Mapping power law distributions in digital health social networks: methods, interpretations, and practical implications

BACKGROUND: Social networks are common in digital health. A new stream of research is beginning to investigate the mechanisms of digital health social networks (DHSNs), how they are structured, how they function, and how their growth can be nurtured and managed. DHSNs increase in value when additional content is added, and the structure of networks may resemble the characteristics of power laws. Power laws are contrary to traditional Gaussian averages in that they demonstrate correlated phenomena. OBJECTIVES: The objective of this study is to investigate whether the distribution frequency in four DHSNs can be characterized as following a power law. A second objective is to describe the method used to determine the comparison. METHODS: Data from four DHSNs—Alcohol Help Center (AHC), Depression Center (DC), Panic Center (PC), and Stop Smoking Center (SSC)—were compared to power law distributions. To assist future researchers and managers, the 5-step methodology used to analyze and compare datasets is described. RESULTS: All four DHSNs were found to have right-skewed distributions, indicating the data were not normally distributed. When power trend lines were added to each frequency distribution, R(2) values indicated that, to a very high degree, the variance in post frequencies can be explained by actor rank (AHC .962, DC .975, PC .969, SSC .95). Spearman correlations provided further indication of the strength and statistical significance of the relationship (AHC .987. DC .967, PC .983, SSC .993, P<.001). CONCLUSIONS: This is the first study to investigate power distributions across multiple DHSNs, each addressing a unique condition. Results indicate that despite vast differences in theme, content, and length of existence, DHSNs follow properties of power laws. The structure of DHSNs is important as it gives insight to researchers and managers into the nature and mechanisms of network functionality. The 5-step process undertaken to compare actor contribution patterns can be replicated in networks that are managed by other organizations, and we conjecture that patterns observed in this study could be found in other DHSNs. Future research should analyze network growth over time and examine the characteristics and survival rates of superusers.

Root distributions of Australian herbaceous perennial legumes in response to phosphorus placement

Many Australian plant species have specific root adaptations for growth in phosphorus-impoverished soils, and are often sensitive to high external P concentrations. The growth responses of native Australian legumes in agricultural soils with elevated P availability in the surface horizons are unknown. The aim of these experiments was to test the hypothesis that increased P concentration in surface soil would reduce root proliferation at depth in native legumes. The effect of P placement on root distribution was assessed for two Australian legumes, Kennedia prorepens F. Muell. and Lotus australis Andrews, and the exotic Medicago sativa L. Three treatments were established in a low-P loam soil: amendment of 0.15 g mono-calcium phosphate in either (i) the top 50 mm (120 µg P g–1) or (ii) the top 500 mm (12 µg P g–1) of soil, and an unamended control. In the unamended soil M. sativa was shallow rooted, with 58% of the root length of in the top 50 mm. K. prorepens and L. australis had a more even distribution down the pot length, with only 4 and 22% of their roots in the 0–50 mm pot section, respectively. When exposed to amendment of P in the top 50 mm, root length in the top 50 mm increased 4-fold for K. prorepens and 10-fold for M. sativa, although the pattern of root distribution did not change for M. sativa. L. australis was relatively unresponsive to P additions and had an even distribution of roots down the pot. Shoot P concentrations differed according to species but not treatment (K. prorepens 2.1 mg g–1, L. australis 2.4 mg g–1, M. sativa 3.2 mg g–1). Total shoot P content was higher for K. prorepens than for the other species in all treatments. In a second experiment, mono-ester phosphatases were analysed from 1-mm slices of soil collected directly adjacent to the rhizosphere. All species exuded phosphatases into the rhizosphere, but addition of P to soil reduced phosphatase activity only for K. prorepens. Overall, high P concentration in the surface soil altered root distribution, but did not reduce root proliferation at depth. Furthermore, the Australian herbaceous perennial legumes had root distributions that enhanced P acquisition from low-P soils.

Testing projected wild bee distributions in agricultural habitats: predictive power depends on species traits and habitat type

