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  • Author: Samo Drobne x
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The use of different objective functions in hierarchical aggregation procedures is examined in this paper. Specifically, we analyse the use of the original Intramax objective function, the sum-of-flows objective function, the sum-of-proportions-to-intra-regional-flows objective function, Smart’s weighted interaction index, the first and second CURDS weighted interaction indices, and Tolbert and Killian’s interaction index. The results of the functional regionalisation have been evaluated by self-containment statistics, and they show that the use of the original Intramax procedure tends to delineate operationally the most persuasive and balanced regions that, regarding the intra-regional flows, homogeneously cover the analysed territory. The other objective functions give statistically better but operationally less suitable results. Functional regions modelled using the original Intramax procedure were compared to the regions at NUTS 2 and NUTS 3 levels, as well as to administrative units in Slovenia. We conclude that there are some promising directions for further research on functional regionalisation using hierarchical aggregation procedures.

Dynamics and local policy in labour commuting

Background: In the paper, the influence of the selected parameters, which are population, travel time to work by car, employment rate and average gross earnings, to labour commuting flows in Slovenia is analysed for the period 2000 - 2009. Furthermore, the dynamics of the analysed parameters have been studied to be implemented in the local policy application. Objectives: The main goal of this research has been to study the stickiness and attractiveness of Slovenian municipalities regarding the analysed parameters to support local labour commuting policy. Methods/Approach: The influence of the analysed parameters to the labour commuting flows has been studied in the extended gravity model. The change of the influence of parameters on commuting flows has been studied separately for each year in the analysed period. Additionally, the calculation of the extended gravity model has been performed for the whole analysed period. Results: The results show that the analysed parameters more attracted than dispatched the inter-municipal labour commuting flows in Slovenia in the study period. The results of the study of the dynamics of the analysed parameters have been implemented in the case study at the local level. Conclusions: The results provide the important empirical contribution to physical planners at the state, regional and/or local level for creating development policies. The results show that some factors in the gravity model can be compensated with the change of the others and vice-versa.


Background: In most countries, data on migration refer only to flows between administratively or statistically defined zones that are changing over time. When different numbers, sizes, and shapes of areas are chosen for analysis of internal migration, different results are generated. This problem is recognised as the Modifiable Areal Unit Problem (MAUP).

Objectives: The paper analyses the impact of inter-municipal migration on population redistribution in Slovenia in 2000–2014 by considering the MAUP. Namely, the number of analysed municipalities increased by 19 in the considered period.

Methods/Approach: We analysed the MAUP effects and estimated internal migration statistics by producing a large number of aggregations using the IMAGE Studio software.

Results: Several statistics that measure the direction and pace of population concentration, as well as the correlation between measures of migration intensity and national development, have been calculated.

Conclusions: The results for Slovenia show that the migration efficiency decreases with the development process measured by the human development index.


Background: Hierarchical functional regions (FRs) can be calculated using data on interactions between basic spatial units (BSUs) and a hierarchical aggregation procedure. However, the results depend on the selected system of initial BSUs. In spatial sciences, this is known as the zonation effect, which is one of the effects of the Modifiable Areal Unit Problem (MAUP). Objectives: In this paper, we analyse the influence of the zonation effect on a system of hierarchical functional regions. Methods/Approach: We compared two systems of hierarchical functional regions of Slovenia modelled by the Intramax aggregation procedure using the inter-municipal labour commuting flows for the same year, but for two different initial sets of municipalities. Besides, we have introduced a new measure to compare systems of hierarchical FRs. Results: The results show that the zonation effect has an influence on hierarchical functional regions. The clustering comparison measure suggested here is a metric measure, which is appropriate for comparing hierarchical FRs. Conclusions: The zonation effect has influence on hierarchical FRs. The clustering comparison measure suggested in this paper is easy to interpret, but it should be adjusted for the number of clusterings


Background: Intramax is a hierarchical aggregation procedure for dealing with the multi-level specification problem and with the association issue of data set reduction, but it was used as a functional regionalization procedure many times in the past.

