Linear non-local diffusion problems in metric measure spaces

The aim of this paper is to provide a comprehensive study of some linear non-local diffusion problems in metric measure spaces. These include, for example, open subsets in ℝN, graphs, manifolds, multi-structures and some fractal sets. For this, we study regularity, compactness, positivity and the spectrum of the stationary non-local operator. We then study the solutions of linear evolution non-local diffusion problems, with emphasis on similarities and differences with the standard heat equation in smooth domains. In particular, we prove weak and strong maximum principles and describe the asymptotic behaviour using spectral methods

Better Health in Times of Hardship?

This paper examines the impact that the Great Recession had on individuals’ health behaviours and risk factors such as diet choices, smoking, alcohol consumption, and Body Mass Index, as well as on intermediate health outcomes in England. We exploit data from the Health Survey for England for the period 2001-2013 and capture the change in macroeconomic conditions using regional Unemployment Rates (URs) and an indicator variable for the onset of the recession. We observe an overall tendency towards moderation in smoking and alcohol intake. Interestingly, the recession indicator itself is associated to a decrease in fruit intake, a shift of the BMI distribution towards obesity, an increase in medicines consumption, and the likelihood of suffering diabetes, heart and mental health problems. These associations are more intense for the less educated and for women. When it exists, the association with UR tends to weaken after 2008. Our findings indicate that some of the health risks and intermediate health outcomes changes are associated with mechanisms not captured solely by worsened URs. We hypothesize that the uncertainty and the negative expectations generated by the recession may have influenced individual health outcomes and behaviours beyond the adjustments induced by the worsened macroeconomic conditions. The net effect translated in the erosion of the propensity to undertake several health risky behaviours but an exacerbation of some morbidity indicators

The impact of the Great Recession on health-related risk factors, behaviour and outcomes in England

This paper examines the impact that the Great Recession had on individuals' health behaviours and risk factors such as diet choices, smoking, alcohol consumption, and Body Mass Index, as well as on intermediate health outcomes in England. We exploit data on about 9000 households from the Health Survey for England for the period 2001-2013 and capture the change in macroeconomic conditions using regional unemployment rates and an indicator variable for the onset of the recession. Our findings indicate that the recession is associated with a decrease in the number of cigarettes smoked - which translated into a moderation in smoking intensity - and a reduction in alcohol intake. The recession indicator itself is associated with a decrease in fruit intake, a shift of the BMI distribution towards obesity, an increase in medicines consumption, and the likelihood of suffering from diabetes and mental health problems. These associations are often stronger for the less educated and for women. When they exist, the associations with the unemployment rate (UR) are nevertheless similar before and after 2008. Our results suggest that some of the health risks and intermediate health outcomes changes may be due to mechanisms not captured by worsened URs. We hypothesize that the uncertainty and the negative expectations generated by the recession may have influenced individual health outcomes and behaviours beyond the adjustments induced by the worsened macroeconomic conditions. The net effect translated into the erosion of the propensity to undertake several health risky behaviours but an exacerbation of some morbidity indicators. Overall, we find that the recession led to a moderation in risky behaviours but also to worsening of some risk factors and health outcomes

Effects of a low-carbohydrate diet on body composition and performance in road cycling: A randomized, controlled trial

