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A prominent characteristic of. COVID-19 is the long incubation period, the lack of symptoms during that period, and significant geographic variation in prevalence and testing. This article investigates the relationship between testing and infection based on an Israeli sample of 193 municipalities and a report from 11 May 2020. Results support an exponential rise in the fraction of positive. COVID-19 outcomes with the fraction of tests. Finally, under conditions of equal socioeconomic ranking, population density and income inequality, the projected efficiency of tests rises with population density and the Gini index and drops with socioeconomic ranking. [ABSTRACT FROM AUTHOR]

A rank-size rule following Zipf's law was tested along a complete urban–rural hierarchy in Greece using 2021 census data released at different administrative levels. Testing five econometric specifications (linear, quadratic, and cubic forms, together with refined logistic and Gompertz forms) on log-transformed population numbers, deviations from the rank-size rule were assumed as an indicator of economic concentration (considering settlements, population, and activities jointly) along the density gradient in Greece. This hypothesis was verified using progressively disaggregated population numbers at (i) regional units (n = 75), (ii) 'Kallikratis' municipalities (n = 333), (iii) 'Kapodistrian' municipalities (n = 1037), and (iv) local communities (n = 6126). Econometric results were stable across geographical levels and indicate a relatively poor fit of linear specifications, the classical formulation of Zipf's law. Quadratic specifications displayed a good fit for all territorial levels outperforming cubic specifications. Gompertz specifications outperformed logistic specifications under aggregate partitions (e.g., regional units and 'Kallikratis' municipalities). Quadratic specifications outperformed both logistic and Gompertz specifications under disaggregated levels of investigation ('Kapodistrian' municipalities and local communities). Altogether, these findings indicate the persistence of non-linear rank-size relationships estimated over a cross-section of population data at progressively detailed observational units. Such evidence enriches the recent literature on Zipf's law, demonstrating the inherent complexity of rank-size rules tested on real data along the whole density gradient in a given country. [ABSTRACT FROM AUTHOR]

An attempt is made to critically study the measuring urbanisation, recent urban growth patterns, Urban Growth Sustainability (UGS) and addresses the question of how the primate city impacts urban growth. The methods of Urban-Rural Growth Differential (URGD), Composite Annual Growth Rate (CAGR) and Index of Primacy (PI) have been used to understand recent urban growth, impact of primate cities in India based on Census. The top-heavy nature of India's metropolitan structure has a negative impact on the country's balanced regional growth. The study recommends that more infrastructure capacity should be granted for the primate cities due to increases in the city's population. [ABSTRACT FROM AUTHOR]

The strategy of geographically diversifying a portfolio of commercial real estate assets is an intuitive approach for risk management. However, due to high concentrations of these assets in major metropolitan areas, investors may face additional constraints in the portfolio optimization process. The rank-size rule, a log-linear relationship between city rank and size, provides one of the greatest empirical regularities in regional science. As such, it serves as a possible theoretical guide to the weights given to properties by location in a commercial real estate portfolio. This paper sets forth some ideas relating to the concentration side of portfolio variance and the limiting effect that large concentrations may have on the ability to diversify risk. Two variants of the rank-size relationship – the Zipf distribution and the parabolic fractal distribution – are fitted to a variety of datasets to provide a sense of the degree of concentration in the commercial real estate industry. These empirical findings suggest the presence of limitations to geographical diversification that have varying degrees of severity across different property types or sectors of the commercial real estate market. [ABSTRACT FROM AUTHOR]

A rank-size rule following Zipf’s law was tested along a complete urban–rural hierarchy in Greece using 2021 census data released at different administrative levels. Testing five econometric specifications (linear, quadratic, and cubic forms, together with refined logistic and Gompertz forms) on log-transformed population numbers, deviations from the rank-size rule were assumed as an indicator of economic concentration (considering settlements, population, and activities jointly) along the density gradient in Greece. This hypothesis was verified using progressively disaggregated population numbers at (i) regional units (n = 75), (ii) ‘Kallikratis’ municipalities (n = 333), (iii) ‘Kapodistrian’ municipalities (n = 1037), and (iv) local communities (n = 6126). Econometric results were stable across geographical levels and indicate a relatively poor fit of linear specifications, the classical formulation of Zipf’s law. Quadratic specifications displayed a good fit for all territorial levels outperforming cubic specifications. Gompertz specifications outperformed logistic specifications under aggregate partitions (e.g., regional units and ‘Kallikratis’ municipalities). Quadratic specifications outperformed both logistic and Gompertz specifications under disaggregated levels of investigation (‘Kapodistrian’ municipalities and local communities). Altogether, these findings indicate the persistence of non-linear rank-size relationships estimated over a cross-section of population data at progressively detailed observational units. Such evidence enriches the recent literature on Zipf’s law, demonstrating the inherent complexity of rank-size rules tested on real data along the whole density gradient in a given country.

