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

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]

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 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]

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]

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]

Summary: Heavy 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. [ABSTRACT FROM AUTHOR]

Research 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. [ABSTRACT FROM AUTHOR]

Piantadosi, Tily, and Gibson analyzed a large‐scale web‐scraping corpus (the Google 1T dataset) and reported that word length is independently predicted from average information content (surprisal) calculated by a 2‐ to 4‐gram model (hereafter, longer‐span surprisal) across 11 Indo‐European languages, namely, Czech, Dutch, English, French, German, Italian, Polish, Spanish, Portuguese, Romanian, and Swedish. However, a recent article by Meylan and Griffiths suggested the importance of preprocessing for studies with large‐scale corpora and reanalyzed the same databases. After their preprocessing, the results in Piantadosi et al. were not replicated in Czech, Romanian, and Swedish. Additionally, a German‐specific study by Koplenig, Kupietz, and Wolfer showed that the strict analysis did not replicate the result in Piantadosi et al. for that language with the preprocessing suggested by Meylan and Griffiths in a large‐scale but less noisy database. These three studies provide evidence from 11 Indo‐European languages and one Afro‐Asiatic language, Hebrew, as relevant in this debate. However, we do not have evidence from other linguistic groups. This study provides evidence about Japanese based on a strict preprocessing of Google's web‐scraping database. The results show that Japanese word length can be predicted independently by 2‐ to 4‐gram surprisal. [ABSTRACT FROM AUTHOR]

Cross‐species communication, where signals are sent by one species and perceived by others, is one of the most intriguing types of communication that functionally links different species to form complex ecological networks. Global change and human activity can affect communication by increasing fluctuations in species composition and phenology, altering signal profiles and intensity, and introducing noise. So far, most studies on cross‐species communication have focused on a few specific species isolated from ecological communities. Scaling up investigations of cross‐species communication to the community level is currently hampered by a lack of conceptual and practical methodologies. Here, we propose an interdisciplinary framework based on information theory to investigate mechanisms shaping cross‐species communication at the community level. We use plants and insects, the cornerstones of most ecosystems, as a showcase and focus on chemical communication as the key communication channel. We first introduce some basic concepts of information theory, then we illustrate information patterns in plant–insect chemical communication, followed by a further exploration of how to integrate information theory into ecological and evolutionary processes to form testable mechanistic hypotheses. We conclude by highlighting the importance of community‐level information as a means to better understand the maintenance and workings of ecological systems, especially during rapid global change. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

These include normalised degree centrality, eigenvector centrality, Katz centrality, betweenness centrality and normalised closeness centrality. I Readership i : Management professionals, marketing analysts, students taking courses in discrete mathematics, networks and associated algorithms. Chapter 1 describes social networks and associated concepts as well as types of analysis in broad terms with some examples and goes on to preview some of the later material. [Extracted from the article]

Summary: Information‐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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

With urbanization and population migration, some Chinese cities fall into decline whereas others prosper. Using nighttime light data, we redefine the city based on economic function and evaluate the city size distribution in representative countries. The results provide evidence not only for Zipf's law, but also for a distortion in China's current city size distribution. This study proposes a feasible method to predict urban population distribution based on the role of geographical factors in regional development, following the idea of spatial equilibrium. This prediction suggests that the divergence of city size in China tends to be pronounced, with inter‐regional income disparity being narrowed and the city size distribution following Zipf's law. The Chinese government should further relax restrictions on population inflow into large cities and prepare for more migration in the future. [ABSTRACT FROM AUTHOR]

In order to shorten the time for users to query news on the Internet, this paper studies and designs a network news data extraction technology, which can obtain the main news information through the extraction of news text keywords. Firstly, the TF-IDF keyword extraction algorithm, TextRank keyword extraction algorithm, and LDA keyword extraction algorithm are analyzed to understand the keyword extraction process, and the TF-IDF algorithm is optimized by Zipf's law. By introducing the idea of model fusion, five schemes based on waterfall fusion and parallel combination fusion are designed, and the effects of the five schemes are verified by experiments. It is found that the designed extraction technology has a good effect on network news data extraction. News keyword extraction has a great application prospect, which can provide the basis for the research fields of news key phrases, news abstracts, and so on. [ABSTRACT FROM AUTHOR]

