A weakly stable algorithm for general Toeplitz systems

We show that a fast algorithm for the QR factorization of a Toeplitz or Hankel matrix A is weakly stable in the sense that R^T.R is close to A^T.A. Thus, when the algorithm is used to solve the semi-normal equations R^T.Rx = A^Tb, we obtain a weakly stable method for the solution of a nonsingular Toeplitz or Hankel linear system Ax = b. The algorithm also applies to the solution of the full-rank Toeplitz or Hankel least squares problem.Comment: 17 pages. An old Technical Report with postscript added. For further details, see http://wwwmaths.anu.edu.au/~brent/pub/pub143.htm

Insights on the source of the 28 September 2018 Sulawesi tsunami, Indonesia based on spectral analyses and numerical simulations

The 28 September 2018 Sulawesi tsunami has been a puzzle because extreme deadly tsunami waves were generated following an Mw 7.5 strike-slip earthquake, while such earthquakes are not usually considered to produce large tsunamis. Here, we obtained, processed and analyzed two sea level records of the tsunami in the near-field (Pantoloan located inside the Palu Bay) and far-field (Mamuju located outside the Palu Bay) and conducted numerical simulations to shed light on the tsunami source. The two tide gauges recorded maximum tsunami trough-to-crest heights of 380 and 24 cm, respectively, with respective dominating wave periods of 3.6-4.4 and 10 min, and respective high-energy wave duration of 5.5 and [14 h. The two observed waveforms were significantly different with wave amplitude and period ratios of *16 and *3, respectively. We infer tsunamigenic source dimen19 sions of 3.4–4.1 km and 32.5 km, for inside and outside of the Palu Bay, respectively. Our numerical simulations fairly well repro21 duced both tsunami observations in Pantoloan and Mamuju; except for the arrival time in Mamuju. However, it was incapable of reproducing the maximum reported coastal amplitudes of 6–11 m. It is possible that these two sources are different parts of the same tectonic source. A bay oscillation mode of *85 min was revealed for the Palu Bay through numerical modeling. Actual sea surface disturbances and landslide-generated waves were captured by two video recordings from inside the Palu Bay shortly after the earthquake. It is possible that a large submarine landslide contributed to and intensified the Sulawesi tsunami. We identify the southern part of the Palu Bay, around the latitude of -0.82o S, as the most likely location of a potential landslide based on our backward tsunami ray tracing analysis. However, marine geological data from the Palu Bay are required to confirm such hypothesis

Mouse Chromosome 11

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46996/1/335_2004_Article_BF00648429.pd

Whole-genome sequencing reveals host factors underlying critical COVID-19

Critical COVID-19 is caused by immune-mediated inflammatory lung injury. Host genetic variation influences the development of illness requiring critical care1 or hospitalization2,3,4 after infection with SARS-CoV-2. The GenOMICC (Genetics of Mortality in Critical Care) study enables the comparison of genomes from individuals who are critically ill with those of population controls to find underlying disease mechanisms. Here we use whole-genome sequencing in 7,491 critically ill individuals compared with 48,400 controls to discover and replicate 23 independent variants that significantly predispose to critical COVID-19. We identify 16 new independent associations, including variants within genes that are involved in interferon signalling (IL10RB and PLSCR1), leucocyte differentiation (BCL11A) and blood-type antigen secretor status (FUT2). Using transcriptome-wide association and colocalization to infer the effect of gene expression on disease severity, we find evidence that implicates multiple genes—including reduced expression of a membrane flippase (ATP11A), and increased expression of a mucin (MUC1)—in critical disease. Mendelian randomization provides evidence in support of causal roles for myeloid cell adhesion molecules (SELE, ICAM5 and CD209) and the coagulation factor F8, all of which are potentially druggable targets. Our results are broadly consistent with a multi-component model of COVID-19 pathophysiology, in which at least two distinct mechanisms can predispose to life-threatening disease: failure to control viral replication; or an enhanced tendency towards pulmonary inflammation and intravascular coagulation. We show that comparison between cases of critical illness and population controls is highly efficient for the detection of therapeutically relevant mechanisms of disease