The article is devoted to determining the conditions for the evolution of central place systems in the early stages – in the framework of the new and classical economic geography. We come to the conclusion that the new economic geography is not operational in relation to evolutionary processes, since it proceeds from postulates that violate the central place theory and based on incorrect assumptions (for example, validity of Bunge’s problem). We postulate the need to revise three main provisions of the classical approach: 1) on the initial correspondence of systems to the rank-size rule; 2) on increasing the compliance of systems with the rank-size rule as the share of urban population increases to 50%; 3) about the striving of central place systems to the state of equilibrium and – upon reaching it, for mature systems – an insignificant in its intensity ‘fluctuation’ around it. The authors define the conditions for the evolution of central place systems as follows: 1) the systems correspond slightly to the rank-size rule in the early stages and much better to the Christaller distribution; 2) as the share of urban population increases, the very slight compliance of systems with the rank-size rule worsens more and more; an increase in the share of urban population is accompanied by an improvement in the fit to the Christaller distribution; 3) systems strive for a state of equilibrium at any stage of their evolution; ‘oscillations’ around it for young systems are characterized by a significantly larger amplitude compared to that for mature systems

In the context of geographical quantitative revolution around the mid-20th century, George K Zipf’s model emerged, which was designed to measure sizes of cities by their population in what is known as the rank-size rule. It is important to apply that scientific base to measure sizes of cities at state level as well as level of administrative regions within the state. This is the scope of this study, which sought to apply the rule to the cities of Qassim region as a geographical unit within Kingdom of Saudi Arabia. The aim of the research is to study the urban system in Qassim and discover the urban hierarchy that runs the governorates within their administrative boundaries. The main question of the study was: What is the balanced geographical rank of the cities of Qassim region? The tools of the geographical statistical method were used to display and analyze data, where most important results were: The urban system in Qassim region is dominated by the city of Buraidah, which contains most of the geographical factors that formed the urban sites and their environmental conditions. The study concluded that the urban system in Qassim enjoys a natural formative background that depends on the fertile lands around its cities, whose characteristics are similar and their main features converge. In spite of this, the consequence of applying Zipf's rank-size rule was that: cities are far from the straight equilibrium line of the vertices of their sizes.

Introduction. In modern Economics, one of the most common and simplest methods of analyzing the balance of urban settlement systems is to assess their compliance with Zipf's law or the rank–size rule. The basis of this pattern is the relationship between urban population and its place in the hierarchy of towns ranked in descending order of size. Based on the results of the study conducted, the article assesses the balance of the urban settlement system of the European North Russia, as one of its regions, by analyzing its compliance with Zipf’s law. Materials and Methods. The official data from the Federal State Statistics Service on the population of towns in the European North of Russia for 1959, 1989 and 2019 were used as materials of the study. The method of constructing a linear regression between the logarithm of the actual population and the logarithm of the rank of the town was used to verify Zipf's law for the urban network of the region in a certain period. In order to substantiate the conclusions drawn, an analysis of the dynamics of the number of towns and the share of the population living in them was carried out. The monographic method, as well as the methods of tabular and graphical data visualization, was used to interpret the results of the calculations. Results. Based on the analysis of data on the application of the rank–size rule for the towns in the European North of Russia, it has been found that Zipf’s law was not fully observed in any time period, which indicates the imbalance of the existing urban settlement system. In the period from 1959 to 2019, there was an increase in the concentration of the population in the major cities of the region. The imbalance is also caused by the growing number of small towns with a population that does not correspond to the optimal value according to Zipf's law. Discussion and Conclusion. Based on the calculations, the author has come to the conclusion that the cities of Arkhangelsk and Cherepovets have the potential for growth, as well as some others with a population of up to 100 thousand people. The practical significance of the study lies in the possibility of using the results obtained to prognosticate the population of towns in the European North of Russia when planning the location of production facilities, as well as transport and social infrastructure in the region.

