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Numerical solution of the heat equation with non-linear, time derivative-dependent source term
(2010)
The mathematical modeling of heat conduction with adsorption effects in coated metal structures yields the heat equation with piecewise smooth coefficients and a new kind of source term. This term is special, because it is non-linear and furthermore depends on a time derivative. In our approach we reformulated this as a new problem for the usual heat equation, without source term but with a new non-linear coefficient. We gave an existence and uniqueness proof for the weak solution of the reformulated problem. To obtain a numerical solution, we developed a semi-implicit and a fully implicit finite volume method. We compared these two methods theoretically as well as numerically. Finally, as practical application, we simulated the heat conduction in coated aluminum fibers with adsorption in the zeolite coating. Copyright © 2010 John Wiley & Sons, Ltd.
Obesity-induced overexpression of miR-802 impairs glucose metabolism through silencing of Hnf1b
(2013)
The contribution of altered post-transcriptional gene silencing to the development of insulin resistance and type 2 diabetes mellitus so far remains elusive. Here, we demonstrate that expression of microRNA (miR)-143 and 145 is upregulated in the liver of genetic and dietary mouse models of obesity. Induced transgenic overexpression of miR-143, but not miR-145, impairs insulin-stimulated AKT activation and glucose homeostasis. Conversely, mice deficient for the miR-143–145 cluster are protected from the development of obesity-associated insulin resistance. Quantitative-mass-spectrometry-based analysis of hepatic protein expression in miR-143-overexpressing mice revealed miR-143-dependent downregulation of oxysterol-binding-protein-related protein (ORP) 8. Reduced ORP8 expression in cultured liver cells impairs the ability of insulin to induce AKT activation, revealing an ORP8-dependent mechanism of AKT regulation. Our experiments provide direct evidence that dysregulated post-transcriptional gene silencing contributes to the development of obesity-induced insulin resistance, and characterize the miR-143–ORP8 pathway as a potential target for the treatment of obesity-associated diabetes.
Suppose we have k samples X₁,₁,…,X₁,ₙ₁,…,Xₖ,₁,…,Xₖ,ₙₖ with different sample sizes ₙ₁,…,ₙₖ and unknown underlying distribution functions F₁,…,Fₖ as observations plus k families of distribution functions {G₁(⋅,ϑ);ϑ∈Θ},…,{Gₖ(⋅,ϑ);ϑ∈Θ}, each indexed by elements ϑ from the same parameter set Θ, we consider the new goodness-of-fit problem whether or not (F₁,…,Fₖ) belongs to the parametric family {(G₁(⋅,ϑ),…,Gₖ(⋅,ϑ));ϑ∈Θ}. New test statistics are presented and a parametric bootstrap procedure for the approximation of the unknown null distributions is discussed. Under regularity assumptions, it is proved that the approximation works asymptotically, and the limiting distributions of the test statistics in the null hypothesis case are determined. Simulation studies investigate the quality of the new approach for small and moderate sample sizes. Applications to real-data sets illustrate how the idea can be used for verifying model assumptions.