本文選題：人類動(dòng)力學(xué) + 速率分布��； 參考：《溫州大學(xué)》2017年碩士論文

【摘要】：本文以馬拉松賽為對(duì)象研究自適應(yīng)個(gè)體的群體運(yùn)動(dòng)特征以及人類行為動(dòng)力學(xué)問題,統(tǒng)計(jì)紐約、芝加哥、倫敦和柏林四個(gè)城市馬拉松賽10多年參賽者的信息,包括全程完成時(shí)間和分賽段完成時(shí)間等數(shù)據(jù)。實(shí)證統(tǒng)計(jì)全程和分段馬拉松賽中全部參賽者的速率分布、紐約馬拉松賽各分賽段內(nèi)全部參賽者的速率分布及全部參賽者的名次變化,分析紐約馬拉松賽各分賽段內(nèi)速率分布與名次變化的關(guān)聯(lián)。本文的主要研究?jī)?nèi)容有以下幾個(gè)部分:1.實(shí)證統(tǒng)計(jì)分析四個(gè)著名城市馬拉松賽全部參賽者的全程速率的統(tǒng)計(jì)分布,發(fā)現(xiàn)四個(gè)城市馬拉松賽的全程速率分布均呈對(duì)數(shù)正態(tài)分布。實(shí)證統(tǒng)計(jì)紐約和芝加哥城市馬拉松賽平均速率最大年齡組的全程速率分布也滿足對(duì)數(shù)正態(tài)分布。2.理論分析發(fā)現(xiàn)紐約馬拉松賽各分賽段中所有參賽者的速率的對(duì)數(shù)值的平均值和標(biāo)準(zhǔn)差近似為常數(shù),由此應(yīng)用最大熵原理導(dǎo)出的馬拉松賽的速率分布為對(duì)數(shù)正態(tài)分布,與實(shí)證統(tǒng)計(jì)結(jié)果一致。3.實(shí)證統(tǒng)計(jì)紐約馬拉松賽各分賽段馬拉松賽中全部參賽者的速率分布、紐約馬拉松賽各分段內(nèi)全部參賽者的速率分布及參賽者的名次變化分布,分析紐約馬拉松賽各分賽段內(nèi)速率分布與名次變化的關(guān)聯(lián)。發(fā)現(xiàn)在總共8個(gè)長(zhǎng)度各為5公里的計(jì)時(shí)賽段中,最初的一個(gè)或幾個(gè)賽段中的速率分布遵守對(duì)數(shù)正態(tài)分布,隨后在中間的幾個(gè)計(jì)時(shí)賽段中轉(zhuǎn)變?yōu)楦咚狗植?而在最后幾個(gè)計(jì)時(shí)賽段中又轉(zhuǎn)變?yōu)閷?duì)數(shù)正態(tài)分布。為此我們實(shí)證統(tǒng)計(jì)各計(jì)時(shí)賽段中全部參賽者的名次變化并計(jì)算其方均根值來描述賽段中的競(jìng)爭(zhēng)激烈強(qiáng)度,分析各分賽段內(nèi)速率分布從初始階段的對(duì)數(shù)正態(tài)分布到中間階段的高斯分布,再到最后階段的對(duì)數(shù)正態(tài)分布的轉(zhuǎn)變與各賽段中競(jìng)爭(zhēng)激烈強(qiáng)度(名次變化方均根值)變化的關(guān)聯(lián)。發(fā)現(xiàn)在初始階段隨著各賽段中名次變化方均根值下降,速率分布相應(yīng)地從對(duì)數(shù)正態(tài)分布轉(zhuǎn)變?yōu)橹虚g階段的高斯分布,在中間階段隨著各賽段中名次變化方均根值增大,速率分布相應(yīng)地從高斯分布轉(zhuǎn)變?yōu)樽詈箅A段的對(duì)數(shù)正態(tài)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.
【學(xué)位授予單位】：溫州大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：O211

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本文編號(hào)：1824006