Scaling laws of human interaction activity

Even though people in our contemporary technological society are depending on communication, our understanding of the underlying laws of human communicational behavior continues to be poorly understood. Here we investigate the communication patterns in 2 social Internet communities in search of statistical laws in human interaction activity. This research reveals that human communication networks dynamically follow scaling laws that may also explain the observed trends in economic growth. Specifically, we identify a generalized version of Gibrat''s law of social activity expressed as a scaling law between the fluctuations in the number of messages sent by members and their level of activity. Gibrat''s law has been essential in understanding economic growth patterns, yet without an underlying general principle for its origin. We attribute this scaling law to long-term correlation patterns in human activity, which surprisingly span from days to the entire period of the available data of more than 1 year. Further, we provide a mathematical framework that relates the generalized version of Gibrat''s law to the long-term correlated dynamics, which suggests that the same underlying mechanism could be the source of Gibrat''s law in economics, ranging from large firms, research and development expenditures, gross domestic product of countries, to city population growth. These findings are also of importance for designing communication networks and for the understanding of the dynamics of social systems in which communication plays a role, such as economic markets and political systems.     

Scaling laws between population and facility densities

When a new facility like a grocery store, a school, or a fire station is planned, its location should ideally be determined by the necessities of people who live nearby. Empirically, it has been found that there exists a positive correlation between facility and population densities. In the present work, we investigate the ideal relation between the population and the facility densities within the framework of an economic mechanism governing microdynamics. In previous studies based on the global optimization of facility positions in minimizing the overall travel distance between people and facilities, it was shown that the density of facility D and that of population ρ should follow a simple power law D ∼ ρ^2/3. In our empirical analysis, on the other hand, the power-law exponent α in D ∼ ρ^α is not a fixed value but spreads in a broad range depending on facility types. To explain this discrepancy in α, we propose a model based on economic mechanisms that mimic the competitive balance between the profit of the facilities and the social opportunity cost for populations. Through our simple, microscopically driven model, we show that commercial facilities driven by the profit of the facilities have α = 1, whereas public facilities driven by the social opportunity cost have α = 2/3. We simulate this model to find the optimal positions of facilities on a real U.S. map and show that the results are consistent with the empirical data.     

