Rank-size Distribution Research Articles

Dinámica reciente del sistema urbano chileno 1970-2002: integración a escala nacional

The analysis of ranksize distributions and internal movement of the system shows that the Chilean urban system is evolving towards integration at national level, as a result of a notable mobility of intermediate cities and the consolidation of larger ones. The driving forces behind this process can be found in the urban reinforcement of the economic base of cities, which adds new functions, and in the effects that decentralization in large urban centres brought about in neighbouring cities.

Pareto’s law and sample size: a case study of China’s urban system 1984–2008

While Pareto’s law has been widely supported by empirical evidence in urban studies, past studies have focused on finding best fits for city rank-size distribution. A main concern with Pareto’s law is the truncation of sample selection, for which few studies have examined it directly. This study tests three existing threshold methods (number threshold, size threshold, and urban population percentage threshold) using China’s city system as a case study. In addition, this study proposes a new method based upon the percentage threshold of the total number of cities. A systematic analysis is applied to examine the relationship between Pareto exponent and sample size using different threshold methods. The results show that Pareto exponent is sensitive to sample size and the truncation point. Including only large cities is problematic because a slight change in the truncation point will yield quite different results of Pareto exponent. In addition, the new method, the percentage threshold of the total number of cities method, presents an advantage over previous methods, in that this method yields a consistent set of results over a wide range of thresholds. Finally, when using this new method with China’s city system, the Pareto exponent presents a turning point in 1996, representing China’s transition from a planned economy to a more market oriented economy during that period.

Study on Rank—Frequency Distribution of Scientific Research Papers by famous teacher teaching in biomedicine domain

Study on Rank Frequency Distribution of Scientific Research Papers by Chinese University famous teacher teaching in biomedicine domain from 2003 to 2009. Whose quantitative indicators of scientific papers were negative logarithmic distribution, exeept provincial-level teaching famous teachers＇ SCI papers were negative exponential distribution. The qualitative index were negative logarithmic, except state-level teaching famous teachers＇ SCI paper yearly average paper cited were linear distribution and provincial-level were negative exponent distribution. The magnitude of concentrations was between 0. 257 and 0. 728, which deviates from the Priee＇s law （0.50）. It indicates that the Rank-frequency distribution model can be applied to the teaching famous teacher. The internal gradation instrument in the top scientists is different from in science community. Scientist＇s gradation in the science community depends on whether the objective of scientific paper evaluation comes true. The state-level teaching famous teacher scientific paper difference is greater than the provincial-level; SCI paper difference is bigger than the CSCD paper. Key words: biomedical; famous teacher in teaching; scientific papers; analyzes

Zipf's Law in Short-Time Timbral Codings of Speech, Music, and Environmental Sound Signals

Timbre is a key perceptual feature that allows discrimination between different sounds. Timbral sensations are highly dependent on the temporal evolution of the power spectrum of an audio signal. In order to quantitatively characterize such sensations, the shape of the power spectrum has to be encoded in a way that preserves certain physical and perceptual properties. Therefore, it is common practice to encode short-time power spectra using psychoacoustical frequency scales. In this paper, we study and characterize the statistical properties of such encodings, here called timbral code-words. In particular, we report on rank-frequency distributions of timbral code-words extracted from 740 hours of audio coming from disparate sources such as speech, music, and environmental sounds. Analogously to text corpora, we find a heavy-tailed Zipfian distribution with exponent close to one. Importantly, this distribution is found independently of different encoding decisions and regardless of the audio source. Further analysis on the intrinsic characteristics of most and least frequent code-words reveals that the most frequent code-words tend to have a more homogeneous structure. We also find that speech and music databases have specific, distinctive code-words while, in the case of the environmental sounds, this database-specific code-words are not present. Finally, we find that a Yule-Simon process with memory provides a reasonable quantitative approximation for our data, suggesting the existence of a common simple generative mechanism for all considered sound sources.

Did Zipf Anticipate Socio-Economic Spatial Networks?

