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  1. Abstract

    Extracting quadrilateral layouts from surface triangulations is an important step in texture mapping, semi-structured quadrilateral meshing for traditional analysis and spline reconstruction for isogeometric analysis. Current methods struggle to yield high-quality layouts with appropriate connectivity between singular nodes (known as “extraordinary points” for spline representations) without resorting to either mixed-integer optimization or manual constraint prescription. The first of these is computationally expensive and comes with no guarantees, while the second is laborious and error-prone. In this work, we rigorously characterize curves in a quadrilateral layout up to homotopy type and use this information to quickly define high-quality connectivity constraints between singular nodes. The mathematical theory is accompanied by appropriate computational algorithms. The efficacy of the proposed method is demonstrated in generating quadrilateral layouts on the United States Army’s DEVCOM Generic Hull vehicle and parts of a bilinear quadrilateral finite element mesh (with some linear triangles) of a 1996 Dodge Neon.

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  2. Wang, Linwei ; Dou, Qi ; Fletcher, P. Thomas ; Speidel, Stefanie ; Li, Shuo (Ed.)
    We presented a novel radiomics approach using multimodality MRI to predict the expression of an oncogene (O6-Methylguanine-DNA methyltransferase, MGMT) and overall survival (OS) of glioblastoma (GBM) patients. Specifically, we employed an EffNetV2-T, which was down scaled and modified from EfficientNetV2, as the feature extractor. Besides, we used evidential layers based to control the distribution of prediction outputs. The evidential layers help to classify the high-dimensional radiomics features to predict the methylation status of MGMT and OS. Tests showed that our model achieved an accuracy of 0.844, making it possible to use as a clinic-enabling technique in the diagnosing and management of GBM. Comparison results indicated that our method performed better than existing work. 
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  3. In this work we present a framework of designing iterative techniques for image deblurring in inverse problem. The new framework is based on two observations about existing methods. We used Landweber method as the basis to develop and present the new framework but note that the framework is applicable to other iterative techniques. First, we observed that the iterative steps of Landweber method consist of a constant term, which is a low-pass filtered version of the already blurry observation. We proposed a modification to use the observed image directly. Second, we observed that Landweber method uses an estimate of the true image as the starting point. This estimate, however, does not get updated over iterations. We proposed a modification that updates this estimate as the iterative process progresses. We integrated the two modifications into one framework of iteratively deblurring images. Finally, we tested the new method and compared its performance with several existing techniques, including Landweber method, Van Cittert method, GMRES (generalized minimal residual method), and LSQR (least square), to demonstrate its superior performance in image deblurring. 
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  4. Optimal transportation maps play fundamental roles in many engineering and medical fields. The computation of optimal transportation maps can be reduced to solve highly non-linear Monge-Ampere equations. This work summarizes the geometric variational frameworks for spherical optimal transportation maps, which offers solutions to the Minkowski problem in convex differential geometry, reflector design and refractor design problems in optics. The method is rigorous, robust and efficient. The algorithm can directly generalized to higher dimensions. 
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