Extended Lorenz majorization and frequencies of distances in an undirected network

Purpose:To contribute to the study of networks and graphs.Design/methodology/approach:We apply standard mathematical thinking.Findings:We show that the distance distribution in an undirected network Lorenz majorizes the one of a chain.As a consequence,the average and median distances in any such network are smaller than or equal to those of a chain.Research limitations:We restricted our investigations to undirected,unweighted networks.Practical implications:We are convinced that these results are useful in the study of small worlds and the so-called six degrees of separation property.Originality/value:To the best of our knowledge our research contains new network results,especially those related to frequencies of distances.

Development of a New Index for Integrating Landscape Patterns with Ecological Processes at Watershed Scale

Understanding the relationship between landscape pattems and ecological processes has been a central yet challenging research theme in landscape ecology. Over the past decades, many landscape metrics have been proposed but few directly incorporated ecological processes. In this paper, we developed a landscape index, namely, location-weighted landscape index （LWLI） to highlight the role of landscape type in ecological processes, such as nutrient losses and soil erosion. Within the framework of the Lorenz curve theory, we develop this index by integrating land- scape pattern and point-based measurements at a watershed scale. The index can be used to characterize the contribution of landscape pattern to ecological processes （e.g. nutrient losses） with respect to a specific monitoring point in a watershed. Through a case study on nutrient losses in an agricultural area in northeastern China, we found that nutrient losses tended to be higher for a watershed with a higher LWLI value, and vice versa. It implied that LWLI can be used to evaluate the potential risk of nutrient losses or soil erosion by comparing their values across watersheds. In addition, this index can be extended to characterize ecological processes, such as the effect of landscape pattern on wildlife inhabitation and urban heat island effect. Finally, we discuss several problems that should be paid attention to when applying this index to a heterogeneous landscape site.

Source-sink landscape spatial characteristics and effect on non-point source pollution in a small catchment of the Three Gorge Reservoir Region

The source and sink landscape patterns refer to landscape types or units that can either promote positive evolvement of non-point source(NPS) pollution process, or can prevent/defer the ecological process, respectively. Therefore, the role of a catchment landscape pattern in nutrient losses can be identified based on the spatial arrangement of source and sink landscapes. To reveal the relations between landscape spatial characteristics and NPS pollution in small catchment, a case study was carried out in a Wangjiagou small catchment of the Three Gorges Reservoir Region(TGRR), China. Google earth imagery for 2015 were processed and used to differentiate source and sink landscape types, and six subcatchments were selected as sample regions for monitoring nitrogen and phosphorus nutrients.Relative elevation, slope gradient and relative flow length was used to construct the Lorenz curves of different source and sink landscape types in the catchment, in order to assess the source and sink landscape spatial characteristics. By calculating the location-weighted landscape indices of each subcatchment and total catchment, the landscape spatial load characteristics affecting the NPS pollution was identified, with a further Pearson correlation analysis for location-weighted landscape indices and nitrogen-phosphorus monitoring indicators. The analysis of Lorenz curve has revealed that the obtained distribution trend of Lorenz curve and curve area quantified well the spatial characteristics of source and sink landscape pattern related to the relative elevation, slope gradient and relative flow length in small catchment. Results of Pearson correction analysis indicated that location-weighted landscape index(LWLI) combining of terrain and landscape type factor did better in reflecting the status of nitrogen and phosphorus loss than the indices related to relative elevation, slope gradient and relative flow length.

Examining the distribution and dynamics of impervious surface in different function zones in Beijing

