Sparse sampling and reconstruction for freeform surface based on low-rank matrix completion

The coordinate measuring machine (CMM) becomes an extensive and effective method for high precision inspection of free-form surfaces due to its ability to measure complex and irregular surfaces. Sampling strategy and surface restoration method have an important influence on the efficiency and precision of CMM. In this paper, a sparse sampling strategy and surface reconstruction method for free-form surfaces based on low-rank matrix completion (LRMC) is proposed. In this method, the free-form surface is sampled randomly with uniform distribution in the cartesian coordinate system to obtain sparse sampling points, and then optimizes the scanning path to obtain the shortest path through all measurement points, and finally, the LRMC algorithm based on alternating root mean square prop was used to reconstruct the surface with high precision. The simulation and experimental results show that under the premise of ensuring accuracy, the number of sampling points is greatly reduced and the measurement efficiency is greatly improved.

Unrecognized introductions of SARS-CoV-2 into the state of Georgia shaped the early epidemic

In early 2020, as SARS-CoV-2 diagnostic and surveillance responses ramped up, attention focused primarily on returning international travelers. Here, we build on existing studies characterizing early patterns of SARS-CoV-2 spread within the U.S. by analyzing detailed clinical, molecular, and viral genomic data from the state of Georgia through March 2020. We find evidence for multiple early introductions into Georgia, despite relatively sparse sampling. Most sampled sequences likely stemmed from a single introduction from Asia at least two weeks prior to the state’s first detected infection. Our analysis of sequences from domestic travelers demonstrates widespread circulation of closely-related viruses in multiple U.S. states by the end of March 2020. Our findings indicate that the early attention directed towards identifying SARS-CoV-2 in returning international travelers may have led to a failure to recognize locally circulating infections for several weeks, and points towards a critical need for rapid and broadly-targeted surveillance efforts in the future.