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.     

Spatio-Temporal Dynamics of Cholera during the First Year of the Epidemic in Haiti

Background

In October 2010, cholera importation in Haiti triggered an epidemic that rapidly proved to be the world''s largest epidemic of the seventh cholera pandemic. To establish effective control and elimination policies, strategies rely on the analysis of cholera dynamics. In this report, we describe the spatio-temporal dynamics of cholera and the associated environmental factors.

Methodology/Principal findings

Cholera-associated morbidity and mortality data were prospectively collected at the commune level according to the World Health Organization standard definition. Attack and mortality rates were estimated and mapped to assess epidemic clusters and trends. The relationships between environmental factors were assessed at the commune level using multivariate analysis. The global attack and mortality rates were 488.9 cases/10,000 inhabitants and 6.24 deaths/10,000 inhabitants, respectively. Attack rates displayed a significantly high level of spatial heterogeneity (varying from 64.7 to 3070.9 per 10,000 inhabitants), thereby suggesting disparate outbreak processes. The epidemic course exhibited two principal outbreaks. The first outbreak (October 16, 2010–January 30, 2011) displayed a centrifugal spread of a damping wave that suddenly emerged from Mirebalais. The second outbreak began at the end of May 2011, concomitant with the onset of the rainy season, and displayed a highly fragmented epidemic pattern. Environmental factors (river and rice fields: p<0.003) played a role in disease dynamics exclusively during the early phases of the epidemic.

Conclusion

Our findings demonstrate that the epidemic is still evolving, with a changing transmission pattern as time passes. Such an evolution could have hardly been anticipated, especially in a country struck by cholera for the first time. These results argue for the need for control measures involving intense efforts in rapid and exhaustive case tracking.     

The new school absentees reporting system for pandemic influenza A/H1N1 2009 infection in Japan

Objective

To evaluate the new Japanese School Absentees Reporting System for Infectious Disease (SARSID) for pandemic influenza A/H1N1 2009 infection in comparison with the National epidemiological Surveillance of Infectious Disease (NESID).

Methods

We used data of 53,223 students (97.7%) in Takamatsu city Japan. Data regarding school absentees in SARSID was compared with that in NESID from Oct 13, 2009 to Jan 12, 2010.

Results

Similar trends were observed both in SARSID and NESID. However, the epidemic trend for influenza in SARSID was thought to be more sensitive than that in NESID.

Conclusion

The epidemic trend for influenza among school-aged children could be easily and rapidly assessed by SARSID compared to NESID. SARSID might be useful for detecting the epidemic trend of influenza.     

Pandemic (H1N1) 2009 Influenza Community Transmission Was Established in One Australian State When the Virus Was First Identified in North America

Background

In mid-June 2009 the State of Victoria in Australia appeared to have the highest notification rate of pandemic (H1N1) 2009 influenza in the world. We hypothesise that this was because community transmission of pandemic influenza was already well established in Victoria at the time testing for the novel virus commenced. In contrast, this was not true for the pandemic in other parts of Australia, including Western Australia (WA).

Methods

We used data from detailed case follow-up of patients with confirmed infection in Victoria and WA to demonstrate the difference in the pandemic curve in two Australian states on opposite sides of the continent. We modelled the pandemic in both states, using a susceptible-infected-removed model with Bayesian inference accounting for imported cases.

Results

Epidemic transmission occurred earlier in Victoria and later in WA. Only 5% of the first 100 Victorian cases were not locally acquired and three of these were brothers in one family. By contrast, 53% of the first 102 cases in WA were associated with importation from Victoria. Using plausible model input data, estimation of the effective reproductive number for the Victorian epidemic required us to invoke an earlier date for commencement of transmission to explain the observed data. This was not required in modelling the epidemic in WA.

Conclusion

Strong circumstantial evidence, supported by modelling, suggests community transmission of pandemic influenza was well established in Victoria, but not in WA, at the time testing for the novel virus commenced in Australia. The virus is likely to have entered Victoria and already become established around the time it was first identified in the US and Mexico.     