Species distribution models (SDM) are increasingly used to understand the factors that regulate variation in biodiversity patterns and to help plan conservation strategies. However, these models are rarely validated with independently collected data and it is unclear whether SDM performance is maintained across distinct habitats and for species with different functional traits. Highly mobile species, such as bees, can be particularly challenging to model. Here, we use independent sets of occurrence data collected systematically in several agricultural habitats to test how the predictive performance of SDMs for wild bee species depends on species traits, habitat type, and sampling technique. We used a species distribution modeling approach parametrized for the Netherlands, with presence records from 1990 to 2010 for 193 Dutch wild bees. For each species, we built a Maxent model based on 13 climate and landscape variables. We tested the predictive performance of the SDMs with independent datasets collected from orchards and arable fields across the Netherlands from 2010 to 2013, using transect surveys or pan traps. Model predictive performance depended on species traits and habitat type. Occurrence of bee species specialized in habitat and diet was better predicted than generalist bees. Predictions of habitat suitability were also more precise for habitats that are temporally more stable (orchards) than for habitats that suffer regular alterations (arable), particularly for small, solitary bees. As a conservation tool, SDMs are best suited to modeling rarer, specialist species than more generalist and will work best in long-term stable habitats. The variability of complex, short-term habitats is difficult to capture in such models and historical land use generally has low thematic resolution. To improve SDMs’ usefulness, models require explanatory variables and collection data that include detailed landscape characteristics, for example, variability of crops and flower availability. Additionally, testing SDMs with field surveys should involve multiple collection techniques.

Generalized convective quasi-equilibrium principle

A generalization of Arakawa and Schubert's convective quasi-equilibrium principle is presented for a closure formulation of mass-flux convection parameterization. The original principle is based on the budget of the cloud work function. This principle is generalized by considering the budget for a vertical integral of an arbitrary convection-related quantity. The closure formulation includes Arakawa and Schubert's quasi-equilibrium, as well as both CAPE and moisture closures as special cases. The formulation also includes new possibilities for considering vertical integrals that are dependent on convective-scale variables, such as the moisture within convection. The generalized convective quasi-equilibrium is defined by a balance between large-scale forcing and convective response for a given vertically-integrated quantity. The latter takes the form of a convolution of a kernel matrix and a mass-flux spectrum, as in the original convective quasi-equilibrium. The kernel reduces to a scalar when either a bulk formulation is adopted, or only large-scale variables are considered within the vertical integral. Various physical implications of the generalized closure are discussed. These include the possibility that precipitation might be considered as a potentially-significant contribution to the large-scale forcing. Two dicta are proposed as guiding physical principles for the specifying a suitable vertically-integrated quantity.

The sensitivity of convective aggregation to diabatic processes in idealized radiative-convective equilibrium simulations

Idealized explicit convection simulations of the Met Office Unified Model exhibit spontaneous self-aggregation in radiative-convective equilibrium, as seen in other models in previous studies. This self-aggregation is linked to feedbacks between radiation, surface fluxes, and convection, and the organization is intimately related to the evolution of the column water vapor field. Analysis of the budget of the spatial variance of column-integrated frozen moist static energy (MSE), following Wing and Emanuel [2014], reveals that the direct radiative feedback (including significant cloud longwave effects) is dominant in both the initial development of self-aggregation and the maintenance of an aggregated state. A low-level circulation at intermediate stages of aggregation does appear to transport MSE from drier to moister regions, but this circulation is mostly balanced by other advective effects of opposite sign and is forced by horizontal anomalies of convective heating (not radiation). Sensitivity studies with either fixed prescribed radiative cooling, fixed prescribed surface fluxes, or both do not show full self-aggregation from homogeneous initial conditions, though fixed surface fluxes do not disaggregate an initialized aggregated state. A sensitivity study in which rain evaporation is turned off shows more rapid self-aggregation, while a run with this change plus fixed radiative cooling still shows strong self-aggregation, supporting a “moisture memory” effect found in Muller and Bony [2015]. Interestingly, self-aggregation occurs even in simulations with sea surface temperatures (SSTs) of 295 K and 290 K, with direct radiative feedbacks dominating the budget of MSE variance, in contrast to results in some previous studies.

Equilibrium behavior of symmetric ABA triblock copolymer melts

Melts of ABA triblock copolymer molecules with identical end blocks are examined using self-consistent field theory (SCFT). Phase diagrams are calculated and compared with those of homologous AB diblock copolymers formed by snipping the triblocks in half. This creates additional end segments which decreases the degree of segregation. Consequently, triblock melts remain ordered to higher temperatures than their diblock counterparts. We also find that middle-block domains are easier to stretch than end-block domains. As a result, domain spacings are slightly larger, the complex phase regions are shifted towards smaller A-segment compositions, and the perforated-lamellar phase becomes more metastable in triblock melts as compared to diblock melts. Although triblock and diblock melts exhibit very similar phase behavior, their mechanical properties can differ substantially due to triblock copolymers that bridge between otherwise disconnected A domains. We evaluate the bridging fraction for lamellar, cylindrical, and spherical morphologies to be about 40%–45%, 60%–65%, and 75%–80%, respectively. These fractions only depend weakly on the degree of segregation and the copolymer composition.

