Fast Cutter Location Surface Computation Using Ray Tracing Cores

By using the cutter location (CL) surface, fast and stable computation of the cutter path for machining complicated molds and dies can be realized. State-of-the-art graphics processing units (GPUs) are equipped with special hardware named ray tracing (RT) cores dedicated to image processing (called ray tracing) for 3D computer graphics. Using RT cores, it is possible to quickly compute the intersection points between a set of straight lines and polygons. In this paper, we propose a novel CL surface computation method using the RT core. The RT core was originally designed to accelerate 3D computer graphics processing. For the development of software using RT cores, it is necessary to use the OptiX application programming interface (API) library for computer graphics. We demonstrate how to use the OptiX API in the development of software for CL surface computations. Computational experiments were carried out, and it was confirmed that it is possible to obtain the CL surface based on a very high-resolution Z-map several times faster than the depth buffer-based method, which has been considered to be the fastest to date.

Quantile Regression for Survival Data

Quantile regression offers a useful alternative strategy for analyzing survival data. Compared with traditional survival analysis methods, quantile regression allows for comprehensive and flexible evaluations of covariate effects on a survival outcome of interest while providing simple physical interpretations on the time scale. Moreover, many quantile regression methods enjoy easy and stable computation. These appealing features make quantile regression a valuable practical tool for delivering in-depth analyses of survival data. This article provides a review of a comprehensive set of statistical methods for performing quantile regression with different types of survival data. The review covers various survival scenarios, including randomly censored data, data subject to left truncation or censoring, competing risks and semicompeting risks data, and recurrent events data. Two real-world examples are presented to illustrate the utility of quantile regression for practical survival data analyses.

2D-FFTLog: efficient computation of real-space covariance matrices for galaxy clustering and weak lensing

ABSTRACT Accurate covariance matrices for two-point functions are critical for inferring cosmological parameters in likelihood analyses of large-scale structure surveys. Among various approaches to obtaining the covariance, analytic computation is much faster and less noisy than estimation from data or simulations. However, the transform of covariances from Fourier space to real space involves integrals with two Bessel integrals, which are numerically slow and easily affected by numerical uncertainties. Inaccurate covariances may lead to significant errors in the inference of the cosmological parameters. In this paper, we introduce a 2D-FFTLog algorithm for efficient, accurate, and numerically stable computation of non-Gaussian real-space covariances for both 3D and projected statistics. The 2D-FFTLog algorithm is easily extended to perform real-space bin-averaging. We apply the algorithm to the covariances for galaxy clustering and weak lensing for a Dark Energy Survey Year 3-like and a Rubin Observatory’s Legacy Survey of Space and Time Year 1-like survey, and demonstrate that for both surveys, our algorithm can produce numerically stable angular bin-averaged covariances with the flat sky approximation, which are sufficiently accurate for inferring cosmological parameters. The code CosmoCov for computing the real-space covariances with or without the flat-sky approximation is released along with this paper.