An avalanche of empirical studies has addressed the validity of the rank-size rule (or Zipf’s law) in a multi-city context in many countries. City size in most countries seems to obey Zipf’s law, but the question under which conditions (e.g. sample size, spatial scale) this ‘law’ holds remained largely underinvestigated. Another complementary question is whether socio-economic networks in space also show a similar hierarchical pattern.Against this background, the present paper investigates – from a methodological viewpoint – the relationship between network connectivity and the rank-size rule (or Zipf’s law) in an urban-economic network constellation. After a review of the literature, we address in particular the following methodological issues: (i) the (aggregate) behavioral foundation underlying the rank-size rule/Zipf’s law in the light of spatial-economic network theories (e.g. entropy maximization, spatial interaction theory, etc.); (ii) the nature of the analytical relationship between social-spatial network analysis and the rank-size rule/Zipf’s law. We argue that the rank size rule is compatible with conventional economic foundations of spatial network models. Consequently, a spatial-economic interpretation – as well as a network connectivity interpretation – of the rank-size rule coefficient is provided.Our methodological contribution forms the foundation for the subsequent empirical analysis applied to spatial networks in a socio-economic context. The aim here is to test the sensitivity of empirical findings for changes in scale, functional forms, time periods, and network structures. Our application is concerned with an extensive spatio-temporal panel database related to the evolution of urban population in Germany. We test the relevance of the rank-size rule/Zipf’s law, and its evolution over the years, and – in parallel – the related ‘socio-economic’ connectivity in these urban networks. In particular, we will show that Zipf’s law (i.e., with the rank-size coefficient equal to 1) is only valid under particular conditions of the sample size. The paper concludes with some retrospective and prospective remarks.

Supporting trust: credit assessment and debt recovery through Trade Protection Societies in Britain and Ireland, 1776–1992

From an initial foundation in London in 1776, Trade Protection Societies grew in numbers to reach a peak of about 120 in 1910. They provided inter-business and some consumer credit assessment, debt management and recovery. From the 1850s they coordinated activities through a national association that covered Britain and Ireland. The societies were processing millions of credit assessments for thousands of members in the 1960s, reaching over 100,000 assessments per day in the 1980s. They provided a voluntary institutional base drawing on networks of mutuality, supplying information between members and societies that was judged privileged by the Courts. This offered transaction costs advantages for the high frequency, short duration activity provided, and hedged against the risks of complex Court actions. They became a large-scale mechanism to encourage honouring of commitments, thus underpinning the trust necessary across an increasingly geographically integrated economy. Their evolution demonstrates the importance of city size and regional centres, with diffusion down the city rank-size distribution. However, some smaller centres, mainly in resorts, also developed TPSs. The spatial process linked individual traders and the smallest places into a national system of credit management. By the 1920s smaller TPSs became difficult to sustain and were taken over or became branches of the larger societies; but overall membership continued to increase. True consolidation occurred after 1971 when demand exploded after the removal of credit controls, with unit costs pressed down, leading to de-mutualisation.

The Entropy of LEGO®

Can the information content of a building be given meaning? Provided it can be modeled as a set of repeating parts the entropy of those parts can be measured. One way to do this is to make a LEGO® model then base the calculation on how many pieces of each type have been used. It is claimed that Lego is a language-like method of representing the built environment and that Lego pieces are analogous to words because their rank–frequency distribution follows a Zipf–Mandelbrot distribution similar to words in English. The zero-order entropy of Lego was measured to be about 8.5 bits, compared with 9.4 bits per word of English. Lego models of famous buildings were found to have entropy of between 6 and 10 bits per piece, giving a quantitative measure of how unusual their pieces were.

The Lambda-structure of Texts. Ioan-Iovitz Popescu, Radek Cech, and Gabriel Altmann.

The book under review, jointly written by three authors with a pronounced expertise in the field of quantitative linguistics and text analysis, is primarily devoted to the analysis of lexical frequency structures in texts. In a way, the book may be said to represent part of an ongoing research project, integrating earlier findings (Popescu et al., 2009), and being elaborated in ongoing research (Popescu et al., 2010). The authors consider it to be a major task of the book to develop, present, and introduce new methodological instruments to quantitative analyses of texts. First and foremost, they concentrate on the frequency occurrence of words, i.e. word forms and/or lexemes, or lemmata. On the one hand, this concerns aspects of lexical rank frequency distributions, on the other hand, issues of lexical richness, derived from such data for purposes of individual stylistics, authorship attribution, quantitative text typology, etc. As is referred to in detail in the introductory part (p. 1ff), a whole variety of indices and indicators have been developed in the past, to calculate lexical richness on the basis of type-token ratios, percentage of hapax legomena, or various specific ratios based on lexical inventory used in a given text. However, all of these indicators suffer from a major theoretical flaw, namely their dependence on sample size, i.e. on the length of the text(s) under study, which renders them rather useless, or eventually even misleading, for any kind of comparative approach.