Breaking the double-edged sword of effort/trying hard: developmental equilibrium and Longitudinal relations among effort, achievement, and academic self-concept

Ever since the classic research of Nicholls (1976) and others, effort has been recognized as a double-edged sword: whilst it might enhance achievement, it undermines academic self-concept (ASC). However, there has not been a thorough evaluation of the longitudinal reciprocal effects of effort, ASC and achievement,in the context of modern self-concept theory and statistical methodology. Nor have there been developmental equilibrium tests of whether these effects are consistent across the potentially volatile early-to-middle adolescence. Hence, focusing on mathematics, we evaluate reciprocal effects models over the first four years of secondary school, relating effort, achievement (test scores and school grades), ASC, and ASCxEffort interactions for a representative sample of 3,421 German students (Mn age = 11.75 years at Wave 1). ASC, effort and achievement were positively correlated at each wave, and there was a clear pattern of positive reciprocal positive effects among ASC, test scores and school grades—each contributing to the other, after controlling for the prior effects of all others. There was an asymmetrical pattern of effects for effort that is consistent with the double-edged sword premise: prior school grades had positive effects on subsequent effort, but prior effort had non-significant or negative effects on subsequent grades and ASC. However, on the basis of a synergistic application of new theory and methodology, we predicted and found a significant ASC-by-effort interaction, such that prior effort had more positive effects on subsequent ASC and school grades when prior ASC was high—thus providing a key to breaking the double-edged sword.

Deterpenation of Bergamot Essential Oil Using Liquid-Liquid Extraction: Equilibrium Data of Model Systems at 298.2 K

The deterpenation of bergamot essential oil can be performed by liquid liquid extraction using hydrous ethanol as the solvent. A ternary mixture composed of 1-methyl-4-prop-1-en-2-yl-cydohexene (limonene), 3,7-dimethylocta-1,6-dien-3-yl-acetate (linalyl acetate), and 3,7-dimethylocta-1,6-dien-3-ol (linalool), three major compounds commonly found in bergamot oil, was used to simulate this essential oil. Liquid liquid equilibrium data were experimentally determined for systems containing essential oil compounds, ethanol, and water at 298.2 K and are reported in this paper. The experimental data were correlated using the NRTL and UNIQUAC models, and the mean deviations between calculated and experimental data were lower than 0.0062 in all systems, indicating the good descriptive quality of the molecular models. To verify the effect of the water mass fraction in the solvent and the linalool mass fraction in the terpene phase on the distribution coefficients of the essential oil compounds, nonlinear regression analyses were performed, obtaining mathematical models with correlation coefficient values higher than 0.99. The results show that as the water content in the solvent phase increased, the kappa value decreased, regardless of the type of compound studied. Conversely, as the linalool content increased, the distribution coefficients of hydrocarbon terpene and ester also increased. However, the linalool distribution coefficient values were negatively affected when the terpene alcohol content increased in the terpene phase.

Vegetable Oils Deacidification by Solvent Extraction: Liquid-Liquid Equilibrium Data for Systems Containing Sunflower Seed Oil at 298.2 K

Liquid-liquid equilibrium experimental data for refined sunflower seed oil, artificially acidified with commercial oleic acid or commercial linoleic acid and a solvent (ethanol + water), were determined at 298.2 K. This set of experimental data and the experimental data from Cuevas et al.,(1) which were obtained from (283.2 to 333.2) K, for degummed sunflower seed oil-containing systems were correlated using NRTL and UNIQUAC models with temperature-dependent binary parameters. The deviation between experimental and calculated compositions presented average values of (1.13 and 1.41) % for NRTL and UNIQUAC equations, respectively, indicating that the models were able to correctly describe the behavior of compounds under different temperature and solvent hydration.

Extraction of free fatty acids from peanut oil and avocado seed oil: Liquid-liquid equilibrium data at 298.2 K

The present paper reports phase equilibrium experimental data for two systems composed by peanut oil or avocado seed oil + commercial oleic acid + ethanol + water at 298.2 K and different water contents in the solvent. The addition of water to the solvent reduces the loss of neutral oil in the alcoholic phase and improves the solvent selectivity. The experimental data were correlated by the NRTL and UNIQUAC models. The global deviations between calculated and experimental values were 0.63 % and 1.08 %, respectively, for the systems containing avocado seed oil. In the case of systems containing peanut oil those deviations were 0.65 % and 0.98 %, respectively. Such results indicate that both models were able to reproduce correctly the experimental data, although the NRTL model presented a better performance.

