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足球动力学的熵分析

Entropy Analysis of Soccer Dynamics.

作者信息

Lopes António M, Tenreiro Machado J A

机构信息

UISPA-LAETA/INEGI, Faculty of Engineering, University of Porto, Rua Dr. Roberto Frias, 4200-465 Porto, Portugal.

Department of Electrical Engineering, Institute of Engineering, Polytechnic of Porto, Rua Dr. António Bernardino de Almeida, 431, 4249-015 Porto, Portugal.

出版信息

Entropy (Basel). 2019 Feb 16;21(2):187. doi: 10.3390/e21020187.

DOI:10.3390/e21020187
PMID:33266902
原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC7514670/
Abstract

This paper adopts the information and fractional calculus tools for studying the dynamics of a national soccer league. A soccer league season is treated as a complex system (CS) with a state observable at discrete time instants, that is, at the time of rounds. The CS state, consisting of the goals scored by the teams, is processed by means of different tools, namely entropy, mutual information and Jensen-Shannon divergence. The CS behavior is visualized in 3-D maps generated by multidimensional scaling. The points on the maps represent rounds and their relative positioning allows for a direct interpretation of the results.

摘要

本文采用信息和分数阶微积分工具来研究国家足球联赛的动态。一个足球联赛赛季被视为一个复杂系统（CS），其状态在离散时刻（即轮次时间）是可观测的。由球队进球数组成的CS状态通过不同工具进行处理，即熵、互信息和詹森 - 香农散度。CS的行为在通过多维缩放生成的三维地图中可视化。地图上的点代表轮次，它们的相对位置允许对结果进行直接解读。

https://cdn.ncbi.nlm.nih.gov/pmc/blobs/0c8c/7514670/f36f1a61d8ac/entropy-21-00187-g010.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/0c8c/7514670/fa54bb0e6cbb/entropy-21-00187-g001.jpg
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https://cdn.ncbi.nlm.nih.gov/pmc/blobs/0c8c/7514670/c98b8947e7b6/entropy-21-00187-g002.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/0c8c/7514670/3114557e5f9d/entropy-21-00187-g003.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/0c8c/7514670/22311938a01b/entropy-21-00187-g004a.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/0c8c/7514670/37e310175aa2/entropy-21-00187-g005.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/0c8c/7514670/85de4d616358/entropy-21-00187-g006.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/0c8c/7514670/dd58f452665d/entropy-21-00187-g007.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/0c8c/7514670/be6c968239f6/entropy-21-00187-g008.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/0c8c/7514670/cac051ab25d0/entropy-21-00187-g009.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/0c8c/7514670/f36f1a61d8ac/entropy-21-00187-g010.jpg

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本文引用的文献

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