Zipf's Law Research Articles

Word Length in Chinese: The Menzerath-Altmann Law is Valid After All

ABSTRACT According to the Menzerath-Altmann law, longer language constructs consist, on average, of shorter constituents. It is most often studied at the level of words and syllables (the mean syllable length gets shorter with the increasing word length). Its validity at this level was corroborated in several languages. However, it was claimed that Chinese is an exception with respect to the validity of the Menzerath-Altmann law. We show that the law is valid if word types are considered, while the behaviour of word tokens is different. This difference can be explained by the fact that the Zipf law of abbreviation is valid not only for words but also for syllables (shorter syllables are used more frequently).

Quantifying basic colors' salience from cross‐linguistic corpora

AbstractA 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.

Double Articulation Analyzer With Prosody for Unsupervised Word and Phone Discovery

Infants acquire words and phonemes from unsegmented speech signals using segmentation cues, such as distributional, prosodic, and co-occurrence cues. Many pre-existing computational models that represent the process tend to focus on distributional or prosodic cues. This paper proposes a nonparametric Bayesian probabilistic generative model called the prosodic hierarchical Dirichlet process-hidden language model (Prosodic HDP-HLM). Prosodic HDP-HLM, an extension of HDP-HLM, considers both prosodic and distributional cues within a single integrative generative model. We conducted three experiments on different types of datasets, and demonstrate the validity of the proposed method. The results show that the Prosodic DAA successfully uses prosodic cues and outperforms a method that solely uses distributional cues. The main contributions of this study are as follows: 1) We develop a probabilistic generative model for time series data including prosody that potentially has a double articulation structure; 2) We propose the Prosodic DAA by deriving the inference procedure for Prosodic HDP-HLM and show that Prosodic DAA can discover words directly from continuous human speech signals using statistical information and prosodic information in an unsupervised manner; 3) We show that prosodic cues contribute to word segmentation more in naturally distributed case words, i.e., they follow Zipf's law.

A Zipf's law-based text generation approach for addressing imbalance in entity extraction

Entity extraction is critical in the intelligent advancement across diverse domains. Nevertheless, a challenge to its effectiveness arises from the data imbalance, where certain entities are common while others are scarce. To address this issue, this study proposes a novel text generation approach that harnesses Zipf's law, which is a powerful tool from informetrics for studying human language. By employing characteristics of Zipf's law, words within the documents are classified as common and rare ones. Subsequently, sentences are classified into common and rare ones, and are further processed by text generation models accordingly. Rare entities within the generated sentences are then labeled using human-designed rules, serving as a supplement to the raw dataset, thereby mitigating the imbalance problem. The study presents a case of extracting entities from technical documents, and the extensive experimental results on two datasets prove the effectiveness of the proposed method. Furthermore, the significance and potential of Zipf's law in driving the progress of artificial intelligence (AI) is discussed, broadening the scope and coverage of informetrics. By incorporating the foundational principles of informetrics into text generation, this study showcases the pivotal role of informetrics in shaping the design and developmental of AI systems.

An innovative two-stage algorithm to optimize Firewall rule ordering

Packet classification activity performed by a FireWall (FW) introduces high latency in network communications due to the computation time required to check whether any packet matches one of the FW rules. Such a classification process is done by sequentially checking the list of rules until a match is found or the end of the list is reached. Given the complexity of FW rules in some environments, this latency could become relevant. This problem is addressed by ordering the list of FW rules to minimize the classification latency, where the rules with higher activation frequencies are placed accordingly starting from the top of the list. This is not always feasible because dependency constraints between rules could exist: swapping the positions of dependent rules results in a loss of the integrity of the implemented security policy. For this reason, the FW rule ordering problem belongs to the realm of constrained combinatorial optimization.This paper proposes a two-stage algorithm to address this problem. The first stage performs an innovative topological sorting algorithm aimed at finding an optimal ordering for the constrained rules, taking into account the fact that rule activation frequencies are influenced by inter-packet arrival time, which typically obeys Zipf's law. The second stage employs a genetic algorithm to find the optimal ordering of all rules within the list. The proposed approach is evaluated using different filtering lists of different complexity provided by ClassBench. A comparison with other state-of-the-art algorithms addressing the same problem is performed. Furthermore, the performance analysis is extended employing an exact optimization method. The results obtained show the effectiveness of the proposed algorithm in minimizing packet classification latency, while a short reordering time is required.

