Zipf's law leads to Heaps' law: analyzing their relation in finite-size systems

Background

Zipf''s law and Heaps'' law are observed in disparate complex systems. Of particular interests, these two laws often appear together. Many theoretical models and analyses are performed to understand their co-occurrence in real systems, but it still lacks a clear picture about their relation.

Methodology/Principal Findings

We show that the Heaps'' law can be considered as a derivative phenomenon if the system obeys the Zipf''s law. Furthermore, we refine the known approximate solution of the Heaps'' exponent provided the Zipf''s exponent. We show that the approximate solution is indeed an asymptotic solution for infinite systems, while in the finite-size system the Heaps'' exponent is sensitive to the system size. Extensive empirical analysis on tens of disparate systems demonstrates that our refined results can better capture the relation between the Zipf''s and Heaps'' exponents.

Conclusions/Significance

The present analysis provides a clear picture about the relation between the Zipf''s law and Heaps'' law without the help of any specific stochastic model, namely the Heaps'' law is indeed a derivative phenomenon from the Zipf''s law. The presented numerical method gives considerably better estimation of the Heaps'' exponent given the Zipf''s exponent and the system size. Our analysis provides some insights and implications of real complex systems. For example, one can naturally obtained a better explanation of the accelerated growth of scale-free networks.     

Random Texts Do Not Exhibit the Real Zipf's Law-Like Rank Distribution

Background

Zipf''s law states that the relationship between the frequency of a word in a text and its rank (the most frequent word has rank , the 2nd most frequent word has rank ,…) is approximately linear when plotted on a double logarithmic scale. It has been argued that the law is not a relevant or useful property of language because simple random texts - constructed by concatenating random characters including blanks behaving as word delimiters - exhibit a Zipf''s law-like word rank distribution.

Methodology/Principal Findings

In this article, we examine the flaws of such putative good fits of random texts. We demonstrate - by means of three different statistical tests - that ranks derived from random texts and ranks derived from real texts are statistically inconsistent with the parameters employed to argue for such a good fit, even when the parameters are inferred from the target real text. Our findings are valid for both the simplest random texts composed of equally likely characters as well as more elaborate and realistic versions where character probabilities are borrowed from a real text.

Conclusions/Significance

The good fit of random texts to real Zipf''s law-like rank distributions has not yet been established. Therefore, we suggest that Zipf''s law might in fact be a fundamental law in natural languages.     

Beyond Word Frequency: Bursts,Lulls, and Scaling in the Temporal Distributions of Words

Background

Zipf''s discovery that word frequency distributions obey a power law established parallels between biological and physical processes, and language, laying the groundwork for a complex systems perspective on human communication. More recent research has also identified scaling regularities in the dynamics underlying the successive occurrences of events, suggesting the possibility of similar findings for language as well.

Methodology/Principal Findings

By considering frequent words in USENET discussion groups and in disparate databases where the language has different levels of formality, here we show that the distributions of distances between successive occurrences of the same word display bursty deviations from a Poisson process and are well characterized by a stretched exponential (Weibull) scaling. The extent of this deviation depends strongly on semantic type – a measure of the logicality of each word – and less strongly on frequency. We develop a generative model of this behavior that fully determines the dynamics of word usage.

Conclusions/Significance

Recurrence patterns of words are well described by a stretched exponential distribution of recurrence times, an empirical scaling that cannot be anticipated from Zipf''s law. Because the use of words provides a uniquely precise and powerful lens on human thought and activity, our findings also have implications for other overt manifestations of collective human dynamics.     

Evolution of scaling emergence in large-scale spatial epidemic spreading

Background

Zipf''s law and Heaps'' law are two representatives of the scaling concepts, which play a significant role in the study of complexity science. The coexistence of the Zipf''s law and the Heaps'' law motivates different understandings on the dependence between these two scalings, which has still hardly been clarified.

Methodology/Principal Findings

In this article, we observe an evolution process of the scalings: the Zipf''s law and the Heaps'' law are naturally shaped to coexist at the initial time, while the crossover comes with the emergence of their inconsistency at the larger time before reaching a stable state, where the Heaps'' law still exists with the disappearance of strict Zipf''s law. Such findings are illustrated with a scenario of large-scale spatial epidemic spreading, and the empirical results of pandemic disease support a universal analysis of the relation between the two laws regardless of the biological details of disease. Employing the United States domestic air transportation and demographic data to construct a metapopulation model for simulating the pandemic spread at the U.S. country level, we uncover that the broad heterogeneity of the infrastructure plays a key role in the evolution of scaling emergence.