Further Analysis of the Zipf's Law: Does the Rank-Size Rule Really Exist?

ABSTRACT Zipf's law has two striking regularities: excellent fit and an exponent close to 1.0. When the exponent equals 1.0, Zipf's law collapses into the rank-size rule. This paper alters the sample size, the truncation point, and the mix of cities in the sample to analyze the Zipf exponent. Our results demonstrate that the exponent is close to 1.0 only for a number of selected sub-samples. Small samples of large cities provide higher values, while samples of small cities produce lower values. Using the estimated values of the exponent derived from the rolling sample method revealed elasticity in the exponent with regard to sample size. Our results also suggest that the rank-size rule should be interpreted with caution. Although it is well-known and commonly used, the rank-size rule may be more of a statistical phenomenon than an economic regularity.

Historical Linguistics and Evolutionary Genetics. Based on Symbol Frequencies in Tamil Texts and DNA Sequences

We have studied the rank frequency distribution (RFD) of letters of the alphabet in Tamil language texts. In a novel application of rank frequencies, we have defined a simple intuitive distance parameter between a pair of strings (text or DNA sequence of codons). This distance correlates well with age difference in historical linguistics and evolutionary genetics. Using a distance matrix of a set of strings, we derive evolutionary trees that are broadly in agreement with historical evidence. The method has potential for refinement and application in evolutionary studies to complement other approaches to evolution. The RFD in a single string conforms to a law called the CMPL (Cumulative Modified Power Law), which we had formulated and applied to RFD's of diverse symbol sets.

Zipf’s law, 1/ f noise, and fractal hierarchy

Fractals, 1/ f noise, and Zipf’s laws are frequently observed within the natural living world as well as in social institutions, representing three signatures of complex systems. All these observations are associated with scaling laws and therefore have created much research interest in many diverse scientific circles. However, the inherent relationships between these scaling phenomena are not yet clear. In this paper, theoretical demonstration and mathematical experiments based on urban studies are employed to reveal the analogy between fractal patterns, 1/ f spectra, and the Zipf distribution. First, the multifractal process empirically suggests the Zipf distribution. Second, a 1/ f spectrum is mathematically identical to Zipf’s law. Third, both 1/ f spectra and Zipf’s law can be converted into a self-similar hierarchy. Fourth, fractals, 1/ f spectra, Zipf’s law can be rescaled with similar exponential laws and power laws. The self-similar hierarchy is a more general scaling method which can be used to unify different scaling phenomena and rules in both physical and social systems such as cities, rivers, earthquakes, fractals, 1/ f noise, and rank-size distributions. The mathematical laws of this hierarchical structure can provide us with a holistic perspective of looking at complexity and complex systems.

입지계층분석을 활용한 산업단지 유치 업종 결정에 관한 연구

ABSTRACT This study aims at listing up those manufacturing activities sensitive to regional characteristics by analyzing locational hierarchy designed on the urban rank-size rule. This locational hierarchy by manufacturing activities is expected to provide a ground for the proper supply of an industrial complex. The analysis of the locational hierarchy by manufacturing activities can work as a method of observing the characteristics of the distribution of location for each economic activity by analyzing the trend in the change of manufacturing location. Consequently, it can be used to determine the appropriate manufacturing activities for the industrial complex of a particular region. Here, the locational hierarchy is analyzed depending on the base of the basic local government such as Gun(district level) and Si(city level), and manufacturing activities are categorized by Korea Standard Industry Code. Those activities demonstrating growth pattern are Manufacture of Electronic Equipment(KSIC 26), Manufacture of Medical․Precision․Optical Instruments․Watch(KSIC 27), Manufacture of Motor Vehicles․(KSIC 30, 31), etc. With proper infrastructures, these activities can be located everywhere. Those sectors on the decline pattern in the locational hierarchy can be summarized as Manufacture of Tobacco Products(KSIC 12), Manufacture of wearing apparel․Fur Articles(KSIC 14), etc. Those sectors scattered widely in the locational hierarchy are Manufacture of Food Products(KSIC 10), Manufacture of Coke․Petroleum Products(KSIC 19), Manufacture of Chemical Products(KSIC 20), Manufacture of Electronic Equipment(KSIC 26). These particular manufacturing activities can be operated in those regions in a sufficient supply of unskilled workers regardless of proper infrastructures. Those activities that have a tendency to reconcentrate on larger cities are Manufacture of Textiles(KSIC 13), Manufacture of Wearing Apparel․Clothing․Fur Articles(KSIC 14), Manufacture of Other Transport Equiptmen(KSIC 31). In most cases, these sectors tend to favor their existing agglomerated areas and concentrate around large cities. Therefore, it is inefficient to promote these sectors in small or medium-sized cities or underdeveloped regions. The establishment of developmental strategies of an industrial complex can gain greater competitiveness by observing such characteristics of the locational hierarchy.Keywords: Supply of industrial site, Industrial complex, Manufacturing activities, Locational hierarchy