Information complexity in animals is an indicator of advanced communication and an intricate socio‐ecology. Zipf's Law of least effort has been used to assess the potential information content of animal repertoires, including whether or not a particular animal communication could be 'language‐like'. As all human languages follow Zipf's law, with a power law coefficient (PLC) close to −1, animal signals with similar probability distributions are postulated to possess similar information characteristics to language. However, estimation of the PLC from limited empirical datasets (e.g. most animal communication studies) is problematic because of biases from small sample sizes.The traditional approach to estimating Zipf's law PLC is to find the slope of a log–log rank‐frequency plot. Our alternative option uses the underlying equivalence between Shannon entropy (i.e. whether successive elements of a sequence are unpredictable, or repetitive) and PLC. Here, we test whether an entropy approach yields more robust estimates of Zipf's law PLC than the traditional approach.We examined the efficacy of the entropy approach in two ways. First, we estimated the PLC from synthetic datasets generated with a priori known power law probability distributions. This revealed that the estimated PLC using the traditional method is particularly inaccurate for highly stereotyped sequences, even at modest repertoire sizes. Estimation via Shannon entropy is accurate with modest sample sizes even for repertoires with thousands of distinct elements. Second, we applied these approaches to empirical data taken from 11 animal species. Shannon entropy produced a more robust estimate of PLC with lower variance than the traditional method, even when the true PLC is unknown. Our approach for the first time reveals Zipf's law operating in the vocal systems of multiple lineages: songbirds, hyraxes and cetaceans.As different methods of estimating the PLC can lead to misleading results in real data, estimating the balance of a communication system between simplicity and complexity is best performed using the entropy approach. This provides a more robust way to investigate the evolutionary constraints and processes that have acted on animal communication systems, and the parallels between these processes and the evolution of language. [ABSTRACT FROM AUTHOR]

We provide new insights on the city size distribution of countries around the world. Using more than 10,000 cities delineated via geospatial data and a globally consistent city identification scheme, we investigate distributional shapes in all countries. In terms of population, we find that Zipf's law holds for many, but not all, countries. Contrasting the distribution of population with the distribution of economic activity, measured by nighttime lights, across cities we shed light on the globally variant magnitude of agglomeration economies. Deviations from Zipf's law are to a large extent driven by an undue concentration in the largest cities. They benefit from agglomeration effects which seem to work through area rather than through density. Examining the cross‐country heterogeneity in the city size distribution, our model selection approach suggests that historical factors play an important role, in line with the time of development hypothesis. [ABSTRACT FROM AUTHOR]

Since its inception, Shannon's information theory has attracted interest for the study of language and music. Recently, a wide range of converging studies have shown how efficient communication pervades language, from phonetics to syntax. Efficient principles imply that more resources should be assigned to highly informative items. For instance, average information content was shown to be a better predictor of word length than frequency, revisiting the famous Zipf's law. However, in spite of the success of the efficient communication framework in the study of language and speech, very little work has investigated its relevance in the analysis of music. Here, we examine the organization of harmonic information in two large corpora of Western music, one made of MIDI files directly sequenced from scores, and the other made of MIDI recordings of live performances of highly skilled piano players. We show that there is a clear positive relationship between (contextual) information content of harmonic sequences and two essential musical properties, namely duration and loudness: the more unexpected a harmonic event is, the longer and the louder it is. [ABSTRACT FROM AUTHOR]