Impervious surface(IS) is often recognized as the indicator of urban environmental changes. Numerous research efforts have been devoted to studying its spatio-temporal dynamics and ecological effects, especially for the IS in Beijing metropolitan region. However, most previous studies primarily considered the Beijing metropolitan region as a whole without considering the differences and heterogeneity among the function zones. In this study, the subpixel impervious surface results in Beijing within a time series(1991, 2001, 2005, 2011 and 2015) were extracted by means of the classification and regression tree(CART) model combined with change detection models. Then based on the method of standard deviation ellipse, Lorenz curve, contribution index(CI) and landscape metrics, the spatio-temporal dynamics and variations of IS(1991, 2001, 2011 and 2015) in different function zones and districts were analyzed. It is found that the total area of impervious surface in Beijing increased dramatically during the study period, increasing about 144.18%. The deflection angle of major axis of standard deviation ellipse decreased from 47.15° to 38.82°, indicating the major development axis in Beijing gradually moved from northeast-southwest to north-south. Moreover, the heterogeneity of impervious surface’s distribution among 16 districts weakened gradually, but the CI values and landscape metrics in four function zones differed greatly. The urban function extended zone(UFEZ), the main source of the growth of IS in Beijing, had the highest CI values. Its lowest CI value was 1.79 that is still much higher than the highest CI value in other function zones. The core function zone(CFZ), the traditional aggregation zone of impervious surface, had the highest contagion index(CONTAG) values, but it contributed less than UFEZ due to its small area. The CI value of the new urban developed zone(NUDZ) increased rapidly, and it increased from negative to positive and multiplied, becoming animportant contributor to the rise of urban impervious surface. However, the ecological conservation zone(ECZ) had a constant negative contribution all the time, and its CI value decreased gradually. Moreover, the landscape metrics and centroids of impervious surface in different density classes differed greatly. The high-density impervious surface had a more compact configuration and a greater impact on the eco-environment.

Modeling relationships between the network distance and travel time dynamics for assessing equity of accessibility to urban parks

Static models of accessibility are usually based on the fixed distance or Average Travel Time(ATT)models.Because of ignoring the traffic as a dynamic process affecting the accessibility through the change of Travel Time(TT),these models lead to unperceived temporal inequities.In contrast to the consideration of the temporal Variation of TT(VTT)in the previous studies,the variation of traffic-related TT and its relations with network distance has not been considered.In this study,relations between VTT and network distance to access urban parks in Tehran megacity has been modeled.Traffic maps at five times of day are used to produce TT maps of Traffic Analysis Zones(TAZs)to their 3-closest parks.Comparison of the Gini coefficients of accessibility show significant inequities of accessibility at different times of day.Relations between the distance,ATT,and TT_(max) are modeled by statistical analysis.Results show both TT and TTmax have significant positive relations with distance and traffic and reach their maximum at 6 p.m.Observation of significant relations between distance,ATT,TT_(max),and VTT provides interesting knowledge for the conversion of temporal measures of equity(TT)to a physical measure of equity(distance).A simple application of these findings for effective management of the spatiotemporal inequities is the definition of critical distances from public services.As an example,to decrease the TT_(max) of TAZs to less than 12 min,their maximum distance to the closest parks should be less than 4 km.The developed approach can be adopted for the accessibility evaluation of the other public services,particularly the health and education centers.

Distribution and equity trends for general practitioners in China from 2012 to 2015

Objective:This study aimed to identify the distribution and equity trends for general practi-tioners(GPs)in China from 2012 to 2015 and to provide evidence to guide the discipline’s develop-ment of general practice and for policy-making.Methods:On the basis of data from the National Health Statistics yearbooks,the distribution and equity trends for GPs from 2012 to 2015 were analyzed with the Lorenz curve and Gini coef-ficient as indictors of health equity.Results:From 2012 to 2015 the number of GPs increased at rates ranging from 9.3%to 32.5%,while the number of registered GPs increased at rates ranging from 32.6%to 37.2%.In 2015 the average number of GPs was 1.38 per 10,000 people(among the 31 provinces the highest rate was 3.90 per 10,000 people in Zhejiang and the lowest rate was 0.50 per 10,000 people in Xizang)and 1.98 per 100 km2(among 31 provinces the highest rate was 89.23 per 100 km2 in Shanghai and the lowest rate was 0.01 per 100 km^(2) in Xizang).From 2012 to 2015 the Gini coefficients weighted by population were 0.31,0.29,0.26,and 0.25 respectively,while the Gini coefficients weighted by geographical area were 0.74,0.72,0.72,and 0.72 respectively.Conclusion:The number of GPs increased rapidly in China;however,the proportion of regis-tered GPs was unsatisfactory,and there were inequities among the different provinces.The govern-ment should launch integrated strategies to encourage GP trainees to become registered GPs and optimize the distribution and equity of GPs.