From the Cover: Scaling laws predict global microbial diversity

Scaling laws underpin unifying theories of biodiversity and are among the most predictively powerful relationships in biology. However, scaling laws developed for plants and animals often go untested or fail to hold for microorganisms. As a result, it is unclear whether scaling laws of biodiversity will span evolutionarily distant domains of life that encompass all modes of metabolism and scales of abundance. Using a global-scale compilation of ∼35,000 sites and ∼5.6⋅10⁶ species, including the largest ever inventory of high-throughput molecular data and one of the largest compilations of plant and animal community data, we show similar rates of scaling in commonness and rarity across microorganisms and macroscopic plants and animals. We document a universal dominance scaling law that holds across 30 orders of magnitude, an unprecedented expanse that predicts the abundance of dominant ocean bacteria. In combining this scaling law with the lognormal model of biodiversity, we predict that Earth is home to upward of 1 trillion (10¹²) microbial species. Microbial biodiversity seems greater than ever anticipated yet predictable from the smallest to the largest microbiome.The understanding of microbial biodiversity has rapidly transformed over the past decade. High-throughput sequencing and bioinformatics have expanded the catalog of microbial taxa by orders of magnitude, whereas the unearthing of new phyla is reshaping the tree of life (1–3). At the same time, discoveries of novel forms of metabolism have provided insight into how microbes persist in virtually all aquatic, terrestrial, engineered, and host-associated ecosystems (4, 5). However, this period of discovery has uncovered few, if any, general rules for predicting microbial biodiversity at scales of abundance that characterize, for example, the ∼10¹⁴ cells of bacteria that inhabit a single human or the ∼10³⁰ cells of bacteria and archaea estimated to inhabit Earth (6, 7). Such findings would aid the estimation of global species richness and reveal whether theories of biodiversity hold across all scales of abundance and whether so-called law-like patterns of biodiversity span the tree of life.A primary goal of ecology and biodiversity theory is to predict diversity, commonness, and rarity across evolutionarily distant taxa and scales of space, time, and abundance (8–10). This goal can hardly be achieved without accounting for the most abundant, widespread, and metabolically, taxonomically, and functionally diverse organisms on Earth (i.e., microorganisms). However, tests of biodiversity theory rarely include both microbial and macrobial datasets. At the same time, the study of microbial ecology has yet to uncover quantitative relationships that predict diversity, commonness, and rarity at the scale of host microbiomes and beyond. These unexplored opportunities leave the understanding of biodiversity limited to the most conspicuous species of plants and animals. This lack of synthesis has also resulted in the independent study of two phenomena that likely represent a single universal pattern. Specifically, these phenomena are the highly uneven distributions of abundance that underpin biodiversity theory (11) and the universal pattern of microbial commonness and rarity known as the microbial “rare biosphere” (12).Scaling laws provide a promising path to the unified understanding and prediction of biodiversity. Also referred to as power laws, the forms of these relationships, y ∼ x^z, predict linear rates of change under logarithmic transformation [i.e., log(y) ∼ zlog(x)] and hence, proportional changes across orders of magnitude. Scaling laws reveal how physiological, ecological, and evolutionary constraints hold across genomes, cells, organisms, and communities of greatly varying size (13–15). Among the most widely known are the scaling of metabolic rate (B) with body size [M; B = B_oM^3/4 (13)] and the rate at which species richness (i.e., number of species; S) scale with area [A; S = cA^z (16)]. These scaling laws are predicted by powerful ecological theories, although evidence suggests that they fail for microorganisms (17–19). Beyond area and body size, there is an equally general constraint on biodiversity, that is, the number of individuals in an assemblage (N). Often referred to as total abundance, N can range from less than 10 individuals in a given area to the nearly 10³⁰ cells of bacteria and archaea on Earth (6, 7). This expanse outstrips the 22 orders of magnitude that separate the mass of a Prochlorococcus cell (3⋅1⁻¹⁶ kg) from a blue whale (1.9·10⁵ kg) and the 26 orders of magnitude that result from measuring Earth’s surface area at a spatial grain equivalent to bacteria (5.1⋅10²⁶ μm²).Here, we consider whether N may be one of the most powerful constraints on commonness and rarity and one of the most expansive variables across which aspects of biodiversity could scale. Although N imposes an obvious constraint on the number of species (i.e., S ≤ N), empirical and theoretical studies suggest that S scales with N at a rate of 0.25–0.5 (i.e., S ∼ N^z and 0.25 ≤ z ≤ 0.5) (20–22). Importantly, this relationship applies to samples from different systems and does not pertain to cumulative patterns (e.g., collector’s curves), which are based on resampling (20–22). Recent studies have also shown that N constrains universal patterns of commonness and rarity by imposing a numerical constraint on how abundance varies among species, across space, and through time (23, 24). Most notably, greater N leads to increasingly uneven distributions and greater rarity. Hence, we expect greater N to correspond to an increasingly uneven distribution among a greater number of species, an increasing portion of which should be rare. However, the strength of the relationships, whether they differ between microbes and macrobes, and whether they conform to scaling laws across orders of magnitude are virtually unknown.If aspects of diversity, commonness, and rarity scale with N, then local- to global-scale predictions of microbial biodiversity could be within reach. Likewise, if these relationships are similar for microbes and macrobes, then we may be closer to a unified understanding of biodiversity than previously thought. To answer these questions, we compiled the largest publicly available microbial and macrobial datasets to date. These data include 20,376 sites of bacterial, archaeal, and microscopic fungal communities and 14,862 sites of tree, bird, and mammal communities. We focused on taxonomic aspects of biodiversity, including species richness (S), similarity in abundance among species (evenness), concentration of N among relatively low-abundance species (rarity), and number of individuals belonging to the most abundant species (absolute dominance, N_max). We use the resulting relationships to predict N_max and S in large microbiomes and make empirically supported and theoretically underpinned estimates for the number of microbial species on Earth.     

