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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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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 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.

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]

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]

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]

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]

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]

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]

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]

We study the number of words that occur exactly once since the beginning of a text. We model it as a stochastic process over the length of the text. The elementary probability model, going back to Bahadur and Karlin, states that the number of words that occur exactly once should grow according to a power law, like the number of different words. The final value of the number of words occurring exactly once is the number of hapaxes of this text. We construct two statistical tests to test Karlin's model under the assumption that the probabilities of words in this model satisfy the generalized Zipf's law. These statistical tests show that some texts fit the model well, but many texts deviate significantly from it. This deviation is that the number of hapaxes is too small relative to the number of different words. [ABSTRACT FROM AUTHOR]

This study explores the behaviour of quantitative motifs in random numerical data, focussing on the property of length. One hundred and twenty sequences of pseudorandomintegers were generated and segmented into quantitative motifs using the standard definition. The length--frequency relationship was modelled in each case using the Zipf-Alekseev function. Different combinations of sequence length, integer range, and pseudorandom number generator were trialled. The model-fitting was successful in all cases (R1² 1 > 0.9 in 118/120 cases and > 0.8 in 2/120), and the model parameters fell in the same range as those obtained in a previous textual study of motifs. Integer range was the main factor affecting the parameter values, with sequence length affecting the degree of spread. Further comparisons between textual and random data are needed, as well as a theoretical explanation of why motifs in random data demonstrate lawful behaviour. In future textual motif studies, particular attention needs to be paid to possible dependencies on value range and text length. [ABSTRACT FROM AUTHOR]

Remote sensing has proven to be an invaluable and effective tool for mapping urban areas. However, further efforts are required to fully utilize remote sensing data in mapping the Chinese urban villages (Chengzhongcun), which are characterized by high population density, irregular shapes and a limited view of the sky. In this study, we integrated deep neural network architectures with GaoFen-2 satellite images at a spatial resolution of 1 metre to investigate the feasibility of using FCN, Unet and ResUnet models for monitoring two categories of urban villages. The results indicate that all three deep learning algorithms demonstrate superiority in identifying and classifying urban villages, surpassing outlier identification. The urban village patches in the study areas adhere to the Zipf's law rule. Particularly, the ResUnet model outperforms FCN and Unet, achieving an overall classification accuracy of over 91% for urban villages. This study suggests that ResUnet is superior to FCN and Unet as it effectively avoids fragmentation and overfitting of individual irregular buildings within urban areas, yielding faster and more accurate results. Overall, this study underscores the significance of the Gaofen-2 dataset as an influential data source for analysing intra-urban structures. Additionally, the implementation of the ResUnet learning algorithm proves to be exceptionally valuable in extracting information across various scales and accurately capturing the intricate nature of irregular urban village patches, even when using satellite images with metre-scale resolution. [ABSTRACT FROM AUTHOR]

With the deepening of urbanization in China, the coordinated development of cities in different regions is an important part of the sustainable development of the country, and the reasonable quantification of the unbalanced development of cities in different regions is an important issue facing the society nowadays. Previous studies usually use population data to analyze the power-law distribution law to quantify the imbalance of urban development in different regions, but China's population data span a large number of years and numerous division criteria, and the results obtained from different population data are widely disparate and have obvious limitations. The paper starts from a fractal perspective and utilizes OpenStreetMap (OSM) data to extract national road intersections from 2015 to 2022, calculates critical distance thresholds for eight years using urban expansion curves, generates urban agglomerations in China, and quantifies the imbalance of urban development in different regions by calculating the urban agglomeration power-law index. The results indicate that (1) the critical distance threshold of urban expansion curves exhibits a slight overall increase and stabilizes within the range of 120–130 m, (2) the number of urban agglomerations in China has been increasing significantly year by year, but the power-law index has been decreasing from 1.49 in 2015 to 1.36 in 2022, and (3) the number of urban agglomerations and the power–law index of the Beijing–Tianjin–Hebei, Yangtze River Delta, Pearl River Delta, and Chengdu–Chongqing regions, which is consistent with the national scale trend, indicates that the scale distribution of urban agglomerations in China at this stage does not conform to Zipf's law, and there is a certain Matthew effect among cities in different geographic areas with a large unevenness. The results of the study can provide new ideas for assessing the coordinated development of cities in different regions. It compensates for the instability of population and economic data in traditional studies. [ABSTRACT FROM AUTHOR]