Khat use is associated with impaired working memory and cognitive flexibility

Rationale

Khat consumption has increased during the last decades in Eastern Africa and has become a global phenomenon spreading to ethnic communities in the rest of the world, such as The Netherlands, United Kingdom, Canada, and the United States. Very little is known, however, about the relation between khat use and cognitive control functions in khat users.

Objective

We studied whether khat use is associated with changes in working memory (WM) and cognitive flexibility, two central cognitive control functions.

Methods

Khat users and khat-free controls were matched in terms of sex, ethnicity, age, alcohol and cannabis consumption, and IQ (Raven''s progressive matrices). Groups were tested on cognitive flexibility, as measured by a Global-Local task, and on WM using an N-back task.

Result

Khat users performed significantly worse than controls on tasks tapping into cognitive flexibility as well as monitoring of information in WM.

Conclusions

The present findings suggest that khat use impairs both cognitive flexibility and the updating of information in WM. The inability to monitor information in WM and to adjust behavior rapidly and flexibly may have repercussions for daily life activities.     

The strength of genetic interactions scales weakly with mutational effects

Background

Genetic interactions pervade every aspect of biology, from evolutionary theory, where they determine the accessibility of evolutionary paths, to medicine, where they can contribute to complex genetic diseases. Until very recently, studies on epistatic interactions have been based on a handful of mutations, providing at best anecdotal evidence about the frequency and the typical strength of genetic interactions. In this study, we analyze a publicly available dataset that contains the growth rates of over five million double knockout mutants of the yeast Saccharomyces cerevisiae.

Results

We discuss a geometric definition of epistasis that reveals a simple and surprisingly weak scaling law for the characteristic strength of genetic interactions as a function of the effects of the mutations being combined. We then utilized this scaling to quantify the roughness of naturally occurring fitness landscapes. Finally, we show how the observed roughness differs from what is predicted by Fisher''s geometric model of epistasis, and discuss the consequences for evolutionary dynamics.

Conclusions

Although epistatic interactions between specific genes remain largely unpredictable, the statistical properties of an ensemble of interactions can display conspicuous regularities and be described by simple mathematical laws. By exploiting the amount of data produced by modern high-throughput techniques, it is now possible to thoroughly test the predictions of theoretical models of genetic interactions and to build informed computational models of evolution on realistic fitness landscapes.     

Size-dependent leaf area ratio in plant twigs: implication for leaf size optimization

Background and Aims

Although many hypotheses have been proposed to explain variation in leaf size, the mechanism underlying the variation remains not fully understood. To help understand leaf size variation, the cost/benefit of twig size was analysed, since, according to Corner''s rule, twig size is positively correlated with the size of appendages the twig bears.

Methods

An extensive survey of twig functional traits, including twig (current-year shoots including one stem and few leaves) and leaf size (individual leaf area and mass), was conducted for 234 species from four broadleaved forests. The scaling relationship between twig mass and leaf area was determined using standardized major axis regression and phylogenetic independent comparative analyses.

Key Results

Leaf area was found to scale positively and allometrically with both stem and twig mass (stem mass plus leaf mass) with slopes significantly smaller than 1·0, independent of life form and habitat type. Thus, the leaf area ratio (the ratio of total leaf area to stem or twig mass) decreases with increasing twig size. Moreover, the leaf area ratio correlated negatively with individual leaf mass. The results of phylogenetic independent comparativeanalyses were consistent with the correlations. Based on the above results, a simple model for twig size optimization was constructed, from which it is postulated that large leaf size–twig size may be favoured when leaf photosynthetic capacity is high and/or when leaf life span and/or stem longevity are long. The model''s predictions are consistent with leaf size variation among habitats, in which leaf size tends to be small in poor habitats with a low primary productivity. The model also explains large variations in leaf size within habitats for which leaf longevity and stem longevity serve as important determinants.