Conclusions/Significance

The analyses of large-scale spatial epidemic spreading help understand the temporal evolution of scalings, indicating the coexistence of the Zipf''s law and the Heaps'' law depends on the collective dynamics of epidemic processes, and the heterogeneity of epidemic spread indicates the significance of performing targeted containment strategies at the early time of a pandemic disease.     

Widening the lens: what the manual modality reveals about language,learning and cognition

The goal of this paper is to widen the lens on language to include the manual modality. We look first at hearing children who are acquiring language from a spoken language model and find that even before they use speech to communicate, they use gesture. Moreover, those gestures precede, and predict, the acquisition of structures in speech. We look next at deaf children whose hearing losses prevent them from using the oral modality, and whose hearing parents have not presented them with a language model in the manual modality. These children fall back on the manual modality to communicate and use gestures, which take on many of the forms and functions of natural language. These homemade gesture systems constitute the first step in the emergence of manual sign systems that are shared within deaf communities and are full-fledged languages. We end by widening the lens on sign language to include gesture and find that signers not only gesture, but they also use gesture in learning contexts just as speakers do. These findings suggest that what is key in gesture''s ability to predict learning is its ability to add a second representational format to communication, rather than a second modality. Gesture can thus be language, assuming linguistic forms and functions, when other vehicles are not available; but when speech or sign is possible, gesture works along with language, providing an additional representational format that can promote learning.     

The Structure and Evolution of Buyer-Supplier Networks

In this paper, we investigate the structure and evolution of customer-supplier networks in Japan using a unique dataset that contains information on customer and supplier linkages for more than 500,000 incorporated non-financial firms for the five years from 2008 to 2012. We find, first, that the number of customer links is unequal across firms; the customer link distribution has a power-law tail with an exponent of unity (i.e., it follows Zipf''s law). We interpret this as implying that competition among firms to acquire new customers yields winners with a large number of customers, as well as losers with fewer customers. We also show that the shortest path length for any pair of firms is, on average, 4.3 links. Second, we find that link switching is relatively rare. Our estimates indicate that the survival rate per year for customer links is 92 percent and for supplier links 93 percent. Third and finally, we find that firm growth rates tend to be more highly correlated the closer two firms are to each other in a customer-supplier network (i.e., the smaller is the shortest path length for the two firms). This suggests that a non-negligible portion of fluctuations in firm growth stems from the propagation of microeconomic shocks – shocks affecting only a particular firm – through customer-supplier chains.     

Children’s and Adults’ On-Line Processing of Syntactically Ambiguous Sentences during Reading

While there has been a fair amount of research investigating children’s syntactic processing during spoken language comprehension, and a wealth of research examining adults’ syntactic processing during reading, as yet very little research has focused on syntactic processing during text reading in children. In two experiments, children and adults read sentences containing a temporary syntactic ambiguity while their eye movements were monitored. In Experiment 1, participants read sentences such as, ‘The boy poked the elephant with the long stick/trunk from outside the cage’ in which the attachment of a prepositional phrase was manipulated. In Experiment 2, participants read sentences such as, ‘I think I’ll wear the new skirt I bought tomorrow/yesterday. It’s really nice’ in which the attachment of an adverbial phrase was manipulated. Results showed that adults and children exhibited similar processing preferences, but that children were delayed relative to adults in their detection of initial syntactic misanalysis. It is concluded that children and adults have the same sentence-parsing mechanism in place, but that it operates with a slightly different time course. In addition, the data support the hypothesis that the visual processing system develops at a different rate than the linguistic processing system in children.     