LABVIEW IN THE RESEARCH OF FRACTAL PROPERTIES OF THE TOPOLOGY OF NETWORKS AND STOCHASTIC PROCESSES

The advancement and utilization of computer technologies for studying and diagnosing the technical state of dynamic systems are closely linked to scientific and technological progress. Among these technologies, fractal technologies hold a prominent position [1]. Time series data, which record changes in controlled parameters over time, are commonly used for diagnosing technical objects and systems. The use of fractals will also be of interest in assessing the resonant frequency characteristics of oscillatory systems [3]. The informational characteristics of topologically distributed networks (e.g., computer, cellular) significantly depend on their geometry, node placement, and inter-node distances. The fractal dimension, a fundamental characteristic of networks, plays a crucial role in this context [2]. The research paper presents a methodology for modeling and synthesizing large networks using the node density function, which follows a power function with a fractal dimension. This characteristic aligns with Zipf's law of population distribution around urban centers. The paper also provides fractality degree indices for the network diagram. Software tools such as LabVIEW play a significant role in scientific research and experiment automation.

Auerbach, Lotka, and Zipf: pioneers of power-law city-size distributions

Power-law city-size distributions are a statistical regularity researched in many countries and urban systems. In this history of science treatise we reconsider Felix Auerbach’s paper published in 1913. We reviewed his analysis and found (i) that a constant absolute concentration, as introduced by him, is equivalent to a power-law distribution with exponent approx 1, (ii) that Auerbach describes this equivalence, and (iii) that Auerbach also pioneered the empirical analysis of city-size distributions across countries, regions, and time periods. We further investigate his legacy as reflected in citations and find that important follow-up work, e.g. by Lotka (Elements of physical biology. Williams & Wilkins Company, Baltimore, 1925) and Zipf (Human behavior and the principle of least effort: an introduction to human ecology, Martino Publishing, Manfield Centre, CT (2012), 1949), does give proper reference to his discovery—but others do not. For example, only approximately 20% of city-related works citing Zipf (1949) also cite Auerbach (Petermanns Geogr Mitteilungen 59(74):74–76, 1913). To our best knowledge, Lotka (1925) was the first to describe the power-law rank-size rule as it is analyzed today. Saibante (Metron Rivista Internazionale di Statistica 7(2):53–99, 1928), building on Auerbach and Lotka, investigated the power-law rank-size rule across countries, regions, and time periods. Zipf’s achievement was to embed these findings in his monumental 1949 book. We suggest that the use of “Auerbach–Lotka–Zipf law” (or “ALZ-law”) is more appropriate than “Zipf’s law for cities”, which also avoids confusion with Zipf’s law for word frequency. We end the treatise with biographical notes on Auerbach.

Price dispersion and the stability of trade*

AbstractResearch on trade relationships has documented a high rate of relationship breakup and churning. We use data on Norwegian exports to document two stylized facts about the stability of trade relationships. First, the probability of relationship breakup increases in the deviation of the relationship‐specific price from a reference price. Second, relationship hazards follow Zipf's law. We propose a search model with limited information and search frictions to explain these facts. Reference prices provide information on outside trade options that inform optimal breakups, leading to the first stylized fact. Strong heterogeneity in breakup frictions across relationships can explain the Zipf's law hazards.

The geography of payment activity on PayPal

AbstractWe 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.

