Preparation for the 2021 US Championship

table of Contents

1. 2021 Meisai competition website and its introduction

https://www.comap.com/undergraduate/contests/

The following is the webpage translated into Chinese: (It is worth attending by college students)

2. Description of the 2020 Meisai summary page

Chinese translation is:

(1) Use this template to start typing the first page (summary page) of the electronic report. This template uses 12-point Times New Roman font. Submit the paper in the form of an Adobe PDF electronic file (such as 1111111.PDF), typed in English, and the font is at least 12-point readable.

(2) Do not write the name of your school, mentor or team member on this page or any page.

(3) The paper must be within the page limit specified in the problem statement.

(4) Please be sure to change the control number and question selection above.

(5) When you start typing the report here, you can delete these instructions.

(6) Please follow us @COMAPMath on Twitter or COMAPCHINAOFFICIAL on Weibo to get the latest competition information.

For templates before 2019, please refer to: https://zhuanlan.zhihu.com/p/92453423

3. Commonly used words and sentences

(1) Words commonly used in abstracts

critical algorithm A method of evaluating a method of evaluating Appropriate Approximate

consider considering configurations, layout, optimal, unified maximize, to maximize

strategy parameter parameter, the main determinant of accuracy, strengths and weaknesses

Contact related contract establishment, construct calculate calculate establish establishment

formula formula modify to improve rational and reasonable countermeasure countermeasure

criterion

(2) Statement

1、 As our team set out to come up with a strategy on what would be the most efficient way to

We have proposed a most effective way to solve...

2、 The first aspect that we took into major consideration was…….

Other important findings through research made it apparent that the standard

First of all, we consider..., the other important thing is that we make

4、We have used mathematical modeling in a……to analyze some of the factors associated with such an activity。

In order to analyze some factors of this type of problem, we use mathematical models...

5、This “cannon problem” has been used in many forms in many differential equations courses in the Department of Mathematical Sciences for several years.

These problems have been applied to the natural science department in different differential equation forms over the years.

6、In conclusion our team is very certain that the methods we came up with in

In short, we are pretty sure that our proposed method

7、We already know how well our results worked for……

We already know that we are right...

8、Now that the problem areas have been defined, we offer some ways to reduce the effect of these problems.

Now that the results have been defined, we propose some methods to reduce the impact on the problem.

9、There are many methods in existence for……Furthermore each is mostly successful in what is sets out to do. However, all of these seem to

There are many ways to study..., so the best is what we want to do, however, all of these seem...

10、While our approaches and models were effective and produced results, there remain several types of model weaknesses:

Our method and model are effective in extending the results, and our model also has some shortcomings.

11、We next developed a detailed simulation engine to perform simulations. Our simulations allowed us to ……

We next study calculations, our simulation allows us...

12、We have reached several valuable conclusions about the nature of……and some of the possible policy solutions that can be implemented to make it more effective ，Most importantly, we believe in the absolute necessity of implementing

We get results on this type of issue, some possible policy results make it effective, and most importantly, we believe that... is quite necessary.

13、We use …to …

14、Thus, we recommend…

15、Considering the…

16、In this paper, we examine the results of some fundamental avaricious in structure:……

17、We also wish to tie our exploration of sensitive……

18、we suspect that such system are in general less effective than simpler ones……

4. Matters needing attention in translation

1.* summary* (complete)

(tab)greatly important.