Conclusions

The diminishing returns in the scaling of total leaf area with twig size can be explained in terms of a very simple model on twig size optimization.Key words: Allometry, leaf size, twig size, leaf area ratio, scaling relationship, broadleaved species     

Dopaminergic Neuronal Imaging in Genetic Parkinson's Disease: Insights into Pathogenesis

Objectives

To compare the dopaminergic neuronal imaging features of different subtypes of genetic Parkinson''s Disease.

Methods

A retrospective study of genetic Parkinson''s diseases cases in which DaTSCAN (123I-FP-CIT) had been performed. Specific non-displaceable binding was calculated for bilateral caudate and putamen for each case. The right:left asymmetry index and striatal asymmetry index was calculated.

Results

Scans were available from 37 cases of monogenetic Parkinson''s disease (7 glucocerebrosidase (GBA) mutations, 8 alpha-synuclein, 3 LRRK2, 7 PINK1, 12 Parkin). The asymmetry of radioligand uptake for Parkinson''s disease with GBA or LRRK2 mutations was greater than that for Parkinson''s disease with alpha synuclein, PINK1 or Parkin mutations.

Conclusions

The asymmetry of radioligand uptake in Parkinsons disease associated with GBA or LRRK2 mutations suggests that interactions with additional genetic or environmental factors may be associated with dopaminergic neuronal loss.     

Public Hygiene Campaign in Denmark during the 2009 H1N1 Pandemic Had No Effect on Hospitalization Rate of Communicable Diseases in Children

Background

During the 2009 H1N1 pandemic the Danish National board of Health carried out massive public hygiene campaigns to limit spread of disease. We aimed to investigate whether this resulted in lower incidences of communicable diseases in the paediatric population.

Methods

The study compared annual hospitalization rates for childhood infections from 2005 to 2011.

Results

Admission rates for infections were higher during the year of the pandemic compared to the rest of the period.

Conclusion

There were no indications of a preventive effect by the hygiene campaign on incidence of severe common childhood infections.     

Forever Love: The Hitherto Earliest Record of Copulating Insects from the Middle Jurassic of China

Background

Mating behaviors have been widely studied for extant insects. However, cases of mating individuals are particularly rare in the fossil record of insects, and most of them involved preservation in amber while only in rare cases found in compression fossils. This considerably limits our knowledge of mating position and genitalia orientation during the Mesozoic, and hinders our understanding of the evolution of mating behaviors in this major component of modern ecosystems.

Principal Finding

Here we report a pair of copulating froghoppers, Anthoscytina perpetua sp. nov., referable to the Procercopidae, from the Middle Jurassic of northeastern China. They exhibit belly-to-belly mating position as preserved, with male''s aedeagus inserting into the female''s bursa copulatrix. Abdominal segments 8 to 9 of male are disarticulated suggesting these segments were twisted and flexed during mating. Due to potential taphonomic effect, we cannot rule out that they might have taken side-by-side position, as in extant froghoppers. Genitalia of male and female, based on paratypes, show symmetric structures.

Conclusions/Significance

Our findings, consistent with those of extant froghoppers, indicate froghoppers'' genitalic symmetry and mating position have remained static for over 165 million years.     

Diagnosis and antiviral intervention strategies for mitigating an influenza epidemic

Background

Many countries have amassed antiviral stockpiles for pandemic preparedness. Despite extensive trial data and modelling studies, it remains unclear how to make optimal use of antiviral stockpiles within the constraints of healthcare infrastructure. Modelling studies informed recommendations for liberal antiviral distribution in the pandemic phase, primarily to prevent infection, but failed to account for logistical constraints clearly evident during the 2009 H1N1 outbreaks.Here we identify optimal delivery strategies for antiviral interventions accounting for logistical constraints, and so determine how to improve a strategy''s impact.

Methods and Findings

We extend an existing SEIR model to incorporate finite diagnostic and antiviral distribution capacities. We evaluate the impact of using different diagnostic strategies to decide to whom antivirals are delivered. We then determine what additional capacity is required to achieve optimal impact. We identify the importance of sensitive and specific case ascertainment in the early phase of a pandemic response, when the proportion of false-positive presentations may be high. Once a substantial percentage of ILI presentations are caused by the pandemic strain, identification of cases for treatment on syndromic grounds alone results in a greater potential impact than a laboratory-dependent strategy. Our findings reinforce the need for a decentralised system capable of providing timely prophylaxis.