Empirical data on the configural architecture of human scene perception and linguistic labels using natural images and ambiguous figures

Purpose: Both local and configural processes play a role in the figure-ground organization of scenes. Local factors include bottom-up edge segmentation enabling small regions to be fused into figural regions. The Berkeley Segmentation Dataset (Martin, Fowlkes, Tal, and Malik (2001)) provides a corpus of images whose contours were hand segmented by humans, making it ideal for studying local processes. Configural factors include top-down processes such as grouping and meaningfulness. Barghout (2009) created a complementary dataset designed to capture the configural information required for studying top-down processes. In this study we collected more data for the images in this corpus to enable rigorous statistical analysis. The data-collection paradigm assumes that asking someone to mark the “center of the subject of the photograph” serves as a proxy of the figural status of the region centered at the point marked. Since the method does not distinguish between a foreground, a single object or an object within an object, we coined the term “spatial taxon” to refer to the object or object group centered at the position indicated. This operational definition is analogous to - but also much broader than - the term “figure” as defined in the literature. Methods: Participants were asked to “mark the center of the subject of the photograph” and label it. K-means clustering was used to determine spatial taxons, as operationally defined above. Rank-frequency distributions for spatial taxons and corresponding word labels were fit via linear regression. Results: Results suggest natural-scene-perception architecture comprised of nested hierarchies whose rank-frequency, and corresponding word rank-frequency are described by inverse power laws. Unlike the results for natural scenes, spatial taxon rank-frequency distribution for two of the three ambiguous figures were uniform and word labels corresponded to their percepts; supporting the assumptions underlying the methodology.

Characteristic Features of Rank-Probability Word Distribution in Scientific and Belletristic Literature

In the present work, an optimal function for the approximation of word probability distribution in natural language is tentatively sought. An analysis of Zipf's rank-frequency distribution and its modifications is performed. The original Lavalette's law is modified to get the most accurate approximation of rank-frequency word distribution in natural language. The suggested modification of Lavalette's function has been tested on a broad variety of belletristic and scientific texts. Implication of text features in fitting parameters of the modified Lavalette's distribution function is suggested. The conclusions are made for the general tendencies and the reasons for possible deviations are discussed.

MODELING SETTLEMENT PATTERNS IN REAL TERRITORIES

This paper, describes an agent based model of the spreading of a population over a territory. The models aims at reproducing a distribution of settlements with statistical and spatial characteristics similar to a historically produced pattern. The model operates on a representation of a real territory, taking into account hydrography and relief. The two main goals are to obtain a rank size distribution of the size of settlements which corresponds to a power law (also known as the Zipf Law of settlements) and to place the settlements in the territory in patterns that are close to the real ones, in zones where settlements were the result of a long historical process. The goal of the project was to demonstrate that a set of relatively simple rules could produce a complex pattern, similar to the result of a long and complex historical process. Therefore, it is an assumed reductionist approach. Our conclusions show that a simple territorial logic, taking into account the quality of land, accessibility, population growth and migration preferences could reproduce Zipf distributions and interesting patterns of agent flow among the settlements created. However, achieving spatial patterns closer to the historical record needs an extra dimension involving field of sight. The best results were achieved by creating an artifical population which chooses to create settlements in places where a wide field of view exists of quality territory.