The first paragraph is to summarize, which method solves what problem, especially important (mostly passive sentences in scientific papers, a few active sentences)

The second paragraph, question one, third paragraph, question two, ending paragraph, summarize three or four key words

(Clear translation; no formula, there can be a small number of values) (text page 20)

2. Arabic numerals

Problem 1 (without question ) Model 1

3. Change the verb

use= take= apply= utilize by= with = by means of establish= develop

4. Plural

establish of models

5. The catalog should be as concise as possible, one page

6. Solution translation

a solution to=a key to a problem=an approach to

7. Capitalize each content word in the title

8. Comparison of translation software

9.we need to /our team

10. Note that the English structure is complete, and the complete Chinese sentence machine translation is used.

11. The margins of the body part and the abstract are different, set to normal values; the body part must have a header

12. Model assumptions should be explained accordingly.

13. Data reference. The whole article seems very thin, giving people such a feeling: After the mathematical model is given, the calculation results are out of thin air, which is suspected of fabricating. The main reason is that the data is rarely cited or not reflected in the paper at all. Looking at the O-prize papers, you will find that the workload is twice that of most M papers, and the amount of information is large. This is mainly based on good ideas in MCM topics, while in ICM, it is inseparable from a large number of accurate and reliable data references. I still remember that more than a day last year was spent on data collection and sorting.

14. Properly verify the rationality of the model. It can be verified by appropriate evaluation systems such as the Human Development Index.

15. Maison attaches importance to the combination of the model and the actual problem. It needs to be expressed as the model and the final solution. The calculation process does not need to be reflected in detail.

16. Don't look scattered as a whole. The most typical manifestation is that there are short sentences in the film.

17. The connection between model and conclusion must be strong. Often only the content of the model is given, or only the name is given, and then a large number of conclusions are obtained. This is not the case. The correct approach should be to first establish a mathematical model, then fill in the analysis with a large amount of fact data to realize the model, and finally obtain the calculation results of the mathematical model, and then the analysis can reach a conclusion.

5. Some suggestions for writing essays

5.1 Team preparation

(1) The team can use any source of data or materials: computers, software, reference materials, websites, books, etc. All information used must be credible. Untrustworthy data sources will result in a team's disqualification (for fear that everyone will use the same data source then, so that the risk of being disqualified during the double check).

(2) Except for other members of the same team, team members are not allowed to seek help or discuss problems from their instructor or anyone else. Any discussion is strictly prohibited. This includes e-mail, telephone contact and personal conversations, communication via web chat or other question and answer systems, or any other form of communication. (I understand this, I understand myself)

(3) Part of the solution is acceptable. There is no cut-off score for passing or failing, and numerical scores will not be assigned. The judges of the MCM / ICM competition are mainly interested in team methods and methods.

(4) **Abstract is an important part of your MCM / ICM paper. **Paper-scoring expert judgement occupies a considerable share of the abstract, and winning papers are usually distinguished from other papers based on the quality of the abstract. To write a good abstract, imagine that readers will choose whether to read the main body of the paper based on your abstract: your concise presentation should inspire readers to understand the details of your work. Therefore, the summary should clearly describe your approach to the problem, and most importantly show your most important conclusions. An abstract that is merely a restatement of a comparative problem, or various cuts to the introduction, is usually considered weak.

5.2 Summary table section

(1) Restate and clarify the problem : Say what you want to do in your own words.

(2) Explain the assumptions and reasons : Emphasize the assumptions about the problem. Clearly list all the variables used in the model.

**(3)** The design and reason of the model: the model to be built/used.

**(4)** describes model testing and sensitivity analysis , including error analysis, etc.

(5) Discuss the advantages and disadvantages of your model or method.

5.3 Focus of the judges

(1) The main statement should present major ideas and results.

(2) Clarify or restate the problem as appropriate.

(3) A clear statement of all variables, assumptions and assumptions.

(4) Analyze the problem, including the motivation or reason for the model used.

(5) The design of the model.

(6) Discuss how to test the model, including error analysis and stability (conditioning, sensitivity, etc.).

(7) Discuss any obvious advantages or disadvantages in your model or method.

(8) The paper must be input in English with a font size of at least 12.

