Spectral Representation for the Effective Macroscopic Response of a Polycrystal: Application to Third-Order Nonlinear Susceptibility

Erratum: In our paper, we show that the spectral representation for isotropic two-component composites also applies to uniaxial polycrystals. We have learned that this result was, in fact, first conjectured by G.W. Milton. While our derivation is more detailed, our result for the spectral function is the same as Milton's. We very much regret not having been aware of this work at the time of writing our paper. Original abstract: We extend the spectral theory used for the calculation of the effective linear response functions of composites to the case of a polycrystalline material with uniaxially anisotropic microscopic symmetry. As an application, we combine these results with a nonlinear decoupling approximation as modified by Ma et al., to calculate the third-order nonlinear optical susceptibility of a uniaxial polycrystal, assuming that the effective dielectric function of the polycrystal can be calculated within the effective-medium approximation.Comment: v2 includes erratum and the original preprin

Dimensional Crossover in the Effective Second Harmonic Generation of Films of Random Dielectrics

The effective nonlinear response of films of random composites consisting of a binary composite with nonlinear particles randomly embedded in a linear host is theoretically and numerically studied. A theoretical expression for the effective second harmonic generation susceptibility, incorporating the thickness of the film, is obtained by combining a modified effective-medium approximation with the general expression for the effective second harmonic generation susceptibility in a composite. The validity of the thoretical results is tested against results obtained by numerical simulations on random resistor networks. Numerical results are found to be well described by our theory. The result implies that the effective-medium approximation provides a convenient way for the estimation of the nonlinear response in films of random dielectrics.Comment: 9 pages, 2 figures; accepted for publication in Phys. Rev.

On the spread of epidemics in a closed heterogeneous population

Heterogeneity is an important property of any population experiencing a disease. Here we apply general methods of the theory of heterogeneous populations to the simplest mathematical models in epidemiology. In particular, an SIR (susceptible-infective-removed) model is formulated and analyzed for different sources of heterogeneity. It is shown that a heterogeneous model can be reduced to a homogeneous model with a nonlinear transmission function, which is given in explicit form. The widely used power transmission function is deduced from a heterogeneous model with the initial gamma-distribution of the disease parameters. Therefore, a mechanistic derivation of the phenomenological model, which mimics reality very well, is provided. The equation for the final size of an epidemic for an arbitrary initial distribution is found. The implications of population heterogeneity are discussed, in particular, it is pointed out that usual moment-closure methods can lead to erroneous conclusions if applied for the study of the long-term behavior of the model.Comment: 23 pages, 2 figure

A mixed effect model for bivariate meta-analysis of diagnostic test accuracy studies using a copula representation of the random effects distribution

Diagnostic test accuracy studies typically report the number of true positives, false positives, true negatives and false negatives. There usually exists a negative association between the number of true positives and true negatives, because studies that adopt less stringent criterion for declaring a test positive invoke higher sensitivities and lower specificities. A generalized linear mixed model (GLMM) is currently recommended to synthesize diagnostic test accuracy studies. We propose a copula mixed model for bivariate meta-analysis of diagnostic test accuracy studies. Our general model includes the GLMM as a special case and can also operate on the original scale of sensitivity and specificity. Summary receiver operating characteristic curves are deduced for the proposed model through quantile regression techniques and different characterizations of the bivariate random effects distribution. Our general methodology is demonstrated with an extensive simulation study and illustrated by re-analysing the data of two published meta-analyses. Our study suggests that there can be an improvement on GLMM in fit to data and makes the argument for moving to copula random effects models. Our modelling framework is implemented in the package CopulaREMADA within the open source statistical environment R

Hybrid copula mixed models for combining case-control and cohort studies in meta-analysis of diagnostic tests

Copula mixed models for trivariate (or bivariate) meta-analysis of diagnostic test accuracy studies accounting (or not) for disease prevalence have been proposed in the biostatistics literature to synthesize information. However, many systematic reviews often include case-control and cohort studies, so one can either focus on the bivariate meta-analysis of the case-control studies or the trivariate meta-analysis of the cohort studies, as only the latter contains information on disease prevalence. In order to remedy this situation of wasting data we propose a hybrid copula mixed model via a combination of the bivariate and trivariate copula mixed model for the data from the case-control studies and cohort studies, respectively. Hence, this hybrid model can account for study design and also due to its generality can deal with dependence in the joint tails. We apply the proposed hybrid copula mixed model to a review of the performance of contemporary diagnostic imaging modalities for detecting metastases in patients with melanoma

Diseño y Evaluación de un programa informático para la educación musical de maestros no especialistas. El caso de EMOLAB.

