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Abstract MotivationHeritability, the proportion of variation in a trait that can be explained by genetic variation, is an important parameter in efforts to understand the genetic architecture of complex phenotypes as well as in the design and interpretation of genome-wide association studies. Attempts to understand the heritability of complex phenotypes attributable to genome-wide single nucleotide polymorphism (SNP) variation data has motivated the analysis of large datasets as well as the development of sophisticated tools to estimate heritability in these datasets. Linear mixed models (LMMs) have emerged as a key tool for heritability estimation where the parameters of the LMMs, i.e. the variance components, are related to the heritability attributable to the SNPs analyzed. Likelihood-based inference in LMMs, however, poses serious computational burdens. ResultsWe propose a scalable randomized algorithm for estimating variance components in LMMs. Our method is based on a method-of-moment estimator that has a runtime complexity O(NMB) for N individuals and M SNPs (where B is a parameter that controls the number of random matrix-vector multiplications). Further, by leveraging the structure of the genotype matrix, we can reduce the time complexity to O(NMBmax( log3N, log3M)).We demonstrate the scalability and accuracy of our method on simulated as well as on empirical data. On standard hardware, our method computes heritability on a dataset of 500 000 individuals and 100 000 SNPs in 38 min. Availability and implementationThe RHE-reg software is made freely available to the research community at: https://github.com/sriramlab/RHE-reg.
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This content will become publicly available on September 23, 2026
Towards a spacelike characterization of the null singularity inside a black hole
Abstract We propose a method for recognizing null singularities in a computer simulation that uses a foliation by spacelike surfaces. The method involves harmonic time slicing as well as rescaled tetrad variables. As a ‘proof of concept’ we show that the method works in Reissner–Nordstrom spacetime.
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- Award ID(s):
- 2102914
- PAR ID:
- 10639644
- Publisher / Repository:
- IOP Publishing
- Date Published:
- Journal Name:
- Classical and Quantum Gravity
- Volume:
- 42
- Issue:
- 19
- ISSN:
- 0264-9381
- Page Range / eLocation ID:
- 195005
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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