Marketing statistical analysis of the website of the University of Customs and Finance

The aim of the article. Analyze the website of the higher education institution (University of Customs and Finance) in Dnipro in comparison with other educational institutions' websites; on the basis of the conducted research, develop the design of the main page of the site. The results of the analyses. Based on the assessment of university websites for 2023, we can conclude that the largest number of visits to the website of the NTU "Dniprovska Polytechnic", and the least number of visits to the website of the University of Customs and Finance. Dnipro State Agrarian and Economic University (DDAEU) spent the longest time on the site and viewed 12 pages, the least interested was the information posted on the Dnipro State Academy of Construction and Architecture, number of pages viewed – 2, 5, Time of stay on the UMSF website is 5 minutes. 7 p. and an average of 2.7 pages were viewed. This is a low value of the indicator and indicates that the content posted on the website of the Dnipro State Agrarian and Economic University was the most interesting, and the least on the website of the Dnipro State Academy of Construction and Architecture, the percentage of rejections on website of the University of Customs and Finance is 46.45%. Foreign users were most interested in information on the website of the Dnipro National University named after O. Honchar, while foreigners were least interested in the website of the University of Customs and Finance. All the universities we studied use social networks to spread information about their calling. Based on the results of the research, we can conclude that the website of the Dnipro University named after A. Nobel has the best design and navigation, and the website of the Dnipro National University named after O. Honchar has the worst indicators. The website of the studied higher education institution (University of Customs and Finance) has 64 points according to experts. In general, it has convenient navigation, simple design, textual content is accompanied by illustrative content, meaningful information content. A negative indicator is the lack of a site search button on the main page. In addition, contacts for feedback and links to social networks are at the very bottom of the page. Based on the results of the SEO analysis of the site content, we can conclude that the Dnipro National University of Railway Transport website has the largest number of symbols. V. Lazaryan, and the smallest - the Dnipro State Academy of Construction and Architecture. The UMSF website has 14,292 characters. The largest number of unique words on the UMSF website. This means that the text has a higher semantic index. Low semantic index on the PDABA website. The highest "nauseousness" of the text on the website of NTU "Dniprovska Polytechnic", so search engines regard such an article as low-quality. The best content for search engines is the text on the website of the Dnipro State Academy of Construction and Architecture. The content of the website of the University of Customs and Finance is within the norm. "Perfect" website according to the Zipf index of Dniprovska Polytechnic National Technical University. The least naturalness of the text on the page is Dnipro University named after A. Nobel. The text on the UMSF website is considered to be spammed if the quality of the text is 47% according to Zipf's law. The highest site quality index is 440 (Dnieper State Academy of Construction and Architecture), meaning users are satisfied with the site. The lowest level of trust in the portal of the University of Customs and Finance. The results of the calculation of the integral index showed that the Dnipro State Agrarian University has a critical condition in the use of the website, and the satisfactory use of the Internet site has the Dnipro University named after A. Nobel, the state of use of the site of the Dnipro State Academy of Construction and Architecture is assessed as tense. Conclusions and perspectives for further research. To improve the functioning of the website of the University of Customs and Finance, it is necessary to: add an analytics counter to the site, remove duplicates of the main page, improve the site architecture and add internal linking, add a separate postal address for placement on the site, develop a strategy to improve the number and quality of backlinks , improve site security, redirect to the main site address, include keywords in the meta title and meta description, increase the page title tag, add an English version of the site, change the site design. The proposed measures will help to improve the technical characteristics of the site, and, therefore, to occupy better positions in Google's search results. The design change will contribute to better recognition of the university, improvement of the communicative component.

Time-series nighttime imagery for measuring the growth of Urban agglomeration in the Guangdong-Hong Kong-Macao Greater Bay Area

This paper studies the structure and dynamics of urban agglomeration between 1992 and 2018 in one of most developed regions in China – the Guangdong-Hong Kong-Macao Greater Bay Area (GBA) – based on the harmonized night-time light (NTL) data from the Defense Meteorological Satellite Program (DMSP) and Visible Infrared Imaging Radiometer Suite (VIIRS) imagery. We adopted Zipf's law as the rule to control the spatial clustering of adjacent lit pixels. The clustered pixels as patches are concentration of human activities and can then be used for regional urbanization analysis. Unlike conventional spatial units that are rarely changed, such as administrative boundaries, these patches change subtly each year and, more importantly, can help us to examine precisely the urbanization pattern in both development mode and intensity. We investigated the urban growth pattern during the 27-year timespan and conducted the analysis at both region and city levels. Interestingly, the results suggest that Zipf's law of derived patch sizes can hold nearly every year, showcasing the consistent spatial coherency of the urban agglomeration process in the entire region. The correlation between urbanization metrics for each city at three stages (1992–2000, 2000–2010, and 2010–2018) can further lead to deep insights towards the synergetic course of the coordinated and multi-center development.

