Difference between revisions of "Virtual society:results"

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We are reporting here some selected results describing properties of our Basic Virtual Society model. In such a system various ranges of quantitative analysis can be considered. However, we focus here on the features essential for ongoing epidemiological and transportation studies, as well as on the planned future investigations. Since the methods used for recreation of a given social nodes, e.g. schools and workplaces are in principle similar, we limit the description here only to one selected type of network structure.
 
We are reporting here some selected results describing properties of our Basic Virtual Society model. In such a system various ranges of quantitative analysis can be considered. However, we focus here on the features essential for ongoing epidemiological and transportation studies, as well as on the planned future investigations. Since the methods used for recreation of a given social nodes, e.g. schools and workplaces are in principle similar, we limit the description here only to one selected type of network structure.
  
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[[Image:guzik_mg.png |frame|'''Fig.4a''':The average time necessary to get to the college in villages or cities (data from the work of Guzik<ref name="guzik2001"/>).]]
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[[Image:guzik_mg.png |frame|left|'''Fig.4a''':The average time necessary to get to the college in villages or cities (data from the work of Guzik<ref name="guzik2001"/>).]]
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| [[Image:dist_LO_malopolskie_hatch_bw.png |frame|'''Fig.4b''':The average household-college distance in communes obtained using the model described in this work.]]
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| [[Image:dist_LO_malopolskie_hatch_bw.png |frame|right|'''Fig.4b''':The average household-college distance in communes obtained using the model described in this work.]]
 
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  || [[Image:num_colleges_malopolskie.png |frame|'''Fig.4c''':The presence of schools in the communes (data from NCB).]]
 
  || [[Image:num_colleges_malopolskie.png |frame|'''Fig.4c''':The presence of schools in the communes (data from NCB).]]
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Figure 4b marks out five regions of rather poor school availability, expressed in long household-college distances. In the case of the South-East and South region, the explanation may be the lack of schools in these regions shown in Figure 4c. This pattern is also visible in Figure 4a in the case of south-eastern region of Malopolskie voivodeship. The North and North-Eastern regions of long household-college distances are also pointed out as the regions characterized by long time necessary to reach the school. There is also a small North-West region visible in all three figures.
 
Figure 4b marks out five regions of rather poor school availability, expressed in long household-college distances. In the case of the South-East and South region, the explanation may be the lack of schools in these regions shown in Figure 4c. This pattern is also visible in Figure 4a in the case of south-eastern region of Malopolskie voivodeship. The North and North-Eastern regions of long household-college distances are also pointed out as the regions characterized by long time necessary to reach the school. There is also a small North-West region visible in all three figures.
  
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=== Mean distance to RSU ===
  
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=== Mean distance to RSU ===
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As we said, the addition of the subsequent RSUs was constrained to the minimal distance of 2 km between the units. Consequently, the maximum number of the located units in any commune (see Figure 5) corresponds to the area of that commune. Therefore, Figure 5 reflects also the area size distribution of communes in the whole country.
  
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As we said, the addition of the subsequent RSUs was constrained to the minimal distance of 2 km between the units. Consequently, the maximum number of the located units in any commune (see <a href="#fig">Figure 8</a>) corresponds to the area of that commune. Therefore, <a href="#fig">Figure 8</a> reflects also the area size distribution of communes in the whole country.  
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Despite the high numbers of RSUs, the regions of northern and western Poland (described by a low population density and relatively big areas of the constituting communes) are represented by the big mean distances to the rescue unit, as shown in Figure 6.
  
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Despite the high numbers of RSUs, the regions of northern and western Poland (described by a low population density and relatively big areas of the constituting communes) are represented by the big mean distances to the rescue unit, as shown in <a href="#fig">Figure 8</a>.
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[[Image:ospMAX_color_small.png |frame|left|'''Fig.5''': Maximal number of the RSUs located in particular commune.]]
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[[Image:osp_dist_color_small.png |frame|right|'''Fig.6''': Mean distance between a household and a rescue unit in a commune when maximum number of RSUs is placed in the commune.]]
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=== Simplified economic analysis of the RSU system ===
 
