Compositional evolution with mass transfer in closed systems

Evolution of compositions in time, space, temperature or other covariates is frequentin practice. For instance, the radioactive decomposition of a sample changes its composition with time. Some of the involved isotopes decompose into other isotopes of thesample, thus producing a transfer of mass from some components to other ones, butpreserving the total mass present in the system. This evolution is traditionally modelledas a system of ordinary di erential equations of the mass of each component. However,this kind of evolution can be decomposed into a compositional change, expressed interms of simplicial derivatives, and a mass evolution (constant in this example). A rst result is that the simplicial system of di erential equations is non-linear, despiteof some subcompositions behaving linearly.The goal is to study the characteristics of such simplicial systems of di erential equa-tions such as linearity and stability. This is performed extracting the compositional differential equations from the mass equations. Then, simplicial derivatives are expressedin coordinates of the simplex, thus reducing the problem to the standard theory ofsystems of di erential equations, including stability. The characterisation of stabilityof these non-linear systems relays on the linearisation of the system of di erential equations at the stationary point, if any. The eigenvelues of the linearised matrix and theassociated behaviour of the orbits are the main tools. For a three component system,these orbits can be plotted both in coordinates of the simplex or in a ternary diagram.A characterisation of processes with transfer of mass in closed systems in terms of stability is thus concluded. Two examples are presented for illustration, one of them is aradioactive decay

Income and body mass index in Europe

The problem of obesity is alarming public health authorities around the world. Therefore, it is important to study its determinants. In this paper we explore the empirical relationship between household income and body mass index (BMI) in nine European Union countries. Our findings suggest that the association is negative for women, but we find no statistically significant relationship for men. However, we show that the different relationship for men and women appears to be driven by the negative relationship for women between BMI and individual income from work. We tentatively conclude that the negative relationship between household income and BMI for women may simply be capturing the wage penalty that obese women suffer in the labor market.

Moderate-Vigorous physical activity across Body Mass Index in females: moderating effect of endocannabinoids and temperament

Background: Endocannabinoids and temperament traits have been linked to both physical activity and body mass index (BMI) however no study has explored how these factors interact in females. The aims of this cross-sectional study were to 1) examine differences among distinct BMI groups on daytime physical activity and time spent in moderate-vigorous physical activity (MVPA), temperament traits and plasma endocannabinoid concentrations; and 2) explore the association and interaction between MVPA, temperament, endocannabinoids and BMI. Methods: Physical activity was measured with the wrist-worn accelerometer Actiwatch AW7, in a sample of 189 female participants (43 morbid obese, 30 obese, and 116 healthy-weight controls). The Temperament and Character Inventory-Revised questionnaire was used to assess personality traits. BMI was calculated by bioelectrical impedance analysis via the TANITA digital scale. Blood analyses were conducted to measure levels of endocannabinoids and endocannabinoid-related compounds. Path-analysis was performed to examine the association between predictive variables and MVPA. Results: Obese groups showed lower MVPA and dysfunctional temperament traits compared to healthy-weight controls. Plasma concentrations of 2-arachidonoylglyceryl (2-AG) were greater in obese groups. Path-analysis identified a direct effect between greater MVPA and low BMI (b = −0.13, p = .039) and high MVPA levels were associated with elevated anandamide (AEA) levels (b = 0.16, p = .049) and N-oleylethanolamide (OEA) levels (b = 0.22, p = .004), as well as high Novelty seeking (b = 0.18, p<.001) and low Harm avoidance (b = −0.16, p<.001). Conclusions: Obese individuals showed a distinct temperament profile and circulating endocannabinoids compared to controls. Temperament and endocannabinoids may act as moderators of the low MVPA in obesity.

The association between obesity and back pain in nine countries: a cross-sectional study

BACKGROUND: The association between obesity and back pain has mainly been studied in high-income settings with inconclusive results, and data from older populations and developing countries are scarce. The aim of this study was to assess this association in nine countries in Asia, Africa, Europe, and Latin America among older adults using nationally-representative data. METHODS: Data on 42116 individuals ≥50 years who participated in the Collaborative Research on Ageing in Europe (COURAGE) study conducted in Finland, Poland, and Spain in 2011-2012, and the World Health Organization's Study on Global Ageing and Adult Health (SAGE) conducted in China, Ghana, India, Mexico, Russia, and South Africa in 2007-2010 were analysed. Information on measured height and weight available in the two datasets was used to calculate Body Mass Index (BMI). Self-reported back pain occurring in the past 30 days was the outcome. Multivariable logistic regression analysis was used to assess the association between BMI and back pain. RESULTS: The prevalence of back pain ranged from 21.5% (China) to 57.5% (Poland). In the multivariable analysis, compared to BMI 18.5-24.9 kg/m(2), significantly higher odds for back pain were observed for BMI ≥35 kg/m(2) in Finland (OR 3.33), Russia (OR 2.20), Poland (OR 2.03), Spain (OR 1.56), and South Africa (OR 1.48); BMI 30.0-34.0 kg/m(2) in Russia (OR 2.76), South Africa (OR 1.51), and Poland (OR 1.47); and BMI 25.0-29.9 kg/m(2) in Russia (OR 1.51) and Poland (OR 1.40). No significant associations were found in the other countries. CONCLUSIONS: The strength of the association between obesity and back pain may vary by country. Future studies are needed to determine the factors contributing to differences in the associations observed.