6. Team requirements

There are two types of people required in the team:

One is familiar with modeling and various algorithm theories. After understanding the background, he can build models and design algorithms for solving various problems in this context.
One is that the algorithm can be programmed to achieve the final result.
The third one is for writing specifically. From a professional point of view, other majors are needed. The more suitable majors are biology, civil engineering, electromechanical, telecommunications or machinery. In mathematical modeling, problems of various backgrounds will appear, so if there are other professional students, you can make up for the lack of professional knowledge. Most teams tend to ignore the writing part, thinking that as long as the model is well established, they can win prizes by writing casually. This is a misunderstanding. Because the paper is the embodiment of all work, if the paper is not well written, it will fall short. Therefore, it is definitely beneficial to write more and practice more, and it is not necessary to finish writing, you have to continue to modify, modify until you are very satisfied, modify it to the paper that can be published in a mathematical journal.
Teams must be based on the division of labor. One of the three people must have a solid foundation in mathematics and solid theory, one must be good at algorithm practice, and the other must have good writing skills (to make up for lack of professional knowledge). If a team can have such personnel The configuration is more reasonable.

7. Software and some modeling website reference

(1) Writing a modeling article generally requires the following skills:

Matlab has three main learning directions: modeling (principles, methods, multiple analysis and multiple applications), programming (matlab, lingo, spss, python), typesetting (word)

Learn to use styles, automatic catalogs, automatic quoting, and formula editing. It is easy to learn. After learning, the efficiency of typesetting is about 5 times higher. In addition, take a look at the format requirements issued by the school, the format of the paper has a great impact! For these software: WeChat search public account "Software Installation Manager" are all free downloads, with tutorials.

(2) Summary of mathematical modeling algorithms

https://www.bilibili.com/video/av20238704?from=search&seid=1699655286238093293

Easy to understand, read the package meeting. It is the resource of station b and does not need to be downloaded. (This true conscience)

(3) Word tutorial

https://www.bilibili.com/video/av9261220?from=search&seid=10960492841415341172

Very practical, word is an important and basic skill. After learning not only modeling, it will also have advantages in other aspects. (It is very helpful for word learning)

data:

(4) Links to the 1982-2018 China Statistical Yearbook

https://pan.baidu.com/s/1wF21ejXyWDePzLHSE3mePQ Extraction code: v4wv (You can also directly access the China Statistical Yearbook)

(5) Links to the U.S. Census Data Collection

https://pan.baidu.com/s/1YIFJ0us9V-GiqN_OCJTcHQ Extraction code: juzc

(6) Link to the Data Book of American Cities

https://pan.baidu.com/s/1ufwlpzDDymHDeMWvW7g4-g Extraction code: w8wh

(7) Global medical statistics

Medical link: https://pan.baidu.com/s/1XHg6m5TolTTE6Pu3odV7Ug Extraction code: xtqy

Check the paper website (domestic reference):

(8) CNKI

https://www.cnki.net/

(9) Chinese-English comparison of mathematics in the Chinese University of Hong Kong

http://www.cmi.hku.hk/Ref/Glossary/Mat/i.htm

Check the paper website (foreign reference):

（10） DOAJ

https://www.doaj.org/application/new (It is in pure English and requires some basic English skills)

(11) US Bureau of Transportation Statistics

http://www.bts.gov/

(12) National Agricultural Statistics Service

http://www.usda.gov/wps/portal/usda/usdahome

(13) United States Census Bureau

http://2010.census.gov/2010census/language/chinesesimplified.php

（14）MathType

Link: https://pan.baidu.com/s/1CRwpaHFRZ0fYeLxBbv5kgw
Extraction code: je0n

（15）Academic Phrasebank

http://www.phrasebank.manchester.ac.uk/

Chinese display:

8. Algorithm

The most important thing for the algorithm is to select the most appropriate one based on the meaning of the question. Each algorithm is introduced on the Internet, so only some evaluation algorithms are given below.