Brand names are a crucial part of the brand equity and marketing strategy of any company. Research suggests that companies spend considerable time and money to create suitable names for their brands and products. This paper uses the Zipf's law (or Principle of Least Effort) to analyze the perceived luxuriousness of brand names. One of the most robust laws in linguistics, Zipf's law describes the inverse relationship between a word's length and its frequency i.e., the more frequently a word is used in language, the shorter it tends to be. Zipf's law has been applied to many fields of science and in this paper, we provide evidence for the idea that because polysyllabic words (and brand names) are rare in everyday conversation, they are considered as more complex, distant, and abstract and that the use of longer brand names can enhance the perception of how luxurious a brand is (compared with shorter brand names, which are considered to be close, frequent, and concrete to consumers). Our results suggest that shorter names (mono‐syllabic) are better suited to basic brands whereas longer names (tri‐syllabic or more) are more appropriate for luxury brands. [ABSTRACT FROM AUTHOR]

Zipf's law is one of the best known empirical regularities in urban economics. There is extensive research on the subject, where each city is treated symmetrically in terms of the cost of transactions with other cities. Recent developments in network theory facilitate the examination of an asymmetric transport network. In a scale‐free network, the chance of observing extremes in network connections becomes higher than the Gaussian distribution predicts and, therefore, it explains the emergence of large clusters. The city‐size distribution shares the same pattern. This paper decodes how accessibility of a city to other cities on the transportation network can boost its local economy and explains the city‐size distribution as a result of its underlying transportation network structure. We confirm our model predictions with US and Belgian data. Finally, we discuss the endogenous evolution of transport networks. [ABSTRACT FROM AUTHOR]

Abstract: This paper examines the distribution of patenting activity across cities in the OECD, using a sample of 218 cities from 2000 to 2008. We obtain three main results. First, patenting activity is more concentrated than population and GDP. Second, patenting activity is less persistent than population and GDP, especially in the middle of the distribution. Third, in a parametric model, patenting does not exhibit mean‐reversion, and is positively associated with GDP and population density. Our results suggest that policymakers can influence the amount of innovative activity through the use of appropriate policies. [ABSTRACT FROM AUTHOR]

Zipf's rank-size rule, lognormal distribution, and Gibrat's urban growth models are considered as summarizing fundamental properties of systems of cities. In this article, they are used as statistical benchmarks for comparing the shapes of urban hierarchies and evolutionary trends of seven systems of cities in the world including BRICS, Europe, and United States. In order to provide conclusions that avoid the pitfalls of too small samples or uncontrolled urban definitions, these models are tested on some 20,000 urban units whose geographically significant delineations were harmonized in each country over 50 years between 1960 and 2010. As a result, if the models appear not always statistically valid, their usefulness is confirmed since the observed deviations from empirical data remain limited and can often be interpreted from the geohistorical context of urbanism proper to each world region. Moreover, the article provides new free software which authorizes the reproducibility of our experiments with our data bases as well as with complementary data. [ABSTRACT FROM AUTHOR]

Let ω0,ω1,…,ωn be a full set of outcomes (symbols) and let positive pi, i=0,…,n, be their probabilities (∑i=0npi=1). Let us treat ω0 as a stop symbol; it can occur in sequences of symbols (we call them words) only once, at the very end. The probability of a word is defined as the product of probabilities of its symbols. We consider the list of all possible words sorted in the nonincreasing order of their probabilities. Let pr be the probability of the rth word in this list. We prove that if at least one of the ratios log⁡pi/log⁡pj, i,j∈1,…,n, is irrational, then the limit limr→∞pr/r-1/γ exists and differs from zero; here γ is the root of the equation ∑i=1npiγ=1. The limit constant can be expressed (rather easily) in terms of the entropy of the distribution (p1γ,…,pnγ). [ABSTRACT FROM AUTHOR]

A table of content for November-December 2016 issue of the journal "Complexity" is presented on topics including cardiac dynamics in heart failure, adaptive cluster synchronization, and Zipf's law for word.