Objectives: In this paper, we analyse the simultaneous use of three different constraints in the original Intramax procedure, i.e. the contiguity constraint, the higher-inner-flows constraint, and the lower-variation-of-inner-flows constraint.

Methods/Approach: The inclusion of constraints in the Intramax procedure was analysed by a programme code developed in Mathematica 10.3 by the processing time, by intra-regional shares of total flows, by self-containment indexes, by numbers of singleton and isolated regions, by the number of aggregation steps where a combination of constraints was applied, by the number of searching steps until the combination of constraints was satisfied, and by surveying the results geographically.

Results: The use of the contiguity constraint is important only at the beginning of the aggregation procedure; the higher-inner-flows constraint gives singleton regions, and the lower-variation constraint forces the biggest employment centre as an isolated region up to a relatively high level of aggregation.

Conclusions: The original Intramax procedure (without the inclusion of any constraint) gives the most balanced and operative hierarchical sets of functional regions without any singletons or isolated regions.


Background: Aging is one of the most serious problems that most developed countries are facing in the 21st century. In the European Union, Member States are responsible for the planning, funding and administration of health care and social protection systems. Local authorities and state governments should undertake research toward developing an appropriate array of community-based care services for old people. Objectives: This study analyses the regions of Slovenia for servicing old people in the 2000-2010 time horizon. Methods/Approach: Sets of functional regions were modelled for each year in the analysed period using the Intramax method. Functional regions were evaluated based on the attractiveness of central places for labour commuters and the propensity to commute between regions. Results: The results show that in addition to the nominally declared regional centres of Slovenia, there are also some other local centres that should be potentially included in the functional areas for servicing old people. Conclusions: The results suggest that the regionalization into seven functional regions is the most convenient for servicing old people in the region. Furthermore, some additional functional regions at a lower level are suggested.


Walkable access is recognised as one of the most important factors for deciding to walk instead of using other modes of transport. Distance has been less accurately taken into consideration in previous walking accessibility measures, however, as they are often based on an isotropic approach or on a fixed distance threshold. The objective of this paper is to present a method of modelling continuous walking accessibility to different amenities in a city, with an integrated network-based and distance-decay approach, applied to a case study of the city of Ljubljana, Slovenia. The approach is based on a web survey to obtain data on acceptable walking distances to different types of amenities. Several distance decay functions were analysed for each type of amenity from the cumulative frequency of responses. The best fitting functions were used to model the walking accessibility surfaces for individual amenities in the network, representing five domains (retail, services, recreation, education and transportation) and an overall walking accessibility index. Despite certain limitations and a further need to assess the validity of the methods, our distance-decay network-based approach is more accurate than the isotropic or even network-based modelling of walking distances in continuous or threshold approaches, as it enables the researcher to take into account the differences in propensities to walk to different amenities. The results can be used by city authorities and planners for implementing actions to improve walking accessibility in the most problematic areas.


Background Determining the location, boundaries and areas of land properties accurately in the land cadastre is essential. The named data are provided using coordinates, acquired from field measurements. Since 2008, the Slovenian land cadastre claims positioning in the national realization of the ETRS89, so the GNSS use is practically indispensable. Objectives: Contrary to real-time, we can change parameters in GNSS post-processing. The aim of this paper is to simulate different measurement conditions for GNSS in order to determine how to acquire the best possible coordinates for further use in land area calculation. Methods/Approach: Simulations of obstacles near points followed the increasing of the cut-off angle. Furthermore, shortening the observation interval resulted in different occupation duration. The final condition evaluation for coordinate quality acquisition followed from fuzzy logic. Results: The results show that for short baselines, occupation duration is the most important factor in acquiring high quality coordinates and avoiding the multipath. Differences in coordinates from specific strategies can sometimes exceed the tolerance and evidently affect the area calculation. Conclusions: The findings confirm that only good measurement conditions lead to high quality coordinates and well-defined areas of land properties, which are the fundamental factor in relation to the issues of property valuation and assessing land taxes or rents.