72,302 research outputs found

    Theater of the Absurd

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    Braid groups and Kleinian singularities

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    We establish faithfulness of braid group actions generated by twists along an ADE configuration of 22-spherical objects in a derived category. Our major tool is the Garside structure on braid groups of type ADE. This faithfulness result provides the missing ingredient in Bridgeland's description of a space of stability conditions associated to a Kleinian singularity.Comment: Section 4 from versions 1 and 2 has been deleted due to an error in the proof of Theorem 2. Renamed the paper and rewrote the other sections to reflect this chang

    Seeing Behind the Camera: Identifying the Authorship of a Photograph

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    We introduce the novel problem of identifying the photographer behind a photograph. To explore the feasibility of current computer vision techniques to address this problem, we created a new dataset of over 180,000 images taken by 41 well-known photographers. Using this dataset, we examined the effectiveness of a variety of features (low and high-level, including CNN features) at identifying the photographer. We also trained a new deep convolutional neural network for this task. Our results show that high-level features greatly outperform low-level features. We provide qualitative results using these learned models that give insight into our method's ability to distinguish between photographers, and allow us to draw interesting conclusions about what specific photographers shoot. We also demonstrate two applications of our method.Comment: Dataset downloadable at http://www.cs.pitt.edu/~chris/photographer To Appear in CVPR 201

    Compositional data analysis of geological variability and process : a case study

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    Developments in the statistical analysis of compositional data over the last two decades have made possible a much deeper exploration of the nature of variability and the possible processes associated with compositional data sets from many disciplines. In this paper, we concentrate on geochemical data. First, we explain how hypotheses of compositional variability may be formulated within the natural sample space, the unit simplex, including useful hypotheses of sub-compositional discrimination and specific perturbational change. Then we develop through standard methodology, such as generalised likelihood ratio tests, statistical tools to allow the systematic investigation of a lattice of such hypotheses. Some of these tests are simple adaptations of existing multivariate tests but others require special construction. We comment on the use of graphical methods in compositional data analysis and on the ordination of specimens. The recent development of the concept of compositional processes is then explained, together with the necessary tools for a staying-in-the-simplex approach, such as the singular value decomposition of a compositional data set. All these statistical techniques are illustrated for a substantial compositional data set, consisting of 209 major oxide and trace element compositions of metamorphosed limestones from the Grampian Highlands of Scotland. Finally, we discuss some unresolved problems in the statistical analysis of compositional processes

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