Low-carbohydrate diets are frequently used to improve performance in endurance sports, often with contradictory results. This study aimed to assess whether a low-carbohydrate diet can outperform an isocaloric conventional diet for improving body composition and performance in a sample of twenty-six trained male road cyclists (previous experience in cyclosportive events, 7.6 ± 4.4 years; age, 26.9 ± 4.9 years; weekly training volume, 7.8 ± 2.9 hours; height, 176 ± 7 centimeters; body fat percentage, 9.7 ± 0.8 %; weight, 65.3 ± 2.3 kg). Detraining and pre-treatment periods in which nutrition and training were standardized were followed by an eight-week long intervention in which cyclists consumed either a low-carbohydrate diet (15 % of calories from carbohydrates) or a conventional endurance sports diet while maintaining the same training volumes and intensities. Body composition was assessed through electrical impedance, and performance was evaluated through a twenty-minute time trial performed on a smart bike trainer. The results revealed an overall improvement over time in absolute and relative power, body mass, and body fat for both groups, whilst the improvement in absolute power was comparable. The improvements seen in relative power (p = 0.042), body mass (p = 0.006), and body fat (p = 0.01) were significantly higher in the low-carbohydrate group. We concluded that eight weeks of a low-carbohydrate diet significantly reduced body weight and body fat percentage, and improved 20-minute relative power values in a sample of road cyclists when compared to an isocaloric conventional diet. Las dietas bajas en carbohidratos se usan con frecuencia para mejorar el rendimiento en los deportes de resistencia, a menudo con resultados contradictorios. Este estudio tuvo como objetivo evaluar si una dieta baja en carbohidratos puede superar a una dieta convencional isocalórica para mejorar la composición corporal y el rendimiento en una muestra de veintiséis ciclistas de carretera masculinos entrenados (experiencia previa en eventos cicloportivos, 7, 6 ± 4, 4 años; edad, 26, 9 ± 4, 9 años; volumen de entrenamiento semanal, 7, 8 ± 2, 9 horas; altura, 176 ± 7 centímetros; porcentaje de grasa corporal, 9, 7 ± 0, 8 %; peso, 65, 3 ± 2, 3 kg). Los períodos de desentrenamiento y pretratamiento, en los que se estandarizaron la nutrición y el entrenamiento, fueron seguidos por una intervención de ocho semanas de duración en la que los ciclistas consumieron una dieta de bajo contenido en carbohidratos (15 % de calorías de los carbohidratos) o una dieta convencional para deportes de resistencia, manteniendo los mismos volúmenes de entrenamiento e intensidades. La composición corporal se evaluó a través de la impedancia eléctrica y el rendimiento se evaluó a través de una prueba contrarreloj de veinte minutos realizada en un rodillo de bicicleta inteligente. Los resultados revelaron una mejora general en el tiempo en cuanto a potencia absoluta y relativa, masa corporal y grasa corporal para ambos grupos, mientras que la mejora en potencia absoluta fue comparable. Las mejoras de la potencia relativa (p = 0, 042), la masa corporal (p = 0, 006) y la grasa corporal (p = 0, 01) fueron significativamente mayores en el grupo bajo en carbohidratos. Se concluye que ocho semanas de una dieta baja en carbohidratos redujeron significativamente el peso corporal y el porcentaje de grasa corporal, y mejoraron los valores de potencia relativa de 20 minutos en una muestra de ciclistas de carretera en comparación con una dieta convencional isocalórica

Time to exhaustion at estimated functional threshold power in road cyclists of different performance levels

This study assessed the functional threshold power and the time to exhaustion estimated from the Allen & Coggan test and verify whether performance level has an influence on this parameter

Intrinsic climatic predictability affects ornamental coloration of adult males: Evidence for compensation among carotenoid- and melanin-based coloration

1. Ornamental coloration is frequently an honest signal of quality associated with sexual selection. While changes in average environmental conditions affect carotenoid-and melanin-based coloration, no evidence exists that changes in intrinsic environmental predictability affect coloration. 2. Here we experimentally manipulated the intrinsic predictability of precipitation in semi-natural populations of common lizards Zootoca vivipara and tested its effect on ornamental coloration and reproduction of adult males. 3. Less predictable precipitation decreased hue of carotenoid-based coloration and the extent of melanin-based coloration. Hue was positively correlated and the extent of melanin-based coloration was negatively correlated with the male's number of confirmed mate partners. 4. Treatment effects on hue were associated with reduced, and treatment effectson the extent of melanin-based coloration with increased access to females, in line with differential effects on sexual selection. 5. Neither survival nor reproductive success of adult males significantly differed among predictability treatments, suggesting that negative effects on reproduction caused by changes in carotenoid-basedcoloration may have been compensated by changes in melanin-based coloration. 6. The results also showed that ornamentation, rather than reproduction and survival of adult males, was affected by less favourable conditions. Together with previous results, this suggests that coloration might be more sensitive to changes in environmental conditions than direct fitness proxies

