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For office use only

Team Control Number

For office use only

91566

T1 F1

T2 F2

Problem Chosen

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.

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Team # 91566 Page 1 of 26

Contents

1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.1

Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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 . . . . . . . . . . .

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

. . . . . . . . . . . . . . . . . . . . . . . . . . . . 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.

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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