It was recently brought to our attention that our paper was missing information regarding when the patient chest computed tomography (CT) scans were obtained and that there were some discrepancies in the clinical metadata, associated with the very large image dataset, that we made publicly available through the China National Center for Bioinformation (http://ncov-ai.big.ac.cn/ download?lang=en). All of the chest CT and clinical metadata used in our prognostic analysis were collected from patients at the time of hospital admission, and we have now added this statement to the STAR Methods section of our paper. We believe that the errors in the clinical metadata were introduced when the chest CT images, clinical metadata, and codes were transferred to the web server, and we have now corrected the errors manually. Although these corrections do not alter any of the conclusions made in the paper, we do apologize for these errors and any confusion that they may have caused.

A barrier certificate is an inductive invariant function which can be used for the safety verification of a hybrid system. Safety verification based on barrier certificate has the benefit of avoiding explicit computation of the exact reachable set which is usually intractable for nonlinear hybrid systems. In this paper, we propose a new barrier certificate condition, called Exponential Condition, for the safety verification of semi-algebraic hybrid systems. The most important benefit of Exponential Condition is that it has a lower conservativeness than the existing convex condition and meanwhile it possesses the property of convexity. On the one hand, a less conservative barrier certificate forms a tighter over-approximation for the reachable set and hence is able to verify critical safety properties. On the other hand, the property of convexity guarantees its solvability by semidefinite programming method. Some examples are presented to illustrate the effectiveness and practicality of our method.

The maize dull1 (du1) gene is a determinant of the structure of endosperm starch, and du1- mutations affect the activity of two enzymes involved in starch biosynthesis, starch synthase II (SSII) and starch branching enzyme IIa (SBEIIa). Six novel du1- mutations generated in Mutator-active plants were identified. A portion of the du1 locus was cloned by transposon tagging, and a nearly full-length Du1 cDNA sequence was determined. Du1 codes for a predicted 1674-residue protein, comprising one portion that is similar to SSIII of potato, as well as a large unique region. Du1 transcripts are present in the endosperm during the time of starch biosynthesis, but the mRNA was undetectable in leaf or root tissue. The predicted size of the Du1 gene product and its expression pattern are consistent with those of maize SSII. The Du1 gene product contains two repeated regions in its unique N terminus. One of these contains a sequence identical to a conserved segment of SBEs. We conclude that Du1 codes for a starch synthase, most likely SSII, and that secondary effects of du1- mutations, such as reduction of SBEIIa, result from the primary deficiency in this starch synthase.

Path planning is a fundamental problem, especially for various AEC applications, such as architectural design, indoor and outdoor navigation, and emergency evacuation. However, the conventional approaches mainly operate path planning on 2D drawings or building layouts by simply considering geometric information, while losing abundant semantic information of building components. To address this issue, this paper introduces a new method to cope with path planning for 3D indoor space through an IFC (Industry Foundation Classes) file as input. As a major data exchange standard for Building Information Modeling (BIM), the IFC standard is capable of restoring both geometric information and rich semantic information of building components to support lifecycle data sharing. The method consists of three main steps: (1) extracting both geometric and semantic information of building components defined within the IFC file, (2) discretizing and mapping the extracted information into a planar grid, (3) and finally finding the shortest path based on the mapping for path planning using Fast Marching Method. The paper aims to process different kinds of building components and their corresponding properties to obtain rich semantic information that can enhance applications of path planning. In addition, the IFC-based distributed data sharing and management is implemented for path planning. The paper also presents some experiments to demonstrate the accuracy, efficiency and adaptability of the method. Video demonstration is available from http://cgcad.thss.tsinghua.edu.cn/liuyushen/ifcpath/.

We describe how a simple way to split input operands allows for fast VLSI implementations of subquadratic GF (2)[x] Karatsuba-Ofman multipliers. The theoretical XOR gate delay of the resulting multipliers is reduced significantly. For example, it is reduced by about 33% and 25% for n = 2 t and n = 3 t (t > 1), respectively. To the best of our knowledge, this parameter has never been improved since the original Karatsuba-Ofman algorithm was first used to design GF (2 n) multipliers in 1990.