Conclusions

We address specific real-world issues that must be considered in order to improve pandemic preparedness policy in a practical and methodologically sound way. Provision of antivirals on the scale proposed for an effective response is infeasible using traditional public health outbreak management and contact tracing approaches. The results indicate to change the transmission dynamics of an influenza epidemic with an antiviral intervention, a decentralised system is required for contact identification and prophylaxis delivery, utilising a range of existing services and infrastructure in a “whole of society” response.     

Incipient cognition solves the spatial reciprocity conundrum of cooperation

Background

From the simplest living organisms to human societies, cooperation among individuals emerges as a paradox difficult to explain and describe mathematically, although very often observed in reality. Evolutionary game theory offers an excellent toolbar to investigate this issue. Spatial structure has been one of the first mechanisms promoting cooperation; however, alone it only opens a narrow window of viability.

Methodology/Principal Findings

Here we equip individuals with incipient cognitive abilities, and investigate the evolution of cooperation in a spatial world where retaliation, forgiveness, treason and mutualism may coexist, as individuals engage in Prisoner''s Dilemma games. In the model, individuals are able to distinguish their partners and act towards them based on previous interactions. We show how the simplest level of cognition, alone, can lead to the emergence of cooperation.

Conclusions/Significance

Despite the incipient nature of the individuals'' cognitive abilities, cooperation emerges for unprecedented values of the temptation to cheat, being also robust to invasion by cheaters, errors in decision making and inaccuracy of imitation, features akin to many species, including humans.     

Identification of Direct and Indirect Social Network Effects in the Pathophysiology of Insulin Resistance in Obese Human Subjects

Objective

The aim of the present study was to examine to what extent different social network mechanisms are involved in the pathogenesis of obesity and insulin-resistance.

Design

We used nonparametric and parametric regression models to analyse whether individual BMI and HOMA-IR are determined by social network characteristics.

Subjects and Methods

A total of 677 probands (EGO) and 3033 social network partners (ALTER) were included in the study. Data gathered from the probands include anthropometric measures, HOMA-IR index, health attitudes, behavioural and socio-economic variables and social network data.

Results

We found significant treatment effects for ALTERs frequent dieting (p<0.001) and ALTERs health oriented nutritional attitudes (p<0.001) on EGO''s BMI, establishing a significant indirect network effect also on EGO''s insulin resistance. Most importantly, we also found significant direct social network effects on EGO''s insulin resistance, evidenced by an effect of ALTERs frequent dieting (p = 0.033) and ALTERs sport activities (p = 0.041) to decrease EGO''s HOMA-IR index independently of EGO''s BMI.

Conclusions

Social network phenomena appear not only to be relevant for the spread of obesity, but also for the spread of insulin resistance as the basis for type 2 diabetes. Attitudes and behaviour of peer groups influence EGO''s health status not only via social mechanisms, but also via socio-biological mechanisms, i.e. higher brain areas might be influenced not only by biological signals from the own organism, but also by behaviour and knowledge from different human individuals. Our approach allows the identification of peer group influence controlling for potential homophily even when using cross-sectional observational data.     

A Novel Approach - The Propensity to Propagate (PTP) Method for Controlling for Host Factors in Studying the Transmission of Mycobacterium Tuberculosis

Rationale

Understanding the genetic variations among Mycobacterium tuberculosis (MTB) strains with differential ability to transmit would be a major step forward in preventing transmission.

Objectives

To describe a method to extend conventional proxy measures of transmissibility by adjusting for patient-related factors, thus strengthening the causal association found with bacterial factors.