血清胱抑素C、血肌酐及血尿素氮对窒息新生儿肾功能损害的临床意义

目的:探讨体外反搏联合言语训练治疗脑性瘫痪并语言发育迟缓儿童的临床疗效。方法:选择2015年12月至2017年12月在上海市儿童医院康复科普通门诊确诊的脑瘫并语言发育迟缓患儿52例,按照随机数字表法将其随机分为治疗组和对照组,每组26例。对照组仅给予言语训练治疗,治疗组给予体外反搏联合言语训练治,以4周1个疗程,两组均治疗3个疗程。治疗前后,采用中国康复研究中心汉语版儿童语言发育评定法s-s法、Gesell发育评分法评价和比较患儿言语发育商和认知发育商的变化。结果:治疗后,两组言语发育商和认知发育商均显著高于治疗前,且治疗组言语发育商和认知发育商均显著高于对照组,差异均有统计学意义(均P0.01)。结论:体外反搏联合言语训练较单纯言语训练可更有效改善脑瘫并语言发育迟缓患儿的言语发育和认知发育。     

Word Decoding of Protein Amino Acid Sequences with Availability Analysis: A Linguistic Approach

The amino acid sequences of proteins determine their three-dimensional structures and functions. However, how sequence information is related to structures and functions is still enigmatic. In this study, we show that at least a part of the sequence information can be extracted by treating amino acid sequences of proteins as a collection of English words, based on a working hypothesis that amino acid sequences of proteins are composed of short constituent amino acid sequences (SCSs) or “words”. We first confirmed that the English language highly likely follows Zipf''s law, a special case of power law. We found that the rank-frequency plot of SCSs in proteins exhibits a similar distribution when low-rank tails are excluded. In comparison with natural English and “compressed” English without spaces between words, amino acid sequences of proteins show larger linear ranges and smaller exponents with heavier low-rank tails, demonstrating that the SCS distribution in proteins is largely scale-free. A distribution pattern of SCSs in proteins is similar among species, but species-specific features are also present. Based on the availability scores of SCSs, we found that sequence motifs are enriched in high-availability sites (i.e., “key words”) and vice versa. In fact, the highest availability peak within a given protein sequence often directly corresponds to a sequence motif. The amino acid composition of high-availability sites within motifs is different from that of entire motifs and all protein sequences, suggesting the possible functional importance of specific SCSs and their compositional amino acids within motifs. We anticipate that our availability-based word decoding approach is complementary to sequence alignment approaches in predicting functionally important sites of unknown proteins from their amino acid sequences.     

Beat gestures influence which speech sounds you hear

Beat gestures—spontaneously produced biphasic movements of the hand—are among the most frequently encountered co-speech gestures in human communication. They are closely temporally aligned to the prosodic characteristics of the speech signal, typically occurring on lexically stressed syllables. Despite their prevalence across speakers of the world''s languages, how beat gestures impact spoken word recognition is unclear. Can these simple ‘flicks of the hand'' influence speech perception? Across a range of experiments, we demonstrate that beat gestures influence the explicit and implicit perception of lexical stress (e.g. distinguishing OBject from obJECT), and in turn can influence what vowels listeners hear. Thus, we provide converging evidence for a manual McGurk effect: relatively simple and widely occurring hand movements influence which speech sounds we hear.     

How Could Language Have Evolved?

The evolution of the faculty of language largely remains an enigma. In this essay, we ask why. Language''s evolutionary analysis is complicated because it has no equivalent in any nonhuman species. There is also no consensus regarding the essential nature of the language “phenotype.” According to the “Strong Minimalist Thesis,” the key distinguishing feature of language (and what evolutionary theory must explain) is hierarchical syntactic structure. The faculty of language is likely to have emerged quite recently in evolutionary terms, some 70,000–100,000 years ago, and does not seem to have undergone modification since then, though individual languages do of course change over time, operating within this basic framework. The recent emergence of language and its stability are both consistent with the Strong Minimalist Thesis, which has at its core a single repeatable operation that takes exactly two syntactic elements a and b and assembles them to form the set {a, b}.It is uncontroversial that language has evolved, just like any other trait of living organisms. That is, once—not so long ago in evolutionary terms—there was no language at all, and now there is, at least in Homo sapiens. There is considerably less agreement as to how language evolved. There are a number of reasons for this lack of agreement. First, “language” is not always clearly defined, and this lack of clarity regarding the language phenotype leads to a corresponding lack of clarity regarding its evolutionary origins. Second, there is often confusion as to the nature of the evolutionary process and what it can tell us about the mechanisms of language. Here we argue that the basic principle that underlies language''s hierarchical syntactic structure is consistent with a relatively recent evolutionary emergence.     