In the context of cognition, categorization is the process through which several elements (i.e., words) are grouped into a single set which by naming becomes an abstraction of its elements. For example, tiger, kitty, and max can be categorized as Cats. In this article, we aim to show how the physical, biological and cognitive dimensions are related in the process of categorization or abstraction through the physics of computation. Drawing on Landauer's principle, we show that the price paid in terms of entropy is higher when grouping elements of low ranking (high probability) than when grouping elements of high ranking (low probability). Therefore, the logic of the cognitive process of abstraction is explained through constraints imposed by memory on the computation of categories. © 2015 Wiley Periodicals, Inc. Complexity 21: 269-274, 2016 [ABSTRACT FROM AUTHOR]

We exploit the bilateral and skill dimensions from recent data sets of international migration to test for the existence of Zipf's and Gibrat's laws in the context of aggregate and high-skilled international immigration and emigration using graphical, parametric and non-parametric analysis. The top tails of the distributions of aggregate and high-skilled immigrants and emigrants adhere to a Pareto distribution with an exponent of unity, that is Zipf's law holds. We find some evidence in favour of Gibrat's law holding for immigration stocks, such that the growth in stocks is independent of their initial values and stronger evidence that immigration densities are diverging over time. Conversely, emigrant stocks are converging in the sense that countries with smaller emigrant stocks are growing faster than their larger sovereign counterparts. Lastly, high-skilled immigration and emigration stocks expressed in levels or as densities all exhibit signs of convergence. We conclude by discussing some competing mechanisms that could be driving the observed patterns including differing fertility rates, reductions in emigration restrictions, migrant sorting and selective immigration policies, immigrant networks and persisting wage differentials. [ABSTRACT FROM AUTHOR]

In this paper, we explore the validity of rank-size rule in the Moroccan urban system. We use data from the 1982, 1994, and 2004 censuses. Three thresholds are considered to truncate the data: 5000, 50000, and 100000 residents. Power law states that the rank ( r) of a city is proportional to a power of its size ( Sr), that is, r ̴ S•α. The ordinary least squares (OLS) method is used to estimate α. Using OLS method without Gabaix-Ibragimov correction (GIC) provides evidence of the validity of Zipf's law for cities of more than 100 000 dwellers.When the GIC is used, it appears that the zipfian distribution ( α = -1) is also valid for cities of more than 50000 inhabitants. Over the period 1982-2004, it seems likely that intermediate cities grew more rapidly than other cities. This may lead to a more balanced distribution of the Moroccan urban system. [ABSTRACT FROM AUTHOR]

This section offers news briefs on complexity as of March 14, 2014. A paper published in the October 2, 2013 issue of "Santa Fe Institute Working Papers" tackles the creation of information by deterministic chaos. Another article published in the October 31, 2013 issue of the same journal discusses Zipf's Law. The coexistence of critical regimes in interconnected networks is discussed in an article published in the November 2013 issue of "arXiv."

Many reports have shown that the access pattern for geospatial tiles follows Zipf's law and that its parameter a represents the access characteristics. However, visits to geospatial tiles have temporal and spatial popularities, and the α-value changes as they change. We construct a mathematical model to simulate the user's access behavior by studying the attributes of frequently visited tile objects to determine parameter estimation algorithms. Because the least squares (LS) method in common use cannot obtain an exact α-value and does not provide a suitable fit to data for frequently visited tiles, we present a new approach, which uses a moment method of estimation to obtain the value of α when α is close to 1. When α is further away from 1, the method uses the associated cache hit ratio for tile access and uses an LS method based on a critical cache size to estimate the value of α. The decrease in the estimation error is presented and discussed in the section on experiment results. This new method, which provides a more accurate estimate of α than earlier methods, promises more effective prediction of requests for frequently accessed tiles for better caching and load balancing. [ABSTRACT FROM AUTHOR]

We examine the complete dataset of baby name popularity collected by U.S. Social Security Administration for the last 131 years (1880-2010). The ranked baby name popularity can be fitted empirically by a piecewise function consisting of Beta function for the high-ranking names and power-law function for low-ranking names, but not power-law (Zipf's law) or Beta function by itself. © 2012 Wiley Periodicals, Inc. Complexity, 2012 [ABSTRACT FROM AUTHOR]