Neural circuits with multiple discrete attractor states could support a variety of cognitive tasks according to both empirical data and model simulations. We assess the conditions for such multistability in neural systems using a firing rate model framework, in which clusters of similarly responsive neurons are represented as single units, which interact with each other through independent random connections. We explore the range of conditions in which multistability arises via recurrent input from other units while individual units, typically with some degree of self-excitation, lack sufficient self-excitation to become bistable on their own. We find many cases of multistability—defined as the system possessing more than one stable fixed point—in which stable states arise via a network effect, allowing subsets of units to maintain each others' activity because their net input to each other when active is sufficiently positive. In terms of the strength of within-unit self-excitation and standard deviation of random cross-connections, the region of multistability depends on the response function of units. Indeed, multistability can arise with zero self-excitation, purely through zero-mean random cross-connections, if the response function rises supralinearly at low inputs from a value near zero at zero input. We simulate and analyze finite systems, showing that the probability of multistability can peak at intermediate system size, and connect with other literature analyzing similar systems in the infinite-size limit. We find regions of multistability with a bimodal distribution for the number of active units in a stable state. Finally, we find evidence for a log-normal distribution of sizes of attractor basins, which produces Zipf's Law when enumerating the proportion of trials within which random initial conditions lead to a particular stable state of the system. [ABSTRACT FROM AUTHOR]

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.

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.

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.

Scientific cooperation on an international level has been well studied in the literature. However, much less is known about this cooperation on an intercontinental level. In this paper, we address this issue by creating a collection of approximately 13.8 × 10 6 publications around the papers by one of the highly cited authors working in complex networks and their applications. The obtained rank-frequency distribution of the probability of sequences describing continents and the number of countries—with which authors of papers are affiliated—follows the power law with an exponent − 1.9108 (15). Such dependence is known in the literature as Zipf's law, and it has been originally observed in linguistics; later, it turned out that it is very commonly observed in various fields. The number of distinct "continent (number of countries)" sequences in a function of the number of analyzed papers grows according to power law with exponent 0.527 (14) ; i.e., it follows Heap's law. [ABSTRACT FROM AUTHOR]

The 'Rilke Cryptogram' is a possible cipher of German, WWII origin. This study summarises the text's history, and examines explanations for its nature. Statistical techniques are applied to an updated transcription. The text consists of 18,760 characters in 3,305 unique groups of four, arranged into 670 rows by seven columns on 33 pages of an otherwise ordinary book. The distribution of these groups is not particularly Zipfian, suggesting the text is likely not a code or monoalphabetic substitution cipher. Its alphabet is longer than English and German (46 characters). Character and N-gram entropy analyses suggest the text is less ordered than English and German, but more ordered than random text. Machine-learning modelling suggests the text is a substitution cipher, but frequency and Kasiski-Kerckhoff analyses suggest otherwise. Sukhotin's algorithm results for the text are somewhat consistent with results for German, though N-gram distributions do not strongly resemble English or German. Statistical analysis of physical typewriter key distances suggest the text's groupings are highly unlikely to appear at random, and are consistent with intentional 'lazy' typing. The text is inconsistent with machine ciphers of its era (e.g., Enigma), and other features are not entirely consistent with non-cipher explanations. Further investigation is required. [ABSTRACT FROM AUTHOR]

We use data from PayPal to study the geography of online payment activity. An empirical gravity model finds a distance elasticity of −0.58 for payment value, a result that is 40% lower than typically observed in conventional trade data. The firm‐extensive margin is approximately half as sensitive to distance. The link between the scale of merchants' exports and transaction distance is considerably weaker than observed in conventional international trade data. Zipf's Law holds for PayPal merchants in some countries, but fails in smaller PayPal markets. Merchants' account ages only marginally affect the scale and average distance of their export sales. [ABSTRACT FROM AUTHOR]

This article analyses the distribution of firms by size in six selected countries in 2012 and 2017. Estimates are always made for the whole economy and two subgroups of firms. We compare the Visegrad Four countries (Czech Republic, Hungary, Poland and Slovakia) with similar economic activities and two neighbouring economically more developed countries (Germany and Austria). As the main objective of the article, we describe the distribution of firms by verifying the validity of Zipf's law in selected economies and their sectors. The results confirm the positively skewed distribution of company sizes measured by sales revenues, but Zipf's law does not apply to the distribution of all companies by the magnitude of sales in the whole economy (or in an economic subgroup), but only to sections in the right tail of the distribution (companies with higher turnover within the whole economy), which is in line with numerous research studies. [ABSTRACT FROM AUTHOR]

