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In linguistics and natural language processing, measuring text features is crucial for representing and revealing the properties of texts in terms of topics, genres, sentiment and more. Current methods predominantly rely on the frequency of linguistic units and rarely consider the syntagmatic properties of these units, which can reflect deeper linguistic characteristics (e.g. syntax and pragmatics). This paper proposes a general method for calculating the sequence complexity of text. By combining the features of word length and word frequency, two specific implementations of this method are provided. Using these two formulas, word sequence complexity of text based on the Brown Corpus and the Gutenberg Corpus is calculated. The results show that word sequence complexity of text indicates a characteristic of gradual stabilization. By comparing random texts with natural texts, it is found that word sequence complexity is influenced by syntactic rules rather than sentence order, and natural texts tend to alternate between words of varying lengths and frequencies. Classification experiment results indicate that the proposed word sequence complexity outperforms commonly used quantitative indicators for representing the genre of text, such as TTR, information entropy, Zipf's law parameters and motifs. [ABSTRACT FROM AUTHOR]

The evolution of the spatiotemporal relationship between urban economic growth and health resources within the Yangtze River Delta urban agglomeration provides an important context for understanding the regional development dynamics in China. Previous studies focused on equity in health-resource allocation and service efficiency, often overlooking the allometric growth relationships between health resources and economic variables. This study employs an allometric growth model to elucidate the changing interactions between the number of medical beds, doctors, and urban economic indicators in the Yangtze River Delta region from 2009 to 2022. Employing Zipf's law and allometric growth modeling, this study analyzed growth trends and revealed significant differences in resource allocation and size changes over time. The main findings suggest that, although resource centralization is a general trend, differences persist, especially in less economically developed regions. This study innovatively introduces an allometric growth model that offers a new perspective on understanding the mechanisms of regional health-resource growth and underscores the significant influence of economic factors on health-resource allocation. This study significantly contributes to the sustainability of urban health systems and provides theoretical support for policy formulations aimed at optimizing the allocation of health resources and strengthening regional economic strategies in the Yangtze River Delta region. [ABSTRACT FROM AUTHOR]

The article explores the quantitative syntactic features of Chinese and English through a comparative study based on dependency relations. It delves into the universality and individuality of languages, emphasizing the dynamic, variable, and ambiguous nature of language. The study employs data-driven research methods, focusing on dependency grammar and valency theory to uncover valuable insights for future research. By utilizing quantitative linguistics, the research aims to define and measure linguistic attributes and units, highlighting the significance of interdisciplinary approaches in language study. [Extracted from the article]

The article "The Impact of Events and Order of Entry" by Nicholas Guthrie explores the concepts of events and launch order in pharmaceutical pipeline forecasting. It discusses how market trends can be influenced by future events and the importance of the order in which brands enter the market. Using real data, the article illustrates how events like product launches and warnings can impact prescription volumes and market shares. The study also delves into Zipf's Law, which suggests that the first product to launch in a market class may have a higher market share. [Extracted from the article]

Efficiency principles are increasingly called upon to study features of human language and communication. Zipf's law of abbreviation is widely seen as a classic instance of a linguistic pattern brought about by language users’ search for efficient communication. The “law”—a recurrent correlation between the frequency of words and their brevity—is a near‐universal principle of communication, having been found in all of the hundreds of human languages where it has been tested, and a few nonhuman communication systems as well. The standard explanation for the law of abbreviation derives from pressures for efficiency: speakers minimize their cumulative effort by using shorter words for frequent occurrences. This explanation, we argue here, fails to explain why long words exist at all. It also fails to explain why the law of abbreviation, despite being robust, is systematically weakened by many short and rare words. We propose an alternative account of the law of abbreviation, based on a simple cultural evolutionary model. Our model does not require any pressure for efficiency. Instead, it derives the law of abbreviation from a general pressure for brevity applying to all words regardless of their frequency. This model makes two accurate predictions that the standard model misses: the correlation between frequency and brevity is consistently weak, and it is characterized by heteroskedasticity, with many short and rare words. We argue on this basis that efficiency considerations are neither necessary nor sufficient to explain the law. [ABSTRACT FROM AUTHOR]

In Probability Proportional to Size (PPS) sampling, size variable associated with the sampling unit leads to the probability selection of units proportional to its size. In the literature, modification to PPS has been proposed by dividing the population in two groups on arranging the units in decreasing order of their frequency. We introduce Stratified Modified Probability Proportional to Size with Replacement (Stratified MPPSWR) sampling and Stratified Modified Rao-Hartley-Cochran (Stratified MRHC) design in case of without replacement sampling where the data are distributed in homogeneous strata such that it follows Zipf's law within each stratum and the units are selected using MPPSWR and MRHC design respectively. In proposed schemes, each stratum is divided into two groups and first group is selected into the sample with probability 1 and units from second group are selected using PPSWR and RHC sampling respectively as in MPPSWR and MRHC sampling design. The relative efficiency of the proposed schemes is carried out and an illustration is given using the real data set. The proposed sampling schemes are seen to be more efficient than existing techniques. [ABSTRACT FROM AUTHOR]

