## 3/20/2013

### The Game of Life

The Game of Life is a ‘cellular automaton’, which was invented by John Conway in 1970.

It consists of a collection of cells which is in one of two possible states, alive or dead. These cells are based on a few mathematical rules as below.

The Rules

"For a space that is ‘populated’ (live cell)"

Each live cell with one or no neighbors dies, as if by under-population.

Each live cell with four or more neighbors dies, as if caused by overcrowding.

Each live cell with two or three neighbors survives.

"For a space that is ‘empty’ or ‘unpopulated’ (dead cell)"

Each dead cell with three live neighbors becomes populated, as if by reproduction.

Intuitive to visualize (2D/3D) spatially

Easy to communicate

Simple to create/ theory is simple

Can model random variation perhaps better than equation

Difficult to analyse

Difficult to apply to real world

Utility of simulation is limited

Cannot make specific predictions

-----------------------------------------------

CA is...

・Good for understanding mechanisms

Simple system which can give highly variable outcomes

Complex global behavior from local interaction

## The Relationship between Obesity and Life Expectancy

On 13th December 2012, CNN reported that obesity is a bigger health crisis globally than hunger, and the leading cause of disabilities around the world according to a new report published in the British medical journal The Lancet.

The report revealed that every country, with the exception of those in sub-Saharan Africa, faces alarming obesity rates an increase of 82% globally in the past two decades. Middle Eastern countries are more obese than ever, seeing a 100% increase since 1990.
(http://edition.cnn.com/2012/12/13/health/global-burden-report/index.html?iref=allsearch)

According to a research of the Ministry of Health, Labor and Welfare, obesity is one of grave concerns in Japan as well. Then, to what extent obesity correlates to life expectancy? In this blog, the relationship between obesity and life duration will be examined.

The ministry shows the data of obesity rate through The National Nutrition Survey carried out in 2010 (http://www.mhlw.go.jp/english/, accessed 23rd Dec 2012). From this survey, the obesity rates by prefecture can be seen. The boundary data are obtained from the ESRI Japan web site (http://www.esrij.com/, accessed 23rd Dec 2012). Below is a distribution map of obesity rate by prefecture.

As shown by above figures, there seems to be regional differences and the rates range widely from under 25 to 45. In order to study the association with life duration, the data of mean life expectancy are got through electronic open database of the Ministry of Health, Labor and Welfare in Japan. The prefectural data are retrieved from the Population Survey Report released in 2010.

As is the case with the obesity rate, differences among regions are likely to be seen on the map of mean life expectancy. In an effort to clarify the spatial relationship between these two variables, a regression analysis is calculated.

A Regression Analysis

For the purpose of testing to see whether there is a statistical relationship between obesity and life expectancy, a following regression analysis is examined in a condition that ‘mean life expectancy’ is set as the dependent variable and ‘obesity rate’ is used as the explanatory variable. Below is the result of the regression analysis.

R-squared value, which indicates how effectively the model fits, is calculated through the regression analysis. The value ranges from 0 to 1. From the above result, the value is 0.2285. It means that it would be interpreted that life expectancy is probable to have a relation with obesity.

The Degree of Spatial Autocorrelation

Two methods of measurement are used on this study so as to know the degree of spatial autocorrelation of life duration. One is Moran’s I, and another is Geary’s C.

Firstly, the degree of spatial autocorrelation can be calculated by Moran’s I. Moran (1950) was the first person to develop the measure of spatial autocorrelation with an aim to clarify stochastic phenomena which are distributed in space. Like a correlation coefficient, the values of Moran's Index range from -1 to +1. While +1 means strong positive spatial autocorrelation, -1 means strong negative spatial autocorrelation and 0 indicates a random pattern. It shows the degree of interdependency between the variables. In this test, the result of Moran’s I is 0.568. Therefore, it can be said that there is spatial clustering of the values because it is relatively near to +1.

Secondly, Geary's C is tested, which is similar to Moran's I but it is non-identical. Geary's C focuses more on local spatial autocorrelation while Moran's I is a way of measuring global spatial autocorrelation. Geary’s C value ranges from 0 to 2. In this analysis, 1 indicates no spatial autocorrelation and values ranging from 0 to 1 means increasing positive spatial autocorrelation, whilst values higher than 1 demonstrate increasing negative spatial autocorrelation. In this case, the result of Geary’s C test is 0.572. Hence, as with Moran’s I, it also means positive spatial autocorrelation on the grounds that the value is between 0 to 1.

Conclusion

Although there seems to be a certain relationship between obesity and life expectancy, the values of spatial analyses are not necessarily enough to conclude. Therefore, further researches are required to elucidate the role of obesity as a factor relating to length of life.

References

Cliff A.D.and Ord J.K. (1981) ‘Spatial processes’, Pion, p. 21.

ESRI Japan, http://www.esrij.com/, accessed 23rd Dec 2012.

Gehlke C.E, Biehl K (1934) ‘Certain effects of grouping upon the size of the correlation coefficient in census tract material’, Journal of the American Statistical Association, 29, pp. 169–170.

Goodchild M.F. (1987) ‘Spatial Autocorrelation’. CATMOG, 47, GEO BOOKS.

Moran, P.A.P. (1950) ‘Notes on continuous stochastic phenomena’. Biometrika, 37, 17.

The Ministry of Health, Labor and Welfare, http://www.mhlw.go.jp/english/, accessed 23rd Dec 2012.