16 research outputs found

    Fast and Robust Retrieval of Minkowski Sums of Rotating Convex Polyhedra in 3-Space

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    We present a novel method for fast retrieval of exact Minkowski sums of pairs of convex polytopes in R³, where one of the polytopes keeps rotating. The algorithm is based on pre-computing a so-called criticality map, which records the changes in the underlying graph-structure of the Minkowski sum, while one of the polytopes rotates. We give tight combinatorial bounds on the complexity of the criticality map when the rotating polytope rotates about one, two, or three axes. The criticality map can be rather large already for rotations about one axis, even for summand polytopes with a moderate number of vertices each. We therefore focus on the restricted case of rotations about a single, though arbitrary, axis. Our work targets applications that require exact collisiondetection such as motion planning with narrow corridors and assembly maintenance where high accuracy is required. Our implementation handles all degeneracies and produces exact results. It efficiently handles the algebra of exact rotations about an arbitrary axis in R³, and it well balances between preprocessing time and space on the one hand, and query time on the other. We use Cgal arrangements and in particular the support for spherical Gaussian-maps to efficiently compute the exact Minkowski sum of two polytopes. We conducted several experiments to verify the correctness of the algorithm and its implementation, and to compare its efficiency with an alternative (static) exact method. The results are reported

    Automatically Identifying Join Candidates in the Cairo Genizah

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    A join is a set of manuscript-fragments that are known to originate from the same original work. The Cairo Genizah is a collection containing approximately 250,000 fragments of mainly Jewish texts discovered in the late 19th century. The fragments are today spread out in libraries and private collections worldwide, and there is an onging effort to document and catalogue all extant fragments. The task of finding joins is currently conducted manually by experts, and presumably only a small fraction of the existing joins have been discovered. In this work, we study the problem of automatically finding candidate joins, so as to streamline the task. The proposed method is based on a combination of local descriptors and learning techniques. To evaluate the performance of various join-finding methods, without relying on the availability of human experts, we construct a benchmark dataset that is modeled on the Labeled Faces in the Wild benchmark for face recognition. Using this benchmark, we evaluate several alternative image representations and learning techniques. Finally, a set of newly-discovered join-candidates have been identified using our method and validated by a human expert

    Defining diurnal fluctuations in mouse choroid plexus and CSF at high molecular, spatial, and temporal resolution

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    Abstract Transmission and secretion of signals via the choroid plexus (ChP) brain barrier can modulate brain states via regulation of cerebrospinal fluid (CSF) composition. Here, we developed a platform to analyze diurnal variations in male mouse ChP and CSF. Ribosome profiling of ChP epithelial cells revealed diurnal translatome differences in metabolic machinery, secreted proteins, and barrier components. Using ChP and CSF metabolomics and blood-CSF barrier analyses, we observed diurnal changes in metabolites and cellular junctions. We then focused on transthyretin (TTR), a diurnally regulated thyroid hormone chaperone secreted by the ChP. Diurnal variation in ChP TTR depended on Bmal1 clock gene expression. We achieved real-time tracking of CSF-TTR in awake Ttr mNeonGreen mice via multi-day intracerebroventricular fiber photometry. Diurnal changes in ChP and CSF TTR levels correlated with CSF thyroid hormone levels. These datasets highlight an integrated platform for investigating diurnal control of brain states by the ChP and CSF
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