Auditory-motor learning during speech production in 9-11-year-old children

Background

Hearing ability is essential for normal speech development, however the precise mechanisms linking auditory input and the improvement of speaking ability remain poorly understood. Auditory feedback during speech production is believed to play a critical role by providing the nervous system with information about speech outcomes that is used to learn and subsequently fine-tune speech motor output. Surprisingly, few studies have directly investigated such auditory-motor learning in the speech production of typically developing children.

Methodology/Principal Findings

In the present study, we manipulated auditory feedback during speech production in a group of 9–11-year old children, as well as in adults. Following a period of speech practice under conditions of altered auditory feedback, compensatory changes in speech production and perception were examined. Consistent with prior studies, the adults exhibited compensatory changes in both their speech motor output and their perceptual representations of speech sound categories. The children exhibited compensatory changes in the motor domain, with a change in speech output that was similar in magnitude to that of the adults, however the children showed no reliable compensatory effect on their perceptual representations.

Conclusions

The results indicate that 9–11-year-old children, whose speech motor and perceptual abilities are still not fully developed, are nonetheless capable of auditory-feedback-based sensorimotor adaptation, supporting a role for such learning processes in speech motor development. Auditory feedback may play a more limited role, however, in the fine-tuning of children''s perceptual representations of speech sound categories.     

Male facial attractiveness,perceived personality,and child-directed speech

This study investigated associations between men's facial attractiveness, perceived personality, attitudes towards children, and the quality of their child-directed (CD) speech. Sixty-three males were photographed and completed a brief questionnaire concerning their family background and attitudes towards children. They then performed a task in which they gave directions to (imaginary) adults and children. Analyses of the acoustic properties of speech produced under each condition were performed in order to determine the extent to which individual men changed their speech to accommodate a child listener (i.e., exhibited CD speech). The men's faces were rated by 59 female participants, who assessed perceived prosociality, masculinity, health, and short- and long-term attractiveness. Although women's ratings of attractiveness and prosociality were related to men's self-reported liking for children, they were negatively correlated to men's use of CD speech (i.e., less attractive men used more features of CD speech when addressing an imaginary child). These findings are discussed in the context of halo effects and strategic pluralism in male mating behaviors.     

Evaluation of a structured test and a parent led method for screening for speech and language problems: prospective population based study

ObjectiveTo evaluate two methods for identifying speech and language problems in preschool children.DesignProspective population based study.SettingInner London.ResultsReference assessments and usable scores were obtained for 458 (97%) of the 474 children screened. 98 (21%) children had severe language problems and 131 (29%) needed therapy. The sensitivity and specificity for the structured screening test were 66% (95% confidence interval 53% to 76%) and 89% (85% to 93%) respectively for severe language problems and 54% (43% to 65%) and 90% (85% to 93%) for those needing therapy. The sensitivity and specificity for referral by the parent led method were 56% (40% to 71%) and 85% (78% to 90%) for severe language problems and 58% (44% to 71%) and 90% (83% to 94%) for those needing speech and language therapy.ConclusionsBoth approaches failed to detect a substantial proportion of children with severe language problems and led to over-referral for diagnostic assessments. Screening is likely to be an ineffective approach to the management of speech and language problems in preschool children in this population.

What is already known on this topic

Moderate to severe language difficulties in young children are predictive of long term problems affecting learning, school achievement, and behaviourFormal screening tests are widely used, but relying on parents'' observations and health professionals'' clinical judgment may be more effective in identifying children needing therapy

What this study adds

A commonly used screening test and an approach based on parents'' observations and health visitors'' judgment fail to identify a substantial proportion of children with serious language problems and lead to the over-referral of children without serious difficulties     

The Biological Origin of Linguistic Diversity

In contrast with animal communication systems, diversity is characteristic of almost every aspect of human language. Languages variously employ tones, clicks, or manual signs to signal differences in meaning; some languages lack the noun-verb distinction (e.g., Straits Salish), whereas others have a proliferation of fine-grained syntactic categories (e.g., Tzeltal); and some languages do without morphology (e.g., Mandarin), while others pack a whole sentence into a single word (e.g., Cayuga). A challenge for evolutionary biology is to reconcile the diversity of languages with the high degree of biological uniformity of their speakers. Here, we model processes of language change and geographical dispersion and find a consistent pressure for flexible learning, irrespective of the language being spoken. This pressure arises because flexible learners can best cope with the observed high rates of linguistic change associated with divergent cultural evolution following human migration. Thus, rather than genetic adaptations for specific aspects of language, such as recursion, the coevolution of genes and fast-changing linguistic structure provides the biological basis for linguistic diversity. Only biological adaptations for flexible learning combined with cultural evolution can explain how each child has the potential to learn any human language.     

