Search Results (59)

Bottlenose dolphins’ broadband click vocalisations are well-studied in the literature concerning their echolocation function. Their potential use for communication among conspecifics has long been speculated but has yet to be conclusively established. In this study, we first categorised dolphins’ click production based on their amplitude contour and then analysed the distribution of individual clicks and click sequences against their duration and length. The results show that the repertoire and composition of clicks and click sequences adhere to the three essential linguistic laws of efficient communication: Zipf’s rank–frequency law, the law of brevity, and the Menzerath–Altmann law. Conforming to the rank–frequency law suggests that clicks may form a linguistic code subject to selective pressures for unification, on the one hand, and diversification, on the other. Conforming to the other two laws also implies that dolphins use clicks according to the compression criterion or minimisation of code length without losing information. Such conformity of dolphin clicks might indicate that these linguistic laws are more general, which produces an exciting research perspective on animal communication. Full article

In the process of Chinese-style modernisation, the socially and culturally coordinated development of cities in the Yangtze River Economic Belt is important for promoting regional coordinated development, enhancing the balance of public services, and strengthening cultural soft power. This study used quantitative methods, including the construction of an indicator system, spatial correlation analysis, and Zipf’s rank-size rule, on data from 2011 to 2021 to analyse the capacity for coordinated social and cultural development and assessed the spatial distribution characteristics of the Yangtze River Economic Belt. The study found that the overall level of social and cultural coordination among the cities in the Yangtze River Economic Belt steadily improved; however, significant regional disparities still exist, particularly in areas such as social security and cultural integration. Spatially, a “high in the east, low in the west” pattern is observed, with the Yangtze River Delta city cluster leading development, the midstream cluster playing a supportive role, and the Chengdu–Chongqing city cluster showing significant internal disparities. Core cities such as Shanghai, Hangzhou, Wuhan, and Chengdu demonstrated driving effects in areas such as culture, education, and healthcare; however, some peripheral cities remain underdeveloped. This study suggests the need to enhance the development of the Yangtze River’s culture, promote the development of cultural industry clusters, foster the integration of various business models, leverage scientific and educational resources, optimise the cultural consumption market, and achieve the coordinated development of the social and cultural sectors, thereby enabling the Yangtze River Economic Belt to play a greater role in Chinese-style modernisation. Full article

We compare the “classical” equations of type-token systems, namely Zipf’s laws, Heaps’ law and the relationships between their indices, with data selected from the Standardized Project Gutenberg Corpus (SPGC). Selected items all exceed 100,000 word-tokens and are trimmed to 100,000 word-tokens each. With the most egregious anomalies removed, a dataset of 8432 items is examined in terms of the relationships between the Zipf and Heaps’ indices computed using the Maximum Likelihood algorithm. Zipf’s second (size) law indices suggest that the types vs. frequency distribution is log–log convex, with the high and low frequency indices showing weak but significant negative correlation. Under certain circumstances, the classical equations work tolerably well, though the level of agreement depends heavily on the type of literature and the language (Finnish being notably anomalous). The frequency vs. rank characteristics exhibit log–log linearity in the “middle range” (ranks 100–1000), as characterised by the Kolmogorov–Smirnov significance. For most items, the Heaps’ index correlates strongly with the low frequency Zipf index in a manner consistent with classical theory, while the high frequency indices are largely uncorrelated. This is consistent with a simple simulation. Full article

This article investigates scaling laws within language families using data from over six thousand languages and analyzes emergent patterns observed in Zipf-like classification graphs. Both macroscopic (based on the number of languages by family) and microscopic (based on the number of speakers by language within a family) aspects of these classifications are examined. Particularly noteworthy is the discovery of a distinct division among the fourteen largest contemporary language families, excluding Afro-Asiatic and Nilo-Saharan languages. These families are found to be distributed across three language family quadruplets, each characterized by significantly different exponents in the Zipf graphs. This finding sheds light on the underlying structure and organization of major language families, revealing intriguing insights into the nature of linguistic diversity and distribution. Full article

A sketch is a probabilistic data structure that can accurately estimate massive network traffic with a small memory overhead. To improve the measurement accuracy, most sketch-based schemes separate elephant flows from mouse flows to accommodate the skewed network traffic. However, the increased algorithmic complexity often results in a sacrifice of measurement throughput. In addition, some improved sketches may be over-reliant on the skewed distribution of traffic, which results in unstable accuracy. To this end, a novel sketch, called Air Sketch, is proposed in this paper. It treats flows of different sizes as air with different temperatures. Meanwhile, a deterministic replacement strategy is applied to elephant flows. In order to improve throughput, an asymmetric insertion and query algorithm with a global hash is designed. The performance of Air Sketch is evaluated using real traffic transaction datasets, anonymized internet traces, and synthetic Zipf datasets. The experimental results demonstrate that Air Sketch can outperform the best typical measurement methods by up to 27 times in flow size measurement and up to 40 times in elephant flow detection. Additionally, Air Sketch achieves high accuracy and stability while achieving high insertion and query throughput. Full article

