Construction algorithms for polynomial lattice rules for multivariate integration

We introduce a new construction algorithm for digital nets for integration in certain weighted tensor product Hilbert spaces. The first weighted Hilbert space we consider is based on Walsh functions. Dick and Pillichshammer calculated the worst-case error for integration using digital nets for this space. Here we extend this result to a special construction method for digital nets based on polynomials over finite fields. This result allows us to find polynomials which yield a small worst-case error by computer search. We prove an upper bound on the worst-case error for digital nets obtained by such a search algorithm which shows that the convergence rate is best possible and that strong tractability holds under some condition on the weights.

We extend the results for the weighted Hilbert space based on Walsh functions to weighted Sobolev spaces. In this case we use randomly digitally shifted digital nets. The construction principle is the same as before, only the worst-case error is slightly different. Again digital nets obtained from our search algorithm yield a worst-case error achieving the optimal rate of convergence and as before strong tractability holds under some condition on the weights. These results show that such a construction of digital nets yields the until now best known results of this kind and that our construction methods are comparable to the construction methods known for lattice rules.

We conclude the article with numerical results comparing the expected worst-case error for randomly digitally shifted digital nets with those for randomly shifted lattice rules.

     

Contextual quantum process theory

A logically complete interpretation of quantum mechanics is given in terms of a theory of quantum processes.Research performed during stays at Utrecht State University, at the Institute for the History and Foundations of Science and at the Department of Philosophy.     

Studies on the chemical constituents of the South China Sea sponge Phacellia fusca

Three pyrrololactam alkaloids have been isolated from the marine sponge Phacellia fusca Schmidt collected from the South China Sea, and their structures were determined as 1–3 , on the grounds of spectral data. This is the first report of these compounds from this sponge. The structure of 1 was confirmed by X-ray analysis.     

Application of color image segmentation to estrusc detection

Automatic segmentation and classification of color images is a problem of great practical interest in different areas. This paper presents an algorithm for this purpose which is divided in three steps. Firstly, the regions of interest are isolated from the rest of the image based on threshold functions defined in theYUV andYIQ color spaces, producing a set of connected components. Then, a set of features is computed to enable a quantitative evaluation of the segmented objects. Finally, the image is classified by means of a decision rule based on the analysis of the differences between the computed measures and a set of ideally segmented images, according to experts’ assessment. The algorithm was applied to a decision support tool for estrus detection in cattle. This approach constitutes a valuable alternative to improve this process, as it may replace the visual observation by the automatic analysis of pictures taken to cows in controlled environments. Experimental results show that the segmentations obtained with this method are highly satisfactory and they allow a precise classification of the images with low computational complexity.     

Krichever-Novikov-like bases on punctured Riemann surfaces

Bases of holomorphic -differentials on N-punctured Riemann surfaces of arbitrary genus are constructed. The resulting extension of the Virasoro algebra on N-punctured spheres is displayed explicitly.     

A Gerischer phase element in the impedance diagram of the polymer electrolyte membrane fuel cell anode

We study the isothermal hydrogen adsorption and reaction at the E-TEK electrode of a polymer electrolyte fuel cell with a Nafion 117 membrane by impedance spectroscopy at 30 degrees C. We find that the impedance diagram must include a Gerischer phase element. Constant phase elements are not sufficient to describe the experimental data. This means that an adsorption reaction takes place in combination with surface diffusion of hydrogen in the carbon layer located before the platinum surface, separate from the charge transfer step at the platinum particle surface. We are not able to distinguish between molecular or atomic hydrogen diffusion on carbon. We predict and find that the relaxation time of the adsorption step is independent of the applied potential. Water may also enter rate-limiting steps in the electrode reaction, but its role needs further clarification.