Scaling laws governing stochastic growth and division of single bacterial cells

Uncovering the quantitative laws that govern the growth and division of single cells remains a major challenge. Using a unique combination of technologies that yields unprecedented statistical precision, we find that the sizes of individual Caulobacter crescentus cells increase exponentially in time. We also establish that they divide upon reaching a critical multiple (≈1.8) of their initial sizes, rather than an absolute size. We show that when the temperature is varied, the growth and division timescales scale proportionally with each other over the physiological temperature range. Strikingly, the cell-size and division-time distributions can both be rescaled by their mean values such that the condition-specific distributions collapse to universal curves. We account for these observations with a minimal stochastic model that is based on an autocatalytic cycle. It predicts the scalings, as well as specific functional forms for the universal curves. Our experimental and theoretical analysis reveals a simple physical principle governing these complex biological processes: a single temperature-dependent scale of cellular time governs the stochastic dynamics of growth and division in balanced growth conditions.Quantitative studies of bacterial growth and division initiated the molecular biology revolution (1) and continue to provide constraints on molecular mechanisms (1–8). However, many basic questions about the growth law, i.e., the time evolution of the size of an individual cell, remain (8–13). Whether cells specifically sense size, time, or particular molecular features to initiate cell division is also unknown (14). Answers to these questions, for individual cells in balanced growth conditions, are of fundamental importance, and they serve as starting points for understanding collective behaviors involving spatiotemporal interactions between many cells (15–18).Cell numbers increase exponentially in bulk culture in balanced growth conditions irrespective of how the size of an individual cell increases with time (1). Thus, observation of the population is insufficient to reveal the functional form of the growth law for a given condition. Bulk culture measurements necessarily average over large numbers of cells, which can conceal cell-to-cell variability in division times, sizes at division, growth rates, and other properties (19). Moreover, the cell cycles of different cells in the population are typically at different stages of completion at a given time of observation. Even when effort is made to synchronize cells at the start of an experiment, so as to have a more tightly regulated initial distribution of growth phases, this dispersion can only be mitigated, not eliminated. These considerations highlight the importance of studying growth and division at the single-cell level.The landmark papers of Schaechter, Koch, and coworkers (2, 20, 21) addressed issues of growth at the single-cell level, but the (statistical) precision of these measurements was not sufficient to characterize the growth law(s) under different conditions. There is evidence that the growth laws for various microorganisms under favorable conditions are exponential (14, 22–25). However, both linear and exponential growth laws have been previously proposed (26–29), and it is estimated that a measurement precision of 6% is required to discriminate between these functional forms for cells that double in size during each division period (5). This precision is difficult to achieve in typical single-cell microscopy studies because cell division leads to rapid crowding of the field of view (30).Various experimental approaches have been introduced to address this issue (25, 31–34). Conventional single-cell measurements on agarose pads are limited to about 10 generations, and the age distribution of the observed cells is skewed toward younger cells because the population numbers grow geometrically (35). Designed confinement of cells allows observation of constant numbers of cells without requiring genetic manipulation (25, 34). The system that we describe here for Caulobacter crescentus allows tracking constant numbers of single cells over many generations at constant (and, if desired, low) number densities. This setup provides the advantages that contacts between cells can be avoided and the environment can be kept invariant over the course of an experiment, such that all cells exhibit equivalent statistics. In fact, in control experiments with this setup, we observe that cells grow at reduced rates when they come in contact with each other. Our extensive data provide the statistical precision needed to transcend previous studies to establish the functional form of the mean growth law under different conditions and to characterize fluctuations in growth and division.     

