Zipf's Law Research Articles

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.

Stochastic Time‐Series Analyses Highlight the Day‐To‐Day Dynamics of Lexical Frequencies

Standard models in quantitative linguistics assume that word usage follows a fixed frequency distribution, often Zipf's law or a close relative. This view, however, does not capture the near daily variations in topics of conversation, nor the short-term dynamics of language change. In order to understand the dynamics of human language use, we present a corpus of daily word frequency variation scraped from online news sources every 20 min for more than 2 years. We construct a simple time-varying model with a latent state, which is observed via word frequency counts. We use Bayesian techniques to infer the parameters of this model for 20,000 words, allowing us to convert complex word-frequency trajectories into low-dimensional parameters in word usage. By analyzing the inferred parameters of this model, we quantify the relative mobility and drift of words on a day-to-day basis, while accounting for sampling error. We quantify this variation and show evidence against "rich-get-richer" models of word use, which have been previously hypothesized to explain statistical patterns in language.

Analysis of Landscape Characteristics and Influencing Factors of Residential Areas on the Qinghai-Tibet Plateau: A Case Study of Tibet, China.

The Qinghai-Tibet Plateau is the largest ecological barrier and one of the most vulnerable areas of the ecological environmental system. However, the increasing frequency of human activities in the Qinghai-Tibet Plateau has led to strong interference. Residential areas are the main places in which human activities are carried out and, as such, can effectively reflect the intensity of activities. Based on this, this research takes the Tibet Autonomous Region as the study area and analyzes the distribution characteristics of Tibetan residential areas using Zipf's law and various landscape indices, as well as discussing the influences of altitude, hydrology, ecological environment, and location on residential area distribution. The obtained results indicate the following: (1) The residential areas in Tibet basically conform to the rank-size principle. The residential areas in central and northwest Tibet are concentrated in size distribution, and the relatively large residential areas are prominent, while the residential areas in the eastern Hengduan mountain region are relatively balanced in size distribution. (2) The landscape index results demonstrate that the counties with an unbalanced distribution of residential areas are mainly concentrated in the northwest of Tibet, while the residential areas in the counties and regions where the administrative stations of each prefecture-level city (or region) are located tend to present a polarization phenomenon, with large patches. The area distribution of residential areas showed a "medium-high-low" pattern from southeast to northwest. The residential areas in eastern Tibet have a high degree of fragmentation and a low degree of aggregation, while the residential areas in northwest Tibet have a low degree of fragmentation and a relatively high degree of aggregation. (3) The residential areas in Tibet are most concentrated in the altitude range of 3000-5000 m above sea level and their water affinity and road-affinity are strong, with the distribution of residential areas within 500 m of roads and water networks accounting for more than one-quarter. The vegetation coverage in the residential areas is low, inconsistent with the surface vegetation coverage rate over the whole of Tibet.

Constructing multi-level urban clusters based on population distributions and interactions

A city (or an urban cluster) is not an isolated spatial unit, but a combination of areas with closely linked socio-economic activities. However, so far, we lack a consistent and quantitative approach to define multi-level urban clusters through these socio-economic connections. Here, using granular population distribution and flow data from China, we propose a bottom-up aggregation approach to quantify urban clusters at multiple spatial scales. We reveal six ‘phases’ (i.e., levels) in the population density-flow diagram, each of which corresponds to a spatial configuration of urban clusters from large to small. Besides, our results show that Zipf's law appears only after the fifth level, confirming the spatially dependent nature of urban laws. Our approach does not need pre-defined administrative boundaries and can be applied effectively on a global scale.

Variable expression of linguistic laws in ape gesture: a case study from chimpanzee sexual solicitation.

Two language laws have been identified as consistent patterns shaping animal behaviour, both acting on the organizational level of communicative systems. Zipf's law of brevity describes a negative relationship between behavioural length and frequency. Menzerath's law defines a negative correlation between the number of behaviours in a sequence and average length of the behaviour composing it. Both laws have been linked with the information-theoretic principle of compression, which tends to minimize code length. We investigated their presence in a case study of male chimpanzee sexual solicitation gesture. We failed to find evidence supporting Zipf's law of brevity, but solicitation gestures followed Menzerath's law: longer sequences had shorter average gesture duration. Our results extend previous findings suggesting gesturing may be limited by individual energetic constraints. However, such patterns may only emerge in sufficiently large datasets. Chimpanzee gestural repertoires do not appear to manifest a consistent principle of compression previously described in many other close-range systems of communication. Importantly, the same signallers and signals were previously shown to adhere to these laws in subsets of the repertoire when used in play; highlighting that, in addition to selection on the signal repertoire, ape gestural expression appears shaped by factors in the immediate socio-ecological context.

