自适应个体的群体运动行为研究

发布时间：2018-04-30 09:27

本文选题：人类动力学 + 速率分布　；参考：《温州大学》2017年硕士论文

【摘要】：本文以马拉松赛为对象研究自适应个体的群体运动特征以及人类行为动力学问题,统计纽约、芝加哥、伦敦和柏林四个城市马拉松赛10多年参赛者的信息,包括全程完成时间和分赛段完成时间等数据。实证统计全程和分段马拉松赛中全部参赛者的速率分布、纽约马拉松赛各分赛段内全部参赛者的速率分布及全部参赛者的名次变化,分析纽约马拉松赛各分赛段内速率分布与名次变化的关联。本文的主要研究内容有以下几个部分:1.实证统计分析四个著名城市马拉松赛全部参赛者的全程速率的统计分布,发现四个城市马拉松赛的全程速率分布均呈对数正态分布。实证统计纽约和芝加哥城市马拉松赛平均速率最大年龄组的全程速率分布也满足对数正态分布。2.理论分析发现纽约马拉松赛各分赛段中所有参赛者的速率的对数值的平均值和标准差近似为常数,由此应用最大熵原理导出的马拉松赛的速率分布为对数正态分布,与实证统计结果一致。3.实证统计纽约马拉松赛各分赛段马拉松赛中全部参赛者的速率分布、纽约马拉松赛各分段内全部参赛者的速率分布及参赛者的名次变化分布,分析纽约马拉松赛各分赛段内速率分布与名次变化的关联。发现在总共8个长度各为5公里的计时赛段中,最初的一个或几个赛段中的速率分布遵守对数正态分布,随后在中间的几个计时赛段中转变为高斯分布,而在最后几个计时赛段中又转变为对数正态分布。为此我们实证统计各计时赛段中全部参赛者的名次变化并计算其方均根值来描述赛段中的竞争激烈强度,分析各分赛段内速率分布从初始阶段的对数正态分布到中间阶段的高斯分布,再到最后阶段的对数正态分布的转变与各赛段中竞争激烈强度(名次变化方均根值)变化的关联。发现在初始阶段随着各赛段中名次变化方均根值下降,速率分布相应地从对数正态分布转变为中间阶段的高斯分布,在中间阶段随着各赛段中名次变化方均根值增大,速率分布相应地从高斯分布转变为最后阶段的对数正态分布。
[Abstract]:In this paper, we study the characteristics of adaptive individual group movement and human behavior dynamics, and analyze the information of the participants in the marathon in four cities, New York, Chicago, London and Berlin, for more than 10 years. Including the completion time of the whole process and the completion time, and so on. The rate distribution of all participants in the full and piecewise Marathon, the rate distribution of all participants in each sub-stage of the New York Marathon, and the change of all the contestants' rankings are analyzed empirically. This paper analyzes the relationship between the velocity distribution and the rank change in the race segments of the New York Marathon. The main contents of this paper are as follows: 1. Based on the statistical analysis of the whole course rate distribution of all the participants in the four famous cities, it is found that the whole course rate distribution of the four famous cities is logarithmic normal distribution. Empirical statistics show that the distribution of the whole process rate in the maximum age group of the average rate of the city Marathon in New York and Chicago also satisfies the logarithmic normal distribution. 2. Theoretical analysis shows that the average value and standard deviation of the logarithmic values of all participants in each segment of the New York Marathon are approximately constant, and the rate distribution of the Marathon derived from the maximum entropy principle is logarithmic normal distribution. Consistent with the empirical results. 3. Empirical statistics show the rate distribution of all the participants in the New York Marathon, the rate distribution of all the participants in the New York Marathon, and the variation distribution of the contestants' ranking. This paper analyzes the relationship between the velocity distribution and the rank change in the race segments of the New York Marathon. It was found that the rate distribution in the first one or more segments followed the logarithmic normal distribution in a total of 8 timing segments, each of which was 5 kilometers in length, and then changed to Gao Si distribution in the middle of the timing segments. In the last few stages, it is transformed into logarithmic normal distribution. In order to describe the intensity of competition, we empirically count the changes of all contestants' positions and calculate their root values. This paper analyzes the relationship between the rate distribution in each segment from the logarithmic normal distribution in the initial stage to the Gao Si distribution in the intermediate stage and the change of the lognormal distribution to the final stage with the change of the competitive intensity (the average root value of the rank changer) in each segment. It was found that in the initial stage, the root value of each side decreased with the change of rank, and the rate distribution changed from lognormal distribution to Gao Si distribution in the middle stage, and the root value increased with the change of rank in the middle stage. The rate distribution is changed from Gao Si distribution to the lognormal distribution in the final stage.
【学位授予单位】：温州大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O211

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