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The Italian primary school-size distribution and the city-size: a complex nexus.

Belmonte A, Di Clemente R, Buldyrev SV - Sci Rep (2014)

Bottom Line: The upper tail of the school-size distribution decreases exponentially and the growth rates are distributed with a Laplace PDF.We propose a novel cluster methodology and a new spatial interaction approach among schools which outline the variety of policies implemented in Italy.Different regional policies are also discussed shedding lights on the relation between policy and geographical features.

View Article: PubMed Central - PubMed

Affiliation: IMT Institute for Advanced Studies Lucca, Piazza S. Ponziano 6, 55100, Lucca, Italy.

ABSTRACT
We characterize the statistical law according to which Italian primary school-size distributes. We find that the school-size can be approximated by a log-normal distribution, with a fat lower tail that collects a large number of very small schools. The upper tail of the school-size distribution decreases exponentially and the growth rates are distributed with a Laplace PDF. These distributions are similar to those observed for firms and are consistent with a Bose-Einstein preferential attachment process. The body of the distribution features a bimodal shape suggesting some source of heterogeneity in the school organization that we uncover by an in-depth analysis of the relation between schools-size and city-size. We propose a novel cluster methodology and a new spatial interaction approach among schools which outline the variety of policies implemented in Italy. Different regional policies are also discussed shedding lights on the relation between policy and geographical features.

No MeSH data available.


School-size distribution conditional on comuni features.(a). School-size distribution for different city-samples clustered according to the number of schools, i.e. to Eq. 3. Only comuni with nk = 1 show a single peak school-size distribution, clustered around m1 (the +-red line on the top). They have an average population of 2000 inhabitants and the 81% are located in mountain territories. (b). School-size distribution for different city-samples clustered according to the altitude. The altitude of the comune shift the school-size distribution (shift location effect) as higher comuni are generally smaller schools. (c). School-size distribution in the six biggest Italian cities. With the exception of Rome, the hypothesis of unimodality may not be rejected in none of the biggest cities. In particular, flatter cities, such as Milano and Torino, mostly contribute to second mode m2, whereas in Genova, Italian city built upon mountains that steeply ended on the sea, all the school-size distribution stands on the left side.
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f4: School-size distribution conditional on comuni features.(a). School-size distribution for different city-samples clustered according to the number of schools, i.e. to Eq. 3. Only comuni with nk = 1 show a single peak school-size distribution, clustered around m1 (the +-red line on the top). They have an average population of 2000 inhabitants and the 81% are located in mountain territories. (b). School-size distribution for different city-samples clustered according to the altitude. The altitude of the comune shift the school-size distribution (shift location effect) as higher comuni are generally smaller schools. (c). School-size distribution in the six biggest Italian cities. With the exception of Rome, the hypothesis of unimodality may not be rejected in none of the biggest cities. In particular, flatter cities, such as Milano and Torino, mostly contribute to second mode m2, whereas in Genova, Italian city built upon mountains that steeply ended on the sea, all the school-size distribution stands on the left side.

Mentions: In Fig. 4 we investigate the school-size distribution according to the comuni features. To this end, Fig. 4(a) draws the distributions of log10xi conditionally on the number of schools, nk, in the comune k. It yields 8 curves, one for each cluster h defined in Eq. 3. The first cluster is drawn in red (+) distributing all the schools located in comuni where only one school is provided. The orange line (○) distributes all the schools provided in comuni with two or three schools (i.e. h = 2); and so on. The interesting point of Fig. 4(a) is that only the school-size distribution of the smallest comuni (with nk = 1) features a unimodal shape. The reason for that relies on the fact that comuni with only one school are geographically similar: they are the 57% of the total, with little more than 2000 inhabitants, the 81% of which are located in mountain territories.


The Italian primary school-size distribution and the city-size: a complex nexus.

Belmonte A, Di Clemente R, Buldyrev SV - Sci Rep (2014)

School-size distribution conditional on comuni features.(a). School-size distribution for different city-samples clustered according to the number of schools, i.e. to Eq. 3. Only comuni with nk = 1 show a single peak school-size distribution, clustered around m1 (the +-red line on the top). They have an average population of 2000 inhabitants and the 81% are located in mountain territories. (b). School-size distribution for different city-samples clustered according to the altitude. The altitude of the comune shift the school-size distribution (shift location effect) as higher comuni are generally smaller schools. (c). School-size distribution in the six biggest Italian cities. With the exception of Rome, the hypothesis of unimodality may not be rejected in none of the biggest cities. In particular, flatter cities, such as Milano and Torino, mostly contribute to second mode m2, whereas in Genova, Italian city built upon mountains that steeply ended on the sea, all the school-size distribution stands on the left side.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4066576&req=5

f4: School-size distribution conditional on comuni features.(a). School-size distribution for different city-samples clustered according to the number of schools, i.e. to Eq. 3. Only comuni with nk = 1 show a single peak school-size distribution, clustered around m1 (the +-red line on the top). They have an average population of 2000 inhabitants and the 81% are located in mountain territories. (b). School-size distribution for different city-samples clustered according to the altitude. The altitude of the comune shift the school-size distribution (shift location effect) as higher comuni are generally smaller schools. (c). School-size distribution in the six biggest Italian cities. With the exception of Rome, the hypothesis of unimodality may not be rejected in none of the biggest cities. In particular, flatter cities, such as Milano and Torino, mostly contribute to second mode m2, whereas in Genova, Italian city built upon mountains that steeply ended on the sea, all the school-size distribution stands on the left side.
Mentions: In Fig. 4 we investigate the school-size distribution according to the comuni features. To this end, Fig. 4(a) draws the distributions of log10xi conditionally on the number of schools, nk, in the comune k. It yields 8 curves, one for each cluster h defined in Eq. 3. The first cluster is drawn in red (+) distributing all the schools located in comuni where only one school is provided. The orange line (○) distributes all the schools provided in comuni with two or three schools (i.e. h = 2); and so on. The interesting point of Fig. 4(a) is that only the school-size distribution of the smallest comuni (with nk = 1) features a unimodal shape. The reason for that relies on the fact that comuni with only one school are geographically similar: they are the 57% of the total, with little more than 2000 inhabitants, the 81% of which are located in mountain territories.

Bottom Line: The upper tail of the school-size distribution decreases exponentially and the growth rates are distributed with a Laplace PDF.We propose a novel cluster methodology and a new spatial interaction approach among schools which outline the variety of policies implemented in Italy.Different regional policies are also discussed shedding lights on the relation between policy and geographical features.

View Article: PubMed Central - PubMed

Affiliation: IMT Institute for Advanced Studies Lucca, Piazza S. Ponziano 6, 55100, Lucca, Italy.

ABSTRACT
We characterize the statistical law according to which Italian primary school-size distributes. We find that the school-size can be approximated by a log-normal distribution, with a fat lower tail that collects a large number of very small schools. The upper tail of the school-size distribution decreases exponentially and the growth rates are distributed with a Laplace PDF. These distributions are similar to those observed for firms and are consistent with a Bose-Einstein preferential attachment process. The body of the distribution features a bimodal shape suggesting some source of heterogeneity in the school organization that we uncover by an in-depth analysis of the relation between schools-size and city-size. We propose a novel cluster methodology and a new spatial interaction approach among schools which outline the variety of policies implemented in Italy. Different regional policies are also discussed shedding lights on the relation between policy and geographical features.

No MeSH data available.