PLoS ONE Alerts: Mathematics

The Astronomical Orientation of Ancient Greek Temples

2009-11-19T08:00:00Z

Despite its appearing to be a simple question to answer, there has been no consensus as to whether or not the alignments of ancient Greek temples reflect astronomical intentions. Here I present the results of a survey of archaic and classical Greek temples in Sicily and compare them with temples in Greece. Using a binomial test I show strong evidence that there is a preference for solar orientations. I then speculate that differences in alignment patterns between Sicily and Greece reflect differing pressures in the expression of ethnic identity.

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

2009-11-11T08:00:00Z

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.

Reduced Physiological Complexity in Robust Elderly Adults with the APOE ε4 Allele

2009-11-05T08:00:00Z

Background

It is unclear whether the loss of physiological complexity during the aging process is due to genetic variations. The APOE gene has been studied extensively in regard to its relationship with aging-associated medical illness. We hypothesize that diminished physiological complexity, as measured by heart rate variability, is influenced by polymorphisms in the APOE allele among elderly individuals.

Methodology/Principal Findings

A total of 102 robust, non-demented, elderly subjects with normal functions of daily activities participated in this study (97 males and 5 females, aged 79.2±4.4 years, range 72–92 years). Among these individuals, the following two APOE genotypes were represented: ε4 non-carriers (n = 87, 85.3%) and ε4 carriers (n = 15, 14.7%). Multi-scale entropy (MSE), an analysis used in quantifying complexity for nonlinear time series, was employed to analyze heart-rate dynamics. Reduced physiological complexity, as measured by MSE, was significantly associated with the presence of the APOE ε4 allele in healthy elderly subjects, as compared to APOE ε4 allele non-carriers (24.6±5.5 versus 28.9±5.2, F = 9.429, p = 0.003, respectively).

Conclusions/Significance

This finding suggests a role for the APOE gene in the diminished physiological complexity seen in elderly populations.

A Modeling Framework to Describe the Transmission of Bluetongue Virus within and between Farms in Great Britain

2009-11-05T08:00:00Z

Background

Recently much attention has been given to developing national-scale micro-simulation models for livestock diseases that can be used to predict spread and assess the impact of control measures. The focus of these models has been on directly transmitted infections with little attention given to vector-borne diseases such as bluetongue, a viral disease of ruminants transmitted by Culicoides biting midges. Yet BT has emerged over the past decade as one of the most important diseases of livestock.

Methodology/Principal Findings

We developed a stochastic, spatially-explicit, farm-level model to describe the spread of bluetongue virus (BTV) within and between farms. Transmission between farms was modeled by a generic kernel, which includes both animal and vector movements. Once a farm acquired infection, the within-farm dynamics were simulated based on the number of cattle and sheep kept on the farm and on local temperatures. Parameter estimates were derived from the published literature and using data from the outbreak of bluetongue in northern Europe in 2006. The model was validated using data on the spread of BTV in Great Britain during 2007. The sensitivity of model predictions to the shape of the transmission kernel was assessed.

Conclusions/Significance

The model is able to replicate the dynamics of BTV in Great Britain. Although uncertainty remains over the precise shape of the transmission kernel and certain aspects of the vector, the modeling approach we develop constitutes an ideal framework in which to incorporate these aspects as more and better data become available. Moreover, the model provides a tool with which to examine scenarios for the spread and control of BTV in Great Britain.

Fast and Flexible Selection with a Single Switch

2009-10-22T07:00:00Z

Selection methods that require only a single-switch input, such as a button click or blink, are potentially useful for individuals with motor impairments, mobile technology users, and individuals wishing to transmit information securely. We present a single-switch selection method, “Nomon,” that is general and efficient. Existing single-switch selection methods require selectable options to be arranged in ways that limit potential applications. By contrast, traditional operating systems, web browsers, and free-form applications (such as drawing) place options at arbitrary points on the screen. Nomon, however, has the flexibility to select any point on a screen. Nomon adapts automatically to an individual's clicking ability; it allows a person who clicks precisely to make a selection quickly and allows a person who clicks imprecisely more time to make a selection without error. Nomon reaps gains in information rate by allowing the specification of beliefs (priors) about option selection probabilities and by avoiding tree-based selection schemes in favor of direct (posterior) inference. We have developed both a Nomon-based writing application and a drawing application. To evaluate Nomon's performance, we compared the writing application with a popular existing method for single-switch writing (row-column scanning). Novice users wrote 35% faster with the Nomon interface than with the scanning interface. An experienced user (author TB, with 10 hours practice) wrote at speeds of 9.3 words per minute with Nomon, using 1.2 clicks per character and making no errors in the final text.