Cross-situational learning has recently gained attention as a plausible candidate for the mechanism that underlies the learning of word-meaning mappings. In a recent study, Blythe and colleagues have studied how many trials are theoretically required to learn a human-sized lexicon using cross-situational learning. They show that the level of referential uncertainty exposed to learners could be relatively large. However, one of the assumptions they made in designing their mathematical model is questionable. Although they rightfully assumed that words are distributed according to Zipf's law, they applied a uniform distribution of meanings. In this article, Zipf's law is also applied to the distribution of meanings, and it is shown that under this condition, cross-situational learning can only be plausible when referential uncertainty is sufficiently small. It is concluded that cross-situational learning is a plausible learning mechanism but needs to be guided by heuristics that aid word learners with reducing referential uncertainty. [ABSTRACT FROM AUTHOR]

Hierarchy of cities reflects the ubiquitous structure frequently observed in the natural world and social institutions. Where there is a hierarchy with cascade structure, there is a Zipf's rank-size distribution, and vice versa. However, we have no theory to explain the spatial dynamics associated with Zipf's law of cities. In this paper, a new angle of view is proposed to find the simple rules dominating complex systems and regular patterns behind random distribution of cities. The hierarchical structure can be described with a set of exponential functions that are identical in form to Horton-Strahler's laws on rivers and Gutenberg-Richter's laws on earthquake energy. From the exponential models, we can derive four power laws including Zipf's law indicative of fractals and scaling symmetry. A card-shuffling model is built to interpret the relation between Zipf's law and hierarchy of cities. This model can be expanded to illuminate the general empirical power-law distributions across the individual physical and social sciences, which are hard to be comprehended within the specific scientific domains. This research is useful for us to understand how complex systems such as networks of cities are self-organized. [ABSTRACT FROM AUTHOR]

proposed that the Lexical Frequency Profile (LFP) can estimate the size of a second-language writer's productive vocabulary. questioned the sensitivity and the reliability of LFPs for estimating vocabulary sizes, based on the results obtained from probabilistic simulations of LFPs. However, the underlying mathematical model for the simulations, based on Zipf's law, allows such an analysis to be done directly, without recourse to simulations. The direct analysis has the further advantage of demonstrating how variability estimates obtained from within the 1k band (the 1,000 most frequent words of English) portion of written texts may explain the simulation results. The findings confirm that the ability of LFPs to distinguish between groups diminishes as vocabulary size increases. However, for fairly homogeneous groups, LFPs are able to provide a coarse but reasonable tool for vocabulary size estimation. We also explore modifications to Zipf's law that may result in a more accurate model of word frequencies in natural language. [ABSTRACT FROM AUTHOR]

Here we sketch a new derivation of Zipf's law for word frequencies based on optimal coding. The structure of the derivation is reminiscent of Mandelbrot's random typing model but it has multiple advantages over random typing: (1) it starts from realistic cognitive pressures, (2) it does not require fine tuning of parameters, and (3) it sheds light on the origins of other statistical laws of language and thus can lead to a compact theory of linguistic laws. Our findings suggest that the recurrence of Zipf's law in human languages could originate from pressure for easy and fast communication. © 2016 Wiley Periodicals, Inc. Complexity 21: 409-411, 2016 [ABSTRACT FROM AUTHOR]

The Matthew effect has that recognition is bestowed on researchers of already high repute. If recognition is measured by citations, this means that often-cited papers or authors are cited more often. I use the statistical theory of the growth of firms to test whether the fame of papers and authors indeed exhibits increasing returns to scale, and confirm this hypothesis for the 100 most prolific economists. [ABSTRACT FROM AUTHOR]

