Super-localized orthogonal decomposition for convection-dominated diffusion problems.

This paper presents a novel multi-scale method for convection-dominated diffusion problems in the regime of large Péclet numbers. The method involves applying the solution operator to piecewise constant right-hand sides on an arbitrary coarse mesh, which defines a finite-dimensional coarse ansatz space with favorable approximation properties. For some relevant error measures, including the -norm, the Galerkin projection onto this generalized finite element space even yields -independent error bounds, being the singular perturbation parameter.

A Novel Tissue-Free Method to Estimate Tumor-Derived Cell-Free DNA Quantity Using Tumor Methylation Patterns.

Estimating the abundance of cell-free DNA (cfDNA) fragments shed from a tumor (i.e., circulating tumor DNA (ctDNA)) can approximate tumor burden, which has numerous clinical applications.

Evaluation of cell-free DNA approaches for multi-cancer early detection.

In the Circulating Cell-free Genome Atlas (NCT02889978) substudy 1, we evaluate several approaches for a circulating cell-free DNA (cfDNA)-based multi-cancer early detection (MCED) test by defining clinical limit of detection (LOD) based on circulating tumor allele fraction (cTAF), enabling performance comparisons. Among 10 machine-learning classifiers trained on the same samples and independently validated, when evaluated at 98% specificity, those using whole-genome (WG) methylation, single nucleotide variants with paired white blood cell background removal, and combined scores from classifiers evaluated in this study show the highest cancer signal detection sensitivities. Compared with clinical stage and tumor type, cTAF is a more significant predictor of classifier performance and may more closely reflect tumor biology.

Circulating Tumor DNA Allele Fraction: A Candidate Biological Signal for Multicancer Early Detection Tests to Assess the Clinical Significance of Cancers.

Current imaging-based cancer screening approaches provide useful but limited prognostic information. Complementary to existing screening tests, cell-free DNA-based multicancer early detection (MCED) tests account for cancer biology [manifested through circulating tumor allele fraction (cTAF)], which could inform prognosis and help assess the cancer's clinical significance. This review discusses the factors affecting circulating tumor DNA (ctDNA) levels and cTAF, and their correlation with the cancer's clinical significance.