Perturbation analysis of the rank-size rule is made for municipalities that are squeezed in a prefecture. Specifically, attention is focused on Japanese prefectures, for which effects of the archipelagoes, municipal consolidations, and coastal inundations due to the future sea-level rise are examined. In each prefecture, typically tens of municipalities are closely packed with a unique configuration that has been arranged according to a self-organized process. With a mind to sustainable development goals, analysis is made from three points of view. First, comparisons between the results of the mainland and those of the entire prefecture with territorial islands suggest that historical interactions over a long period become a key factor to enhance the statistical rule. Next, to cope with rapidly increasing rural depopulation, simulations are made on the basis of three consolidatory schemes. Of prefectures with extremely depopulated areas, particular emphasis is laid on Fukushima Prefecture, the east coast of which was damaged by the nuclear disaster on 11 March 2011. Lastly, analysis is made implying perturbations due to global warming. Among three parameters that characterize the rank-size relation, stabilities are confirmed for the scaling exponent.

Effectively monitoring the size of a city in real time enables the scientific planning of urban development. Models that utilize the distribution and variations in city size generally use population data as inputs, which cannot be obtained in a timely and rapid manner. However, night-time light (NTL) remote sensing may be an alternative method. A case study was carried out on the Yangtze River Delta (YRD) in China, and the rank–size rule, the law of primate cities, and the Gini coefficient were employed to monitor the variation in city size in the study area. The urban areas extracted based on NTL remote sensing were utilized instead of the traditionally used population data to evaluate the variations in city size from 2012 to 2017. Considering the empiricism and subjectivity of the thresholding method, urban areas were extracted from NTL data combined with the normalized differential vegetation index and land-surface temperature data based on the artificial neural network algorithm. Based on the results, the YRD did not fit the distribution of the primate cities from 2012 to 2017. However, this region satisfied the rank–size rule well, which indicated that the development of medium–small cities was more prominent than that of larger cities, and the dispersed force was larger than the concentrated force. Notably, the city size reached a relatively balanced level in the study area. Further, sensitivity analysis revealed that the relatively low extraction accuracy of urban areas of few small cities had little effect on the results of city size variations. Moreover, the validation of city size computed from statistical population data and its comparison with results calculated based on the statistical data of urban areas aligned with the results of this study, which indicates the rationality and applicability of monitoring the variations in city size using the urban areas extracted from NTL remote sensing instead of population data. [ABSTRACT FROM AUTHOR]

This paper offers a new numerical approach to model the effects of archaeological site placement and population density on environmental suitability using two ecological models, the Ideal Free Distribution (IFD) and Ideal Despotic Distribution (IDD), treating the Oued Loukkos in northern Morocco as an example. This method incorporates local resource depletion with increasing population density consistent with the predictions of the IFD. It also incorporates the potential for the exclusion of part of the population from certain productive areas consistent with the IDD. In this study, we propose a dynamic approach to the impact of site placement on habitat suitability and therefore broader application for understanding changes in settlement distribution with population density through time. Furthermore, resulting settlements can be parameterized by a Zipf-Mandelbrot distribution, entailing a direct relationship between the ecological, demographic, and political factors and the resulting rank-size distribution of sites. This approach allows for a broader range of applications among foraging and agricultural economies. [ABSTRACT FROM AUTHOR]

The sole well-recognized United States (US) urban hierarchy articulation essentially is outdated, even though selected recent work seeks to upgrade it. The primary goal of this paper is to update it in a definitive and comprehensive fashion. This paper describes the conceptual framework underlying such observed orderings, itemizes certain strengths and weaknesses of the existing articulation, and then posits a justifiable renovated US urban hierarchy. Next, recapped analyses expose both contiguity and urban hierarchy spatial autocorrelation components of the upper tiers of the 2020 US metropolitan area population rank size distribution. Noteworthy is that these descriptions entail positive-negative spatial autocorrelation mixtures. Inventoried output from the research efforts leading to this paper includes: a contemporary US urban hierarchy articulation that should prove serviceable for at least the next few decades; and, an apparatus providing a practical contribution for improving cultural, environmental, and social aspects of systems of cities through, for example, better cost containment and more efficient/effective delivery of urban public health services and utilization/consumption. The Earth's scientists need this category of tool to incorporate into methodology combating negative effects of globalization that materialize via spatial diffusion.

