an illustrating example system. Upon this system, its macrostate is discovered by having a nonlinear global ranking hierarchy as its deterministic component, while its constrained randomness component is embraced within the nearly completely recovered conference schedule . Based on the computed microstate ensemble, we are able to conclude that the NCAA FBS is overall a fragile competition system because it retains highly heterogeneous degrees of sensitivity with its ranking hierarchy.
机译：流行的现实世界竞赛系统真的可以脆弱吗？为了解决这个问题，我们通过有向二进制网络来表示这样的系统。根据观察到的网络数据（通常以损益矩阵的形式），我们的计算开发始于共同提取网络的信息流。然后我们计算并发现网络的宏状态。该可计算的宏状态进一步显示为包含嵌入有随机性机制的确定性结构。这样的确定性和随机性耦合成为生成微状态集合的基础。具体而言，提出了一种网络模仿算法，以根据统计力学原理生成微状态集合：所有生成的微观状态必须符合目标系统的宏观状态。我们证明这种微状态合奏是探索系统敏感性的有效平台。在整个计算开发过程中，我们采用NCAA足球碗细分（FBS）作为示例系统。在该系统上，通过将非线性全局排名层次结构作为其确定性组件来发现其宏状态，而将其受约束的随机性组件包含在几乎完全恢复的会议日程中。基于计算出的微状态集合，我们可以得出结论，NCAA FBS总体上是一个脆弱的竞争系统，因为它保留了高度异质的排名等级。

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