Autonomic Nervous System Influences on Cardiovascular Self-Organized Criticality.

Cardiovascular self-organized criticality has recently been demonstrated. We studied a model of autonomic nervous system changes to better characterize heart rate variability self-organized criticality. The model included short and long-term autonomic changes associated with body position and physical training, respectively. Twelve professional soccer players took part in a 5-week training session divided into "Warm-up", "Intensive", and "Tapering" periods. A stand test was carried out at the beginning and end of each period. Heart rate variability was recorded beat by beat (Polar Team 2). Bradycardias, defined as successive heart rates with a decreasing value, were counted according to their length in number of heartbeat intervals. We checked whether bradycardias were distributed according to Zipf's law, a feature of self-organized criticality. Zipf's law draws a straight line when the rank of occurrence is plotted against the frequency of occurrence in a log-log graph. Bradycardias were distributed according to Zipf's law, regardless of body position or training. Bradycardias were much longer in the standing position than the supine position and Zipf's law was broken after a delay of four heartbeat intervals. Zipf's law could also be broken in some subjects with curved long bradycardia distributions by training. Zipf's law confirms the self-organized nature of heart rate variability and is strongly linked to autonomic standing adjustment. However, Zipf's law could be broken, the significance of which remains unclear.

Location matters: High-speed railway (HSR) stations in city evolution

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

Heavy tailed but not Zipf: Firm and establishment size in the United States

SummaryHeavy tails play an important role in modern macroeconomics and international economics. Previous work often assumes a Pareto distribution for firm size, typically with a shape parameter approaching Zipf's law. This convenient approximation has dramatic consequences for the importance of large firms in the economy. But we show that a lognormal distribution, or better yet, a convolution of a lognormal and a non‐Zipf Pareto distribution, provides a better description of the US economy, using confidential Census Bureau data. These findings hold even far in the upper tail and suggest that heterogeneous firm models should more systematically explore deviations from Zipf's law.

A Quantitative Approach to the Study on Length-Frequency Relationship of English Patterns

As a master of lexicology and corpus-driven linguistic studies, pattern grammar shares the features of concern on collocation and approximation to natural language, which provides an optimization idea for the extensively used phrase structure grammar and dependency grammar in natural language processing. This research adopts the methods of quantitative linguistics, taking patterns as the research focus to explore the length-frequency relationship of patterns, verify Zipf law and synergic linguistic model in respect of patterns, and analyze the usage characteristics of patterns in different registers. The results have demonstrated that Zipf's law is also applicable to patterns, and the synergic linguistic model shows a preferable goodness of fit on the description of the pattern length-frequency relations. This study provides bidirectional contributions to pattern grammar and the synergic relationship between length and frequency. In addition, it offers a refinement method for the application of patterns in different registers.

The Role of Compliance System in Monitoring and Controlling Public Administration


 
 
 Objective: The objective of this study is to survey the state of the art of Public Administration Compliance in the national scientific domain, analyzing its scope, evolution, and authorship network.
 Problem: While there are several studies and surveys on Compliance, they are primarily aimed at the private administration, with limited attention given to its application in the public sector. As such, this study aims to address the gap in knowledge regarding Compliance in Public Administration and contribute to the understanding of its current state of the art in the national context.
 Method: This study employs a quantitative and descriptive approach, utilizing bibliographic research to collect data. The content analysis technique was applied to selected scientific journals from the SPELL electronic library to analyze the state of the art of Compliance in Brazilian Public Administration. The study also utilizes bibliometric laws to verify the authorship network and identify trends in publication over the years.
 Results: The study identified the Revista de Administração Pública as the journal that most reported on the subject, with a significant growth in publications over the years, particularly in 2019 and 2020. The analyzed articles fitted Lotka's law, but there was no applicability of Bradfort's and Zipf's law. The authorship network had a density of 0.037, which is considered weak. The study also identified the most cited articles on Compliance in the national domain, serving as an introductory guide for researchers in this area.
 Conclusions: This study contributes to the mapping and identification of the state of the art of Compliance in Brazilian Public Administration, highlighting its evolution over the years, the contributions, and the authorship network. The findings serve as a useful guide for researchers in this area and provide insights into the current state of knowledge on the subject in the national context.
 