MODELLING OF HIGH-PRESSURE PHASE EQUILIBRIUM IN SYSTEMS OF INTEREST IN THE FOOD ENGINEERING FIELD USING THE PENG-ROBINSON EQUATION OF STATE WITH TWO DIFFERENT MIXING RULES

In this work, thermodynamic models for fitting the phase equilibrium of binary systems were applied, aiming to predict the high pressure phase equilibrium of multicomponent systems of interest in the food engineering field, comparing the results generated by the models with new experimental data and with those from the literature. Two mixing rules were used with the Peng-Robinson equation of state, one with the mixing rule of van der Waals and the other with the composition-dependent mixing rule of Mathias et al. The systems chosen are of fundamental importance in food industries, such as the binary systems CO(2)-limonene, CO(2)-citral and CO(2)-linalool, and the ternary systems CO(2)-Limonene-Citral and CO(2)-Limonene-Linalool, where high pressure phase equilibrium knowledge is important to extract and fractionate citrus fruit essential oils. For the CO(2)-limonene system, some experimental data were also measured in this work. The results showed the high capability of the model using the composition-dependent mixing rule to model the phase equilibrium behavior of these systems.

The impact of smoke from forest fires on the spectral dispersion of cloud droplet size distributions in the Amazonian region

In this paper, the main microphysical characteristics of clouds developing in polluted and clean conditions in the biomass-burning season of the Amazon region are examined, with special attention to the spectral dispersion of the cloud droplet size distribution and its potential impact on climate modeling applications. The dispersion effect has been shown to alter the climate cooling predicted by the so-called Twomey effect. In biomass-burning polluted conditions, high concentrations of low dispersed cloud droplets are found. Clean conditions revealed an opposite situation. The liquid water content (0.43 +/- 0.19 g m(-3)) is shown to be uncorrelated with the cloud drop number concentration, while the effective radius is found to be very much correlated with the relative dispersion of the size distribution (R(2) = 0.81). The results suggest that an increase in cloud condensation nuclei concentration from biomass-burning aerosols may lead to an additional effect caused by a decrease in relative dispersion. Since the dry season in the Amazonian region is vapor limiting, the dispersion effect of cloud droplet size distributions could be substantially larger than in other polluted regions.

Dynamic picture of the inner asteroid belt: implications for the density, size and taxonomic distributions of real objects

In this paper, we construct a dynamic portrait of the inner asteroidal belt. We use information about the distribution of test particles, which were initially placed on a perfectly rectangular grid of initial conditions, after 4.2 Myr of gravitational interactions with the Sun and five planets, from Mars to Neptune. Using the spectral analysis method introduced by Michtchenko et al., the asteroidal behaviour is illustrated in detail on the dynamical, averaged and frequency maps. On the averaged and frequency maps, we superpose information on the proper elements and proper frequencies of real objects, extracted from the data base, AstDyS, constructed by Milani and Knezevic. A comparison of the maps with the distribution of real objects allows us to detect possible dynamical mechanisms acting in the domain under study; these mechanisms are related to mean-motion and secular resonances. We note that the two- and three-body mean-motion resonances and the secular resonances (strong linear and weaker non-linear) have an important role in the diffusive transportation of the objects. Their long-lasting action, overlaid with the Yarkovsky effect, may explain many observed features of the density, size and taxonomic distributions of the asteroids.

Caesium, potassium and ammonium distributions in different organs of tropical plants

In the present work the distribution of ions in aboveground plant parts was studied in order to establish the suitability of using radiocaesium as a tracer for the plant absorption of nutrients, such as potassium (K(+)) and ammonium (NH(4)(+)). We present the results for the distributions of (137)Cs, (40)K and NH(4)(+) from four tropical plant species: lemon (Citrus aurantifolia), orange (Citrus sinensis), guava (Psidium guajava) and chili pepper (Capsicum frutescens). Activity concentrations of (137)Cs and (40)K were measured by gamma spectrometry and concentrations of free NH(4)(+) ions by a colorimetric method. Similarly to potassium and ammonium, caesium showed a high mobility within the plants, exhibiting the highest values of concentration in the growing parts of the tree (fruits, new leaves, twigs, and barks). A significant correlation between activity concentrations of (137)Cs and (40)K was observed in these tropical plants. The K/Cs discrimination ratios were approximately equal to unity in different compartments of each individual plant, suggesting that caesium could be a good tracer for (40)K in tropical woody fruit species. Despite the similarity observed for the behaviour of caesium and ammonium in the newly grown plant compartments, (137)Cs was not well correlated with NH(4)(+). Significant temporal changes in the NH(4)(+) concentrations were observed during the development of fruits, while the (137)Cs activity concentration alterations were not of great importance, indicating, therefore, that Cs(+) and free NH(4)(+) ions could have distinct concentration ratios for each particular plant organ. (C) 2008 Elsevier B.V. All rights reserved.