Purpose: This study investigates the application of the principle of least effort in the usage of printed resources among students at Razi University. The principle posits that actions are performed in ways that minimize effort. Methodology: A quantitative research design employing a survey method was used. Data were collected from 375 students using a structured questionnaire. Findings: The study revealed that the use of printed resources by Razi University students aligns significantly with the principle of least effort. Undergraduate students exhibited greater adherence to this principle compared to postgraduate levels. Statistical analyses, including Pearson’s correlation and multivariate regression, indicated that the principle of least effort significantly predicts printed resource usage. Conclusion: The principle of least effort appears to be a valid framework for understanding students' resource usage behaviors. The findings underscore its importance for library and information center management. Value: This study introduces a novel exploration of the principle of least effort within the Iranian academic context. [ABSTRACT FROM AUTHOR]

The article explores the quantitative syntactic features of Chinese and English through a comparative study based on dependency relations. It delves into the universality and individuality of languages, emphasizing the dynamic, variable, and ambiguous nature of language. The study utilizes authentic data from treebanks and employs quantitative linguistics research methods to uncover underlying language structures. By applying rigorous mathematical techniques, the research offers valuable insights for future studies in the field of linguistic analysis. [Extracted from the article]

City size and growth are the subject of a substantial literature in economic geography and urban economics, but consensus remains elusive on the extent to which key regularities such as Zipf's Law or Gibrat's Law holds across space and time. We contribute to this literature by examining city size, rank and growth in Britain 1801–2011, the first country in the world to urbanize. Across Zipf, Gibrat and Gini analyses, we find that urban concentration in Britain peaked in the mid-nineteenth century before falling 1861–1911 and again 1951–1991. The evolving relationship between city size, rank and growth in Britain since 1801 strongly suggests that drivers mentioned in the literature, such as random growth, increasing returns to scale and the importance of location fundamentals, are not constant over time. There is some evidence of increasing returns to scale 1801–1861, then offset by factors favouring smaller cities, possibly related to new transport technologies. Further, we show that conclusions about both Zipf's and Gibrat's Law would change if weaker city definitions, sample cutoffs and regression methods were used, a likely factor in understanding the often contradictory results in the literature on city dynamics. [ABSTRACT FROM AUTHOR]

This study examines the integrity of financial statements within the Romanian gambling and betting industry, employing Benford's, Zipf's and Universal Law and distribution distances tests. Data from the financial statements of active gambling and betting companies in 2013, classified under NACE code 9200, were analysed The primary focus was on the absolute values of declared gross profit or loss. Our analysis involved visual inspections, Chi-square tests, and the application of Zipf's and Universal laws for distribution conformity. Results indicated that the empirical distributions of the first and second digits, as well as the combined first two digits of gross profit or loss, align with Benford's Law. Surprisingly, the distribution did not conform to the expected Zipf's type but instead followed the specific pattern of the Universal law. Furthermore, while the Zipf's model was not a fit, the Universal law effectively captured the distribution of the reported financial data, suggesting a power-law concentration of gross profit values in the industry. [ABSTRACT FROM AUTHOR]

Copyright of Revista Foco (Interdisciplinary Studies Journal) is the property of Revista Foco 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.)

HAZOP is a paradigm of industrial safety, and the introduction of deep learning-based HAZOP text categorization marks the arrival of an intelligent era of safety analysis. However, existing risk analysis methods have limitations in processing complex texts and extracting deep risk features. To solve this problem, this paper proposes a novel HAZOP risk event classification model based on BERT, BiLSTM, and TextCNN. The complexity of HAZOP text is revealed by introducing statistical laws of natural language, such as Zipf's law and Heaps' law, and the outputs of different levels of BERT are further combined linearly to collaborate with BiLSTM and TextCNN to capture long-term dependency and local contextual information for a more accurate classification task. Meanwhile, an improved loss function is proposed to effectively solve the deficiencies of the traditional cross-entropy loss function in the mislabeling process and improve the generalization ability of the model. It is experimentally demonstrated that the accuracy of the model is improved by 3% to 4% compared to the traditional BERT model in the task of severity and possibility classification of HAZOP reports. This study not only improves the accuracy and efficiency of HAZOP risk analysis, but also provides new ideas and methods for the application of natural language processing in industrial safety. [ABSTRACT FROM AUTHOR]

The common assumption is that genetic information is built on a four-symbol alphabet, i.e., DNA nucleotides, the smallest meaningful blocks of genomes are codon triplets, and the record of genetic information does not contain any asserted symbols playing the role of the space. It is, however, well known that some nucleotides in some codons are redundant. Our study, therefore, tests the alternative scenario. As the same nucleotide may play various semiotic roles, the genomic alphabet actually contains seven semiotic symbols. Consequently, the meaningful fragments of genomes (words) can be of different sizes, and there are asserted symbols in the record of genomic information. If this is true, then, similarly to natural languages, the frequency-range of these genomic words should follow the power-law distribution. The presented hypothesis was tested, in comparison to competitive (codon-based and n-tuple) forms of tokenization, on a wide range of genomic texts. [ABSTRACT FROM AUTHOR]