Influenza A Gradual and Epochal Evolution: Insights from Simple Models

2009-10-20T07:00:00Z

The recurrence of influenza A epidemics has originally been explained by a “continuous antigenic drift” scenario. Recently, it has been shown that if genetic drift is gradual, the evolution of influenza A main antigen, the haemagglutinin, is punctuated. As a consequence, it has been suggested that influenza A dynamics at the population level should be approximated by a serial model. Here, simple models are used to test whether a serial model requires gradual antigenic drift within groups of strains with the same antigenic properties (antigenic clusters). We compare the effect of status based and history based frameworks and the influence of reduced susceptibility and infectivity assumptions on the transient dynamics of antigenic clusters. Our results reveal that the replacement of a resident antigenic cluster by a mutant cluster, as observed in data, is reproduced only by the status based model integrating the reduced infectivity assumption. This combination of assumptions is useful to overcome the otherwise extremely high model dimensionality of models incorporating many strains, but relies on a biological hypothesis not obviously satisfied. Our findings finally suggest the dynamical importance of gradual antigenic drift even in the presence of punctuated immune escape. A more regular renewal of susceptible pool than the one implemented in a serial model should be part of a minimal theory for influenza at the population level.

Balancing with Vibration: A Prelude for “Drift and Act” Balance Control

2009-10-20T07:00:00Z

Stick balancing at the fingertip is a powerful paradigm for the study of the control of human balance. Here we show that the mean stick balancing time is increased by about two-fold when a subject stands on a vibrating platform that produces vertical vibrations at the fingertip (0.001 m, 15–50 Hz). High speed motion capture measurements in three dimensions demonstrate that vibration does not shorten the neural latency for stick balancing or change the distribution of the changes in speed made by the fingertip during stick balancing, but does decrease the amplitude of the fluctuations in the relative positions of the fingertip and the tip of the stick in the horizontal plane, A(x,y). The findings are interpreted in terms of a time-delayed “drift and act” control mechanism in which controlling movements are made only when controlled variables exceed a threshold, i.e. the stick survival time measures the time to cross a threshold. The amplitude of the oscillations produced by this mechanism can be decreased by parametric excitation. It is shown that a plot of the logarithm of the vibration-induced increase in stick balancing skill, a measure of the mean first passage time, versus the standard deviation of the A(x,y) fluctuations, a measure of the distance to the threshold, is linear as expected for the times to cross a threshold in a stochastic dynamical system. These observations suggest that the balanced state represents a complex time–dependent state which is situated in a basin of attraction that is of the same order of size. The fact that vibration amplitude can benefit balance control raises the possibility of minimizing risk of falling through appropriate changes in the design of footwear and roughness of the walking surfaces.

Using Dynamic Stochastic Modelling to Estimate Population Risk Factors in Infectious Disease: The Example of FIV in 15 Cat Populations

2009-10-16T07:00:00Z

Background

In natural cat populations, Feline Immunodeficiency Virus (FIV) is transmitted through bites between individuals. Factors such as the density of cats within the population or the sex-ratio can have potentially strong effects on the frequency of fight between individuals and hence appear as important population risk factors for FIV.

Methodology/Principal Findings

To study such population risk factors, we present data on FIV prevalence in 15 cat populations in northeastern France. We investigate five key social factors of cat populations; the density of cats, the sex-ratio, the number of males and the mean age of males and females within the population. We overcome the problem of dependence in the infective status data using sexually-structured dynamic stochastic models. Only the age of males and females had an effect (p = 0.043 and p = 0.02, respectively) on the male-to-female transmission rate. Due to multiple tests, it is even likely that these effects are, in reality, not significant. Finally we show that, in our study area, the data can be explained by a very simple model that does not invoke any risk factor.

Conclusion

Our conclusion is that, in host-parasite systems in general, fluctuations due to stochasticity in the transmission process are naturally very large and may alone explain a larger part of the variability in observed disease prevalence between populations than previously expected. Finally, we determined confidence intervals for the simple model parameters that can be used to further aid in management of the disease.

Empirical Bayes Analysis of Quantitative Proteomics Experiments

2009-10-14T07:00:00Z

Background

Advances in mass spectrometry-based proteomics have enabled the incorporation of proteomic data into systems approaches to biology. However, development of analytical methods has lagged behind. Here we describe an empirical Bayes framework for quantitative proteomics data analysis. The method provides a statistical description of each experiment, including the number of proteins that differ in abundance between 2 samples, the experiment's statistical power to detect them, and the false-positive probability of each protein.