Objectives: As the acceleration of global urbanization, traffic congestion and environmental degradation have emerged in the urban area. Based on the light and statistical data, this paper studied the spatial evolution between urban people and land, and revealed the significance of its coupling and coordination characteristics for the sustainable development of cities. Methods: For primary data, a series of preprocessing are needed to eliminate the problems of supersaturation and discontinuity of inter‑annual data. Based on the lighting threshold, this paper excerpted the built‑up areas of urban agglomeration in Zhejiang Province year by year, compared them with the statistical data, and analyzed the corrected data source relatively. Firstly, based on the order‑scale distribution model of urban order and urban population in Zhejiang Province from 1992 to 2020, we made a dynamic analysis on population aggregation and distribution in its development process. Then, we constructed the population‑land urbanization allometric growth model by using population and light area, as well as judged the spatialization of man‑land relationship in urban development. Finally, according to the lag phenomenon of population growth relative to land development, we proposed an allometric growth model with lag factor, and used the lag term model to judge the characteristics of unequal growth of people and land in different cities. Results: The structural system of urban agglomeration is relatively mature in Zhejiang Province, and the distribution of cities is reasonable. However, the primacy of city is gradually improved, and the population is gradually gathering. The results of allometric growth model show that the man‑land relationship of urban agglomeration in Zhejiang Province is generally low in the eastern coastal cities and high in the western inland cities, and the planning of the four metropolitan areas is reasonable. The improvement of fitting accuracy of the proposed model with lag factor obviously shows that there is lag effect between population urbanization and land urbanization, with an average increase of 6.47% and the highest increase of 12.61%. Among the influencing factors on land urbanization, the dominant factor in Hangzhou is the existing population in urban areas, while the dominant factor in Ningbo is the new population in urban areas. Conclusions: The proposed allometric growth model with lag factor can correct the model errors and improve the fitting accuracy of urban man‑land relationship. It can also effectively evaluate the temporal and spatial evolution characteristics of man‑land relationship in regional system, explore its development and put forward countermeasures. [ABSTRACT FROM AUTHOR]

Objectives: It is important to know the pattern of Pakistan̓s regional development for the construction of China‑Pakistan Economic Corridor. Methods: We used visible infrared imager radiometer suite (VIIRS) nighttime light remote sensing image as the main data source, and implemented Savitzky ‑ Golay (SG) filtering algorithm to repair the missing values of the images. Night time light change ratio (NLCR), Mann ‑ Kendall(MK) trend test method and rank ‑ size rule were carried out to study the nighttime light change patterns of province level, city level, geographic grid level, and east‑west zone in Pakistan. Results: The analysis result of NLCR shows that from 2012 to 2019, NLCR of the entire Pakistan is 47.96% and all provincal regions has developed to a certain degree with NLCR larger than 15%. NLCR of Gwadar Port is 126.94%, which is the highest in 15 node cities on east and west lines of China‑Pakistan Economic Corridor. Additionally, the development of 15 node cities on east and west lines of China ‑ Pakistan Economic Corridor was unbalanced. The results of MK trend test show that at the geographic grid scale of 5 km, there are 1 905 grids with the total nighttime light upward trend in Punjab and 338 grids with the total nighttime light downward trend in Sindh. It is found that most grids with the total nighttime light downward trend are located in rural areas of Sindh, which is consistent to the fact that there is a serious power shortage problem in rural areas of Sindh. The analysis results of rank‑size rule show that the Pareto indexes of both eastern and western zones are gradually decreased, indicating that the distribution of urban size in Pakistan becomes more balanced. And the lack of stable power supply may be the reasons for the low brightness of nighttime light in some areas. Conclusions: The regional development patterns of Pakistan under long‑term time series and multiple spatial scales can provide a certain scientific basis for the planning of China‑Pakistan Economic Corridor. [ABSTRACT FROM AUTHOR]

At the present stage, urban economists widely use Zipf ’s law to assess the urban regional and national systems. Zipf ’s law or the rank–size rule is a pattern linking the population of a city with its place in the hierarchy of cities arranged in descending order depending on their size. Using Zipf ’s law, the study aims to analyse the uniformity of the distribution of population, employees, enterprises and organisations in Russian cities. The research is based on the data of the Federal State Statistics Service. We selected a sample of cities from each Federal District and Russia as a whole. The sample included settlements with the status cities and more than 100 thousand inhabitants in 2016. The maximum values of the Zipf coefficient were calculated for the indicators “population size” and “average annual number of employees of enterprises”. Regarding the Federal Districts, the estimated Zipf coefficients ranges from 0.5 to 0.9 in terms of the population size; from 0.4 to 0.8 in terms of the average annual number of the employees of enterprises; from 0.4 to 0.8 in terms of the number of enterprises and organisations. For reducing the identified interregional differentiation in the Federal Districts of Russia, we advise to develop small and medium cities. Further research should focus on the application of Zipf ’s law to create a method for determining the optimal size of a city in a territorial space.