Most studies on size distributions focus on examining rank-size distributions at urban or regional scale, but they often overlook their spatial dependencies, distributions, and neighboring relationships. This study aims to test Zipf 's Law at the neighborhood scale of Metropolitan Istanbul, analyze its spatial dependencies, and investigate their spatial behavioral patterns in urban areas over the past decade. Initially, we found that Zipf 's Law is not valid at the neighborhood scale of Istanbul. Secondly, we identified significant spatial dependencies in neighborhood population densities, observed clustering of high- and lowdensity neighborhoods in different locations, and detected their influences from adjacent neighborhood densities. Thirdly, we observed that population dynamics are directly affected by urban policies. Based on these findings, when spatial dependencies are considered as essential factors and analyzed in detail at lower scales, population density can provide preliminary insight into the social, economic, and political processes occurring in the city. [ABSTRACT FROM AUTHOR]

We aim to systematize the elements of sustainable development of cities and their social and ecological components in the theoretical and methodological basis of measuring the effectiveness of post-war reconstruction of the country. We study the theoretical and practical aspects of the economic growth of cities, and we systematize the components of implementing the strategy for achieving sustainable development of cities in the post-war period. We present the main characteristic features of the effective regional policy of the EU and Ukraine, highlighting the revitalization of polluted land plots in cities, the modernization of industrial facilities, the integrated regeneration of urban and rural areas, the development of environmentally friendly urban transport, and the development of residential construction. We indicate the key aspects of the industrial waste management system in the city and the main directions: production-oriented, socially-oriented, and marketing management approaches. We find that organizational decisions should reflect the harmonious interaction of enterprises in handling industrial waste from the city-forming, city-maintenance, and city-building spheres. We characterize the key aspects of the industrial waste management system in the city and describe a set of methods for evaluating the sustainable development of cities. We substantiate the importance of applying the scientific and methodological foundations of Zipf’s Law, considering it universal for measuring the effectiveness of the functioning of local communities and territories. We note that for the benefit of future generations, the strategy of sustainable development of cities should satisfy their own needs, covering social, economic, and ecological dimensions. We highlight the interrelationship of the components and present a scientific and methodological approach to determining the level of urbanization of the city, taking into account the index of sustainable development of the city based on Zipf’s law, which we have developed.

Speech acts, as basic communication units in pragmatics, are highly correlated to speakers' communicative intentions. It is a worthwhile goal to explore whether they obey some linguistic laws that reflect people's cognitive mechanisms, e.g. Zipf's Law. However, few studies have examined whether the Zipf distribution can capture the frequencies of speech acts, and whether the parameters of it can show how speakers' attributes (e.g. gender and education level) relate to the use of speech acts. As a preliminary attempt to bridge this gap, the current study finds from the data sample of the Switchboard Dialog Act Corpus that: (1) the Zipf distribution well captures the distribution of speech acts; (2) the parameter a can distinguish the dialogs between speakers of different genders, and it shows a regularity of the highest frequency of an SA in a dialigue to some degree; (3) the parameter b can differentiate speakers of different education levels – people with college-level education may have higher expressivity of SAs compared with those with higher-than-college-level education. This study shows that Zipf's Law can be extended to the analysis of pragmatic phenomena, which may become part of the synergetic system of language through the approach of Quantitative Linguistics. [ABSTRACT FROM AUTHOR]

Emojis in digital communication have drawn increasing academic attention. Qualitative studies mainly rely on a presumption that emojis share similar properties with units of natural language. It remains to be explored with quantitative methods whether emojis exhibit the same or similar behaviour from linguistic units (like words, morphemes). This study investigates emoji features in relation to language properties based on Zipf's law and linear regression models. Results show that, firstly, the rank frequency distribution of emojis can be well fitted by Zipf's law, and the parameters of emoji distribution are closer to those of written language. Secondly, most emoji categories tend to occur in the latter half of the tweet; while in some cases, they can also be at the beginning or in the middle of a tweet. Thirdly, the relative position of the more frequently-used emojis will be further back in the tweet. When emojis' frequencies are relatively greater, their categories vary more in terms of their positions. In general, our quantitative findings suggest that emojis display linguistic properties to some extent. Our exploratory study demonstrates the value of applying linguistic laws and quantitative methods to investigate emoji features, extending the application of quantitative linguistic methods into emoji studies. [ABSTRACT FROM AUTHOR]

The studies of international scientific cooperation have been present in the literature since the early 1990s. However, much less is known about this cooperation at the intercontinental level. Very recently Krawczyk and Malarz (Chaos 33(11):111102, 2023), showed that the rank-based probability distribution of the sequences of 'continents (number of countries)' in the authors' affiliations shows a clear power law with an exponent close to 1.9. In this paper, we focus on the analysis of almost 14 million papers. Based on the affiliations of their authors, we created lists of sequences 'continent (number of countries)'—at the intercontinental level—and 'country (number of authors)' sequences—at the international level—and analysed them in terms of their frequency. In contrast to the intercontinental level, the rank-based probability distribution of the 'country (number of authors)' sequences in the authors' affiliations reveals a broken power law distribution. [ABSTRACT FROM AUTHOR]

A region has a certain area within which there is a certain number of cities that are different in the number of the inhabitants, located at different distances from each other, forming an urban system that is based on the multitude of relationships between them. This study investigates the hierarchy of the 16 cities that make up the regional urban system of Dobrogea, as well as the spatial interaction between them. To achieve these goals, several models were used, such as those of Zipf, Beckman, and Reilly-Converse, and the Jefferson index. The results of the study indicate the urban primacy (hypertophy) of the largest city in the territory located between the Danube and the Black Sea, Constanța, as well as the macrocephaly of its regional urban system. Zipf's law shows the incoherence, the imbalance of the urban system and divides its cities into plethoric cities and deficit cities. The same characteristics of the urban system are also confirmed by Beckman's law. By applying the Reilly-Converse law, the zone of influence of the city of Constanța was delimited, almost 38% of the entire area of the Dobrogea region. [ABSTRACT FROM AUTHOR]