Les lois linguistiques de la brièveté : conformité chez le lémurien chanteur Indri indri

Vocal and gestural sequences of many primate species conform to two principles of compression: the compensation between the length of a construct and that of its constituents (Menzerath-Altmann law) and an inverse relationship between signal length and occurrence (Zipf's law of abbreviation). Although Zipf's law is considered a universal in animal communicative systems, evidence for the adherence of non-human primate vocal behavior to linguistic laws is debated, and information on strepsirrhines is absent. We investigated the vocal behavior of the only singing lemur (Indri indri) to test whether the song of this species shows indication for compression. Because roars have a chaotic structure that prevents the recognition of each individual emission, and long notes are mainly emitted by males, we relied on the core part of the song (i.e., descending phrases, composed of two to six units). Our results indicate that songs conform to both laws. Indeed, shorter phrases are more likely included in the songs, in conformity to Zipf’s law, and unit length decreases with increasing phrase size, in line with Menzerath-Altmann law. Furthermore, despite a sexual dimorphism of both units and phrases duration, these laws characterize the vocal sequences of both sexes. In conclusion, we provide the first evidence for a compromise between signal duration and occurrence in the vocal system of a strepsirrhine species, suggesting that, in primates, selective pressures for compression are more ancestral than previously assumed.

City Size Distribution Analyses Based on the Concept of Entropy Competition

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.

Quantitative methods to determine the student workload. I. Empirical study based on digital platforms.

We present a quantitative study of an online course developed during COVID19 sanitary emergency in Chile. We reconstruct the teaching-learning process considering the activity logs on digital platforms in order to answer the question of How do our students study? The results from the analysis evidence the complex adaptive character of the academic environment, which exhibits regularities similar to those found in financial markets (e.g., distributions of the daily time devoted to learning activities follow patterns like Pareto's or Zipf's law). Our empirical results illustrate (i) the relevance of economic notions in the understanding of the teaching-learning processes and (ii) the reliability of quantitative methods based on digital platforms to conduct experimental studies in this framework. We introduce in the present work a series of indicators to characterize the performance of professors, students' follow-up of the course, and their learning progress by crossing information with the results of assessments. In this context, the learning rate appears as a key statistical descriptor for the allocation of the student workload.

Compression principle and Zipf's Law of brevity in infochemical communication.

Compression has been presented as a general principle of animal communication. Zipf's Law of brevity is a manifestation of this postulate and can be generalized as the tendency of more frequent communicative elements to be shorter. Previous works supported this claim, showing evidence of Zipf's Law of brevity in animal acoustical communication and human language. However, a significant part of the communicative effort in biological systems is carried out in other transmission channels, such as those based on infochemicals. To fill this gap, we seek, for the first time, evidence of this principle in infochemical communication by analysing the statistical tendency of more frequent infochemicals to be chemically shorter and lighter. We analyse data from the largest and most comprehensive open-access infochemical database known as Pherobase, recovering Zipf's Law of brevity in interspecific communication (allelochemicals) but not in intraspecific communication (pheromones). Moreover, these results are robust even when addressing different magnitudes of study or mathematical approaches. Therefore, different dynamics from the compression principle would dominate intraspecific chemical communication, defying the universality of Zipf's Law of brevity. To conclude, we discuss the exception found for pheromones in the light of other potential communicative paradigms such as pressures on successful communication or the Handicap principle.

Cross-Domain Empirical Risk Minimization for Unbiased Long-Tailed Classification

We address the overlooked unbiasedness in existing long-tailed classification methods: we find that their overall improvement is mostly attributed to the biased preference of "tail" over "head", as the test distribution is assumed to be balanced; however, when the test is as imbalanced as the long-tailed training data---let the test respect Zipf's law of nature---the "tail" bias is no longer beneficial overall because it hurts the "head" majorities. In this paper, we propose Cross-Domain Empirical Risk Minimization (xERM) for training an unbiased test-agnostic model to achieve strong performances on both test distributions, which empirically demonstrates that xERM fundamentally improves the classification by learning better feature representation rather than the "head vs. tail" game. Based on causality, we further theoretically explain why xERM achieves unbiasedness: the bias caused by the domain selection is removed by adjusting the empirical risks on the imbalanced domain and the balanced but unseen domain.

Perbandingan Kata Kunci Abstrak Skripsi dengan Subjek Menggunakan Dalil ZIPF pada Skripsi Prodi Teknologi Informasi Politeknik Caltex Riau Tahun 2018

This research aims to find out the comparison of keywords in thesis abstracts with subjects using zipf law in the thesis of students of IT program of Politeknik Caltex Riau 2018. The research method used in this study is a quantitative method with a comparative approach. Population and sample in this study is the entire thesis of 82 students in 2018. Based on data from the results of subjects indexing with zipf law and keywords in thesis abstracts have a relatively high level of relevance compared to relevant and irrelevant marginal. The relevant level (the resulting subject is entirely and precisely the same) of the comparison result is 79% or 65 theses, for marginal relevant (the resulting subject has similarities) of 17% or 14 theses, and for irrelevant (the resulting subject has absolutely no similarity) by 4% or three theses.