For representative observational stations on the globe, rank-size analyses are made for vectors arising from sequences of the monthly distributions of temperatures and precipitations. The ranking method has been shown to be useful for revealing a statistical rule inherent in complex systems such as texts of natural languages. Climate change is detectable through the rotation angle between two 12-dimensional vectors. The rankings of the angle data for the entire station are obtained and compared between the former (from 1931 to 1980) and the latter (from 1951 to 2010) period. Independently of the period, the variation of the angles is found to show a long tail decay as a function of their ranks being aligned in descending order. Furthermore, it is shown that for the temperatures, nonlinearities in the angle-rank plane get stronger in the latter period, confirming that the so-called snow/ice-albedo feedback no doubt arises. In contrast to the temperatures, no sign of a feedback is found for the precipitations. Computed results for Japan show that the effect is consistent with the global counterpart.

As the first step for revealing potential rules inherent in cities that are closely squeezed in a sectioned domain, municipalities in the entire prefecture in Japan are considered and their distributions of the areas are analyzed in details according to a rank-size procedure. Computed results suggest that among the population, area, and population density, the last becomes the most important factor in finding the rank-size rule. Indeed, of the 47 Japanese prefectures the Metropolis of Tokyo and Fukuoka Prefecture exhibit the most typical rank-size rules, where the former possesses the exceptionally high population density as well as urbanized rate. The underlying mechanism of the rule can be supported by a toy model with a tournament game using a sequence of random numbers, where teams (municipalities) are highly competitive in gaining the final wins (broadest territory). A stability analysis implying perturbations due to global warming allows one to confirm unexpected robustness of the rank-size relation. Finally, the authenticity of the log-log relation in the rank-area data of Tokyo Metropolis is tested statistically.

The aim of this paper is the study of the functional and demographic hierarchy in the metropolitan area of Malaga (Spain). For this purpose, we will use analysis techniques commonly used in urban geography, such as the Davies index and the rank-size rule. The metropolitan area of Malaga consists of a polycentric area with two sub-centres of major functional and demographic importance: the cities of Malaga and Marbella, as well as some urban sub-centres located on the urban coastal axis. All of them share a functional specialisation based on tourist activity that generates important synergies in other sectors within the area. Among the results obtained, we highlight the functional primacy of the city of Malaga followed, at some distance, by the city of Marbella, but with an absence of demographic hierarchy, which is the result of an unequal balance between flows of inputs and outputs between the urban coast and its rural inland hinterland, due to the orographic difficulties that hinder exchanges between the two areas, conditioned by the difficulty in land communications between the rural inland and the urban coast, with the exception of the sub-centres of the Guadalhorce valley, which is considered the natural expansion area of the Malaga metropolis. [ABSTRACT FROM AUTHOR]

Effectively monitoring the size of a city in real time enables the scientific planning of urban development. Models that utilize the distribution and variations in city size generally use population data as inputs, which cannot be obtained in a timely and rapid manner. However, night-time light (NTL) remote sensing may be an alternative method. A case study was carried out on the Yangtze River Delta (YRD) in China, and the rank–size rule, the law of primate cities, and the Gini coefficient were employed to monitor the variation in city size in the study area. The urban areas extracted based on NTL remote sensing were utilized instead of the traditionally used population data to evaluate the variations in city size from 2012 to 2017. Considering the empiricism and subjectivity of the thresholding method, urban areas were extracted from NTL data combined with the normalized differential vegetation index and land-surface temperature data based on the artificial neural network algorithm. Based on the results, the YRD did not fit the distribution of the primate cities from 2012 to 2017. However, this region satisfied the rank–size rule well, which indicated that the development of medium–small cities was more prominent than that of larger cities, and the dispersed force was larger than the concentrated force. Notably, the city size reached a relatively balanced level in the study area. Further, sensitivity analysis revealed that the relatively low extraction accuracy of urban areas of few small cities had little effect on the results of city size variations. Moreover, the validation of city size computed from statistical population data and its comparison with results calculated based on the statistical data of urban areas aligned with the results of this study, which indicates the rationality and applicability of monitoring the variations in city size using the urban areas extracted from NTL remote sensing instead of population data.

