Zipf's Law Research Articles

Information consumption and firm size.

Social and biological collectives exchange information through internal networks to function. Less studied is the quantity and variety of information transmitted. We characterize the information flow into organizations, primarily business firms. We measure online reading using a large dataset of articles accessed by employees across millions of firms. We measure and relate quantitatively three aspects: reading volume, variety and firm size. We compare volume with size, showing that firm sizes grow sublinearly with reading volume. This is like an economy of scale in information consumption that exaggerates the classic Zipf's law inequality for firm economics. We connect variety and volume to show that reading variety is limited. Firms above a threshold size read repetitively, consistent with the onset of a coordination problem between teams of employees in a simple model. Finally, we relate reading variety to size. The relationship is consistent with large firms that accumulate interests as they grow. We argue that this reflects structural constraints. Taking the scaling relations as a baseline, we show that excess reading is strongly correlated with returns and valuations. The results indicate how information consumption reflects internal structure, beyond individual employees, as is likewise important for collective information processing in other systems.

Improving Word Embedding on Malayalam Corpus

Abstract: NLP is natural language processing or neuro linguis-tic programming.Natural languages like malayalam are highly inflectional and agglutinative in nature.This is problematic whendealing with nlp based malayalam applications.So that inorder toimprove performance of malayalam nlp based applications, wordembedding improvement on malayalam corpus is needed.The improvement is based on converting the words contained inthe malayalam corpus into a standardised means removingall inflectional parts in the words in the existing malayalamcorpus ie taking root words only.All that needed is a stemmer.Inthis project i have used a malayalam morphological analyserfor taking root words of all words in the existing malayalam corpus.The advanatge of removing inflectional parts from allwords is that we can reduce the sparsity in the existing malayalam corpus.Also there will be a high hike in frequency of wordsin the resulting corpus,then the space and time complexity of wordembedding representation of the existing corpus willdecreases.According to zipfs law by increasing frequency ofwords performance of neural word embedding will increases. Zipfs Law is a discrete probability distribution that tells you the probability of encountering a word in a given corpus.By applying zipfs law am proposing there will be improvement on malyalam wordembedding.Here using fasttext, word embeddingsare performed and capture dense word vector representation ofthe malayalam corpus with dimensionality reduction from thesparse word co-occurence matrix.The improvement is mainly used for wordnet,analogy,ontology based malayalam applications.Index Terms—Morphological Analyzer,Zipfs law, Preprocessing, Testing, Training

Mapping The Growth of ESG Research: A Bibliometric Analysis Using Bradford's, Lotka's, and Zipf's Laws

Objective: The objective of this study is to investigate the growth and development of research on Environmental, Social, and Governance (ESG) factors using bibliometric analysis. The aim is to understand the publication trends in ESG research and identify influential authors, key themes, and opportunities for future studies. Theoretical Framework: The research is grounded in key bibliometric laws such as Bradford's law (journal productivity), Lotka's law (scientific productivity of authors), and Zipf's law (word frequency analysis). These laws form the basis of the study and provide a solid framework for understanding the evolution of ESG research. Method: This study adopts a bibliometric analysis approach, using data from the Web of Science and Scopus databases. A total of 699 articles from 345 journals and 1,574 authors were analyzed. Techniques like citation analysis, co-citation analysis, bibliographic coupling, and network analysis were employed to assess publication patterns and collaborations. Data was processed using R software and Bibliometrix. Results and Discussion: The results reveal a significant increase in ESG-related publications, particularly after 2013, with annual growth of 39.97%. The study identifies influential authors, such as Hebbe and Buallay, and explores the themes of sustainability, corporate social responsibility, and governance. In the discussion, the results are contextualized within the broader ESG framework, highlighting the role of ESG in corporate behavior and investment strategies. Research Implications: The study provides insights into how ESG research can inform policy-making and corporate decision-making. The findings highlight the importance of ESG factors in sustainable development and suggest future research avenues in areas like digital transformation, entrepreneurship, and innovation. Originality/Value: This study contributes to the literature by offering a comprehensive overview of ESG research, utilizing innovative bibliometric techniques to track its evolution. The originality lies in the use of multiple bibliometric laws to analyze ESG trends, making it valuable for researchers and practitioners looking to understand current and future directions in ESG.