This paper ranks Asian universities in two related economics fields: international economics and development economics. A key finding is that new latecomers rank atop the two specialty areas of economics. The results of the university ranking also establish that Zipf's law applies to research-based school ranks. [ABSTRACT FROM AUTHOR]

Zipf's law states that if words of language are ranked in the order of decreasing frequency in texts, the frequency of a word is inversely proportional to its rank. It is very reliably observed in the data, but to date it escaped satisfactory theoretical explanation. This article suggests that Zipf's law may result from a hierarchical organization of word meanings over the semantic space, which in turn is generated by the evolution of word semantics dominated by expansion of meanings and competition of synonyms. A study of the frequency of partial synonyms in Russian provides experimental evidence for the hypothesis that word frequency is determined by semantics. [ABSTRACT FROM AUTHOR]

Many economic and non-economic variables such as income, wealth, firm size, or city size often distribute Pareto in the upper tail. It is well established that Gibrat's law can explain this phenomenon, but Gibrat's law often does not hold. This note characterizes a class of processes, one that includes Gibrat's law as a special case, that can explain Pareto distributions. Of particular importance is a parsimonious generalization of Gibrat's law that allows size to affect the variance of the growth process but not its mean. This note also shows that under plausible conditions Zipf's law is equivalent to Gibrat's law. [ABSTRACT FROM AUTHOR]

The rank-size rule and Zipf's law for city sizes have been traditionally examined by means of OLS estimation and the t test. This paper studies the accurate and approximate properties of the OLS estimator and obtains the distribution of the t statistic under the assumption of Zipf's law (i.e., Pareto distribution). Indeed, we show that the t statistic explodes asymptotically even under the null, indicating that a mechanical application of the t test yields a serious type I error. To overcome this problem, critical regions of the t test are constructed to test the Zipf's law. Using these corrected critical regions, we can conclude that our results are in favor of the Zipf's law for many more countries than in the previous researches such as Rosen and Resnick (1980) or Soo (2005) . By using the same database as that used in Soo (2005) , we demonstrate that the Zipf law is rejected for only one of 24 countries under our test whereas it is rejected for 23 of 24 countries under the usual t test. We also propose a more efficient estimation procedure and provide empirical applications of the theory for some countries. [ABSTRACT FROM AUTHOR]

In this paper a rationale for choosing how many and what types of spelling-to-sound units of English to teach children to learn to read is introduced. The rationale is based on an analysis of the frequency with which various units of spelling-to-sound mapping occur in monosyllabic words of the English language. Analysis of spelling-to-sound mappings at three levels (whole words, onsets and rimes and graphemes) reveals that the distribution of these mappings in English text approximates Zipf's Law. Further analyses reveal that a substantial proportion of text can be read if knowledge of the most frequent mappings at each level is assumed. It is suggested that viewing reading from this perspective can be useful in developing reading instruction so that children are taught information that is most useful in achieving the endpoint of learning to read. Copyright © 2007 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this article concentration (i.e., inequality) aspects of the functions of Zipf and of Lotka are studied. Since both functions are power laws (i.e., they are mathematically the same) it suffices to develop one concentration theory for power laws and apply it twice for the different interpretations of the laws of Zipf and Lotka. After a brief repetition of the functional relationships between Zipf's law and Lotka's law, we prove that Price's law of concentration is equivalent with Zipf's law. A major part of this article is devoted to the development of continuous concentration theory, based on Lorenz curves. The Lorenz curve for power functions is calculated and, based on this, some important concentration measures such as the ones of Gini, Theil, and the variation coefficient. Using Lorenz curves, it is shown that the concentration of a power law increases with its exponent and this result is interpreted in terms of the functions of Zipf and Lotka. [ABSTRACT FROM AUTHOR]