Urban population distribution in China: Evidence from internet population

Based on mobile internet user data, we construct an “Internet population” measure and reexamine spatial population distribution in China. The location based service (LBS) data of mobile internet uses is able to capture the accurate location of users' residence and solve the underestimation problem of missing migrants. We have three main findings. First, contrary to previous studies based on traditional population statistics, city size distribution of Internet population fits well into Zipf's law with a R2 of 90.7%. Second, the Internet population indicator is superior to traditional population statistics in explaining inelastic household consumption such as water consumption, electricity consumption, and garbage disposal. It suggests that the “Internet population” is a better proxy of actual city population. Third, the traditional population statistics systematically overestimate population in small cities and underestimate population in large cities. It indicates that the public resource distortions will continue to exist or even worsen off in China if the allocation process relies greatly on traditional population statistics. Although no measures are perfect, our new population measure provides important incremental information for future discussion.

Humanization of nursing care for people with tuberculosis: Bibliometric Study

Objective: To analyze the scientific production on tuberculosis and the humanization of nursingcare. Methods: Bibliometric, descriptive quantitative study, carried out in the Web Of Science databasewith a time frame from January 2010 to July 2021. The laws of lotka and zipf were applied and the analysisoccurred with the aid of vosviewer software. Results: We recovered 309 scientific productions ontuberculosis and the humanization of nursing care, the majority published in 2019, with the predominanceof the English language. According to lotka law among the 1,381 authors who publish on the subject, 276(20%) are responsible for 30.3% of productivity, but only eight have a total strength of co-authorship bond.Through zipf's law, 761 keywords with a predominance of "tuberculosis" and "nursing" were found. TheCountries united states of America (USA) (25%) and Brazil (22%) have the highest number of publicationson the theme addressed here. Conclusion: There is a tendency to increase in publications on tuberculosis,however, little is studied about humanization aimed at the treatment of people who experience thisdisease. More evidence should be produced in this context because the end of tuberculosis depends on theimplementation of what is contained in the global strategy plan, regarding the intensification pillar ofresearch and innovation. Such actions will contribute to the execution of more humanized practices of thecare of the nursing professional, reflecting on the success of the treatment of people suffering fromtuberculosis.

Languages are efficient, but for whom?

Human languages evolve to make communication more efficient. But efficiency creates trade-offs: what is efficient for speakers is not always efficient for comprehenders. How do languages balance these competing pressures? We focus on Zipf's meaning-frequency law, the observation that frequent wordforms have more meanings. On the one hand, this law could reflect a speaker-oriented pressure to reuse frequent wordforms. Yet human languages still maintain thousands of distinct wordforms, suggesting a countervailing, comprehender-oriented pressure. What balance of these pressures produces Zipf's meaning-frequency law? Using a neutral baseline, we find that frequent wordforms in real lexica have fewer homophones than predicted by their phonotactic structure: real lexica favor a comprehender-oriented pressure to reduce the cost of frequent disambiguation. These results help clarify the evolutionary drive for efficiency: human languages are subject to competing pressures for efficient communication, the relative magnitudes of which reveal how individual-level cognitive constraints shape languages over time.

Literature Review on Control Charts for Autocorrelated Processes

This research aims to present a literature review (LR) on control charts for autocorrelated processes, intending to contribute to the scientific knowledge of the process management area. The article was constructed having a research question defined ex-ante, elaborated based on the literature, where a research protocol adapted from Tranfield, Denyer, and Smart (2003) was systematized according to the methodological rigor demanded in the literature review, which resulted in the composition of the research corpus. The research corpus was evaluated in detail using the bibliometric packages HistCite, VOSviewer, package R and Iramuteq. It was evaluated the validity of the 3 bibliometric laws were verified: Lotka's Law, Bradford's Law, and Zipf's Law based on the authors’ citation and co-citation techniques. This study is considered as relevant and original since it is the first literature review on control charts for autocorrelated processes. The results confirmed the 3 classical bibliometric laws for the researched corpus. As a practical implication, this review provides support for quality management scholars to unlock potential research gaps. The main limitation of the work refers to the composition of the textual corpus, given that databases of national journals were not consulted due to the difficulty in terms of compatibility of the software used in this research.

