Program snapshot. Application of the spring-block model for partition of counties in USA. Blocks are modeling the counties (or group of counties) and they are represented as circles. The blue lines are the springs connecting the blocks.

Spring-block model reveals region-like structures

Regions are regarded as basic units of social and economic life. They are complex socio-economic structures and in order to define them complex methods are needed. There are two basic and much debated questions that should be clarified: how do they emerge and how may be they defined and delimited in space? The present work contributes to this topic by offering a novel quantitative method for geographical space-partition. The elaborated method applies the classical spring-block model of physics for revealing a hierarchical organization of settlements in region-like structures. Spring-block type models were previously used with success to describe fragmentation at different spatial scales. Due to the fact the partition of a geographical space in region-like structures is also a hierarchical fragmentation process, the use of spring-block models is motivated. The spring-block model consists of sliding blocks interconnected by springs as main elements. The blocks will model the settlements, and they are interconnected with their neighbors through abstracts springs. The mass of the blocks are naturally the sizes of the settlements, while the interaction strength in the springs is defined through the similarity strength of the neighboring elements.  This measure can be determined from Pearson-type correlations of relevant long-time settlement-level data (population census data, GDP data, tax data, etc...). The fragments which result from the relaxation of the tension-field in the spring-block system are accounted as regions of the corresponding geographical system.

To illustrate the applicability of the method, a user-friendly and interactive JAVA program was created. The program was then used for detecting region-like structures in the case of USA, Hungary and Transylvania. In the case of USA and Transylvania, long-term population census data was considered for constructing the connectivity measure, while in the case of Hungary taxation data for the last 20 years (1990-2009) were used. All these applications proved that the method works well, and the obtained space partitions proved to be reasonable ones, revealing some historically, politically or geographically motivated region-structures.

Figure 1 . Results of the method for Transylvania using census data between 1850 and 2002. The picture on the right illustrates a rough partition, confirming the particular situation of the Banat region. The picture on the right shows a finer partition in four, revealing four main regions.

Figure 2. Results of the method for Hungary using settlement level tax data between 1990 and 2009. The picture on the left illustrates a first partition, revealing East and West Hungary separated by the line of the Danube. The picture in the middle shows a partition in 19 territorial units, and the picture on the right illustrates a structure which is highly corresponding with the actual territorial-administrative partition of Hungary. 

Links:

http://www.plosone.org/article/info%3Adoi%2F10.1371%2Fjournal.pone.0016518

http://atom.ubbcluj.ro/~gmate/regions/

Gabriell Máté^1,2 , Zoltán Néda¹ and József Benedek³

¹Interdisciplinary Center for Scientific Computing, University of Heidelberg, Speyererstr 6, 69115 Heidelberg, Germany
²Department of Theoretical and Computational Physics. BabeÅŸ-Bolyai University, str. Kogalniceanu 1, RO-400084, Cluj-Napoca, Romania
³Department of Geography, BabeÅŸ-Bolyai University, str. Kogalniceanu 1, RO-400084, Cluj-Napoca, Romania