Read Before You Cite!

We report a method for estimating what percentage of people who cited a paper had actually read it. The method is based on a stochastic modeling of the citation process that explains empirical studies of misprint distributions in citations (which we show follows a Zipf law). Our estimate is that only about 20% of citers read the original.

In-depth analysis of music structure as a text network

Music, enchanting and poetic, permeates every corner of human civilization. Although music is not unfamiliar to people, our understanding of its essence remains limited, and there is still no universally accepted scientific description. This is primarily due to music being regarded as a product of reason and emotion, making it difficult to define. This article treats musical texts as a complex system. This view echoes linguist John Rupert Firth's insight that understanding a word involves defining it through its surrounding relationships. To construct the network we first build a linear regression model with threshold values to assign conditions to the links among note, time, and volume. Then a clustering coefficient representing regional characteristics is utilized to define the word. Finally, the statistical distribution of the text is strictly required to adhere to the grammatical properties of statistical linguistics, such as Zipf's law, to adjust the weights of the linear regression model and achieve optimal results. These processes enable us to comprehend the structural differences in music across different periods with scientific rigor. Relying on the advantages of structuralism, we concentrate on the relationships and order between the physical elements of music, rather than getting entangled in the blurred boundaries of science and philosophy. Aside from serving as a bridge connecting music to natural language processing and knowledge graphs, the technical methods developed in this work offer a more intuitive approach to elucidate the relationships among elements of a complex network. Published by the American Physical Society 2024

Trends in Multicomponent Training Research in the Aged Population: A Bibliometric Analysis.

The proportion of aged populations is increasing worldwide. Exercise has a palliating effect on some adverse implications of aging. Multicomponent training (MCT) is a recommended form of exercise for the aged population. The aims of this research were to (1) study the number of publications regarding MCT in the aged population following an exponential growth rate; (2) identify the journals, authors, and countries that stand out the most in this area; and (3) describe the most common themes and used keywords in this field. The analysis was performed through the traditional laws of bibliometrics, including, Price's, Lotka's, Bradford's, and Zipf's law. All documents published in journals indexed in the Web of Science (WoS) Core Collection from 2001 to November 2023 that met the inclusion criteria were included. The 485 documents included in this review revealed that the number of annual publications experienced an exponential growth phase, 15 journals with six or more publications formed the core journals on this topic, and the author Mikel Izquierdo and his collaborative network topped the lists of prominent and prolific co-authors. Spain was the leading country in number of publications. Various thematic lines and keywords regarding strength, sarcopenia, quality of life, falls, balance, dual-task exercise, and cognitive and physical functioning were identified. In conclusion, this work confirmed that research on this topic is going through an exponential growth phase and provided detailed information about the journals, authors, and countries involved in the subject, as well as the keywords most frequently used in the subject matter.

New cyclic Jensen type bounds via weighted HH inequalities and Montgomery identity with application to information inequalities

In this article a new method is introduced to give weighted estimations of the differences of cyclic refinements of Jensen functionals. We utilize weighted form of Hermite–Hadamard (HH) inequality along with the approximations of Montgomery two- and one-point formulae with Peano type kernel along with the consequences of the n-times differentiable convex functions. As a result, we present new upper and lower bounds that are also verified with concrete examples to show the correctness of the bounds obtained for special cases. As a result, we provide estimations in terms of cyclic power means. We also improvise our results to give new uniform estimations for useful distance functions in information theory. Finally, some estimations of Zipf and Hybrid Zipf law are provided as well.