An archaeological signature of multi-level social systems: The case of the Irish Bronze Age

Recent research suggests that contemporary human social groups are structured according to principles of fission and fusion that are also observed in some of our primate relatives, raising the possibility that such social systems have been a feature of hominin society throughout prehistory. The current paper examines the possibility of identifying archaeological signatures of multi-level social structures through the examination of site size distributions. Data on the sizes of Irish Bronze Age stone circles and predictions for the size of aggregations they could accommodate are compared with simulations parameterized using data on modern human groups. The results suggest that the presence of hierarchically inclusive, multi-level social structures provides a better explanation for the data than more traditional archaeological accounts based on the rank-size rule and related inferences concerning the emergence of political elites.

Using Power-Law Science to Enhance Knowledge for Practical Relevance

The debates about knowledge relevance have been around for years and several calls have been issued to change the methods used by researchers to improve the translation of academic research to management. We think a change in perspective about what phenomenon we study and how we study them is key to enhance knowledge for practical relevance. Specifically, most research produced by academics focuses on Gaussian science - the science of normal distributions, stable means, finite variance, and statistical significance. These help produce knowledge about normal phenomena but fails to provide solutions for organizations as truly dynamic systems. In contrast, we argue that research ontology and epistemology need to shift in some significant measure to the study of Paretian rank frequencies; what we call power-law science. This paper introduces Pareto rank frequency distributions and how they differ from normal methods of conducting research and suggests methods to use at various points on Pareto distributions to offer practical knowledge about phenomena faced by managers.

The application of characteristic scores and scales to the evaluation and ranking of scientific journals

Characteristic scores and scales (CSS) were introduced by Glänzel and Schubert in 1988. CSS can be applied to analyse the citation impact of any subset of a system in comparison with citation patterns of the complete system. In this present study, CSS will be applied to individual subfields as systems and journals and papers as corresponding subunits. CSS are used as parameter-free tools to identify top journals within science fields, to identify highly cited papers within fields and journals and to compare the rank frequency distribution of highly cited papers over journals with the journal ranking according to traditional impact measures. The second part of the study is devoted to the possible normalisation of journal impact. In this study, threshold values of CSS are used to re-scale the journal-impact distributions. The underlying methodology and the outcomes for different subfields representing the life sciences, engineering and mathematics are discussed.

Study on the rank-size distribution and variation of crude oil flow in China

This study takes crude oil flow in China as the research subjects,and takes provincial-level administrative units as the nodes of crude oil flow.Meanwhile,selecting five typical years in 1985-2007 as the time points for research and with Zipf law,this paper discusses the rank-size distribution variation of input and output flow of crude oil in China.Some results are obtained as follows.(1) The rank-size distributions of input and output flow is consistent with Zipf law in the five typical years.(2) The non-scaling range of the output flow varies very little,while the one of input flow is narrowed at first and then enlarged gradually.(3) As to the spatial fractal structure,the output flow has no segmentation in its non-scaling range,and appears as a single fractal all along.However,the input flow experiences a process from double fractals to single fractal.(4) There are differences between the spatial distribution pattern of input flow and output flow.The one of input flow changed from lognormal distribution in 1985 to Pareto distribution in 1995,then lognormal distribution again in 1999,and it finally became Pareto distribution in 2003 and 2007.Meanwhile,the spatial distribution pattern of output flow maintains Pareto distribution.(5) Generally,the variations of output flow and input flow are not synchronous,which is closely related to the spatial distribution of huge oil fields,the distribution of petrochemical industries,the oil distribution system and so on in China.

Research on China’s Urban Development Strategy Based on Arable Land Preservation

This paper studies the trend of urbanization in China, examines the evolution of the urban scale structure in China through the development of a quadratic regression model for the urban rank-size rule and significantly improves the fitness of large-sized cities to the model, formulates a power function to simulate the relationship between urban size and urban population density, and studies the evolution trend of the function in China. This paper also includes the design of a scenario of compact urban growth according to the evolution trend of urban scale structure and urban size–population density function based on farmland preservation. In contrast to express-highway-based urban sprawl, the author advocates a railway-based compact urban growth mode in China and provides related measures to implement it, such as large city in-advance development, concentrated urban growth, urban subway system construction, high-population-density community building, filling in urban growth, and intercity high-speed railway system construction. It provides a way of urbanization with higher land-use efficiency and lower energy consumption for developing countries in the new era.