Methodology/Principal Findings

We analyzed 2 types of mass spectrometric experiments. First, we showed that the method identified the protein targets of small-molecules in affinity purification experiments with high precision. Second, we re-analyzed a mass spectrometric data set designed to identify proteins regulated by microRNAs. Our results were supported by sequence analysis of the 3′ UTR regions of predicted target genes, and we found that the previously reported conclusion that a large fraction of the proteome is regulated by microRNAs was not supported by our statistical analysis of the data.

Conclusions/Significance

Our results highlight the importance of rigorous statistical analysis of proteomic data, and the method described here provides a statistical framework to robustly and reliably interpret such data.

Evolution with Stochastic Fitness and Stochastic Migration

2009-10-09T07:00:00Z

Background

Migration between local populations plays an important role in evolution - influencing local adaptation, speciation, extinction, and the maintenance of genetic variation. Like other evolutionary mechanisms, migration is a stochastic process, involving both random and deterministic elements. Many models of evolution have incorporated migration, but these have all been based on simplifying assumptions, such as low migration rate, weak selection, or large population size. We thus have no truly general and exact mathematical description of evolution that incorporates migration.

Methodology/Principal Findings

We derive an exact equation for directional evolution, essentially a stochastic Price equation with migration, that encompasses all processes, both deterministic and stochastic, contributing to directional change in an open population. Using this result, we show that increasing the variance in migration rates reduces the impact of migration relative to selection. This means that models that treat migration as a single parameter tend to be biassed - overestimating the relative impact of immigration. We further show that selection and migration interact in complex ways, one result being that a strategy for which fitness is negatively correlated with migration rates (high fitness when migration is low) will tend to increase in frequency, even if it has lower mean fitness than do other strategies. Finally, we derive an equation for the effective migration rate, which allows some of the complex stochastic processes that we identify to be incorporated into models with a single migration parameter.

Conclusions/Significance

As has previously been shown with selection, the role of migration in evolution is determined by the entire distributions of immigration and emigration rates, not just by the mean values. The interactions of stochastic migration with stochastic selection produce evolutionary processes that are invisible to deterministic evolutionary theory.

Metagenomic Analysis of Respiratory Tract DNA Viral Communities in Cystic Fibrosis and Non-Cystic Fibrosis Individuals

2009-10-09T07:00:00Z

The human respiratory tract is constantly exposed to a wide variety of viruses, microbes and inorganic particulates from environmental air, water and food. Physical characteristics of inhaled particles and airway mucosal immunity determine which viruses and microbes will persist in the airways. Here we present the first metagenomic study of DNA viral communities in the airways of diseased and non-diseased individuals. We obtained sequences from sputum DNA viral communities in 5 individuals with cystic fibrosis (CF) and 5 individuals without the disease. Overall, diversity of viruses in the airways was low, with an average richness of 175 distinct viral genotypes. The majority of viral diversity was uncharacterized. CF phage communities were highly similar to each other, whereas Non-CF individuals had more distinct phage communities, which may reflect organisms in inhaled air. CF eukaryotic viral communities were dominated by a few viruses, including human herpesviruses and retroviruses. Functional metagenomics showed that all Non-CF viromes were similar, and that CF viromes were enriched in aromatic amino acid metabolism. The CF metagenomes occupied two different metabolic states, probably reflecting different disease states. There was one outlying CF virome which was characterized by an over-representation of Guanosine-5′-triphosphate,3′-diphosphate pyrophosphatase, an enzyme involved in the bacterial stringent response. Unique environments like the CF airway can drive functional adaptations, leading to shifts in metabolic profiles. These results have important clinical implications for CF, indicating that therapeutic measures may be more effective if used to change the respiratory environment, as opposed to shifting the taxonomic composition of resident microbiota.

The Impact of Nature Experience on Willingness to Support Conservation

2009-10-07T07:00:00Z

We hypothesized that willingness to financially support conservation depends on one's experience with nature. In order to test this hypothesis, we used a novel time-lagged correlation analysis to look at times series data concerning nature participation, and evaluate its relationship with future conservation support (measured as contributions to conservation NGOs). Our results suggest that the type and timing of nature experience may determine future conservation investment. Time spent hiking or backpacking is correlated with increased conservation contributions 11–12 years later. On the other hand, contributions are negatively correlated with past time spent on activities such as public lands visitation or fishing. Our results suggest that each hiker or backpacker translates to $200–$300 annually in future NGO contributions. We project that the recent decline in popularity of hiking and backpacking will negatively impact conservation NGO contributions from approximately 2010–2011 through at least 2018.

