A New Algorithm for Computing the Actions of Trigonometric and Hyperbolic Matrix Functions

A new algorithm is derived for computing the actions $f(tA)B$ and $f(tA^{1/2})B$, where $f$ is cosine, sinc, sine, hyperbolic cosine, hyperbolic sinc, or hyperbolic sine function. $A$ is an $n\times n$ matrix and $B$ is $n\times n_0$ with $n_0 \ll n$. $A^{1/2}$ denotes any matrix square root of $A$ and it is never required to be computed. The algorithm offers six independent output options given $t$, $A$, $B$, and a tolerance. For each option, actions of a pair of trigonometric or hyperbolic matrix functions are simultaneously computed. The algorithm scales the matrix $A$ down by a positive integer $s$, approximates $f(s^{-1}tA)B$ by a truncated Taylor series, and finally uses the recurrences of the Chebyshev polynomials of the first and second kind to recover $f(tA)B$. The selection of the scaling parameter and the degree of Taylor polynomial are based on a forward error analysis and a sequence of the form $\|A^k\|^{1/k}$ in such a way the overall computational cost of the algorithm is optimized. Shifting is used where applicable as a preprocessing step to reduce the scaling parameter. The algorithm works for any matrix $A$ and its computational cost is dominated by the formation of products of $A$ with $n\times n_0$ matrices that could take advantage of the implementation of level-3 BLAS. Our numerical experiments show that the new algorithm behaves in a forward stable fashion and in most problems outperforms the existing algorithms in terms of CPU time, computational cost, and accuracy.Comment: 4 figures, 16 page

Regression modelling in hospital epidemiology: a statistical note

Barnett and Graves [1], in their commentary on our report recently published in Critical Care [2], suggested that timediscrete methods should be used to address time-dependent risk factors and competing risks. In this letter we comment on two statements by those authors. First, Barnett and Graves claim that, ‘An alternative method to the competing risks model is a multistate model. ’ In fact, a multistate model is not an alternative to modelling competing risks, but a competing risks model is an example of a multistate model. This is explained in the tutorial by Putter and coworkers [3]. However, competing risks only model the time to first event and the event type (for example, time to nosocomial infection [NI]) or discharge/death, whatever comes first. To model subsequent events also, more complex multistate models are needed. Barnett and Graves give a

Association between women's authorship and women's editorship in infectious diseases journals : a cross-sectional study

Funding: The European Society of Clinical Microbiology and Infectious Diseases.Background Gender inequity is still pervasive in academic medicine, including journal publishing. We aimed to ascertain the proportion of women among first and last authors and editors in infectious diseases journals and assess the association between women's editorship and women's authorship while controlling for a journal's impact factor. Methods In this cross-sectional study, we randomly selected 40 infectious diseases journals (ten from each 2020 impact factor quartile), 20 obstetrics and gynaecology journals (five from each 2020 impact factor quartile), and 20 cardiology journals (five from each 2020 impact factor quartile) that were indexed in Journal Citation Reports, had an impact factor, had retrievable first and last author names, and had the name of more than one editor listed. We retrieved the names of the first and last authors of all citable articles published by the journals in 2018 and 2019 that counted towards their 2020 impact factor and collected the names of all the journals' editors-in-chief, deputy editors, section editors, and associate editors for the years 2018 and 2019. We used genderize.io to predict the gender of each first author, last author, and editor. The outcomes of interest were the proportions of women first authors and women last authors. We assessed the association between women's editorship and women's authorship by fitting quasi-Poisson regression models comprising the variables: the proportion of women last authors or women first authors; the proportion of women editors; the presence of a woman editor-in-chief; and journal 2020 impact factor. Findings We found 11 027 citable infectious diseases articles, of which 167 (1·5%) had an indeterminable first author gender, 155 (1·4%) had an indeterminable last author gender, and seven (0·1%) had no authors indexed. 5350 (49·3%) of 10 853 first authors whose gender could be determined were predicted to be women and 5503 (50·7%) were predicted to be men. Women accounted for 3788 (34·9%) of 10 865 last authors whose gender could be determined and men accounted for 7077 (65·1%). Of 577 infectious diseases journal editors, 190 (32·9%) were predicted to be women and 387 (67·1%) were predicted to be men. Of the 40 infectious diseases journals, 13 (32·5%) had a woman as editor-in-chief. For infectious diseases journals, the proportion of women editors had a significant effect on women's first authorship (incidence rate ratio 1·32, 95% CI 1·06–1·63; p=0·012) and women's last authorship (1·92, 1·45–2·55; p<0·0001). The presence of a woman editor-in-chief, the proportion of women last or first authors, and the journal's impact factor exerted no effect in these analyses. Interpretation The proportion of women editors appears to influence the proportion of women last and first authors in the analysed infectious diseases journals. These findings might help to explain gender disparities observed in publishing in academic medicine and suggest a need for revised policies towards increasing women's representation among editors.PostprintPeer reviewe