2018美赛O奖论文B题-B79002-How many languages-解密.pdf
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For office use only
T1
T2
T3
T4
Team Control Number
79002
Problem Chosen
B
For office use only
F1
F2
F3
F4
2018
MCM/ICM
How many languages?
To predict the number of the one language, we assume that native speakers are related to natural growth rate of its native
speaker and number of the its second speakers. Based on the data we collected, we use
time series languages speakers
difference equation model
to describe the dynamic change of both native and second language speakers, considering the
influence of foreign language taught in school, social media, economics, cultural communication and so on.
The difference equation model can apply our collected indicators to the prediction of change of language distribution over
time. 50 years later, top 10 languages in order of total speakers change from [Mandarin, English, Hindustani, Spanish, Arabic,
Malay, Russian, Bengali, Portuguese French] to [Mandarin ,English, Spanish, Hindustani, Arabic, Bengali, Portuguese, Malay,
Russian, French]; the rank of top 10 native languages speakers changes from [Mandarin, Spanish, English, Hindustani, Arabic,
Bengali, Portuguese, Russian, Punjabi, Japanese] to [Mandarin, Spanish, English, Hindustani, Arabic, Bengali, Portuguese,
Punjabi, Russian and Hausa]. By analyzing these changes, we find some reasonable explanations, such as the rapid natural
growth rate of some developing countries and some languages’ increasing speaking-power.
Given the global population growth and migration pattern, we establish
geographical distribution of difference equation
model, to predict the geographical distribution of different languages. Through the establishment of the difference equation,
we consider the relationship between the distribution of languages on different continents and main migration routes. We use
MATLAB to calculate language proportion changes on each continent over the next 50 years, finding some reasonable
predictions. For example, Mandarin will become the No.2 native language in North America and Australia. The proportion
of Mandarin and Arabic speakers in Europe will increase significantly.
In Part II, based on the requirement and the feature of service company, we choose six suitable cities based on our prediction
of language speakers. Also, we find that the cities are different depending on whether the company is long-term oriented (6
suggested cities: Shanghai, New York, Calcutta, Madrid, Dubai, and Rio de Janeiro) or short-term oriented (6 cities: Shanghai,
New York, Calcutta, Madrid, Dubai, and Singapore).
Moreover, we build the
cost-benefit analysis model
to calculate the suitable number of offices that this company should
build. Given the level of company’s profitability and cost, we set a new parameter, cost-profitability ratio. If the value of c-
p ratio is less than 281, we think 6 offices should be built. If the value of this ratio is between 281 and 422, we think 5 offices
should be built. If the value is between 422-527, 4 offices are best; if it is between 527 and 544, 3 office should be built; if>
544, we should only maintain two offices.
Finally, we analyze the performance of our model and the sensitivity of our model, proving that our model is relatively stable
for different parameters.
Key words: Language distribution, Time Series Difference Equation Model, Dynamic simulation, site selection
Cost-profit analysis
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