The study of the land use optimization of urban agglomerations is of great significance to the rational utilization of land resources and the sustainable development of urban agglomerations. Previous studies have simply regarded the urban agglomeration as a whole area or each city as an isolated individual, without considering the regional coordinated development of urban agglomerations in land use optimization objectives. This study proposed the first attempt to couple Zipf's law and a multiobjective optimization model of land use in an urban agglomeration. Zipf's law was applied to quantify the coordinated development of urban agglomeration and use it as one of the objectives of land use optimization. The genetic algorithm was adopted to establish the optimization model, and different future development scenarios were designed for comparison. The Beijing–Tianjin–Hebei (BTH) urban agglomeration was selected as the study area, and the proposed model obtained effective results within an acceptable time. The Zipf's law–based optimization objective provided a more coordinated scale structure for urban growth and led the urban structure to develop toward the optimized state. There was a conflict, however, between the coordination and the other two objectives (compactness and suitability). Different stakeholders need to consider the trade-offs among these optimization objectives in urban planning. Finally, based on the optimization patterns of local areas, we suggest the following: Some large-scale cities (e.g., Beijing and Tianjin) should strictly control their new urban expansion or transfer part of their resources and population; Langfang and Xingtai should accelerate their development or take over part of the noncapital function of Beijing; and Zhangjiakou and Chengde should optimize their urban morphology and suitability. [ABSTRACT FROM AUTHOR]

Information compression is widely regarded as a fundamental principle that applies to human language. Zipf's law of abbreviation and Menzerath–Altmann's law are two linguistic laws related to information compression and have been demonstrated in human language and other communication systems. Female choice and male-male competition in anurans (frogs and toads) depend heavily on vocal communication. However, it remains unclear whether the laws reflecting information compression apply to vocal communication in anurans. Hainan frilled treefrogs, Kurixalus hainanus , are suitable anuran species to test Zipf's law of abbreviation and Menzerath–Altmann's law as male K. hainanus can emit either monosyllabic or multisyllabic calls with three types of notes (i.e. A, B and C notes). In the present study, we mathematically examined whether the vocalizations of K. hainanus conform to these laws. We found that the note type duration was positively correlated with its frequency of occurrence, which was the opposite finding to that predicted by Zipf's law of abbreviation. We also found that the note duration was negatively correlated with call size (the number of notes in a call), but only A notes exhibited patterns consistent with Menzerath–Altmann's law when analysed separately. These results may be caused by the different physical characteristics or different functions and selection pressures of different note types. Further linear mixed model analysis showed that the duration of A notes was significantly negatively correlated with note position in a call, which suggests that the conformity to Menzerath–Altmann's law in A note is caused by energetic or breathing constraints on vocal production. Lastly, we observed a negative correlation between internote interval duration and call size. Our findings support the existence of information compression in vocal communication systems in anurans, among other communication principles, and contribute to increasing our understanding of universal patterns in communication systems. • We found information compression in an anuran vocal communication system. • The duration of a specific note type was negatively correlated with call size. • The internote interval duration was negatively correlated with call size. • The note type duration was positively correlated with its frequency of occurrence. [ABSTRACT FROM AUTHOR]

Incorporating artificial intelligence (AI) into library science has significantly transformed information management and retrieval. This study explores AI in libraries, focusing on subject mapping and bibliometric laws, using data from 2014 to 2023. This paper provides insights into the evolution of scholarly communication, knowledge dissemination, and information retrieval." The study reveals patterns in library and information science distribution, productivity, and impact by examining bibliometric laws such as Bradford's, Lotka's, and Zipf's. This study utilised systematic searches, robust databases, and bibliometric tools to ensure methodological rigour. Seventy-six documents meeting predefined criteria were selected, with Scopus Elsevier as the primary data source. Analysis was performed using Bibliometrix software in RStudio, supplemented by Python code for visualisation and statistical analysis. Bradford's law highlighted the concentration of AI literature in specific journals, while Lotka's Law confirmed the unequal productivity among authors. The study concludes with recommendations for future research, offering a comprehensive understanding of AI's implications in library science. [ABSTRACT FROM AUTHOR]

Copyright of Journal Public Administration & Social Management / Administração Pública e Gestão Social is the property of Administracao Publica e Gestao Social 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 extends the concept of granularity from firms to cities, examining how large cities influence national economic dynamics beyond their relative size. By applying Zipf's law, which describes the power law distribution of city sizes, we investigate the interplay between granularity and business cycles. Our aim is to test the granular hypothesis that large cities have a significant impact on the business cycle beyond their relative size. We analyze data from American and Brazilian cities between 2003 and 2019 assessing the granular residuals and their explanatory power. Our findings reveal that in the United States, the granular city size is three metropolitan areas or five counties when redefined. In Brazil, it equates to three municipalities. These results emphasize the substantial role large cities play in national economic fluctuations, suggesting that policy interventions that target infrastructure, education, and innovation in major urban centers could have widespread economic benefits. This paper's contribution to the literature is to highlight a spatial component of granularity not considered so far. [ABSTRACT FROM AUTHOR]

