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2018美赛O奖论文B题-B91566-Forecasting the Language Distribution-解密.pdf
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美国大学生数学竞赛获奖论文,历届,单项文件,内容丰富,大学生数学,数学竞赛,参考资料,极具参考价值
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For office use only
Team Control Number
For office use only
91566
T1
F1
T2
F2
T3
Problem Chosen
F3
T4
B
F4
2018
MCM/ICM
Summary Sheet
Forecasting the Language Distribution
Summary
Language shift is a common and complicated phenomenon since ancient times, which
has far-reaching influence on the development of the human civilization. The language
shift is influenced by many factors. We study the geographically distributed language
shift model and provide solutions based on language shift and economic benefits to
the locations of new international offices for a service company.
To get the geographical language transformation model, we start off by creating a
simple model, and then make it more sophisticated.
The Worldwide Language Shift Model reflects the situation when two or more
languages communicate. The model takes into account factors such as government
support, tourism, international business relations and technological progress.
The Domestic Language Shift Model is the application of the worldwide
language shift model in country. We adjust some parameters to make this model
fit the domestic situation better.
The Geographical Language Shift Model is based on the domestic language
shift model. This model contains the impact of migration on language shift.
We collect rich and effective data, fit the unknown parameters and get the
geographical distribution of various languages in the future. Through the sensitivity
analysis, we prove the stability and error tolerance of the model. By the model
implementation, we found that the geographical language distribution remains
basically stable in the next 50 years.
To address the locations of international offices, we take into account the predicted ge-
ographical language distribution and the economic need. In our opinion, choosing the
location of an international office should make the company more profitable. To this
end, we establish a model of the impact of geographical language distribution on the
company’s effectiveness. We identify the six cities most suitable for hosting interna-
tional offices in both short and long terms are: Paris, Tokyo, Milan, Toronto, Bombay,
Brussels. We also put forward our own ideas about the company’s long-term plan.
In a word, we predict the language development for the next 50 years according to the
geographical distribution language shift model, and provide effective reference for the
locations of international offices.
Team # 91566 Page 1 of 26
Contents
1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4
1.1
Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4
1.2
Restatement of the problem . . . . . . . . . . . . . . . . . . . . . . . . . . .
4
1.3
Related Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4
2 Assumptions and Notations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5
2.1
Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5
2.2
Notations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6
3 Model Construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6
3.1
Worldwide Language Shift Model . . . . . . . . . . . . . . . . . . . . . . .
6
3.1.1 Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6
3.1.2
Data Pre-processing . . . . . . . . . . . . . . . . . . . . . . . . . . .
7
3.1.3
Worldwide Language Shift Model Construction . . . . . . . . . . .
8
3.2
Domestic Language Shift Model . . . . . . . . . . . . . . . . . . . . . . . .
11
3.2.1
Domestic Language Shift Model Construction . . . . . . . . . . . .
11
3.3
Migration Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
12
3.3.1
Data Pre-processing . . . . . . . . . . . . . . . . . . . . . . . . . . .
12
3.3.2
Migration Model Construction . . . . . . . . . . . . . . . . . . . . .
12
3.4
Geographic Language Shift Model . . . . . . . . . . . . . . . . . . . . . . .
13
3.4.1 Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
3.4.2 Geographic Language Shift Model Construction . . . . . . . . . . .
13
4 Model Implementation and Results . . . . . . . . . . . . . . . . . . . . . . . . . . . .
14
4.1 Part I Problem A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
4.2 Part I Problem B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
4.3 Part I Problem C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
4.4
Part II Problem A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
17
4.5
Part II Problem B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
18
5 Sensitivity Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
18
5.1 Sensitivity Analysis for K
i
. . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
5.2 Sensitivity Analysis for domestic language distribution . . . . . . . . . . . 18
5.3 Sensitivity Analysis for Fitting Parameters . . . . . . . . . . . . . . . . . . . 19
Team # 91566 Page 2 of 26
6 Strengths and weaknesses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
19
6.1 Strengths . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
6.2
Weaknesses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
20
6.3
Further work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
20
7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
20
Appendices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
22
Team # 91566
Page 3 of 26
To: Chief Operating Officer
From: Investigation Team
Date: 12 February, 2018
Subject: Suggestions for New Office Locations
We have completed an analysis of the locations of your company’s international offices
as well as the trends of global languages.
First, we set up a model of global language competition and summed up the rules of global
language shift by collecting considerable and reliable data. We analyzed and pre-dicted
the geographical distribution of global languages in the next 50 years. Second, based on
the changes of languages, the recruitment cost and the development level of the city
where the office is located in, we provided 6 suitable office locations. Finally, we combined
scientific and technological development factors, and gave reasonable sugges-tions to the
long-term plan of setting up new offices in the future.
Based on our analysis, here are some suggestions:
It is advisable to set up offices in the following six cities. The languages
correspond to each office are as follows:
City
Country
Corresponding language
Paris
France
France, Spanish, English
Tokyo
Japan
Japanese, English
Milan
Italy
Italian, France, English
Toronto
Canada
English, French
Bombay
India
English, Hindustani, Bengali
Brussels
Belgium
France, Dutch,English
We do not recommend frequent replacements of office sites, because there is a
cer-tain stability of the distribution of the world’s languages, no major changes
would occur within a short time. At the same time, replacing an office is costly,
and ad-versely affecting the company’s profits.
Profits brought by language advantages will be reduced due to the rapid
expansion of global communications. While the cost of employing may increase,
the amount of existing offices may no longer be optimal. If you can provide more
specific data, we will be able to give more reasonable advice on the long-term
plans for the new offices.
Our modeling analysis report contains more detailed theoretical information. Please
contact us promptly if there are any questions.
Team # 91566 Page 4 of 26
1
Introduction
1.1 Background
It is generally taken for granted that language, as a concomitant of culture, can spread.
With the trend of globalization and the world’s cultural exchange, language transfer
and integration are also more common. Nowadays more and more people can speak
two or even more languages.
The shift and spread of language can be seen through the amount of speakers, includ-
ing native speakers plus second or third, etc. language speakers. However, the total
number of speakers of a language fluctuates under the influence of various
complicated factors. These factors involve political, economic, diplomatic, social
relations and other aspects, such as government-mandated official languages, tourism
among nations, mi-gration and population movements, the promotion of new social
media (facebook, Twit-ter, etc.) and so on.
1.2 Restatement of the problem
We are required to predict the spread and development of languages all over the world
under the influence of several factors and help a large multinational service company
to determine the locations of new offices.
The problem can be analyzed into three parts:
Develop a model of the distribution of various language speakers over time
based on impact factors and predict what will happen to the number of speakers
of each language in the next 50 years.
Use the model to predict the geographic distributions of languages in the next 50
years.
Determine the locations of new international offices and the languages used in
the new offices based on the modeling results.
1.3 Related Work
Mcmahon(1994) and Mufwene(2001) proposed that the languages change of a region
is caused by a mechanism named language shift. Language shift is a process that
takes place in the region where obsess more than one language. The members of the
region abandon their initial language in favor of another. So, despite the migration.
Accord-ing to Abrams and Strogatz(2003), Anna and Roman(2010), Katharina and
Gero(2017), language shift is modeled as a competition between two communities
who use differ-ent languages, and the motivation of the language shift is to chase to
better opportunity provided by another language. Abrams-Strogatz (A-S) Model is the
most widely math-ematic model of describing the changes in the patterns of language
shift between two language communities. The A-S Model shows the temporal
population shift of both languages, which results in
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