1,374,462 research outputs found

    On the representation of polyhedra by polynomial inequalities

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    A beautiful result of Br\"ocker and Scheiderer on the stability index of basic closed semi-algebraic sets implies, as a very special case, that every dd-dimensional polyhedron admits a representation as the set of solutions of at most d(d+1)/2d(d+1)/2 polynomial inequalities. Even in this polyhedral case, however, no constructive proof is known, even if the quadratic upper bound is replaced by any bound depending only on the dimension. Here we give, for simple polytopes, an explicit construction of polynomials describing such a polytope. The number of used polynomials is exponential in the dimension, but in the 2- and 3-dimensional case we get the expected number d(d+1)/2d(d+1)/2.Comment: 19 pages, 4 figures; revised version with minor changes proposed by the referee

    Model-based learning of local image features for unsupervised texture segmentation

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    Features that capture well the textural patterns of a certain class of images are crucial for the performance of texture segmentation methods. The manual selection of features or designing new ones can be a tedious task. Therefore, it is desirable to automatically adapt the features to a certain image or class of images. Typically, this requires a large set of training images with similar textures and ground truth segmentation. In this work, we propose a framework to learn features for texture segmentation when no such training data is available. The cost function for our learning process is constructed to match a commonly used segmentation model, the piecewise constant Mumford-Shah model. This means that the features are learned such that they provide an approximately piecewise constant feature image with a small jump set. Based on this idea, we develop a two-stage algorithm which first learns suitable convolutional features and then performs a segmentation. We note that the features can be learned from a small set of images, from a single image, or even from image patches. The proposed method achieves a competitive rank in the Prague texture segmentation benchmark, and it is effective for segmenting histological images

    Soiling and other optical losses in solar-tracking PV plants in Navarra

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    Field data of soiling energy losses on PV plants are scarce. Furthermore, since dirt type and accumulation vary with the location characteristics (climate, surroundings, etc.), the available data on optical losses are, necessarily, site dependent. This paper presents field measurements of dirt energy losses (dust) and irradiance incidence angle losses along 2005 on a solar-tracking PV plant located south of Navarre (Spain). The paper proposes a method to calculate these losses based on the difference between irradiance measured by calibrated cells on several trackers of the PV plant and irradiance calculated from measurements by two pyranometers (one of them incorporating a shadow ring) regularly cleaned. The equivalent optical energy losses of an installation incorporating fixed horizontal modules at the same location have been calculated as well. The effect of dirt on both types of installations will accordingly be compared

    The heat of atomization of sulfur trioxide, SO3_3 - a benchmark for computational thermochemistry

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    Calibration ab initio (direct coupled cluster) calculations including basis set extrapolation, relativistic effects, inner-shell correlation, and an anharmonic zero-point energy, predict the total atomization energy at 0 K of SO3_3 to be 335.96 (observed 335.92±\pm0.19) kcal/mol. Inner polarization functions make very large (40 kcal/mol with spdspd, 10 kcal/mol with spdfgspdfg basis sets) contributions to the SCF part of the binding energy. The molecule presents an unusual hurdle for less computationally intensive theoretical thermochemistry methods and is proposed as a benchmark for them. A slight modification of Weizmann-1 (W1) theory is proposed that appears to significantly improve performance for second-row compounds.Comment: Chem. Phys. Lett., in pres
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