This paper attempts to verify the hierarchy of towns in Lower Silesia on the basis of population data from the second decade of the 17th century, assuming that a statistically described distribution law applies. The analysis of the city size distribution was based on Gibrat's law and Zipf's rank‐size rule. This made it possible to verify the assumptions made at the outset and to estimate the population of towns of unknown size and designated rank. The research carried out suggests a revision of the estimates, especially for the largest cities in the region, which tend to be underestimated. Studies have also shown that the method can be extremely useful for verifying uncertain and incomplete historical demographic data. [ABSTRACT FROM AUTHOR]

Self-organized criticality is a universal theory for dynamical systems that has recently been applied to the cardiovascular system. Precise methodological approaches are essential for understanding the dynamics of cardiovascular self-organized criticality. This study examines how the duration and quality of data recording affect the analysis of cardiovascular self-organized criticality, with a focus on the beat-by-beat heart rate variability time series obtained from seven healthy subjects in a standing position. Drawing a Zipf diagram, we evaluated the distribution of cardiovascular events of bradycardia and tachycardia. We identified tipping points for the distribution of both bradycardia and tachycardia events. By varying the recording durations (1, 2, 5, 10, 20, 30, and 40 min) and sampling frequencies (500, 250, and 100 Hz), we investigated their influence on the observed distributions. While shorter recordings can effectively capture cardiovascular events, they may underestimate the variables describing their distribution. Additionally, the tipping point of the Zipf distribution differs between bradycardia and tachycardia events. Comparisons of the distribution of bradycardia and tachycardia events should be conducted using long data recordings. Utilizing devices with lower sampling frequencies may compromise data fidelity. These insights contribute to refining experimental protocols and advancing our understanding of the complex dynamics underlying cardiovascular regulation. [ABSTRACT FROM AUTHOR]

Scholarship demonstrates that urban systems follow a power law population distribution if the population has full labor mobility. Theoretically, subpopulations should also follow a power law population distribution if that subpopulation also has full labor mobility. Examining city population distributions for White and Black Americans across US metropolitan areas from 1910 to 2020 shows that the White distribution mostly conforms to both Zipf's and Gibrat's laws throughout this period. In contrast, the Black population does not follow either law until the second half of the 20th century, a result that is consistent with theories of restricted mobility out of the South for Black Americans during the Jim Crow era. [ABSTRACT FROM AUTHOR]

The definition of cities from the physical view in China is lacking. Most research regarding Chinese cities relies on the definition from the administrative view, which is often inconsistent as there are serious discrepancies between the administrative boundaries and the physical extent of Chinese cities. This study aims to delineate Chinese urbanised areas using population census data at the township level and analyse the identified urbanised areas' characteristics. The results show that the numbers of Chinese urbanised areas in 2000, 2010, and 2020 were 758, 942, and 1058, respectively, indicating there are several 'cities outside the system' that meet the requirements of urban agglomeration but are constrained by the city designation system. The degree of population aggregation and the growth rate of urbanised areas are greater than those of administrative cities. This indicates that the geographical scopes of administrative cities cannot accurately reflect the 'real' urban areas. Additionally, the city-size distribution follows Zipf's law, with the Zipf coefficient moving closer to one if we fit the Zipf model based on the urbanised areas. It is necessary to establish official urbanised areas and publish statistical data based on urbanised areas, which could have significant implications both for policymakers and researchers. [ABSTRACT FROM AUTHOR]

The hierarchical structure of geographic or urban space can be well-characterized by the concept of living structure, a term coined by Christopher Alexander. All spaces, regardless of their size, possess certain degrees of livingness that can be mathematically quantified. While previous studies have successfully quantified the livingness of small spaces such as images or artworks, the livingness of geographic space has not yet been characterized in a recursive manner. Zipf’s law has been observed in urban systems and intra-urban structures. However, whether Zipf’s law is applicable to the hierarchical substructures of geographic space has rarely been investigated. In this study, we recursively extract the substructures of geographic space using global nighttime light imagery. We quantify the livingness of global cities considering the number of substructures (S) and their inherent hierarchy (H). We further investigate the scaling properties of the extracted substructures across scales and the relationships between livingness and population for global cities. The results demonstrate that all substructures of global cities form a living structure that conforms to Zipf’s law. The degree of livingness better captures population distribution than nighttime light intensity values for the global cities. This study contributes in three aspects: First, it considers global cities as a whole to quantify spatial livingness. Second, it applies the concept of livingness to cities to better capture the spatial structure of the population using nighttime light data. Third, it introduces a novel method to recursively extract substructures from nighttime images, offering a valuable tool to investigate urban structures across multiple spatial scales.