Caching scheme for information‐centric networks with balanced content distribution

SummaryInformation‐centric network (ICN) emphasizes on content retrieval without much bothering about the location of its actual producer. This novel networking paradigm makes content retrieval faster and less expensive by shifting data provisioning into content holder rather than content owner. Caching is the feature of ICN that makes content serving possible from any intermediate device. An efficient caching is one of the primary requirements for effective deployment of ICN. In this paper, a caching approach with balanced content distribution among network devices is proposed. The selection of contents to be cached is determined through universal and computed using Zipf's law. The dynamic change in popularity of contents is also considered to take make caching decisions. For balancing the cached content across the network, every router keeps track of its neighbor's cache status. Three parameters, the proportionate distance of the router from the client (pd), the router congestion (rc), and the cache status (cs), are contemplated to select a router for caching contents. The new caching approach is evaluated in the simulated environment using ndnSIM‐2.0. Three state‐of‐the‐art approaches, Leave Copy Everywhere (LCE), centrality measures‐based algorithm (CMBA), and a probability‐based caching (probCache), are considered for comparison. The proposed method of caching shows the better performance compared to the other three protocols used in the comparison.

Cultural Evolution of Precise and Agreed-Upon Semantic Conventions in a Multiplayer Gaming App.

The amount of information conveyed by linguistic conventions depends on their precision, yet the codes that humans and other animals use to communicate are quite ambiguous: they may map several vague meanings to the same symbol. How does semantic precision evolve, and what are the constraints that limit it? We address this question using a multiplayer gaming app, where individuals communicate with one another in a scaled-up referential game. Here, the goal is for a sender to use black and white symbols to communicate colors. We expected that the players' mappings between symbols and colors would grow more specific over time, through a selection process whereby precise mappings are preferentially copied. We found that players become increasingly more precise in their use of symbols over the course of their interactions. This trend did not, however, result from selective copying of precise mappings. We explore the implications of this result for the study of lexical ambiguity, Zipf's Law of Meaning, and disagreements over semantic conventions.

What do analyses of city size distributions have in common?

In this article, I conduct a textual and contextual meta-analysis of the empirical literature on Zipf's law for cities. Combining citation network analysis and bibliometrics, this meta-analysis explores the link between publication bias and reporting bias in the multidisciplinary field of quantitative urban studies. To complement a set of metadata already available, I collect the full-texts and reference lists of 66 scientific articles published in English and construct similarity networks of the terms they use as well as of the references and disciplines they cite. I use these networks as explanatory variables in a model of the similarity network of the distribution of Zipf estimates reported in the 66 articles. I find that the proximity in words frequently used by authors correlates positively with their tendency to report similar values and dispersion of Zipf estimates. The reference framework of articles also plays a role, as articles which cite similar references tend to report similar average values of Zipf estimates. As a complement to previous meta-analyses, the present approach sheds light on the scientific text and context mobilized to report on city size distributions. It allows to identified gaps in the corpus and potentially overlooked articles. It confirms the relationship between publication and reporting biases.

BEmoC: A Corpus for Identifying Emotion in Bengali Texts.

Emotion classification in text has growing interest among NLP experts due to the enormous availability of people’s emotions and its emergence on various Web 2.0 applications/services. Emotion classification in the Bengali texts is also gradually being considered as an important task for sports, e-commerce, entertainments, and security applications. However, It is a very critical task to develop an automatic emotion classification system for low-resource languages such as, Bengali. Scarcity of resources and deficiency of benchmark corpora make the task more complicated. Thus, the development of a benchmark corpus is the prerequisite to develop an emotion classifier for Bengali texts. This paper describes the development of an emotional corpus (hereafter called ‘BEmoC’) for classifying six emotions in Bengali texts. The corpus development process consists of four key steps: data crawling, pre-processing, labelling, and verification. A total of 7000 texts are labelled into six basic emotion categories such as anger, fear, surprise, sadness, joy, and disgust, respectively. Dataset evaluation with 0.969 Cohen’s κ score indicates the close agreement between the corpus annotators and the expert. The analysis of evaluation also represents that the distribution of emotion words obeys Zipf’s law. Moreover, the results of BEmoC analysis shown in terms of coding reliability, emotion density, and most frequent emotion words, respectively.

Trump's COVID-19 tweets and Dr. Fauci's emails.

The paper features an analysis of former President Trump’s early tweets on COVID-19 in the context of Dr. Fauci’s recently revealed email trove. The tweets are analysed using various data mining techniques, including sentiment analysis. These techniques facilitate exploration of content and sentiments within the texts, and their potential implications for the national and international reaction to COVID-19. The data set or corpus includes 159 tweets on COVID-19 that are sourced from the Trump Twitter Archive, running from 24 January 2020 to 2 April 2020. In addition we use Zipf and Mandelbrot’s power law to calibrate the extent to which they differ from normal language patterns. A context for the emails is provided by the recently revealed email trove of Dr. Fauci, obtained by Buzzfeed on 1 June 2021 obtained under the Freedom of Information Act.