Based on the assumption that the economic integration process contributes, via market reforms, to the dynamics of the space distribution in candidate countries, this study examines (i) whether agglomeration forces or dispersion forces are dominant; (ii) whether EU-integration causes a structural break to the space distribution over time; (iii) whether EU-integration makes the city-size distribution more even or uneven in eight eastern European Union members (EU–8). To carry out the analysis, the Ziwot-Andrew and Cusum Square tests are used to detect structural breaks; the ARDL Bound test is used to reveal the interaction between long-run and short-run equilibrium; and the Granger test is used to determine the direction of the causality among the variables. The main results are: the integration with the EU (i) caused a structural break to the city-size distribution, (ii) made the city-size distribution more uneven and (iii) stimulated the agglomerating forces over the spreading forces in the EU–8.

We present a comprehensive agent-based model of a closed system of cities. The model includes two types of agents—employees and firms. Firms compete for workers and make decisions concerning what to produce and whether to adopt innovations. Individual employees make migration decisions. Some migrants become intrapreneurs when their employers adopt production process innovations that they propose. Some migrants become entrepreneurs when the product innovations that they propose are implemented by their employers in new subsidiary firms. These firms tend to be technological leaders. The decisions of individuals and of firms generate innovation–migration dynamics that generate a variety of city sizes. A city that is home to firms that are currently relatively attractive to migrating innovators experience moderate or fast growth. Because of particular decision patterns by individuals and firms, this growth may decline and stop, and the city may stagnate and loose workers as its relative attractiveness decreases. Cities that remain unattractive for long periods can stop growing and shrink. We model explicitly the extent to which cities attract immigrants and innovators and demonstrate that the size distribution of cities is defined by the ability of its resident firms to adopt the innovations and to let the product innovators establish technologically advanced enterprises. These decisions result in high market value of the most productive firms, of the entire industrial system the city where the firm is located, and of the entire urban system. [ABSTRACT FROM AUTHOR]

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The popularity of polycentricity has been increasing in recent years. European spatial planning literature and policy documents that emphasize the positive effects of polycentricity can be one of the reason increase in the popularity of the concept. Although not as clear and planned as in European countries, it is argued that, Turkey's metropolitan cities are also evolving from monocentric spatial structure to polycentric ones. However, there is no empirical study on the measurement of this spatial evolution at national and micro-regional scale in Turkey. From this point of view, this study aims to clarify changes in the morphological structure of Turkey from 2000 to 2016 at national and micro-regional scales and to examine the proposition of 'the spatial configurations of the settlements, especially metropolitans, have been evolving from monocentric to polycentric as results of the dynamics of the 21st century' in Turkey case. The results of empirical analyses show that there is a possibility for Turkey to be a more monocentric in following years if the historical trends continuous.

In this paper we study Zipf’s law, which postulates that the product of a city’s population and its rank (the number of cities with a larger or equal population) is constant for every city in a given region. We show that the empirical literature indicates that the law may not always hold, although its general form, the rank-size rule, could be a good first approximation of city size distribution. We perform our own empirical analysis of the distribution of the population of Polish cities on the largest possible sample to find that Zipf’s law is rejected for Poland as the city sizes are less evenly distributed than it predicts.

Urban system is the special manifestation of political economy and the land management method of a country. The manner of distribution and the level of balance of the cities’ population get clearer by examining the urban system. The urban system of Iran tended to change from the traditional pattern before 1921 because of the centralization of facilities and services in big cities. This pattern distracted the logical relationships among small, medium and big cities and led to disorder in the urban system. The research purpose is to assess the Iranian urban hierarchy based on population during the period of 1956-2012. To measure the urban hierarchy, the Entropy coefficient, the rank-size rule, the primate city- Lorenz curve and Gini coefficient were employed. The statistical data cover all cities of Iran in six census periods. The findings of the current study show that the urban system is becoming more balanced with regard to the indices of concentration coefficient, rank-size, primate city, and entropy index; but with regard to Gini Coefficient and population distribution in urban classes, there has been an imbalance compared to the situation in 1956. In fact, according to the Lorenz curve, the Iranian cities have been near the normal line in 1956 but got away from this line in 2012. This is because of the increase in number of small cities with little population and the increase in population of big cities. To reach a balance in urban system of Iran, strategies to decentralize metropolises and boost small and medium-sized cities are suggested.