Self-organized criticality (SOC) describes natural systems spontaneously tuned at equilibrium yet capable of catastrophic events or avalanches. The cardiovascular system, characterized by homeostasis and vasovagal syncope, is a prime candidate for SOC. Power laws are the cornerstone for demonstrating the presence of SOC. This study aimed to provide evidence of power-law behavior in cardiovascular dynamics. We analyzed beat-by-beat blood pressure and heart rate data from seven healthy subjects in the head-up position over 40 min. Cardiovascular avalanches were quantified by their duration (in beats), and symbolic sequences were identified. Five types of distributions were assessed for power-law behavior: Gutenberg–Richter, classical Zipf, modified Zipf, Zipf of time intervals between avalanches, and Zipf of symbolic sequences. A three-stage approach was used to show power laws: (1) regression coefficient r > 0.95, (2) comparison with randomized data, and (3) Clauset’s statistical test for power law. Numerous avalanches were identified (13.9 ± 0.8 per minute). The classical and modified Zipf distributions met all the criteria (r = 0.99 ± 0.00 and 0.98 ± 0.01, respectively), while the others showed partial agreement, likely due to the limited data duration. These findings reveal that Zipf’s distributions of cardiovascular avalanches strongly support SOC, shedding light on the organization of this complex system. Full article

The observation of randomness patterns serves as guidance for the craft of probabilistic modelling. The most used count models—Binomial, Poisson, Negative Binomial—are the discrete Morris’ natural exponential families whose variance is at most quadratic on the mean, and the solutions of Katz–Panjer recurrence relation, aside from being members of the generalised power series and hypergeometric distribution families, and this accounts for their many advantageous characteristics. Some other basic count models are also described, as well as models with less obvious but useful randomness patterns in connection with maximum entropy characterisations, such as Zipf and Good models. Simple tools, such as truncation, thinning, or parameter randomisation, are straightforward ways of constructing other count models. Full article

This study extends the concept of granularity from firms to cities, examining how large cities influence national economic dynamics beyond their relative size. By applying Zipf’s law, which describes the power law distribution of city sizes, we investigate the interplay between granularity and business cycles. Our aim is to test the granular hypothesis that large cities have a significant impact on the business cycle beyond their relative size. We analyze data from American and Brazilian cities between 2003 and 2019 assessing the granular residuals and their explanatory power. Our findings reveal that in the United States, the granular city size is three metropolitan areas or five counties when redefined. In Brazil, it equates to three municipalities. These results emphasize the substantial role large cities play in national economic fluctuations, suggesting that policy interventions that target infrastructure, education, and innovation in major urban centers could have widespread economic benefits. This paper’s contribution to the literature is to highlight a spatial component of granularity not considered so far. Full article

Large-scale forest restoration projects significantly reduce the net rates of forest loss. However, as a key component of forest restoration, planted forests have failed to restore biodiversity. China has implemented a large-scale afforestation program, which includes pure planted forests in particular, leading to various changes in ecosystem processes. Despite this, a comprehensive analysis of understory vegetation diversity patterns in these pure planted forests is still lacking. This study aimed to analyze the data on understory vegetation diversity from three typical pure and natural forest ecosystems of Hunan ecological forests to reveal their diversity patterns. The results revealed no significant difference in the understory diversity index between natural and pure forest types, although natural forests had a bigger species pool. The Zipf–Mandelbrot model was a better fit for species abundance distribution. The fitted results suggested that both environmental filtering and neutral processes affected the species abundance distribution and pure understory communities during restoration succession. Natural forests had the most stable understory diversity structure, whereas pure Phyllostachys heterocycla (Carr.) Mitford forests had the least stable structure. Multivariate regression tree analysis identified indicator species for each community. The gradient boosting model indicated that isothermality and slope direction were the most important factors affecting diversity. The β-diversity analysis showed that community establishment in the four forest types was affected via different mechanisms. The findings of this study have significant implications for understanding the impact of afforestation on the mechanisms for maintaining diversity. Full article