Inferring the Transcriptional Landscape of Bovine Skeletal Muscle by Integrating Co-Expression Networks

2009-10-01T07:00:00Z

Background

Despite modern technologies and novel computational approaches, decoding causal transcriptional regulation remains challenging. This is particularly true for less well studied organisms and when only gene expression data is available. In muscle a small number of well characterised transcription factors are proposed to regulate development. Therefore, muscle appears to be a tractable system for proposing new computational approaches.

Methodology/Principal Findings

Here we report a simple algorithm that asks “which transcriptional regulator has the highest average absolute co-expression correlation to the genes in a co-expression module?” It correctly infers a number of known causal regulators of fundamental biological processes, including cell cycle activity (E2F1), glycolysis (HLF), mitochondrial transcription (TFB2M), adipogenesis (PIAS1), neuronal development (TLX3), immune function (IRF1) and vasculogenesis (SOX17), within a skeletal muscle context. However, none of the canonical pro-myogenic transcription factors (MYOD1, MYOG, MYF5, MYF6 and MEF2C) were linked to muscle structural gene expression modules. Co-expression values were computed using developing bovine muscle from 60 days post conception (early foetal) to 30 months post natal (adulthood) for two breeds of cattle, in addition to a nutritional comparison with a third breed. A number of transcriptional landscapes were constructed and integrated into an always correlated landscape. One notable feature was a ‘metabolic axis’ formed from glycolysis genes at one end, nuclear-encoded mitochondrial protein genes at the other, and centrally tethered by mitochondrially-encoded mitochondrial protein genes.

Conclusions/Significance

The new module-to-regulator algorithm complements our recently described Regulatory Impact Factor analysis. Together with a simple examination of a co-expression module's contents, these three gene expression approaches are starting to illuminate the in vivo transcriptional regulation of skeletal muscle development.

The Risk of Virologic Failure Decreases with Duration of HIV Suppression, at Greater than 50% Adherence to Antiretroviral Therapy

2009-09-29T07:00:00Z

Background

We hypothesized that the percent adherence to antiretroviral therapy necessary to maintain HIV suppression would decrease with longer duration of viral suppression.

Methodology

Eligible participants were identified from the REACH cohort of marginally housed HIV infected adults in San Francisco. Adherence to antiretroviral therapy was measured through pill counts obtained at unannounced visits by research staff to each participant's usual place of residence. Marginal structural models and targeted maximum likelihood estimation methodologies were used to determine the effect of adherence to antiretroviral therapy on the probability of virologic failure during early and late viral suppression.

Principal Findings

A total of 221 subjects were studied (median age 44.1 years; median CD4+ T cell nadir 206 cells/mm³). Most subjects were taking the following types of antiretroviral regimens: non-nucleoside reverse transcriptase inhibitor based (37%), ritonavir boosted protease inhibitor based (28%), or unboosted protease inhibitor based (25%). Comparing the probability of failure just after achieving suppression vs. after 12 consecutive months of suppression, there was a statistically significant decrease in the probability of virologic failure for each range of adherence proportions we considered, as long as adherence was greater than 50%. The estimated risk difference, comparing the probability of virologic failure after 1 month vs. after 12 months of continuous viral suppression was 0.47 (95% CI 0.23–0.63) at 50–74% adherence, 0.29 (CI 0.03–0.50) at 75–89% adherence, and 0.36 (CI 0.23–0.48) at 90–100% adherence.

Conclusions

The risk of virologic failure for adherence greater than 50% declines with longer duration of continuous suppression. While high adherence is required to maximize the probability of durable viral suppression, the range of adherence capable of sustaining viral suppression is wider after prolonged periods of viral suppression.

Home Educating in an Extended Family Culture and Aging Society May Fare Best during a Pandemic

2009-09-28T07:00:00Z

Large cities can contain populations that move rapidly from one section to another in an efficient transportation network. An emerging air-borne or contact based pathogen could use these transportation routes to rapidly spread an infection throughout an entire population in a short time. Further, in many developed countries, the aging population is increasing. The family structure in these societies may also affect the course of a disease. To help understand the impact of an epidemic on family structure in a networked population, an individual based computer model that randomly generates networked cities with a specified range of population and disease characteristics and individual schedules, infectivity, transmission and hygiene factors was developed. Several salient issues emerged. First, a city of highly active individuals may in fact diminish the number of fatalities because the average duration of the interactions between agents is reduced. Second, home schooling can significantly improve survival because the institutional clustering of weak individuals is minimized. Third, the worst scenario for an aging population is the nuclear family where the aged population is confined to large housing facilities. Naturally, hygiene is the first barrier to infection. The results suggest that societies where extended families and small groups manage most of their own affairs may also be the most suitable for defense against a pandemic. This may prove applicable in city planning and policy making.