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Given a collection of science-based computational models that all estimate states of the same environmental system, we compare the forecast skill of the average of the collection to the skills of the individual members. We illustrate our results through an analysis of regional climate model data and give general criteria for the average to perform more or less skillfully than the most skillful individual model, the “best” model. The average will only be more skillful than the best model if the individual models in the collection produce very different forecasts; if the individual forecasts generally agree, the average will not be as skillful as the best model. [ABSTRACT FROM AUTHOR]

Many problems in science and engineering require the solution of the steady-state diffusion equation with a highly oscillatory coefficient. In this paper, we propose an analytical approximation ũ(x) ϵ Lp(Ω), 1 ≤ p ≤ ∞, for the generalized Laplace equation ∇ · (K (x) ∇u(x)) = 0 in Ω ⊂ Rn, with prescribed boundary conditions and the coefficient function K(x) ϵ Lp(Ω) defined as a step function, not necessarily periodic. The proposed solution can be regarded as an approximation to the weak solution belonging to W¹,p(Ω), the Sobolev space. When the coefficient function describes inclusions in a main matrix, then K(x) is a periodic function, and such formulation leads to an approximation, in Lp(Ω), to the solution of the periodic cell-problem, ∇ · (K(ε-1x)∇w(ε-1x)) = ∇ · (K(ε-1x)1). The solution to the cell-problem is the key information needed to obtain the upscaled coefficient and therefore the zeroth-order approximation for a generalized elliptic equation with highly oscillating coefficient in Ω ⊂ Rn. Our numerical computation of the error between the proposed analytical approximation for the cell-problem, w˜(ε-1x) in Lp(Ω), and the solution w(ε-1x) in W1,2(Ω), demonstrates to converge in the L2-norm, when the scale parameter e approaches zero. The proposed approximation leads to the lower bound of the generalized Voigt-Reiss inequality, which is a more accurate two-sided estimate than the classical Voigt-Reiss inequality. As an application, we compute our approximate value for the homogenized coefficient when the heterogeneous coefficients are inclusions such as squares, circles, and lozenges, and we demonstrate that the results underestimate the effective coefficient with an error of 10% on average, when compared with published numerical results. [ABSTRACT FROM AUTHOR]

Explores ways to improve the status of stochastic theories and models as routine tools for studying hydrology. Reasons why stochastic approaches have not been extensively used as routine tools; Need for hydrogeologists to acknowledge the objective need for stochastic models in many applications; Need for more extensive methods of collecting data.

Merosin deficient congenital muscular dystrophy 1A (MDC1A) is a very rare autosomal recessive disorder caused by mutations in the LAMA2 gene leading to severe and progressive muscle weakness and atrophy. Although over 350 causative mutations have been identified for MDC1A, no treatment is yet available. There are many therapeutic approaches in development, but the lack of natural history data of the mouse model and standardized outcome measures makes it difficult to transit these pre-clinical findings to clinical trials. Therefore, in the present study, we collected natural history data and assessed pre-clinical outcome measures for the dy2J/dy2J mouse model using standardized operating procedures available from the TREAT-NMD Alliance. Wild type and dy2J/dy2J mice were subjected to five different functional tests from the age of four to 32 weeks. Non-tested control groups were taken along to assess whether the functional test regime interfered with muscle pathology. Respiratory function, body weights and creatine kinase levels were recorded. Lastly, skeletal muscles were collected for further histopathological and gene expression analyses. Muscle function of dy2J/dy2J mice was severely impaired at four weeks of age and all mice lost the ability to use their hind limbs. Moreover, respiratory function was altered in dy2J/dy2J mice. Interestingly, the respiration rate was decreased and declined with age, whereas the respiration amplitude was increased in dy2J/dy2J mice when compared to wild type mice. Creatine kinase levels were comparable to wild type mice. Muscle histopathology and gene expression analysis revealed that there was a specific regional distribution pattern of muscle damage in dy2J/dy2J mice. Gastrocnemius appeared to be the most severely affected muscle with a high proportion of atrophic fibers, increased fibrosis and inflammation. By contrast, triceps was affected moderately and diaphragm only mildly. Our study presents a complete natural history dataset which can be used in setting up standardized studies in dy2J/dy2J mice. [ABSTRACT FROM AUTHOR]