DIAGNOSIS OF SCHIZOPHRENIA IN YOUNG CHILDREN

Schizophrenia can be discovered in pre-school children by observation of: Social indifference; uneven and intermittent motor or physical development; irregularity in speech development with tendency toward infantile speech; early fear of falling or rising, giving way to obsession with jumping and falling; excessive interest in spinning toys and circular motility; and preoccupation with body periphery—hands, feet and hair.When the physician observes these symptoms, or is consulted about them by the parents, clinical appraisal in consultation with a pediatric psychiatrist will usually suffice for diagnosis. Early treatment—before school age—is important for the child''s future development.     

Wernicke's area homologue in chimpanzees (Pan troglodytes) and its relation to the appearance of modern human language

Human language is distinctive compared with the communication systems of other species. Yet, several questions concerning its emergence and evolution remain unresolved. As a means of evaluating the neuroanatomical changes relevant to language that accompanied divergence from the last common ancestor of chimpanzees, bonobos and humans, we defined the cytoarchitectonic boundaries of area Tpt, a component of Wernicke''s area, in 12 common chimpanzee brains and used design-based stereologic methods to estimate regional volumes, total neuron number and neuron density. In addition, we created a probabilistic map of the location of area Tpt in a template chimpanzee brain coordinate space. Our results show that chimpanzees display significant population-level leftward asymmetry of area Tpt in terms of neuron number, with volume asymmetry approaching significance. Furthermore, asymmetry in the number of neurons in area Tpt was positively correlated with asymmetry of neuron numbers in Brodmann''s area 45, a component of Broca''s frontal language region. Our findings support the conclusion that leftward asymmetry of Wernicke''s area originated prior to the appearance of modern human language and before our divergence from the last common ancestor. Moreover, this study provides the first evidence of covariance between asymmetry of anterior and posterior cortical regions that in humans are important to language and other higher order cognitive functions.     

Duration and variability of speech segments in fluent speech of children with and without stuttering

The purpose of this study was to compare the duration and variability of speech segments of children who stutter with those of children who do not stutter and to identify changes in duration and variability of speech segments due to the effect of utterance length. Eighteen children participated (ranging from 6.3 to 7.9 years of age). The experimental task required the children to repeat a single word in isolation and the same word embedded in a sentence. Durations of speech segments and Coefficients of variation (Cv) were defined to assess temporal parameters of speech. Significant differences were found in the variability of speech segments on the sentence level, but not in duration. The findings supported the assumption that linguistic factors pose direct demands on the speech motor system and that the extra duration of speech segments observed in the speech of stuttering adults may be a kind of compensation strategy.     

The sound symbolism bootstrapping hypothesis for language acquisition and language evolution

Sound symbolism is a non-arbitrary relationship between speech sounds and meaning. We review evidence that, contrary to the traditional view in linguistics, sound symbolism is an important design feature of language, which affects online processing of language, and most importantly, language acquisition. We propose the sound symbolism bootstrapping hypothesis, claiming that (i) pre-verbal infants are sensitive to sound symbolism, due to a biologically endowed ability to map and integrate multi-modal input, (ii) sound symbolism helps infants gain referential insight for speech sounds, (iii) sound symbolism helps infants and toddlers associate speech sounds with their referents to establish a lexical representation and (iv) sound symbolism helps toddlers learn words by allowing them to focus on referents embedded in a complex scene, alleviating Quine''s problem. We further explore the possibility that sound symbolism is deeply related to language evolution, drawing the parallel between historical development of language across generations and ontogenetic development within individuals. Finally, we suggest that sound symbolism bootstrapping is a part of a more general phenomenon of bootstrapping by means of iconic representations, drawing on similarities and close behavioural links between sound symbolism and speech-accompanying iconic gesture.