Correlation of clinical score to pulmonary function and oxygen saturation in children with asthma attack

BackgroundThe aim of this study is to demonstrate the importance of the relation between clinical score, pulse oximetry and spirometric tests in an asthma attack.MethodsIn this randomized, double blind, observational study, 110 children (age 2-15 years) with an asthma attack who were admitted to emergency room were evaluated. Patient history, physical examination, clinical score and oxygen saturation were recorded in all patients; however pulmonary function tests were obtained only in 54 children who were over 5 years of age. The clinical score was derived from respiratory rate, wheezing, dyspnea and retractions.ResultsBoth oxygen saturation and spirometric tests were found to be significantly correlated with the clinical score in children.ConclusionThe clinical score could be used for assessing the severity of the asthma attack particularly in developing countries where laboratory facilities are not available or pulmonary function tests are not feasible.     

Hospitalizations for asthma among adults exposed to the September 11, 2001 World Trade Center terrorist attack

Objective: We described the patterns of asthma hospitalization among persons exposed to the 2001 World Trade Center (WTC) attacks, and assessed whether 9/11-related exposures or comorbidities, including posttraumatic stress disorder (PTSD) and gastroesophageal reflux symptoms (GERS), were associated with an increased rate of hospitalization. Methods: Data for adult enrollees in the WTC Health Registry, a prospective cohort study, with self-reported physician-diagnosed asthma who resided in New York State on 9/11 were linked to administrative hospitalization data to identify asthma hospitalizations during September 11, 2001–December 31, 2010. Multivariable zero-inflated Poisson regression was used to examine associations among 9/11 exposures, comorbid conditions, and asthma hospitalizations. Results: Of 11 471 enrollees with asthma, 406 (3.5%) had ≥1 asthma hospitalization during the study period (721 total hospitalizations). Among enrollees diagnosed before 9/11 (n = 6319), those with PTSD or GERS had over twice the rate of hospitalization (adjusted rate ratio (ARR) = 2.5, 95% CI = 1.4–4.1; ARR = 2.1, 95% CI = 1.3–3.2, respectively) compared to those without. This association was not statistically significant in enrollees diagnosed after 9/11. Compared to higher educational attainment, completing less than college was associated with an increased hospitalization rate among participants with both pre-9/11- and post-9/11-onset asthma (ARR = 1.9, 95% CI = 1.2–2.9; ARR = 2.6, 95% CI = 1.6–4.1, respectively). Sinus symptoms, exposure to the dust cloud, and having been a WTC responder were not associated with asthma hospitalization. Conclusions: Among enrollees with pre-9/11 asthma, comorbid PTSD and GERS were associated with an increase in asthma hospitalizations. Management of these comorbidities may be an important factor in preventing hospitalization.     

Antistreptolysin-titre under the use of traditional methods and after saturation with dextran sulfate]

1,700 blood samples of healthy test persons without clinically and paraclinically provable streptococcal diseases were examined for their content of antistreptolysin. Beside the usual method parallel determinations were carried out after addition of dextran sulfate. Thus increases of unspecific antistreptolysin titres shall be in most cases excluded, above all by the influence of the lipoproteins. The absorption of dextran sulfate led to the decrease of the antistreptolysin titre by 12.33%. Furthermore could be proved that the average antistreptolysin titre of female test persons is ca. 20 antistreptolysin units below the titre of male test persons, that seasonal variations of the antistreptolysin titre with the highest titres appear in the first and third quarter which may be explained by a bad unspecific defensive condition, that, furthermore, the antistreptolysin titres increase to the 14th year and then continuously decrease and that in new-born children the arithmetic mean value of the antistreptolysin units is significantly higher than in their mothers. Hereby an active influence of the placenta on the transmission of antibodies seems to be possible. Though a slightly increased financial expenditure is necessary for dextran sulfate, temporarily and concerning working technique, however, no larger loads appear, it is justifiable to perform the determination of antistreptolysin titres only by means of dextran sulfate-absorbed sera, since in this way a considerable number of unspecific and misleading reactions can be excluded.     