Social security and pension trends. A bibliometric study

This article presents a bibliometric analysis of trends in pension studies in the field of social security, using Zipf's law, Lotka's law and the h-index. The research focused on identifying productivity and citation patterns and determining the main research themes and trends. Through term frequency analysis, it was observed that the words "pensions," "social security," and "sustainability" are predominant, confirming Zipf's law. Lotka's law was validated by finding that a small group of authors is responsible for most of the publications, indicating a concentration in scientific production. The h-index calculation showed that the most prolific authors are also the most cited, reflecting their influence in the field. Thematic trends reveal a shift from implementing pension systems towards sustainability and reforms for regime changes. Furthermore, the geographical distribution highlighted a high concentration in developed countries with increasing international collaborations. These findings provide a comprehensive overview of research dynamics and offer recommendations for future research and policies in social security

Human Versus Machine Intelligence: Assessing Natural Language Generation Models Through Complex Systems Theory.

The introduction of Transformer architectures - with the self-attention mechanism - in automatic Natural Language Generation (NLG) is a breakthrough in solving general task-oriented problems, such as the simple production of long text excerpts that resemble ones written by humans. While the performance of GPT-X architectures is there for all to see, many efforts are underway to penetrate the secrets of these black-boxes in terms of intelligent information processing whose output statistical distributions resemble that of natural language. In this work, through the complexity science framework, a comparative study of the stochastic processes underlying the texts produced by the English version of GPT-2 with respect to texts produced by human beings, notably novels in English and programming codes, is offered. The investigation, of a methodological nature, consists first of all of an analysis phase in which the Multifractal Detrended Fluctuation Analysis and the Recurrence Quantification Analysis - together with Zipf's law and approximate entropy - are adopted to characterize long-term correlations, regularities and recurrences in human and machine-produced texts. Results show several peculiarities and trends in terms of long-range correlations and recurrences in the last case. The synthesis phase, on the other hand, uses the complexity measures to build synthetic text descriptors - hence a suitable text embedding - which serve to constitute the features for feeding a machine learning system designed to operate feature selection through an evolutionary technique. Using multivariate analysis, it is then shown the grouping tendency of the three analyzed text types, allowing to place GTP-2 texts in between natural language texts and computer codes. Similarly, the classification task demonstrates that, given the high accuracy obtained in the automatic discrimination of text classes, the proposed set of complexity measures is highly informative. These interesting results allow us to add another piece to the theoretical understanding of the surprising results obtained by NLG systems based on deep learning and let us to improve the design of new informetrics or text mining systems for text classification, fake news detection, or even plagiarism detection.

Ethical leadership and employee behavior. Scientometric analysis in scientific production

This scientometric study seeks to analyze scientific articles on ethical business leadership from a social-scientific perspective, considering its relationship or influence with the different behaviors of workers. Using the VOSWiever program, an analysis is carried out on 1000 articles published in Web of Science (WoS) journals from 1987 to May 2023. The results show the five main contributing countries, these being: China, the United States, England, Canada, and Pakistan and the year 2022 will be the year of greatest scientific production. There are no records of studies in Latin America; however, scientific production is found in academic sites in Venezuela, Chile, Ecuador, and Argentina. Using the Laws of Lotka, Price, and the Bradford model, the most prolific authors and the productivity of countries and magazines are discovered. Using Zipf's law and the Hirsch index, the most frequent keywords and the best-known articles are revealed. The article has sought to contribute to the eighth goal of sustainable development (SDG), that is, with the study of ethical leaders who model behaviors that favor economic growth, work well-being, and sustainability of their organizations. For future research, it is suggested that specific effects produced by this leadership as a mediator related to job performance in Latin companies be examined.

Password Strength Evaluation via Zipf's Law and Password Entropy

Password Strength Evaluation via Zipf's Law and Password Entropy

Purported Self-Organized Criticality of the Cardiovascular Function: Methodological Considerations for Zipf's Law Analysis.

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.

Defining urban boundaries through DBSCAN and Shannon's entropy: The case of the Mexican National Urban System

A novel method is proposed to define cities' boundaries within a given national urban system. Point Volunteered Geographic Information, such as the OpenStreetMap road network nodes, together with national geospatial information, like economic units, are recursively clustered using DBSCAN at different distance thresholds; clusters smaller than a threshold reflecting the rural settlements pattern are filtered, and then Shannon's entropy for the entire system is calculated. The system of percolated nodes obtained when this entropy reaches its maximum is compared against the current definition of what is officially urban. It is found to be very similar to the actual urban-nonurban classification, and also to have a very high correspondence with the current classification of the Mexican National Urban System (SUN). An additional finding is that the percolated system at the maximum entropy value has a very high correspondence with Zipf's law, while the current Mexican SUN does not.