 

Zipfian Distributions in Child-Directed Speech.

Across languages, word frequency and rank follow a power law relation, forming a distribution known as the Zipfian distribution. There is growing experimental evidence that this well-studied phenomenon may be beneficial for language learning. However, most investigations of word distributions in natural language have focused on adult-to-adult speech: Zipf's law has not been thoroughly evaluated in child-directed speech (CDS) across languages. If Zipfian distributions facilitate learning, they should also be found in CDS. At the same time, several unique properties of CDS may result in a less skewed distribution. Here, we examine the frequency distribution of words in CDS in three studies. We first show that CDS is Zipfian across 15 languages from seven language families. We then show that CDS is Zipfian from early on (six-months) and across development for five languages with sufficient longitudinal data. Finally, we show that the distribution holds across different parts of speech: Nouns, verbs, adjectives and prepositions follow a Zipfian distribution. Together, the results show that the input children hear is skewed in a particular way from early on, providing necessary (but not sufficient) support for the postulated learning advantage of such skew. They highlight the need to study skewed learning environments experimentally.

The Applicability of Zipf's Law in Report Text

The Applicability of Zipf's Law in Report Text

Number theory, borderline dimension and extensive entropy in distributions of ranked data.

The consideration of an existing stochastic approach for the reproduction of ranked data pointed at a formal equivalence between its key mathematical expression and that for trajectories at the tangent bifurcation. This fact led to a nonlinear dynamical approach for rank distributions that shows similarities with universality classes in critical phenomena. The renormalization group (RG) fixed-point map f*(x) for a tangent bifurcation of arbitrary nonlinearity z > 1 has proved to be a powerful tool into which the formalism can be couched. The source distribution P(N) of the stochastic approach can be linked to f*(x) while the size-rank N(k) and frequency-rank F(k') distributions are obtained, respectively, from the map trajectories xt and the sums of its positions. We provide now an extension to Number Theory as we obtain from the trajectories xt of f*(x) the numbers, or asymptotic approximations of them, for the Factorial, Natural, Prime and Fibonacci sets. A measure of the advance of these numbers towards infinity is given by sums of positions that represent their reciprocals. We specify rank distribution universality classes, already associated with real data, to these number sets. We find that the convergence of the series of number reciprocals occurs first at nonlinearity z = 2, that which corresponds to the classical Zipf law, and link this transition edge to the action of the attractor when it first reduces the fractal dimension of trajectory positions to zero. Furthermore, the search of logarithmic corrections common to borderline dimensions provides a link to the Prime numbers set. Finally, we find corroborating evidence of these logarithmic corrections from the analysis of large data sets for ranked earthquake magnitudes. The formalism links all types of ranked distributions to a generalized extensive entropy.

A multi-level exploration of the relationship between temperature and species diversity: Two cases of marine phytoplankton.

The relationship between temperature (T) and diversity is one of the most important issues in ecology. It provides a key direction not only for exploring the determinants of diversity's patterns, but also for understanding diversity's responses to climate change. Previous studies suggested that T-diversity relationships could be positive, negative, or unimodal. Although these studies accumulated many informative achievements, they might be unsatisfied due to (1) investigating inadequate range of T, (2) selecting incomplete diversity metrics, and (3) making insufficiently detailed analysis of correlation. In this study, species diversity is estimated by four most commonly used diversity metrics and three parameters of species abundance distribution (SAD), and two global datasets of marine phytoplankton (covering a wider range of T) are used to evaluate the T-diversity relationships according to a piecewise model. Results show that all aspects of diversity (except evenness) have the similar relationship with T in the range of lower T, noting that diversity significantly increases as T increases. However, in the range of higher T, diversity may significantly decrease or nearly constant, which indicates that their relationships may be the unimodal or asymptotic. The asymptotic relationship found by this study is assumed that increasing diversity with T will gradually approach the Zipf's law (1:1/2:1/3…). If such assumption can be verified by future investigations, the intrinsic mechanism of the asymptotic relationship is likely to be crucial in understanding the T-diversity relationships.