Este trabajo expone el diseño, desarrollo y evaluación de un software como apoyo docente en una materia de formación musical básica para futuros maestros generalistas. La evaluación del programa fue realizada por estudiantes de primer año del Grado de Maestro en Educación Primaria. Cumplimentaron un cuestionario que recogió sus opiniones (versatilidad, eficacia, facilidad de uso, calidad del entorno gráfico, adecuación, interés, facilitación del aprendizaje, feedback, funcionalidad) y percepciones sobre aspectos más generales (control, orientación, afectividad, consulta, verificación, seguimiento). Los resultados sugieren que el alumnado percibe EMOLab como herramienta de gran ayuda en el desarrollo de sus habilidades musicales

A case study evaluation of competitors undertaking an antarctic ultra-endurance event: nutrition, hydration and body composition variables

Background: The nutritional demands of ultra-endurance racing are well documented. However, the relationship between nutritional consumption and performance measures are less obvious for athletes competing in Polar conditions. Therefore, the aim of this study was to evaluate dietary intake, hydration status, body composition and performance times throughout an 800-km Antarctic race. Methods: The event organisers declared that 17 competitors would participate in the South Pole race. Of the 17 competitors, pre-race data were collected from 13 participants (12 males and 1 female (M±SD): age: 40.1±8.9 years; weight 83.9±10.3kg; and body fat percentage: 21.9±3.8%). Dietary recall, body composition and urinary osmolarity were assessed pre-race, midway checkpoint and end race. Data were compared on the basis of fast finishers (the Norwegian team (n=3) who won in a record of 14 day) and slower finishers (the remaining teams (n=10) reaching the South Pole between 22 and 28 days). Results: The percentage contribution of macronutrients to daily energy intake for all participants was as follows: carbohydrate (CHO) - 23.7% (221±82 g.day-1), fat = 60.6% (251±127g.day-1) and protein = 15.7% (117±52g.day-1). Energy demands were closer met by faster finishers compared to slower finishers (5,332±469 vs. 3,048±1,140kcal.day-1, p=0.02). Average reduction in body mass throughout the race was 8.3±5.5kg, with an average loss of lean mass of 2.0±4.1kg. There as a significant negative correlation between changes in lean mass and protein intake (p=0.03), and lean mass and energy intake (p=0.03). End-race urinary osmolarity was significantly elevated for faster finishers compared to slower finishers and control volunteers (faster finishers: 933±157mOsmol.L-1; slower finishers: 543±92mOsmol.L-1; control: 515±165mOsmol.L-1, p+0.04). Conclusions: Throughout the race, both groups were subjected to a negative change in energy balance which partly explained reduced body mass. Carbohydrate availability was limited inferring a greater reliance on fat and protein metabolism. Consequently, loss in fat-free mass was more prevalent with insufficient protein and caloric intake, which may relate to performance

A comparison of the metabolic effects of sustained strenuous activity in polar environments on men and women

This study investigates differences in pre- to post-expedition energy expenditure, substrate utilisation and body composition, between the all-male Spear17 (SP-17) and all-female Ice Maiden (IM) transantarctic expeditions (IM: N = 6, 61 days, 1700 km; SP-17: N = 5, 67 days, 1750 km). Energy expenditure and substrate utilisation were measured by a standardised 36 h calorimetry protocol; body composition was determined using air displacement plethysmography. Energy balance calculation were used to assess the physical challenge. There was difference in the daily energy expenditure (IM: 4,939 kcal day−1; SP-17: 6,461 kcal day−1, p = 0.004); differences related to physical activity were small, but statistically significant (IM = 2,282 kcal day−1; SP-17 = 3,174 kcal day−1; p = 0.004). Bodyweight loss was modest (IM = 7.8%, SP-17 = 6.5%; p > 0.05) as was fat loss (IM = 30.4%, SP-17 = 40.4%; p > 0.05). Lean tissue weight change was statistically significant (IM = − 2.5%, SP-17 = + 1.0%; p = 0.05). No difference was found in resting or sleeping energy expenditure, normalised to lean tissue weight (p > 0.05); nor in energy expenditure when exercising at 80, 100 and 120 steps min−1, normalised to body weight (p > 0.05). Similarly, no difference was found in the change in normalised substrate utilisation for any of the activities (p > 0.05). Analysis suggested that higher daily energy expenditures for the men in Spear-17 was the result of higher physical demands resulting in a reduced demand for energy to thermoregulate compared to the women in Ice Maiden. The lack of differences between men and women in the change in energy expenditure and substrate utilisation, suggests no sex difference in response to exposure to extreme environments