8.1 Support Vector Machine

clearclcX0=xlsread('Excel文件位置','B2:E19');for i=1:3    X(:,i)=(X0(:,i)-mean(X0(:,i)))/std(X0(:,i));%数据标准化end[m,n]=size(X);e=ones(m,1);D=[X0(:,4)];B=zeros(m,m);C=zeros(m,m);for i=1:m    B(i,i)=1;    C(i,i)=D(i,1);endA=[-X(:,1).*D,-X(:,2).*D,-X(:,3).*D,D,-B];b=-e;f=[0,0,0,0,ones(1,m)];lb=[-inf,-inf,-inf,-inf,zeros(1,m)]';x=linprog(f,A,b,[],[],lb);W=[x(1,1),x(2,1),x(3,1)];CC=x(4,1);X1=[X(:,1),X(:,2),X(:,3)];R1=X1*W'-CC;R2=sign(R1);disp('程序输出结果:');disp('超平面方程为:');disp(['X1:',num2str(x(1,1))]);disp(['X2:',num2str(x(2,1))]);disp(['X3:',num2str(x(3,1))]);disp(['intercept:',num2str(x(4,1))]);disp('超平面分类结果:');R=[R1,R2]
1

8.2 Gray forecast GM (1,1)

clearclcsyms a b;c=[a b]';A=[89677 99215 109655 120333 135823 159878 182321 209407 246619 300670];B=cumsum(A);       %原始数据累加n=length(A);for i=1:(n-1)    C(i)=(B(i)+B(i+1))/2;    %生成累加矩阵endD=A;D(1)=[];D=D';E=[-C;ones(1,n-1)];c=inv(E*E')*E*D;c=c';a=c(1);b=c(2);%预测后续数据F=[];F(1)=A(1);for i=2:(n+10)    F(i)=(A(1)-b/a)/exp(a*(i-1))+b/a;endfor i=2:(n+10)       %向后预测10年    G(i)=F(i)-F(i-1);endt1=1999:2008;t2=1999:2018;Gplot(t1,A,'o',t2,G)  %原始数据与预测数据的比较
1

8.3 Comprehensive principal component analysis

The data selected in this article comes from the "Statistical Yearbook-Shenzhen Bureau of Statistics". Due to the limited data given in the yearbook, this article only counts the data of 5 indicators from 2011 to 2016:

First, import 5 indicators into SPSS , and use principal component analysis to extract comprehensive indicators, as shown below:

It can be seen from Table 2 that the first and second principal components have accumulated to 89.549%, which can represent most of the data.

According to Table 3 and Table 4, according to the formula:

It can be calculated that the characteristic roots of principal components 1 and 2 are approximately 7.15 and 3.12 respectively. The two principal components can be expressed as:

The calculation formula of the principal component synthesis model is:

So it can $F_{x}$ be:

First find the standardized data in the SPSS data set:

Then, according to the year, Z1 to Z5 are respectively corresponded, and finally the comprehensive evaluation table is obtained as:

Then using 2011 as the time point t=1, and so on, $F$ the regression equation over time can be calculated , using SPSS linear regression to get the following:

It can be seen from Tables 7 and 8 that the significance is satisfied, and the degree of fitting is relatively good. Finally, the regression equation for the comprehensive evaluation of the sports industry's health level is:

For the comprehensive health value, the larger the comprehensive value, the higher the health level.

8.4 Grey Relational Degree Algorithm

https://blog.csdn.net/fanjufei123456/article/details/104003589

8.5 Data Envelopment Analysis (DEA) Analysis of Economy and Environment

https://blog.csdn.net/fanjufei123456/article/details/104008422

8.6 Analytic Hierarchy Process Model (AHP)

https://blog.csdn.net/fanjufei123456/article/details/104008717

8.7 Stepwise regression algorithm

https://blog.csdn.net/fanjufei123456/article/details/104128813

8.8 Particle Swarm Algorithm

https://blog.csdn.net/fanjufei123456/article/details/84779353

2021 Meisai Information Preparation