"Understanding Corpus Linguistics" is a textbook that provides an introduction to the goals, methods, and achievements of corpus linguistics. It is written primarily for undergraduate and graduate students, but advanced scholars can also benefit from reading it. The book covers various topics, including the basic concepts of corpus linguistics, corpus composition and types, corpus studies in different fields of linguistics, strategies for searching and analyzing data, corpus building and annotation, statistical description and analysis, the use of corpus linguistics in sociolinguistics, language documentation, and linguistic typology. The book is user-friendly, with exercises and recommendations for further reading in each chapter, making it a valuable resource for anyone interested in corpus linguistics. [Extracted from the article]

The present work pursues theoretical and empirical objectives. With regards to the former, it is demonstrated that the natural tendency to uniformity of both the probability distribution of a city to have a certain number of inhabitants and that of a person to reside in a town of a given number of citizens leads to a competition between their information entropies, which provides the power law distribution as the most probable one for city size. It is also shown that Zipf's law reflects the significant control of the existence of interconnections between cities on the self‐organization of their size. With regards to the empirical objectives, based on population data of European countries and Italian municipalities, the theoretical approach proposed is validated. At the Italian scale, city distribution is shown to be a power law for cities above 10,000 inhabitants. In the 20 Italian regions, the breakpoint in the distribution is generally lower. Finally, the geographical control on city distribution is discussed based on the results achieved in some regions. [ABSTRACT FROM AUTHOR]

Geography, for example because of the presence of rivers, ravines, or peaks, can subdivide a city. These subdivisions raise the question of identifying the area occupied by the city, of deciding whether or not they are aggregates of distinct built-up areas, and whether or not geographical separations are merely asperities in a certain continuum of built-up areas. The city as a union of administrative units allows for jurisdictional practices, but for public policy in health for example, identification by built-up areas is more operational. The study of urban populations thus requires that cities be circumscribed on objective criteria. Circumscribing a city requires knowledge of commuting flows, but in the absence of this piece of information, circumscribing it relies on the fact that it is made up of close built-up areas. This is reflected in the intersection of the convex envelopes of the spatial extent of these built-up areas. The algorithm treats coordinates of the vertices of polygons encompassing built-up areas provided by the Census Bureau for the United States or the National Institute of Statistics and Geography for Mexico. It allows for computing whether convex hulls of polygons intersect or not. If they do, then the built-up areas circumscribed by these polygons are part of the same city. The result is that cities now reflect the geographic extent of urban areas rather than their administrative areas. With this delineation method applied to Mexico's 2020 census data, the population sizes of urban areas with at least 2,126 inhabitants follow a power law, with exponent 0.954 (standard deviation = 0.016), whereas this is no longer the case when considering only the administrative extents of cities with more than 15,000 inhabitants. [ABSTRACT FROM AUTHOR]

A central concern of the cognitive science of language since its origins has been the concept of the linguistic system. Recent approaches to the system concept in language point to the exceedingly complex relations that hold between many kinds of interdependent systems, but it can be difficult to know how to proceed when "everything is connected." This paper offers a framework for tackling that challenge by identifying *scale* as a conceptual mooring for the interdisciplinary study of language systems. The paper begins by defining the scale concept—simply, the possibility for a measure to be larger or smaller in different instances of a system, such as a phonemic inventory, a word's frequency value in a corpus, or a speaker population. We review sites of scale difference in and across linguistic subsystems, drawing on findings from linguistic typology, grammatical description, morphosyntactic theory, psycholinguistics, computational corpus work, and social network demography. We consider possible explanations for scaling differences and constraints in language. We then turn to the question of *dependencies between* sites of scale difference in language, reviewing four sample domains of scale dependency: in phonological systems, across levels of grammatical structure (Menzerath's Law), in corpora (Zipf's Law and related issues), and in speaker population size. Finally, we consider the implications of the review, including the utility of a scale framework for generating new questions and inspiring methodological innovations and interdisciplinary collaborations in cognitive‐scientific research on language. [ABSTRACT FROM AUTHOR]

Human language follows statistical regularities or linguistic laws. For instance, Zipf's law of brevity states that the more frequently a word is used, the shorter it tends to be. All human languages adhere to this word structure. However, it is unclear whether Zipf's law emerged de novo in humans or whether it also exists in the non-linguistic vocal systems of our primate ancestors. Using a vocal conditioning paradigm, we examined the capacity of marmoset monkeys to efficiently encode vocalizations. We observed that marmosets adopted vocal compression strategies at three levels: (i) increasing call rate, (ii) decreasing call duration and (iii) increasing the proportion of short calls. Our results demonstrate that marmosets, when able to freely choose what to vocalize, exhibit vocal statistical regularities consistent with Zipf's law of brevity that go beyond their context-specific natural vocal behaviour. This suggests that linguistic laws emerged in non-linguistic vocal systems in the primate lineage. [ABSTRACT FROM AUTHOR]