=== Simplified economic analysis of the RSU system ===
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Based on the models described so far, it is possible to carry out the preliminary economic analysis of the geo-referenced structure of RSUs distribution.
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The most important factors that need to be balanced are the benefits related to a decrease of the mean distance between RSU and household, and the costs of creating any additional RSU in a commune. However, due to the inhomogeneous structure of the population density, it is not a straight forward task to correctly estimate general benefits of establishing another RSU in any commune.
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The mean distance from a household to the closest unit as a function of the number of RSUs in a commune is described here by a decaying function (named herein D). Function D is hyperbolic, since the mean distance to RSU is inversely proportional to the number of located RSUs. It also depends on a given commune topology. The following factors, among others, strongly affect the D-function: commune type (village, city, city-village), area of the commune and population density. Selected cases of D-function, presented as fits to the data, are shown in Figure 7.
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[[Image:dist_vs_nosp_color.png |frame|center|'''Fig.7''':Examples of different decay character of the mean distance from household to rescue unit versus number of rescue units. Fits presented in the plot regard only the case of villages.]]
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A good measure of the non-linearity of the function in this case is a RMSD (Root Mean Square Deviation) calculated between the linear function fitted to the initial and final point of the decay, and the decay data. Initial point's coordinates are defined by the mean household-RSU distance at one RSU located, final point's - by the mean household-RSU distance at the maximum number of RSU located. When RMSD values are small, any addition of a rescue unit in the commune results with the significant improvement of the accessibility to the RSUs. When RMSD values are high, only few initial rescue units are beneficial because adding another RSU does not change much the mean distance to RSU.
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One can search for correlations between communes' descriptors, namely population and area statistics, and D-function properties in order to establish possible commune clusters. The proposed descriptors, and values used to characterize the D-function are listed in Table 1, below.
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The correlation function may constitute an efficient analysis tool for a proper assignment of similarity among many communes. However, the set of proposed in this work communes' descriptors is not significantly correlated with the character of a D-function, namely it is not possible to deduce the economic properties of adding new RSU. However, we believe, it will reveal its usefulness in a further analysis. In the case of RSU, the correlation matrices indicate that the direct studies of a D-function might be a proper source of knowledge for such economic assessments.
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The correlations that we observed (see Figure 8) show, that there is no significant correlation between the general statistical properties of communes of the same type and the decreasing distance to RSU due to increased number of RSUs.
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[[Image:cmatrix2_g1_part.png |frame|left|'''Fig8a''': Correlation matrices. For the sake of clarity, correlation values lying in the range [-0.370;0.370] are colored uniformly. The indices correspond to the properties given in Table 1.]]
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[[Image:cmatrix2_part.png |frame|right|'''Fig8b''']]
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{| class="rtable" align="center" width=60%
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|+ align="left" | '''tab.1'''
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! colspan="2" | Statistical descriptors and RSU assignment characteristics for Polish communes
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||'''Position''' || '''RSU characteristics'''
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|| 1  || Number of located RSUs
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|| 2  || Mean household-RSU distance, assuming one RSU located
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|| 3  || Mean household-RSU distance, assuming two RSUs located
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|| 4  || Mean household-RSU distance, assuming max RSUs located
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|| 5  || Slope of the linear function 
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|| 6  || RMSD between linear and the D-function
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||  || '''Commune descriptor'''
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|| 7  || Population
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|| 8  || Area
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|| 9  || Minimal population in a node
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|| 10 || Maximal population in a node
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|| 11 || Mean population density (in commune)
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|| 12 || Standard Deviation (of the above mean)
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|| 13 || Range
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|| 14 || Mode
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|| 15 || First Quartile   
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|| 16 || Median
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|| 17 || Third Quartile
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|| 18 || Minimal area conveying 25% of population   
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|| 19 || As above in % of the commune are
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|| 20 || Minimal area conveying 50% of population
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|| 21 ||As above in % of the commune area
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|| 22 ||    Minimal area conveying 75% of population
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|| 23 || As above in % of the commune area
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|}
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On the other hand, the graphs resulting from our models, presented in Figure 7 give a good predicative ability of the benefits coming out of establishing subsequent RSUs in the same commune, and it may constitute possibly a good tool for administrative planning.
  
 
== References ==
 
== References ==

Latest revision as of 13:01, 14 November 2008

Virtual society | Virus spread | Literature | Version Polish.png
Data | Model | Results





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