A long-term, regional-level analysis of Zipf's and Gibrat's laws in the United States

We test the validity of Zipf's and Gibrat's laws for city size distributions at the regional level from 1900 to 2010 by considering US states. Zipf's law is satisfied for a majority of states, but for the United States as a whole it only held during the first half of the twentieth century. The null hypothesis of a power law is not rejected at the national level or for most states (the maximum number of rejections in one year is 13 states out of 48). There is evidence supporting a weak version of Gibrat's law in the long-term; mean growth is independent of initial population for most city sizes over the entire United States and in 27 states, while the variance of growth is size-dependent.

Racing to Zipf's law: Race and metropolitan population size 1910–2020

AbstractScholarship 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.

Relevansi Pemeringkatan Kata Kunci Dengan Menggunakan Dalil Zipf Pada Abstrak Skripsi Hukum Perdata Fakultas Hukum Universitas Sriwijaya Tahun 2018-2022

This study aims to see the relevance of the results of subject indexing through the zipf argument with thesis keywords in several thesis abstracts for the Civil Law Department, Faculty of Law, Sriwijaya University 2018-2022 and also to find out the topic of the thesis. This research uses a quantitative descriptive approach with a bibliometric measurement method using the zipf theorem. The object is the undergraduate student thesis of the Department of Civil Law, Faculty of Law, University of Sriwijaya from 2018 to 2022 as many as 60 thesis abstracts. The research sample is the entire research object. The results of the research apply the use of the zipf argument as a method for determining keywords in the thesis abstracts of the civil law study program, Faculty of Law, Sriwijaya University, 2018-2022. Keywords as a result of zipf ranking are then compared with the author's keywords to obtain the level of relevance of these keywords. From the calculation of the relevance, it can be said that indexing through Zipf's law shows a high level of marginal relevance when equated with the relevant level and irrelevant index results. The proof is through estimatio

Multistability in neural systems with random cross-connections.

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.

Relationship between the principle of least effort and the average cost of information in a zipfian context

From an informetrics perspective, we discuss the relationship between the Least Effort Principle and information cost minimisation, and discuss the implications for Zipf's law. We propose a mathematical proof of a theorem demonstrating that if one minimises the average cost per unit of information, the Least Effort Principle (LEP) will be verified regardless of the effort function chosen. We then show that Zipf's law can be demonstrated on the basis of the two models studied, namely Average Cost per Unit of Information and the Least Effort Principle (LEP).

Scale in Language.

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.

Determinants of IPO´s underpricing: A systematic review

In an Initial Public Offering (IPO) process, it is expected that there will be different share price valuations by professionals, due to market flaws, meaning information asymmetry among investors. For stockholders – who previously formed the corporate structure of the company – an IPO opens up possibilities of immediate gains, as they can purchase at prices lower than established by the structuring agent. On the other hand, underpricing is an indirect cost for the company, as, part of the offer is not collected. Identifying these determinants thus becomes relevant, as this information may be essential for defining the most appropriate share price. Consequently, the purpose of this study is to perform a bibliometric analysis (including the Zipf, Bradford and Lotka Laws), followed by a systematic review of papers analyzing this theme. This analysis uses the VOSviewer and Biblioshiny software packages. As a result, informational asymmetry is confirmed as the main theory clarifying the underpricing event. Noteworthy among the determinants are the reputations of the underwriter and share issuer, the presence of corporate governance mechanisms, and the offering size. Among the knowledge gaps opening up opportunities for further studies on this topic are: investigation of the phenomenon in companies in Latin America or comparatively in emerging countries worldwide, use of a behavioral approach to analyze investor motivations, and the presence of institutional investors as IPO inducers.