Urban sprawl is the most prominent characteristic of urbanization, and increasingly affects local and regional sustainable development. The observation and analysis of urban sprawl dynamics and their relationship with urbanization quality are essential for framing integrative urban planning. In this study, the urban areas of the West Taiwan Strait Urban Agglomeration (WTSUA) were extracted using nighttime light imagery from 1992 to 2013. The spatio-temporal characteristics and pattern of urban sprawl were quantitatively analyzed by combining an urban expansion rate index and a standard deviation ellipse model. The urbanization quality was assessed using an entropy weight model, and its relationship with urban sprawl was calculated by a coupling coordination degree model. The results showed that the urban area in the WTSUA experienced a significant increase, i.e., 18,806.73 km2, during the period 1992–2013. The central cities grew by 11.08% and noncentral cities by 27.43%, with a general uneven city rank-size distribution. The urban sprawl showed a circular expansion pattern, accompanied by a gradual centroid migration of urban areas from the southeast coast to the central-western regions. The coupling coordination level between urban expansion and urbanization quality increased from serious incoordination in 1992 to basic coordination in 2013. Dual driving forces involving state-led policies and market-oriented land reform had a positive influence on the harmonious development of urban sprawl and urbanization quality of the WTSUA. This research offers an effective approach to monitor changes in urban sprawl and explore the coupling coordination relationship between urban sprawl and urbanization quality. The study provides important scientific references for the formulation of future policies and planning for sustainable development in urban agglomerations.

Copyright of Comparative Economic Research is the property of Wydawnictwo Uniwersytetu Lodzkiego and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

This study examines the nexus between high-speed rail (HSR) stations and city evolution from an urban science perspective. We analyzed 1627 HSR stations built from 1976 to 2021 in 533 Chinese and European cities. Node or activity clusters in cities are identified through the street network. Then, the urban forms of Chinese and European cities are compared and the Zipf's law is tested. We found that activity clusters in Europe tend to be more contiguous and clustered, suggesting a clear downtown. In Chinese cities, these clusters are more scattered, suggesting polycentric urban development. When the Zipf's law is applied to the size distribution of activity clusters, the rank-size rule is supported both at the aggregate and country levels. Generally, it takes roughly two decades for an HSR station to be able to mature in attracting related development, such as residence and businesses, to complete the exploration process of city evolution. Finally, contributory factors for the integration of HSR stations with the urban fabrics are examined. Apart from the size of the city, economic power, station features and the spatial pattern of activity clusters, the relative location of the HSR station in relation to the urban form matters. Our study contributes both to the HSR and urban science literature, and has practical implications for locational decisions about HSR stations. • Analyzed 1627 HSR stations built from 1976 to 2021 in 533 cities • Measured activity clusters from an urban science perspective • Urban forms of Chinese and European cities are compared and Zipf's law is tested. • Contributory factors for integration HSR stations with urban fabrics are identified. • City size, GDP, station features, and size of nearest node clusters matter [ABSTRACT FROM AUTHOR]

This paper analyses the relation between socio-economic and institutional factors and the dynamics of city populations, the hierarchy of city systems and the urbanization. Particular attention is devoted on the integration process that several European Countries, often structurally so different, have experimented from the beginning of ’90s. Results show that the hierarchical structures of Member States is more even than expected. Moreover, the analysis have provided evidence that the integration process of the European Union had a mixed impact on the way in which people gathered across the territory of the EU. In details, the entry into force of the Schengen treaty has promoted a process of agglomeration of the population in the larger cities. On the contrary, the introduction of euro has led people to spread over the territory. [ABSTRACT FROM AUTHOR]

Megaregions have become the principal geographic units for countries to participate in the global economy, which is often a composite of numerous urban clusters which are distributed in different cities. In China, a megaregion is regarded as a key urbanization platform, according to the National Plan on New Urbanization published in 2014. In this context, it is imperative to understand the spatial patterns of and the changes occurring in megaregions. For instance, what are the universal rules or differences related to urban cluster growth between different megaregions in the process of rapid urbanization, and are there differences in the growth of urban clusters with different sizes? Focusing on these issues, this study discusses the uneven growth of clusters in five of the largest megaregions in China using the rank-size rule, based on land-cover data interpreted from time-series satellite imagery during the period 1990–2010. The results show that the cluster size distribution of each of these megaregions obeyed the rank-size rule, and the size distribution of the clusters became more uneven and was tilted toward larger clusters between 1990 and 2010. These factors should be considered in the implementation of the National Plan on New Urbanization in China and the designation of urban macro planning and urban layout optimization in other countries those are experiencing rapid urbanization. [ABSTRACT FROM AUTHOR]

