Reply to Janssen et al. Comment on “Sobczyk, M.K.; Gaunt, T.R. The Effect of Circulating Zinc, Selenium, Copper and Vitamin K1 on COVID-19 Outcomes: A Mendelian Randomization Study. Nutrients 2022, 14, 233

In their correspondence arising from our recent manuscript [...

The Effect of Circulating Zinc, Selenium, Copper and Vitamin K1 on COVID-19 Outcomes:A Mendelian Randomization Study

Background & Aims: Previous results from observational, interventional studies and in vitro experiments suggest that certain micronutrients possess anti-viral and immunomodulatory activities. In particular, it has been hypothesized that zinc, selenium, copper and vitamin K(1) have strong potential for prophylaxis and treatment of COVID-19. We aimed to test whether genetically predicted Zn, Se, Cu or vitamin K(1) levels have a causal effect on COVID-19 related outcomes, including risk of infection, hospitalization and critical illness. Methods: We employed a two-sample Mendelian Randomization (MR) analysis. Our genetic variants derived from European-ancestry GWAS reflected circulating levels of Zn, Cu, Se in red blood cells as well as Se and vitamin K(1) in serum/plasma. For the COVID-19 outcome GWAS, we used infection, hospitalization or critical illness. Our inverse-variance weighted (IVW) MR analysis was complemented by sensitivity analyses including a more liberal selection of variants at a genome-wide sub-significant threshold, MR-Egger and weighted median/mode tests. Results: Circulating micronutrient levels show limited evidence of association with COVID-19 infection, with the odds ratio [OR] ranging from 0.97 (95% CI: 0.87–1.08, p-value = 0.55) for zinc to 1.07 (95% CI: 1.00–1.14, p-value = 0.06)—i.e., no beneficial effect for copper was observed per 1 SD increase in exposure. Similarly minimal evidence was obtained for the hospitalization and critical illness outcomes with OR from 0.98 (95% CI: 0.87–1.09, p-value = 0.66) for vitamin K(1) to 1.07 (95% CI: 0.88–1.29, p-value = 0.49) for copper, and from 0.93 (95% CI: 0.72–1.19, p-value = 0.55) for vitamin K(1) to 1.21 (95% CI: 0.79–1.86, p-value = 0.39) for zinc, respectively. Conclusions: This study does not provide evidence that supplementation with zinc, selenium, copper or vitamin K(1) can prevent SARS-CoV-2 infection, critical illness or hospitalization for COVID-19

Critical Exponent for the Density of Percolating Flux

This paper is a study of some of the critical properties of a simple model for flux. The model is motivated by gauge theory and is equivalent to the Ising model in three dimensions. The phase with condensed flux is studied. This is the ordered phase of the Ising model and the high temperature, deconfined phase of the gauge theory. The flux picture will be used in this phase. Near the transition, the density is low enough so that flux variables remain useful. There is a finite density of finite flux clusters on both sides of the phase transition. In the deconfined phase, there is also an infinite, percolating network of flux with a density that vanishes as $T \rightarrow T_{c}^{+}$. On both sides of the critical point, the nonanalyticity in the total flux density is characterized by the exponent $(1-\alpha)$. The main result of this paper is a calculation of the critical exponent for the percolating network. The exponent for the density of the percolating cluster is $\zeta = (1-\alpha) - (\varphi-1)$. The specific heat exponent $\alpha$ and the crossover exponent $\varphi$ can be computed in the $\epsilon$-expansion. Since $\zeta < (1-\alpha)$, the variation in the separate densities is much more rapid than that of the total. Flux is moving from the infinite cluster to the finite clusters much more rapidly than the total density is decreasing.Comment: 20 pages, no figures, Latex/Revtex 3, UCD-93-2

On Pólya's random walk constants

A celebrated result in probability theory is that a simple symmetric random walk on the d-dimensional lattice Zd is recurrent for d=1,2 and transient for d ≥ 3. In this note, we derive a closed-form expression, in terms of the Lauricella function of type C, for the return probability for all d ≥ 3. Previously, a closed-form formula had only been available for d=3

English Political Propaganda, 1377–1485.

Previous historiography on propaganda has focused on particular themes or time periods; this thesis provides a comprehensive and inclusive analysis drawing on a multidisciplinary approach to encompass the period c.1377-1485. The main conclusion is that propaganda was more prevalent and involved a larger proportion of the polity than previously thought. A conceptual framework based upon certain criteria used in Jacques Ellul’s, Propaganda the Formation of Men’s Attitudes, has been adopted to help define and identify propaganda. One of the dominant themes is the prerequisite of communication to enable the propagandist to reach his audience and the opportunities available to do so. An examination of the various methods available, from official sources to rebel manifestoes, together with the physical communication network required demonstrates that there existed a nationwide environment where this was possible. The literary media used for propaganda include proclamations, poetry, letters, and bills. The political audience was broad in terms of understanding of literary and visual forms of communication and their ability to use the available mechanisms to convey their opinions. Whether it was a disgruntled magnate, merchant or yeoman farmer, there was a method of communication suited to their circumstances. Visual propaganda was particularly important in politically influencing an audience, particularly for a largely illiterate population. This is an area that is often overlooked in terms of political influence until the Tudor period. The use of the human body will be a particular focus along with the more traditional aspects of art, such as heraldry. The thesis considers the relationship between kings’ personality, policy and propaganda. What emerges is that the personality of the monarch was essentially more influential than the use of propaganda. Finally, incorporating the analysis of the previous chapters, the North, is examined as a regional example of the presence and impact of propaganda. The North was a subject of propaganda itself and there was a two-way flow of communication and propaganda between the North and Westminster revealing the political consciousness of the region and its role as an audience. The overall argument of the thesis is that communication within the late medieval polity was essential and extensive. Propaganda was frequently used through a variety of media that could reach the whole polity, whether literate or not and not only in times of crisis

A cost analysis of surgery for ruptured abdominal aortic aneurysm

AbstractObjective: this study compares our costs of salvaging patients with ruptured abdominal aortic aneurysms (AAA) with the costs for unruptured AAAs. Methods: details of all AAAs presenting over 18 months were obtained. Costs of repair were carefully calculated for each case and were based upon ITU and ward stay and the use of theatre, radiology and pathology services. We compared the costs in unruptured AAAs with both uncomplicated ruptures and ruptures with one or more system failure. Results: the mortality rate for ruptures undergoing repair was 18% and for elective repairs was 1.6%. The median cost for uncomplicated ruptures was £6427 (range £2012-13 756). For 12 complicated ruptures, it was £20 075 (range £13 864-166 446), and for 63 unruptured AAAs, was £4762 (range £2925-47 499). Conclusion: relatively low operative mortality rates for ruptured AAA repair can be achieved but this comes at substantial cost. On average, a ruptured AAA requiring system support costs four times as much as an elective repair.Eur J Vasc Endovasc Surg 26, 299-302 (2003

Planar lattice gases with nearest-neighbour exclusion

We discuss the hard-hexagon and hard-square problems, as well as the corresponding problem on the honeycomb lattice. The case when the activity is unity is of interest to combinatorialists, being the problem of counting binary matrices with no two adjacent 1's. For this case we use the powerful corner transfer matrix method to numerically evaluate the partition function per site, density and some near-neighbour correlations to high accuracy. In particular for the square lattice we obtain the partition function per site to 43 decimal places.Comment: 16 pages, 2 built-in Latex figures, 4 table