Search

For control nets outlining a large class of topological polyhedra, not just tensor-product grids, bi-cubic polyhedral splines form a piecewise polynomial, first-order differentiable space that associates one function with each vertex. Akin to tensor-product splines, the resulting smooth surface approximates the polyhedron. Admissible polyhedral control nets consist of quadrilateral faces in a grid-like layout, star-configuration where n ≠ 4 quadrilateral faces join around an interior vertex, n-gon configurations, where 2n quadrilaterals surround an n-gon, polar configurations where a cone of n triangles meeting at a vertex is surrounded by a ribbon of n quadrilaterals, and three types of T-junctions where two quad-strips merge into one. The bi-cubic pieces of a polyhedral spline have matching derivatives along their break lines, possibly after a known change of variables. The pieces are represented in Bernstein-Bézier form with coefficients depending linearly on the polyhedral control net, so that evaluation, differentiation, integration, moments, and so on, are no more costly than for standard tensor-product splines. Bi-cubic polyhedral splines can be used both to model geometry and for computing functions on the geometry. Although polyhedral splines do not offer nested refinement by refinement of the control net, polyhedral splines support engineering analysis of curved smooth objects. Coarse nets typically suffice since the splines efficiently model curved features. Algorithm 1032 is a C++ library with input-output example pairs and an IGES output choice. [ABSTRACT FROM AUTHOR] more...

More than 50 000 papers have been published about COVID-19 since the beginning of 2020 and several hundred new papers continue to be published every day. This incredible rate of scientific productivity leads to information overload, making it difficult for researchers, clinicians and public health officials to keep up with the latest findings. Automated text mining techniques for searching, reading and summarizing papers are helpful for addressing information overload. In this review, we describe the many resources that have been introduced to support text mining applications over the COVID-19 literature; specifically, we discuss the corpora, modeling resources, systems and shared tasks that have been introduced for COVID-19. We compile a list of 39 systems that provide functionality such as search, discovery, visualization and summarization over the COVID-19 literature. For each system, we provide a qualitative description and assessment of the system's performance, unique data or user interface features and modeling decisions. Many systems focus on search and discovery, though several systems provide novel features, such as the ability to summarize findings over multiple documents or linking between scientific articles and clinical trials. We also describe the public corpora, models and shared tasks that have been introduced to help reduce repeated effort among community members; some of these resources (especially shared tasks) can provide a basis for comparing the performance of different systems. Finally, we summarize promising results and open challenges for text mining the COVID-19 literature. [ABSTRACT FROM AUTHOR] more...

The Covid-19 Open Research Dataset (CORD-19) is a growing resource of scientific papers on Covid-19 and related historical coronavirus research. CORD-19 is designed to facilitate the development of text mining and information retrieval systems over its rich collection of metadata and structured full text papers. Since its release, CORD-19 has been downloaded over 200K times and has served as the basis of many Covid-19 text mining and discovery systems. In this article, we describe the mechanics of dataset construction, highlighting challenges and key design decisions, provide an overview of how CORD-19 has been used, and describe several shared tasks built around the dataset. We hope this resource will continue to bring together the computing community, biomedical experts, and policy makers in the search for effective treatments and management policies for Covid-19. more...