A Gravitational Wave Background from Reheating after Hybrid Inflation

The reheating of the universe after hybrid inflation proceeds through the nucleation and subsequent collision of large concentrations of energy density in the form of bubble-like structures moving at relativistic speeds. This generates a significant fraction of energy in the form of a stochastic background of gravitational waves, whose time evolution is determined by the successive stages of reheating: First, tachyonic preheating makes the amplitude of gravity waves grow exponentially fast. Second, bubble collisions add a new burst of gravitational radiation. Third, turbulent motions finally sets the end of gravitational waves production. From then on, these waves propagate unimpeded to us. We find that the fraction of energy density today in these primordial gravitational waves could be significant for GUT-scale models of inflation, although well beyond the frequency range sensitivity of gravitational wave observatories like LIGO, LISA or BBO. However, low-scale models could still produce a detectable signal at frequencies accessible to BBO or DECIGO. For comparison, we have also computed the analogous gravitational wave background from some chaotic inflation models and obtained results similar to those found by other groups. The discovery of such a background would open a new observational window into the very early universe, where the details of the process of reheating, i.e. the Big Bang, could be explored. Moreover, it could also serve in the future as a new experimental tool for testing the Inflationary Paradigm.Comment: 22 pages, 18 figures, uses revtex

Evolución histórica de las metáforas en el concepto de función

El conocimiento matemático está constituido por conceptos, metáforas, procesos y hábitos o actitudes, y se puede decir que un texto es bueno o un programa es completo cuando todos estos elementos son adecuadamente atendidos. Desde que Lakoff y Johnson (1991) pusieron de manifiesto la importancia del pensamiento metafórico, entendido como la interpretación de un campo de experiencias en términos de otro ya conocido, el papel de este en la formación de los conceptos matemáticos, es un tema que cada vez tiene más relevancia para la investigación en didáctica de las matemáticas. En este trabajo, enmarcado en un Proyecto de Investigación sobre los Obstáculos Epistemológicos, se analiza y discute la evolución histórica de las metáforas ligadas al concepto de función, en particular las asociadas a la gráfica de una función

Characteristics of pedaling muscle stiffness among cyclists of different performance levels

Background and Objectives: The aim of the present study was to compare the impact of an incremental exercise test on muscle stiffness in the rectus femoris (RF), vastus lateralis (VL), biceps femoris (BF), and gastrocnemius (GL) among road cyclists of three performance levels. Materials and Methods: The study group consisted of 35 cyclists grouped according to their performance level; elite (n = 10; professional license), sub-elite (n = 12; amateur license), and recreational (n = 13; cyclosportive license). Passive muscle stiffness was assessed using myometry before and after an incremental exercise test. Results: There was a significant correlation between time and category in the vastus lateralis with stiffness increases in the sub-elite (p = 0.001, Cohen’s d = 0.88) and elite groups (p = 0.003, Cohen’s d = 0.72), but not in the recreational group (p = 0.085). Stiffness increased over time in the knee extensors (RF, p < 0.001; VL, p < 0.001), but no changes were observed in the knee flexors (GL, p = 0.63, BF, p = 0.052). There were no baseline differences among the categories in any muscle. Conclusions: Although the performance level affected VL stiffness after an incremental exercise test, no differences in passive stiffness were observed among the main muscles implicated in pedaling in a resting state. Future research should assess whether this marker could be used to differentiate cyclists of varying fitness levels and its potential applicability for the monitoring of training load. © 2021 by the authors. Licensee MDPI, Basel, Switzerland