17,561 research outputs found

    Semi-dynamic connectivity in the plane

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    Motivated by a path planning problem we consider the following procedure. Assume that we have two points ss and tt in the plane and take K=\mathcal{K}=\emptyset. At each step we add to K\mathcal{K} a compact convex set that does not contain ss nor tt. The procedure terminates when the sets in K\mathcal{K} separate ss and tt. We show how to add one set to K\mathcal{K} in O(1+kα(n))O(1+k\alpha(n)) amortized time plus the time needed to find all sets of K\mathcal{K} intersecting the newly added set, where nn is the cardinality of K\mathcal{K}, kk is the number of sets in K\mathcal{K} intersecting the newly added set, and α()\alpha(\cdot) is the inverse of the Ackermann function

    A Bayesian Approach to Manifold Topology Reconstruction

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    In this paper, we investigate the problem of statistical reconstruction of piecewise linear manifold topology. Given a noisy, probably undersampled point cloud from a one- or two-manifold, the algorithm reconstructs an approximated most likely mesh in a Bayesian sense from which the sample might have been taken. We incorporate statistical priors on the object geometry to improve the reconstruction quality if additional knowledge about the class of original shapes is available. The priors can be formulated analytically or learned from example geometry with known manifold tessellation. The statistical objective function is approximated by a linear programming / integer programming problem, for which a globally optimal solution is found. We apply the algorithm to a set of 2D and 3D reconstruction examples, demon-strating that a statistics-based manifold reconstruction is feasible, and still yields plausible results in situations where sampling conditions are violated

    Neural View-Interpolation for Sparse Light Field Video

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    We suggest representing light field (LF) videos as "one-off" neural networks (NN), i.e., a learned mapping from view-plus-time coordinates to high-resolution color values, trained on sparse views. Initially, this sounds like a bad idea for three main reasons: First, a NN LF will likely have less quality than a same-sized pixel basis representation. Second, only few training data, e.g., 9 exemplars per frame are available for sparse LF videos. Third, there is no generalization across LFs, but across view and time instead. Consequently, a network needs to be trained for each LF video. Surprisingly, these problems can turn into substantial advantages: Other than the linear pixel basis, a NN has to come up with a compact, non-linear i.e., more intelligent, explanation of color, conditioned on the sparse view and time coordinates. As observed for many NN however, this representation now is interpolatable: if the image output for sparse view coordinates is plausible, it is for all intermediate, continuous coordinates as well. Our specific network architecture involves a differentiable occlusion-aware warping step, which leads to a compact set of trainable parameters and consequently fast learning and fast execution

    Purification of Curcumin from Ternary Extract-Similar Mixtures of Curcuminoids in a Single Crystallization Step

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    Crystallization-based separation of curcumin from ternary mixtures of curcuminoids having compositions comparable to commercial extracts was studied experimentally. Based on solubility and supersolubility data of both, pure curcumin and curcumin in presence of the two major impurities demethoxycurcumin (DMC) and bis(demethoxy)curcumin (BDMC), seeded cooling crystallization procedures were derived using acetone, acetonitrile and 50/50 (wt/wt) mixtures of acetone/2-propanol and acetone/acetonitrile as solvents. Starting from initial curcumin contents of 67–75% in the curcuminoid mixtures single step crystallization processes provided crystalline curcumin free of BDMC at residual DMC contents of 0.6–9.9%. Curcumin at highest purity of 99.4% was obtained from a 50/50 (wt/wt) acetone/2-propanol solution in a single crystallization step. It is demonstrated that the total product yield can be significantly enhanced via addition of water, 2-propanol and acetonitrile as anti-solvents at the end of a cooling crystallization process

    Exact Lagrangian submanifolds in simply-connected cotangent bundles

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    We consider exact Lagrangian submanifolds in cotangent bundles. Under certain additional restrictions (triviality of the fundamental group of the cotangent bundle, and of the Maslov class and second Stiefel-Whitney class of the Lagrangian submanifold) we prove such submanifolds are Floer-cohomologically indistinguishable from the zero-section. This implies strong restrictions on their topology. An essentially equivalent result was recently proved independently by Nadler, using a different approach.Comment: 28 pages, 3 figures. Version 2 -- derivation and discussion of the spectral sequence considerably expanded. Other minor change