Nocturnal 6-hydroxymelatonin sulfate excretion in female workers exposed to magnetic fields

The objective of this study was to determine whether daytime occupational exposure to extremely low frequency magnetic fields (MFs) suppresses nocturnal melatonin production. Sixty female volunteers were recruited. Thirty-nine worked in a garment factory, and 21 office workers served as a reference group. Exposure assessment was based on the type of sewing machine used and MF measurements around each type of machine. Eye-level MF flux density was used to classify the operators to higher (>1 μT) and lower (0.3–1 μT) exposure categories. A third group of factory workers had diverse MF exposures from other sources. The reference group had average exposure of about 0.15 μT. Urine samples were collected on Friday and Monday for three consecutive weeks. Melatonin production was assessed as urinary 6-hydroxymelatonin sulfate (6-OHMS) excretion. The ratio of Friday morning/Monday morning 6-OHMS was used to test the hypothesis that melatonin production is suppressed after 4 days of occupational MF exposure with significant recovery during the weekend. Possible chronic suppression of melatonin production was evaluated by studying exposure-related differences in the Friday values by multivariate regression analysis. The Monday/Friday ratios were close to 1.0, suggesting that there is no increase in melatonin production over the weekend. The average 6-OHMS excretion on Friday was lower among the factory workers than in the reference group, but no monotonous dose–response was observed. Multivariate regression analysis identified MF exposure, smoking, and age as significant explanatory variables associated with decreased 6-OHMS excretion.     

Scaling expectations for the time to establishment of complex adaptations

Although the vast majority of research in evolutionary biology is focused on adaption, a general theory for the population-genetic mechanisms by which complex adaptations are acquired remains to be developed. The issue explored here is the procurement of novel traits that specifically require multiple mutations to achieve a fitness advantage. By highlighting the roles played by the forces of mutation, recombination, and random genetic drift, and drawing from observations on the joint constraints on these factors, the ways in which rates of acquisition of specific types of adaptations scale with population size are explored. These general results provide insight into a number of ongoing controversies regarding the molecular basis of adaptation, including the adaptive utility of recombination and the role of drift in the passage through adaptive valleys.     

Scaling laws for fully developed turbulent flow in pipes: Discussion of experimental data

We compare mean velocity profiles measured in turbulent pipe flows (and also in boundary layer flows) with the predictions of a recently proposed scaling law; in particular, we examine the results of the Princeton “superpipe” experiment and assess their range of validity.     

Statins and cerebrovascular disease: plaque attack to prevent brain attack

Stroke is the third leading cause of death in the USA and in the developed world. The beneficial role of cholesterol reduction in decreasing stroke has been uncertain. However, recent data indicate that statin treatment in patients with a history of myocardial infarction not only reduces the risk of a second myocardial infarction, coronary heart disease, revascularization procedures and death, but also significantly reduces the risk of stroke. However, the mechanism(s) by which statins reduce stroke remain uncertain. Thus, the therapeutic armamentarium for the reduction of stroke in secondary prevention now includes cholesterol reduction with statins.     

Emergency response to a smallpox attack: the case for mass vaccination

In the event of a smallpox bioterrorist attack in a large U.S. city, the interim response policy is to isolate symptomatic cases, trace and vaccinate their contacts, quarantine febrile contacts, but vaccinate more broadly if the outbreak cannot be contained by these measures. We embed this traced vaccination policy in a smallpox disease transmission model to estimate the number of cases and deaths that would result from an attack in a large urban area. Comparing the results to mass vaccination from the moment an attack is recognized, we find that mass vaccination results in both far fewer deaths and much faster epidemic eradication over a wide range of disease and intervention policy parameters, including those believed most likely, and that mass vaccination similarly outperforms the existing policy of starting with traced vaccination and switching to mass vaccination only if required.     

The chest pain center strategy for delivering community heart attack care by shifting the paradigm of heart attack care to earlier detection and treatment

Heart attack remains the number one health problem in the United States and throughout the world. It has been that way for more than 100 years. Unless we change our course, heart attack will continue to exert its horrendous casualties, not only in the United States but also throughout the world. Our present strategy in dealing with this problem needs both leadership and a change in direction. In an effort to search "outside the box" for the solution to this problem, this symposium is a call to action that challenges us to approach the heart attack problem with a mindset bent on winning this war against heart disease, and not coexisting and accepting the problem as an inescapable fate.