4,481 research outputs found

    Optimal algorithms for constructing knight's tours on arbitrary n×m chessboards

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    AbstractThe knight's tour problem is an ancient puzzle whose goal is to find out how to construct a series of legal moves made by a knight so that it visits every square of a chessboard exactly once. In previous works, researchers have partially solved this problem by offering algorithms for subsets of chessboards. For example, among prior studies, Parberry proposed a divided-and-conquer algorithm that can build a closed knight's tour on an n×n, an n×(n+1) or an n×(n+2) chessboard in O(n2) (i.e., linear in area) time on a sequential processor. In this paper we completely solve this problem by presenting new methods that can construct a closed knight's tour or an open knight's tour on an arbitrary n×m chessboard if such a solution exists. Our algorithms also run in linear time (O(nm)) on a sequential processor

    MPT: Mesh Pre-Training with Transformers for Human Pose and Mesh Reconstruction

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    We present Mesh Pre-Training (MPT), a new pre-training framework that leverages 3D mesh data such as MoCap data for human pose and mesh reconstruction from a single image. Existing work in 3D pose and mesh reconstruction typically requires image-mesh pairs as the training data, but the acquisition of 2D-to-3D annotations is difficult. In this paper, we explore how to leverage 3D mesh data such as MoCap data, that does not have RGB images, for pre-training. The key idea is that even though 3D mesh data cannot be used for end-to-end training due to a lack of the corresponding RGB images, it can be used to pre-train the mesh regression transformer subnetwork. We observe that such pre-training not only improves the accuracy of mesh reconstruction from a single image, but also enables zero-shot capability. We conduct mesh pre-training using 2 million meshes. Experimental results show that MPT advances the state-of-the-art results on Human3.6M and 3DPW datasets. We also show that MPT enables transformer models to have zero-shot capability of human mesh reconstruction from real images. In addition, we demonstrate the generalizability of MPT to 3D hand reconstruction, achieving state-of-the-art results on FreiHAND dataset

    A three-phase parallel algorithm for solving linear recurrences

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    AbstractWe present in this paper a three-phase parallel algorithm on the unshuffle network for solving linear recurrences. Through a detailed analysis on the special matrix multiplications involved in the computation we show that the first n terms of an mth order linear recurrence can be computed in O(m3 log nm) time using Θ(nm log nm) processors. For the usual case when m is a small constant. the algorithm achieves cost optimality

    IMPACT EXPERIMENTS IN ORTHOPAEDIC BIOMECHANICS

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    A better understanding of the fracture mechanism, kinematics of the anatomic structure and tissue tolerances can improve clinical prognosis and design of anthropomorphic test devices. An impact apparatus was designed to do experiments in vitro in the areas of orthopaedic biomechanics, either in hard tissue or soft tissue. METHODS: The specimens were subjected to high-speed trauma produced by an impact apparatus. This testing setup is a falling weight system which can do axial and eccentric impacts for different objectives of the orthopaedic studies. A special design was installed to assure only one impact on the specimen for biomechanical analysis. A high-speed camera was placed in front of the specimen to record the trauma event. In this study, the specimens included porcine vertebras, rabbit achilles tendons and human leg cadavers. Observations were also made to get more details by X-ray and/or by CT scan. RESULTS: Spinal fractures similar to those found clinically were successfully produced in porcine spines by impact testing. The deformations of the discs and the kinematical stability of the spinal experimental segments were also found. For the experiment on the achilles tendon, the high speed traction mechanism could produce strain injury to the specimen and get the immediate tensile force in the traction process. For the study on internal fixation for calcaneal fractures, clinically-relevant fractures under high speed impact were produced. The specimens with both longitudinal and transverse primary fracture lines were selected for simulated open reduction and internal fixation. All mechanical failures of the reconstructed calcanens occurred through the transverse primary fracture line. CONCLUSION: Impact experiment is a useful method to do fundamental research in orthopaedic biomechanics. The results in the animal model offer useful insight into bone fractures in human. The repeatability and reproducibility of animal tests offer a great opportunity to evaluate spinal fracture mechanics. The test on the achilles tendon injury was just a pilot study, and a well-designed protocol is needed to improve the results. The study on calcaneal fractures resulted in adding a longitudinal. Transfixing screw is recommended to enhance the strength of internal fixation in the presence of a transverse primary fracture line. From the above three studies, it was concluded that the impact method is an excellent experiment to produce tissue failure and/or fractures for further orthopaedic research

    Integrated nanophotonic hubs based on ZnO-Tb(OH)3/SiO2 nanocomposites

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    Optical integration is essential for practical application, but it remains unexplored for nanoscale devices. A newly designed nanocomposite based on ZnO semiconductor nanowires and Tb(OH)3/SiO2 core/shell nanospheres has been synthesized and studied. The unique sea urchin-type morphology, bright and sharply visible emission bands of lanthanide, and large aspect ratio of ZnO crystalline nanotips make this novel composite an excellent signal receiver, waveguide, and emitter. The multifunctional composite of ZnO nanotips and Tb(OH)3/SiO2 nanoparticles therefore can serve as an integrated nanophotonics hub. Moreover, the composite of ZnO nanotips deposited on a Tb(OH)3/SiO2 photonic crystal can act as a directional light fountain, in which the confined radiation from Tb ions inside the photonic crystal can be well guided and escape through the ZnO nanotips. Therefore, the output emission arising from Tb ions is truly directional, and its intensity can be greatly enhanced. With highly enhanced lasing emissions in ZnO-Tb(OH)3/SiO2 as well as SnO2-Tb(OH)3/SiO2 nanocomposites, we demonstrate that our approach is extremely beneficial for the creation of low threshold and high-power nanolaser
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