Methods

Clinical, demographic and molecular fingerprinting data were obtained during routine surveillance of verified MTB cases reported in the Netherlands between 1993 and 2011, and the phylogenetic lineages of the isolates were inferred. Odds ratios for host risk factors for clustering were used to obtain a measure of each patient''s and cluster''s propensity to propagate (CPP). Mean and median cluster sizes across different categories of CPP were compared amongst four different phylogenetic lineages.

Results

Both mean and median cluster size grew with increasing CPP category. On average, CPP values from Euro-American lineage strains were higher than Beijing and EAI strains. There were no significant differences between the mean and median cluster sizes among the four phylogenetic lineages within each CPP category.

Conclusions

Our finding that the distribution of CPP scores was unequal across four different phylogenetic lineages supports the notion that host-related factors should be controlled for to attain comparability in measuring the different phylogenetic lineages'' ability to propagate. Although Euro-American strains were more likely to be in clusters in an unadjusted analysis, no significant differences among the four lineages persisted after we controlled for host factors.     

Prevalence of 2009 pandemic influenza A (H1N1) virus antibodies, Tampa Bay Florida--November-December, 2009

Background

In 2009, a novel influenza virus (2009 pandemic influenza A (H1N1) virus (pH1N1)) caused significant disease in the United States. Most states, including Florida, experienced a large fall wave of disease from September through November, after which disease activity decreased substantially. We determined the prevalence of antibodies due to the pH1N1 virus in Florida after influenza activity had peaked and estimated the proportion of the population infected with pH1N1 virus during the pandemic.

Methods

During November-December 2009, we collected leftover serum from a blood bank, a pediatric children''s hospital and a pediatric outpatient clinic in Tampa Bay Florida. Serum was tested for pH1N1 virus antibodies using the hemagglutination-inhibition (HI) assay. HI titers ≥40 were considered seropositive. We adjusted seroprevalence results to account for previously established HI assay specificity and sensitivity and employed a simple statistical model to estimate the proportion of seropositivity due to pH1N1 virus infection and vaccination.

Results

During the study time period, the overall seroprevalence in Tampa Bay, Florida was 25%, increasing to 30% after adjusting for HI assay sensitivity and specificity. We estimated that 5.9% of the population had vaccine-induced seropositivity while 25% had seropositivity secondary to pH1N1 virus infection. The highest cumulative incidence of pH1N1 virus infection was among children aged 5–17 years (53%) and young adults aged 18–24 years (47%), while adults aged ≥50 years had the lowest cumulative incidence (11–13%) of pH1N1 virus infection.

Conclusions

After the peak of the fall wave of the pandemic, an estimated one quarter of the Tampa Bay population had been infected with the pH1N1 virus. Consistent with epidemiologic trends observed during the pandemic, the highest burdens of disease were among school-aged children and young adults.     

Effect of the H1N1 influenza pandemic on the incidence of epidemic keratoconjunctivitis and on hygiene behavior: a cross-sectional study

Background

EKC is transmitted chiefly by direct hand contact. It is suspected that the 2009/2010 influenza pandemic influenced hand washing. This study aims to examine the relationship between the 2009/2010 H1N1 influenza pandemic and hygiene behavior.

Methods

We compared the EKC prevalence trends before, during and after the 2009/2010 influenza pandemic by using a t-test comparison of EKC sentinel surveillance.

Results

During the pre-pandemic period, the incidence of EKC increased from the 21st to the 44th week each year. However, during the pandemic period in 2009, there was no epidemic peak. In the post-pandemic period, the epidemic curve was similar to that in the pre-pandemic period. Compared to the pre-pandemic period, the total number of EKC patients during the pandemic period showed a decrease of 44.9% (t value = −7.23, p = 0.002). Comparing the pre-pandemic and pandemic periods by age group, we found there to be a significant decrease in the number of EKC patients for all age groups (−4.12≤t value≤−7.23, all P<0.05). This finding was most evident in the teenage group (62%) compared to the other age groups (decreases of 29 to 44%).

Conclusions

A continuing effort should be made to educate the public on basic infection prevention behaviors in the aftermath of the pandemic, particularly to teenagers.