In the realm of linguistics, the concept of "semanticity" was recently introduced as a novel measure designed to study linguistic networks. In a given text, semanticity is defined as the ratio of the potential number of meanings associated with a word to the number of different words with which it is linguistically linked. This concept provides a quantitative indicator that reflects a word's semantic complexity and its role in a language. In this pilot study, we applied the semanticity measure to the Catalan language, aiming to investigate its effectiveness in automatically distinguishing content words from function words. For this purpose, the measure of semanticity has been applied to a large corpus of texts written in Catalan. We show that the semanticity of words allows us to classify the word classes existing in Catalan in a simple way so that both the semantic and syntactic capacity of each word within a language can be integrated under this parameter. By means of this semanticity measure, it has been observed that adverbs behave like function words in Catalan. This approach offers a quantitative and objective tool for researchers and linguists to gain insights into the structure and dynamics of languages, contributing to a deeper understanding of their underlying principles. The application of semanticity to Catalan is a promising pilot study, with potential applications in other languages, which will allow progress to be made in the field of theoretical linguistics and contribute to the development of automated linguistic tools. [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]

• The high frequencies of CFTR variants can be explained by a selective advantage for healthy carriers (4–6 % per generation). • Spreading of disease-causing allele carriers was accelerated towards the end of the 18th century. • The most widespread variant (F508del) is estimated to have appeared approximately 190 generations ago. The French region of Brittany presents one of the highest cystic fibrosis (CF)-causing allele frequency in Europe. Here, we tested two hypotheses: i) CF-causing allele carriers arrived by sea in the middle of the 1st millennium AD, and ii) a selective advantage for healthy carriers explains this high rate. From the census of cystic fibrosis patients, frequency maps of the most widespread alleles were established. A mathematical model was developed, based on birth date and place of the ancestors of these patients over 5 centuries, to determine the distribution of local migrations and their parameters for inter-generational intervals of 32 years. This model was applied to simulate the spread of CF-causing variant carriers, according to different scenarios that corresponded to the immigration of a given number of variant carriers at different times (year) and places, and to compare their results to current frequency maps. Migrants carrying a CFTR variant settled in several locations, around which they spread, notably in Central Brittany (F508del variant), Léon (G551D variant) and Cornouaille (1078delT variant). Until the end of the 18th century, the spreading of disease-causing allele carriers was relatively slow, and allele frequencies progressively increased. Then, the mean migration distances increased rapidly, leading to a decline in local frequencies. The main CFTR variants could only have reached their current frequencies through a selective advantage for healthy carriers of the order of 4–6 % at each generation. For the most widespread variant (F508del), the model supports the hypothesis that it appeared around 190 generations ago. [ABSTRACT FROM AUTHOR]

We investigate the market value of rarity theoretically and empirically. Prior studies find that the market value of rarity follows a power law, but this finding lacks a theoretical foundation. We provide a micro-foundation for this finding, demonstrating that the observed power law emerges in a competitive market where agents have rank-dependent utility preferences. The model leads to two new theoretical insights: (i) the rank of an item within a set of close substitutes and the quantity of that item known to exist are both natural measures of rarity, but rank is predicted to perform better; (ii) there is a systematic relationship between the estimated slope and intercept from a regression of log price on log rank. When we test the model on data from over 4000 auction records of rare baseball cards, we find that a regression with only log rank and grading company explains 60% of the variation in log price. [ABSTRACT FROM AUTHOR]

The article extends the theoretical and applicative analysis of Zipf's law. We are concerned with a set of properties of Zipf's law that derive directly from the power law expression and from the discrete nature of the objects to which the law is applied, when the objects are words, lemmas, and the like. We also search for variations of Zipf's law that can help explain the noisy results empirically reported in the literature and the departures of the empirically obtained nonlinear graph from the theoretical linear one, with the variants analyzed differing from Mandelbrot and lognormal distributions. A problem of interest that we deal with is that of mixtures of populations obeying Zipf's law. The last problem has relevance in the analysis of texts with words with various etymologies. Computational aspects are also addressed. [ABSTRACT FROM AUTHOR]

"The Music in the Data" is a book that explores the use of corpus studies in music theory. It introduces various quantitative methods and models to analyze musical data and argues that a sense of key in music is learned implicitly through exposure to different musical styles. The book also discusses the differences between music and language perception and serves as an introduction to corpus studies, a reference for quantitative methods, a reflection on data-oriented studies, and a pedagogical resource. It encourages a plurality of interpretations and provides a framework for analyzing different musical styles. [Extracted from the article]

The common assumption is that genetic information is built on a four-symbol alphabet, i.e., DNA nucleotides, the smallest meaningful blocks of genomes are codon triplets, and the record of genetic information does not contain any asserted symbols playing the role of the space. It is, however, well known that some nucleotides in some codons are redundant. Our study, therefore, tests the alternative scenario. As the same nucleotide may play various semiotic roles, the genomic alphabet actually contains seven semiotic symbols. Consequently, the meaningful fragments of genomes (words) can be of different sizes, and there are asserted symbols in the record of genomic information. If this is true, then, similarly to natural languages, the frequency-range of these genomic words should follow the power-law distribution. The presented hypothesis was tested, in comparison to competitive (codon-based and n-tuple) forms of tokenization, on a wide range of genomic texts.

Complex systems research has chiefly investigated language change from a social dynamics perspective, with undeniable success. However, there is more to language change than social diffusion, i.e., a one-off adoption of an innovative variant by language users. Language use indeed factors in, besides prevalence (the percentage of adopters of the form in the community), lexical diversity (the number of different lexical items a conventionalized pattern combines with), and entrenchment (the average rate at which speakers choose the form in suitable pragmatic environments). Changes in token frequency may reflect changes in any of these three variables. To sort them out, we defined proxies to factor entrenchment out of empirical measures of prevalence and lexical diversity. From a French corpus, we analyzed 25 schematic constructions, featuring an open slot that hosts a variety of fillers. We show that their rise of token frequency across a change episode is mostly explained by entrenchment; however, the magnitude of the change is uniquely explained by the final extent of its lexical diversity. Furthermore, the fillers obey a construction-specific Zipf-Mandelbrot organization, that robustly holds throughout the change episode. We also show that in some cases, the fillers arise simultaneously, hinting at the possibility that such a complex organization emerges all at once, highlighting the role of structural features in language change.