This study provides new comparative evidence on city size distribution in OECD (the Organisation for Economic Co-operation and Development) countries, by using consistently defined functional urban areas (FUAs). FUAs are identified by an algorithm based on population density at grid level and commuting patterns and are thought to better approximate economic agglomerations and their internal spatial organisation. Results show that Zipf's law provides a better description of city size distribution when cities are measured in terms of FUAs rather than using traditional administrative definitions. In addition, Zipf's law describes well city size distribution both at country level and wider spatial scales, that is, by continent and for the whole OECD. Finally, the power law hypothesis – of which Zipf's law is a particular case – was not rejected in most of the countries. [ABSTRACT FROM AUTHOR]

In 1981 the author published the article The heading of the national urban systems: a revision, analyzing the degree of prominence of the largest city (or urban agglomeration) in all countries whose data made it possible. The analysis was also conducted in time scale, when allowed by the available information, arriving in that study till 1970. In the present article the question is taken again, focusing the period from that year until 2010, in order to appreciate the continuity or not of the evolutive tendencies then perceived. Already in the previous paper it was found out that the number of countries with an outstanding dimensional position of the largest city (or urban agglomeration) grew during the time, a propensity that, according to the present research, was maintained in the recent decades. By an index and classification criterion created by the author, the number of cases with the mentioned primacy arose from about one half of the urban systems, in 1970, to about two thirds in recent years. [ABSTRACT FROM AUTHOR]

This paper introduces a statistical and other analysis of peer reviewers in order to approach their 'quality' through some quantification measure, thereby leading to some quality metrics. Peer reviewer reports for the Journal of the Serbian Chemical Society are examined. The text of each report has first to be adapted to word counting software in order to avoid jargon inducing confusion when searching for the word frequency: e.g. C must be distinguished, depending if it means Carbon or Celsius, etc. Thus, every report has to be carefully 'rewritten'. Thereafter, the quantity, variety and distribution of words are examined in each report and compared to the whole set. Two separate months, according when reports came in, are distinguished to observe any possible hidden spurious effects. Coherence is found. An empirical distribution is searched for through a Zipf-Pareto rank-size law. It is observed that peer review reports are very far from usual texts in this respect. Deviations from the usual (first) Zipf's law are discussed. A theoretical suggestion for the 'best (or worst) report' and by extension 'good (or bad) reviewer', within this context, is provided from an entropy argument, through the concept of 'distance to average' behavior. Another entropy-based measure also allows to measure the journal reviews (whence reviewers) for further comparison with other journals through their own reviewer reports. [ABSTRACT FROM AUTHOR]

An avalanche of empirical studies has addressed the validity of the rank-size rule (or Zipf's law) in a multicity context in many countries. Under which conditions (eg, sample size, spatial scale) this 'law' holds remains as yet largely underinvestigated, while spatial network constellations also deserve more attention. Against this background, we investigate the relationship between network connectivity and the rank-size rule (or Z ip f's law) in an urban economic network constellation. In particular, we address the following methodological issues: (i) the (aggregate) behavioural foundation underlying the rank-size rule (Zipf's law) in the light of spatial-economic network theories (eg, entropy maximization, spatial interaction theory); (ii) the nature of the analytical relationship between social-spatial network analysis and the rank-size rule (Zipf's law). We argue that the ranksize rule is compatible w ith conventional economic foundations of spatial network models. We test the sensitivity of rank-size rules for changes in scale, functional forms, time periods, and connectivity structures. Our application uses an extensive spatiotemporal panel database on the evolution of the urban population in Germany. We test the relevance of the rank-size rule (Zipf's law), and--in parallel--the related 'socioeconomic' connectivity in these urban networks. In particular, we will show th at Zipf's law (ie, with the rank-size coefficient equal to 1) is only valid under particular conditions of the sample size. [ABSTRACT FROM AUTHOR]

The article discusses a three-step model-selection framework for size distributions in empirical data. It describes a method and shows its usefulness with a sample of commercial cattle farms in Namibia. It suggests that the proposed three-step model-selection framework has the potential to settle the ongoing debate about size distribution models in empirical data.

This paper discusses the size distribution–in economic terms–of the Italian municipalities over the period 2007–2011. Yearly data are rather well fitted by a modified Lavalette law, while Zipf–Mandelbrot–Pareto law seems to fail in this doing. The analysis is performed either at a national as well as at a local (regional and provincial) level. Deviations are discussed as originating in so called king and vice-roy effects. Results confirm that Italy is shared among very different regional realities. The case of Lazio is puzzling. [ABSTRACT FROM AUTHOR]