Limb-girdle muscular dystrophy types 2D and 2F (LGMD 2D and 2F) are autosomal recessive disorders caused by mutations in the alpha- and delta sarcoglycan genes, respectively, leading to severe muscle weakness and degeneration. The cause of the disease has been well characterized and a number of animal models are available for pre-clinical studies to test potential therapeutic interventions. To facilitate transition from drug discovery to clinical trials, standardized procedures and natural disease history data were collected for these mouse models. Implementing the TREAD-NMD standardized operating procedures, we here subjected LGMD2D (SGCA-null), LGMD2F (SGCD-null) and wild type (C57BL/6J) mice to five functional tests from the age of 4 to 32 weeks. To assess whether the functional test regime interfered with disease pathology, sedentary groups were taken along. Muscle physiology testing of tibialis anterior muscle was performed at the age of 34 weeks. Muscle histopathology and gene expression was analysed in skeletal muscles and heart. Muscle histopathology and gene expression was analysed in skeletal muscles and heart. Mice successfully accomplished the functional tests, which did not interfere with disease pathology. Muscle function of SGCA- and SGCD-null mice was impaired and declined over time. Interestingly, female SGCD-null mice outperformed males in the two and four limb hanging tests, which proved the most suitable non-invasive tests to assess muscle function. Muscle physiology testing of tibialis anterior muscle revealed lower specific force and higher susceptibility to eccentric-induced damage in LGMD mice. Analyzing muscle histopathology and gene expression, we identified the diaphragm as the most affected muscle in LGMD strains. Cardiac fibrosis was found in SGCD-null mice, being more severe in males than in females. Our study offers a comprehensive natural history dataset which will be useful to design standardized tests and future pre-clinical studies in LGMD2D and 2F mice. [ABSTRACT FROM AUTHOR]

We perform a set of detailed numerical simulations of single-phase, fully saturated flow in stochastically generated, three-dimensional pore structures with diverse porosities (?) and degrees of connectivity, and analyze the probability density functions (PDFs) of the pore sizes, S, and vertical velocity components, w, which are aligned with the mean flow direction. Both of the PDFs are markedly skewed with pronounced positive tails. This feature of the velocity PDF is dictated by the pore structure and determines the shortest travel times, one of the key transport attributes that underpins the success or the failure of environmental remediation techniques. Using a maximum likelihood approach, we determine that the PDFs of S and w decay according to an exponential and a stretched exponential model, respectively. A strong correlation between the key parameters governing the decay of the upper tails of the two PDFs is found, which provides a quantitative result for this analogy that so far has been stated only qualitatively. The parameter governing the concavity of the tail of the velocity PDF varies linearly with porosity over the entire range of tested values (0.2=?=0.6). The parameters controlling the spread of the upper tails of the PDFs of S and w appear to be linked by a power-law relationship. [ABSTRACT FROM AUTHOR]

We study two-dimensional flow in a layered heterogeneous medium composed of two materials whose hydraulic properties and spatial distribution are known statistically but are otherwise uncertain. Our analysis relies on the composite media theory, which employs random domain decomposition in the context of groundwater flow moment equations to explicitly account for the separate effects of material and geometric uncertainty on ensemble moments of head and flux. Flow parallel and perpendicular to the layering in a two-material composite layered medium is considered. The hydraulic conductivity of each material is log-normally distributed with a much higher mean in one material than in the other. The hydraulic conductivities of points within different materials are uncorrelated. The location of the internal boundary between the two contrasting materials is random and normally distributed with given mean and variance. We solve the equations for (ensemble) moments of hydraulic head and flux and analyze the impact of unknown geometry of materials on statistical moments of head and flux. We compare the composite media approach to approximations that replace statistically inhomogeneous conductivity fields with pseudo-homogeneous random fields. [ABSTRACT FROM AUTHOR]