The sampling strategies in many randomized matrix algorithms are, either explicitly or implicitly, controlled by statistical quantities called leverage scores. We present four bounds for the sensitivity of leverage scores as well as an upper bound for the principal angles between two matrices. These bounds are expressed by considering two real m×n matrices of full column rank, A and B. Our boun...

The only approved clot-busting medical treatment in ischemic stroke, intravenous thrombolysis (IVT), is not without complications. One of the major reasons for withholding the therapy remains fear of symptomatic intracranial hemorrhage (sICH), which can worsen patients’ outcomes. The number needed for IVT to cause fatal sICH is 36.5, and to cause any worsening of outcome (≥1 grade on modified R...

GNPKVKAH Here we discuss standard ways of assigning a score to each amino acid pair, i.e., to each possible column of a gap-free pairwise protein alignment. Examples of such scoring matrices include the PAM30, PAM70, BLOSUM80, BLOSUM62 and BLOSUM45 matrices that are available on NCBI’s blastp server. Such scores are appropriate for comparing two sequences about which we have no other informatio...

In the ranking of the teaching effectiveness of staff members through their student feedback scores, there can be a problem if it is perceived to be more difficult to obtain high scores in some courses than others. The result would be, therefore, that staff taking ‘difficult’ courses are disadvantaged. For example, it is often claimed that GEM and courses at the 1000 level are more difficult to...

GNPKVKAH Here we discuss standard ways of assigning a score to each amino acid pair, i.e., to each possible column of a gap-free pairwise protein alignment. Examples of such scoring matrices include the PAM30, PAM70, BLOSUM80, BLOSUM62 and BLOSUM45 matrices that are available on NCBI’s blastp server. Such scores are appropriate for comparing two sequences about which we have no other informatio...