Wobec genologii. Gatunek indywidualny Julii Hartwig

Hartwig symbols

Response to Hartwig and Davies

and indeed many of the other analyses reported in our paper do not suffer from potential bias due to weak instruments. Hartwig and Davies did, however, suggest that we could have used estimates from an external source to obtain less biased results in our MR-Egger analyses. Whereas we agree that this would be good practice in most situations, we do not feel that it would have been appropriate in...

The Fisher-Hartwig Conjecture and Toeplitz Eigenvalues

The conjecture of Fisher and Hartwig, published in 1968, describes the asymptotic expansion of Toeplitz determinants with singular generating functions. For more than twenty years progress was made in extending the validity of the conjecture, but recent computer experiments led to counter-examples that show the limits of the original conjecture and pointed the way to a revised conjecture. This ...

On a Question of Hartwig and Luh

In 1977 Hartwig and Luh asked whether an element a in a Dedekind-finite ring R satisfying aR = a2R also satisfies Ra = Ra2. In this paper, we answer this question in the negative. We also prove that if a is an element of a Dedekind-finite exchange ring R and aR = a2R, then Ra = Ra2. This gives an easier proof of Dischinger’s theorem that left strongly π-regular rings are right strongly π-regula...

Authors’ response to Hartwig and Davies

1. Davey Smith G, Ebrahim S. ‘Mendelian randomization’: can genetic epidemiology contribute to understanding environmental determinants of disease? Int J Epidemiol 2003;32:1–22. 2. Burgess S, Timpson NJ, Ebrahim S, Davey Smith G. Mendelian randomization: where are we now and where are we going? Int J Epidemiol 2015;44:379–88. 3. Haycock PC, Burgess S, Wade KH, Bowden J, Relton C, Davey Smith G....