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.

     

Left versus right canonical Wiener-Hopf factorization and realization

For an arbitrary rational matrix function, not necessarily analytic at infinity, the existence of a right canonical Wiener-Hopf factorization is characterized in terms of a left canonical Wiener-Hopf factorization. Formulas for the factors in a right factorization are given in terms of the formulas for the factors in a given left factorization. All formulas are based on a special representation of a rational matrix function involving a quintet of matrices.     

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.