There has recently been an increasing interest in the quantification of success in different fields of human activities. However, most of the research in this field solely focuses on success as a collective phenomenon to be understood in terms of a network structure or overall statistics. Moreover, research in this field rarely attempts to predict success. In this work, we consider real data in the Turkish movie industry, with a focus on individual criteria of success and predict annus mirabilis, also known as the miracle year of the performers, through several machine learning algorithms. We find that this prediction can be achieved best by using a random forest model yielding 92 and 90 percent accuracy for actresses and actors, respectively. Next, we provided a novel q-deformed generalization of the k-Nearest Neighbor (kNN) algorithm, which yields the unnormalized kNN algorithm when the parameter q = 0 , and logarithmic normalized kNN algorithm for q = 1 . This generalization increases the prediction accuracy of the miracle year by one percent for the optimal value q = - 3 of the parameter compared to the random forest algorithm. In addition, we found out that the probability of career length follows an exponential distribution in the intermediate region, hence distinguishing two outlier groups. The former group is formed by those with only one movie credit (almost seventy five percent of the acting guild), and the latter group corresponds to those with a career length exceeding thirty five years (almost one percent). The probability distribution of acting in n movies, on the other hand, is observed to be a power law with an exponent corresponding to Zipf's law if ordered in rank. This behavior seems to be the norm in the film industry and is a signature of the memory-dependent (namely, popularity-dependent) choices of directors and producers. We investigated whether gender plays a role in the Turkish fılm industry, and found out that it does, favoring actors in terms of duration of activity. However, after a certain threshold of career length, namely L = 55 years, it is more likely to find active actresses. [ABSTRACT FROM AUTHOR]

The science of complexity aims to answer the question of what rules nature chooses when assembling the basic constituents of matter and energy into structures and dynamical patterns that cascade through the entire hierarchy of scales in the Universe. A related phenomenon – natural language – can successfully mirror such structures as reflected by its ability to encode and transmit information about them and among them. It is thus legitimate to expect that natural language carries the essence of complexity. And indeed, in the human's speaking and writing it is particularly true that more is different. Natural language thus deserves a central place in the related quantitative study within the science of complexity. With this in mind the present review summarizes the main methodological concepts used in this domain and documents their applicability and utility in identifying universal as well as system-specific features of natural language in its written representation in several major Western languages. In particular, three main complexity-related current research trends in quantitative linguistics are exhaustively covered. The first part addresses the issue of word frequencies in texts and, in particular, demonstrates that taking punctuation into consideration largely restores scaling whose violation in the Zipf's law for the most frequent words is commonly modelled by the so-called Mandelbrot's correction. The second part introduces methods inspired by time series analysis, used in studying various kinds of long-range correlations in written texts. The related time series are generated on the basis of text partition into sentences or into phrases between consecutive punctuation marks. It turns out that these series develop features often found in signals generated by complex systems: the presence of long-range correlations along with fractal or even multifractal structures. Moreover, it appears that the distances between consecutive punctuation marks quite universally across languages comply with the discrete variant of the Weibull distribution, often appearing in survival analysis. In the third part, the application of the network formalism to natural language is reviewed, particularly in the context of word-adjacency networks whose structure reflects the word co-occurrence in texts. Various parameters characterizing topology of such networks can be used for classification of texts, for example, from a stylometric perspective. Network approach can also be applied in semantic analysis to represent a hierarchy of words and associations between them based on their meaning. Structure of such networks turns out to be significantly different from that observed in random networks, revealing genuine properties of language. Finally, punctuation appears to have a significant impact not only on the language's information-carrying ability but also on its key statistical properties, hence it seems recommended to consider punctuation marks on a par with words. [ABSTRACT FROM AUTHOR]

This paper tests how digital inclusive finance affects the scale distribution of firms in China. The full-sample registration information of approximately 30 million firms in China is utilized for this investigation. The main findings suggest that, as a developing country, the scale distribution of China's firms significantly deviates from Zipf's law. However, digital inclusive finance helps to correct this deviation. A nonlinear test shows that the above positive effect is rising, meaning it is necessary to further develop digital inclusive finance. The impact of digital inclusive finance is better in the relatively backward central and western regions. Also, no obvious heterogeneity exists among industries, highlighting the due meaning of the word 'inclusive'. [ABSTRACT FROM AUTHOR]

The book "Quantitative Approaches to Universality and Individuality in Language" explores the investigation of universality and individuality in language through quantitative approaches. It highlights 16 studies that demonstrate the perspectives, ambitions, and contributions of quantitative investigations in linguistics. The studies cover topics such as universal language laws, lexical distribution, machine learning, and analytic methods. The book provides insights into the nature and mechanisms of language, emphasizing the importance of both universality and individuality in understanding human beings and the biological and physical basis behind language. It is a valuable resource for researchers interested in combining quantitative and qualitative approaches in linguistics. [Extracted from the article]