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. Full article

The definition of cities from the physical view in China is lacking. Most research regarding Chinese cities relies on the definition from the administrative view, which is often inconsistent as there are serious discrepancies between the administrative boundaries and the physical extent of Chinese cities. This study aims to delineate Chinese urbanised areas using population census data at the township level and analyse the identified urbanised areas’ characteristics. The results show that the numbers of Chinese urbanised areas in 2000, 2010, and 2020 were 758, 942, and 1058, respectively, indicating there are several ‘cities outside the system’ that meet the requirements of urban agglomeration but are constrained by the city designation system. The degree of population aggregation and the growth rate of urbanised areas are greater than those of administrative cities. This indicates that the geographical scopes of administrative cities cannot accurately reflect the ‘real’ urban areas. Additionally, the city-size distribution follows Zipf’s law, with the Zipf coefficient moving closer to one if we fit the Zipf model based on the urbanised areas. It is necessary to establish official urbanised areas and publish statistical data based on urbanised areas, which could have significant implications both for policymakers and researchers. Full article

In this work we suggest that the common cause for the development of various power laws is the existence of a suitable exchangeable quantity between the agents of a set. Examples of such exchangeable quantities, leading to eponymous power laws, include money (Pareto’s Law), scientific knowledge (Lotka’s Law), people (Auerbach’s Law), and written or verbal information (Zipf’s Law), as well as less common cases like bullets during deadly conflicts, recognition in social networks, heat between the atmosphere and sea-ice floes, and, finally, mass of water vapors between pores in solids. This last case is examined closely in the present article based on extensive experimental data. It is shown that the transferred mass between pores, which eventually grow towards a power law distribution, may be expressed using different parameters, either transferred surface area, or transferred volume, or transferred pore length or transferred pore anisotropy. These distinctions lead to different power laws of variable strength as reflected by the corresponding exponent. The exponents depend quantitatively on the spread of frequency distribution of the examined parameter and tend to zero as the spread of distribution tends to a single order of magnitude. A comparison between the energy and the entropy of different kinds of pore distributions reveals that these two statistical parameters are linearly related, implying that the system poise at a critical state and the exchangeable quantities are the most convenient operations helping to keep this balance. Full article

The article extends the theoretical and applicative analysis of Zipf’s law. We are concerned with a set of properties of Zipf’s law that derive directly from the power law expression and from the discrete nature of the objects to which the law is applied, when the objects are words, lemmas, and the like. We also search for variations of Zipf’s law that can help explain the noisy results empirically reported in the literature and the departures of the empirically obtained nonlinear graph from the theoretical linear one, with the variants analyzed differing from Mandelbrot and lognormal distributions. A problem of interest that we deal with is that of mixtures of populations obeying Zipf’s law. The last problem has relevance in the analysis of texts with words with various etymologies. Computational aspects are also addressed. Full article

In this paper, word length in the texts of public speeches by USA and UK politicians is analyzed. More than 300 speeches delivered over the past two hundred years were studied. It is found that the lognormal distribution better describes the distribution of word length than do the Weibull and Poisson distributions, for example. It is shown that the length of words does not change significantly over time (the average value either does not change or slightly decreases, and the mode slightly increases). These results are fundamentally different from those obtained previously for sentence lengths and indicate that, in terms of quantitative linguistic analysis, the word length in politicians’ speech has not evolved over the last 200 years and does not obey the principle of least effort proposed by G. Zipf. Full article

Fire is one of the principal factors influencing subalpine ecosystem succession. Species numbers and plant compositions are used to determine postfire disturbance, vegetation, structural change, and succession. Ecologists also integrate species diversity and mathematical models to enable researchers to obtain increasingly detailed insights into habitats during post-disturbance restoration processes. This study employed five species-abundance models, namely the niche preemption model, the broken-stick model, the log-normal model, the Zipf model, and the Zipf–Mandelbrot model, to perform fitting analysis on the abundance data of postfire species coverage in shrub grasslands near 369 Hut at Xue Mountain in Shei-Pa National Park, Taiwan. We performed the logarithmic transformation on plant-coverage areas for each period of postfire shrub-grassland succession, and then, based on histograms drawn for species–coverage distribution modes, the test results consistently showed normal distributions (p < 0.05). Species-coverage histograms measuring various periods showed that there were comparatively higher numbers of common species during postfire succession and that the numbers of rare species progressively increased. The fitting results of the five species-abundance models showed that although the most suitable abundance models for each period of postfire succession varied, the majority of these periods demonstrated decent fitting with respect to the Zipf–Mandelbrot model. These findings showed that fuel consumption provided nutrients in a manner that facilitated postfire regeneration. Moreover, dominant species, such as Yushania niitakayamensis, and Miscanthus transmorrisonensis, did not fully occupy growing spaces and resource availabilities; consequently, seeded species were able to grow. Full article