A New Approach to Testing Marginal Productivity Theory

We address the long standing question of whether production factors are paid their marginal products. We propose a new approach that circumvents the need to specify production functions and to compare marginal products to factor payments. Our approach is based on a simple equation that directly relates firms' profits to discrepancies between factor payments and marginal products. Our empirical application using data on manufacturing firms suggests that capital receives more than its marginal product, intermediate inputs receive less, and labor receives about its marginal product. Although there are differences with respect to firm size, deviations from marginal productivity theory generally seem limited. Our results have important implications for the distribution of income, the presence of optimizing behavior, and the existence of market power.marginal productivity theory, distribution of income, robust statistics

Ceramic processing: Experimental design and optimization

The objectives of this paper are to: (1) gain insight into the processing of ceramics and how green processing can affect the properties of ceramics; (2) investigate the technique of slip casting; (3) learn how heat treatment and temperature contribute to density, strength, and effects of under and over firing to ceramic properties; (4) experience some of the problems inherent in testing brittle materials and learn about the statistical nature of the strength of ceramics; (5) investigate orthogonal arrays as tools to examine the effect of many experimental parameters using a minimum number of experiments; (6) recognize appropriate uses for clay based ceramics; and (7) measure several different properties important to ceramic use and optimize them for a given application

Adaptive Gaussian Process Regression for Efficient Building of Surrogate Models in Inverse Problems

In a task where many similar inverse problems must be solved, evaluating costly simulations is impractical. Therefore, replacing the model $y$ with a surrogate model $y_s$ that can be evaluated quickly leads to a significant speedup. The approximation quality of the surrogate model depends strongly on the number, position, and accuracy of the sample points. With an additional finite computational budget, this leads to a problem of (computer) experimental design. In contrast to the selection of sample points, the trade-off between accuracy and effort has hardly been studied systematically. We therefore propose an adaptive algorithm to find an optimal design in terms of position and accuracy. Pursuing a sequential design by incrementally appending the computational budget leads to a convex and constrained optimization problem. As a surrogate, we construct a Gaussian process regression model. We measure the global approximation error in terms of its impact on the accuracy of the identified parameter and aim for a uniform absolute tolerance, assuming that $y_s$ is computed by finite element calculations. A priori error estimates and a coarse estimate of computational effort relate the expected improvement of the surrogate model error to computational effort, resulting in the most efficient combination of sample point and evaluation tolerance. We also allow for improving the accuracy of already existing sample points by continuing previously truncated finite element solution procedures.Comment: 28 pages, 10 figure

Efficient adaptivity for simulating cardiac electrophysiology with spectral deferred correction methods

The locality of solution features in cardiac electrophysiology simulations calls for adaptive methods. Due to the overhead incurred by established mesh refinement and coarsening, however, such approaches failed in accelerating the computations. Here we investigate a different route to spatial adaptivity that is based on nested subset selection for algebraic degrees of freedom in spectral deferred correction methods. This combination of algebraic adaptivity and iterative solvers for higher order collocation time stepping realizes a multirate integration with minimal overhead. This leads to moderate but significant speedups in both monodomain and cell-by-cell models of cardiac excitation, as demonstrated at four numerical examples.Comment: 12 pages, 12 figure

Convergence Properties of Newton's Method for Globally Optimal Free Flight Trajectory Optimization

The algorithmic efficiency of Newton-based methods for Free Flight Trajectory Optimization is heavily influenced by the size of the domain of convergence. We provide numerical evidence that the convergence radius is much larger in practice than what the theoretical worst case bounds suggest. The algorithm can be further improved by a convergence-enhancing domain decomposition

Herbal extracts modulate the amplitude and frequency of slow waves in circular smooth muscle of mouse small intestine

Background: Herbal preparations like STW 5 (Iberogast(R)) are widely used drugs in the treatment of dyspepsia and motility-related disorders of the gastrointestinal tract. STW 5 is a phytotherapeutic agent consisting of a fixed mixture of 9 individual plant extracts. The electrophysiological mechanisms of action of STW 5 remain obscure. Aim: The aim of the present study was to investigate whether herbal extracts influence electrophysiological parameters of the small intestine. For this purpose, the resting membrane potential (RMP) and the slow wave rhythmicity of smooth muscle cells of mouse small intestine were observed. Methods: Intracellular recordings of smooth muscle cells of the circular muscle layer of mouse small intestine were performed using standard microelectrode techniques. After dissection of the mucosa, the small intestine was placed in an organ bath and a microelectrode was applied on a circular smooth muscle cell. The RMP and the amplitude of slow waves were measured in millivolts. Results: The RMP of smooth muscle cells was - 59 +/- 1.3 mV. This RMP was significantly depolarized by STW 5 ( 9.6 +/- 1.6 mV); the depolarizing effects can be mainly attributed to the constituents of matricariae flos, angelicae radix and chelidonii herba. The basal frequency of small intestinal slow waves was 39.5 +/- 1.4 min(-1) and the amplitude was 23.1 +/- 0.9 mV. STW 5 significantly reduced the amplitude and frequency of the slow waves ( 11.7 +/- 0.8 mV; 33.5 +/- 3.4 min(-1)). This effect on slow waves represents the sum of the effects of the 9 phytoextracts. Whereas angelicae radix and matricariae flos completely blocked slow wave activity, Iberis amara increased the frequency and amplitude, chelidonii herba reduced the frequency and amplitude of the slow waves, mentae piperitae folium reduced the frequency and left amplitude unchanged and liquiritae radix, carvi fructus and melissae folium had no effects. Conclusion: Herbal extracts cause changes in smooth muscle RMP and slow wave rhythmicity, up to reversible abolition, by blockade of large conductance Ca2+ channels and other not yet identified mechanisms. In herbal preparations like STW 5 these effects add up to a total effect and this study indicates that herbal preparations which are widely used in dyspepsia and motility-related disorders have characteristic, reproducible, reversible effects on small intestinal electrophysiology. Copyright (C) 2005 S. Karger AG, Basel