We report on a study that was undertaken to better understand search and navigation behavior by exploiting the close association between the process underlying users' query submission and the navigational trails emanating from query clickthroughs. To our knowledge, there has been little research towards bridging the gap between these two important processes pertaining to users' online information searching activity. Based on log data obtained from a search and navigation documentation system called AutoDoc, we propose a model of user search sessions and provide analysis on users' link or clickthrough selection behavior, reformulation activities, and search strategy patterns. We also conducted a simple user study to gauge users' perceptions of their information seeking activity when interacting with the system. The results obtained show that analyzing both the query submissions and navigation starting from query clickthrough, reveals much more interesting patterns than analyzing these two processes independently. On average, AutoDoc users submitted only one query per search session and entered approximately two query terms. Specifically, our results show how AutoDoc users are more inclined to submit new queries or resubmit modified queries than to navigate by link-following. We also show that users' behavior within this search system can be approximated by Zipf's Law distribution. [ABSTRACT FROM AUTHOR]

Jung's theory of synchronicity is seen as a step in the development of a complete theory of the symbol. In so doing, a number of proposals are made for modelling the symbolic process along lines already in use for modelling a variety of other phenomena, ranging from language to the behaviour of earthquakes. These modelling techniques involve processes of self-organization, and raise issues of scaling in systems including symbolic systems. The proposal is made that symbolic systems obey the same rules of scaling that these other systems obey, and that symbolic systems can therefore be understood as exhibiting the characteristics of a power law distribution—a concept that is explained and developed in the paper. It is finally proposed that synchronicity is an aspect of the symbolic that can be characterized as exhibiting a high degree of‘symbolic density’. [ABSTRACT FROM AUTHOR]

In regard to the scalable service control platform needed for realization of future mobile communication service, a new method of efficiently accessing distributed databases (DB) is proposed. Previously, as an access system plan to distributed DBs, a unicast-type system in which the access request to a DB received from the network is transferred to the destination DB (System A) and a multicast system with multicast delivery (System B) have been proposed. In the former, the increased size of the destination decision table puts pressure on main memory. In the latter, multicast communication applies pressure every time on processor process capacity. Hence, sufficient scalability has not been obtained in either method. In the present paper, the existence of locality in the requirement for DB access among users is recognized. A hybrid system (System C) is proposed here in which unicast communication is applied for access by a few users with high access frequency, but multicast communication is used for access by the other, majority users. A system control parameter is introduced to select these communication methods. By choosing the value of this parameter optimally, the user accommodation limits in the conventional system are resolved. It is shown quantitatively that operation with a minimum amount of equipment is possible in a wide accommodation range. © 2003 Wiley Periodicals, Inc. Electron Comm Jpn Pt 1, 87(4): 1–15, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecja.10164 [ABSTRACT FROM AUTHOR]

ABSTRACT. Zipf's law for cities is one of the most conspicuous and robust empirical facts in the social sciences. It says that for most countries, the size distribution of cities must fit the power law: the number of cities with populations greater than S is inversely proportional to S. The present paper answers three questions related to Zipf's law: (1) does the Danish case refute Zipf's law for cities?, (2) what are the implications of Zipf's law for models of local growth?, and (3) do we have a Zipf's law for firms? Based on empirical data on the 61 largest Danish cities for year 2000, the answer to (1) is NO--the Danish case is not the exception which refutes Zipf's law. The consideration of (2) then leads to an empirical test of (3). The question of the existence of Zipf's law for firms is tested on a sample of 14,541 Danish production companies (the total population for 1997 with 10 employees or more). Based on the empirical evidence, the answer to (3) is YES in the sense that the growth pattern of Danish production companies follows a clean rank-size distribution consistent with Zipf's law. [ABSTRACT FROM AUTHOR]

Studies the probabilities of the occurrence of multi-word phrases in relation to the probabilities of occurrence of the single words. Validity of the law of Zipf in the latter case; Approximation of the sound distribution by Zipf's law; Fractal argument of Mandelbrot for two-word phrases.

Offers a general-equilibrium economic approach to Zipf's law or the empirical regularity concerning the size of distribution of cities. Incorporation of negative feedbacks in a model of economic geography and international trade; Enhancement of the understanding of the existence of rank-size distribution of cities.