Urban Agglomeration (UA) is regarded as an emerging complex urban system in China. The development of UA demands a reasonable scale structure, which can be investigated by Zipf's law. However, few studies have been conducted to quantify the optimal scale of UA and how its development deviates from the optimal scale. With the continuous urban expansion, the problem of UAs' scale structure has received increasing attention. In this study, we propose a method based on Zipf's law for estimating the theoretical optimal scale of UAs in China and assessing the deviation rate from their optimal scales. Twelve typical UAs in China are selected, and their development is assessed via urban impervious surface data from 2000 to 2018. The results show that the average deviation rate of the investigated UAs decreased from 3.40% in 2000 to 2.32% in 2018, demonstrating that these UAs are on a positive evolution trajectory. Furthermore, according to the development stage, we make recommendations on "large cities vs. medium/small-sized cities and promoting vs. restraining" to each UA based on its size. The conceptual and analytical knowledge, as well as the results from this study, are expected to offer valuable insights and new references for regulating and managing UAs' development in China. [ABSTRACT FROM AUTHOR]

The massive growth in scholarly outputs during the last few decades has resulted into the creation of several scholarly databases to index the outputs. These scholarly databases index publication records and provide different metadata fields for different kinds of usage ranging from retrieval and research evaluation to various scientometric analysis. The 'author keywords' is one such important metadata field provided by many databases and used for different text-based and thematic structure analysis. The Dimensions database, however, does not provide 'author keywords' metadata field, instead it provides automatically generated terms from the article full texts, called 'concepts'. Therefore, it is not clear whether different text-based analysis can be done with data provided by Dimensions database. Therefore, this article explores the distributional characteristics of Dimensions concepts. The Dimensions concept data obtained for a sufficiently large sample of scholarly articles is analysed through rank frequency distribution plots in the log–log space. Existence of Zipfian distribution is explored. The results indicate that Dimensions concepts adhere to the Zipfian properties which in turn indicates that Dimensions concepts have similar distributional characteristics as author keywords and hence they may have the same expressive power as that of author or index keywords for scientometric exercises. The study is novel as it is the first study to explore the distributional characteristics of the Dimensions concepts, particularly with respect to Zipfian properties, which provide the statistical foundation for understanding the Dimensions concepts and help to model and analyse them. [ABSTRACT FROM AUTHOR]

A corpus‐based quantitative assessment of Berlin and Kay's proposal is presented. We refine the Basic Color Terms hierarchy proposed by Berlin and Kay, through the concept of salience. A cross‐linguistic study with 57 different languages and 136 different linguistic corpora has been conducted. This study uses KonText tool and the corpora included in it. The color labels in different languages have been obtained using a unified methodology from PanLex. We have obtained an individual hierarchy for each of the languages analyzed, as well as a general hierarchy that captures the universal trend. Results show that there is a close relationship between the evolutionary stages in the Berlin and Kay proposal and their frequency in our corpora study, which we could also relate to Zipf's Law. The only color that we certify behaves differently compared to such a proposal is yellow. The main advantage of our approach compared to previous corpora studies is taking into account the anglocentric bias by using a representative typological set of different languages from the world. [ABSTRACT FROM AUTHOR]

Through content analysis of articles published in library and information science journals, this work aims to analyse, determine, and apply Zipf's Law in the technical writing of library and information science. DESIDOC Journal of Library and Information Technology, Annals of Library and Information Studies, and Library Herald are the journals that were picked for this research. The examination of the 573 articles that were published in the three mentioned journals during the years 2013 to 2017 is the primary focus of the study. If we assume that an abstract should be between 100 and 200 words in length, then 342 articles fall within that range as per the result of this analysis. There are one to five keywords found in 390 articles. In percent, this is 68.06%. The set hypothesis is rejected in the present study which conclude that Zipf's Law in Library and Information Science technical writing is applicable. [ABSTRACT FROM AUTHOR]

Accurate and timely urban boundaries can effectively quantify the spatial characteristics of urban evolution and are essential for understanding the impacts of urbanization processes and land-use changes on the environment and biodiversity. Currently, there is a lack of long time-series, high-resolution, nationally consistent Chinese urban boundary data for urban research. In this study, the city clustering algorithm was used to generate urban settlement boundaries in China based on the local density, size, and spatial relationships of impervious surfaces. The results showed that both the area and the number of urban settlements in China revealed an upward trend from 1985 to 2020, with East China (EC) being much higher than other regions and South China showing the most significant growth rate. The average area ratio of urban green space in China was 41.68%, with the average area ratio in EC being higher than in other regions. Meanwhile, Zipf's law was used to verify the universality of urban settlement rank–size; the changes in the Zipf index from 1985 to 2020 also revealed that China's urban size tended to be concentrated, and the development of large urban settlements was relatively prominent. The urban definition method we propose in this study can divide urban boundaries efficiently and accurately, identify urban expansion hotspots, and promote research on farmland loss and ecological land degradation, further exploring the impacts of urbanization on food security, biodiversity, and carbon sequestration. By coupling big data such as economy, energy, and population with urban evolution patterns, urban managers can analyze current and future problems in urban development, thereby providing scientific decision-making for urban sustainability. [ABSTRACT FROM AUTHOR]