Whole-genome sequencing (WGS) information has played a crucial role in the SARS-CoV-2 (COVID-19) pandemic by providing evidence about variants to inform public health policy. The purpose of this study was to assess the representativeness of sequenced cases compared with all COVID-19 cases in England, between March 2020 and August 2021, by demographic and socio-economic characteristics, to evaluate the representativeness and utility of these data in epidemiological analyses. To achieve this, polymerase chain reaction (PCR)-confirmed COVID-19 cases were extracted from the national laboratory system and linked with WGS data. During the study period, over 10% of COVID-19 cases in England had WGS data available for epidemiological analysis. With sequencing capacity increasing throughout the period, sequencing representativeness compared to all reported COVID-19 cases increased over time, allowing for valuable epidemiological analyses using demographic and socio-economic characteristics, particularly during periods with emerging novel SARS-CoV-2 variants. This study demonstrates the comprehensiveness of England’s sequencing throughout the COVID-19 pandemic, rapidly detecting variants of concern, and enabling representative epidemiological analyses to inform policy.

Realizing packaged state-of-the-art performance of monolithic microwave integrated circuits (MMICs) operating at millimeter wavelengths presents significant challenges in terms of electrical interface circuitry and physical construction. For instance, even with the aid of modern electromagnetic simulation tools, modeling the interaction between the MMIC and its package embedding circuit can lack the necessary precision to achieve optimum device performance. Physical implementation also introduces inaccuracies and requires iterative interface component substitution that can produce variable results, is invasive and risks damaging the MMIC. This paper describes a novel method for in situ optimization of packaged millimeter-wave devices using a pulsed ultraviolet laser to remove pre-selected areas of interface circuit metallization. The method was successfully demonstrated through the optimization of a 183 GHz low noise amplifier destined for use on the MetOp-SG meteorological satellite series. An improvement in amplifier output return loss from an average of 12.9 dB to 22.7 dB was achieved across an operational frequency range of 175–191 GHz and the improved circuit reproduced. We believe that our in situ tuning technique can be applied more widely to planar millimeter-wave interface circuits that are critical in achieving optimum device performance.

A major goal of Gardner, Ryan, and Snoeyink (2018) was to determine what steps are needed moving forward in examining gender representation in industrial and organizational (I-O) psychology. Specifically, on the topic of pay differences, we highlight that gender differences in pay are in part due to differences in negotiation behaviors and/or experiences. Prior research demonstrates that female negotiators receive greater backlash than male negotiators—a possible explanation to why men tend to negotiate more often and more successfully than women (Bowles, Babcock, & Lai, 2007). Based on this evidence, one next step in moving forward should involve providing resources and knowledge to improve negotiation skills and practices specifically aimed at eliminating differences between women and men in both propensity to negotiate and the evaluation/consequences of negotiating.

Poly(3,4-ethylenedioxythiophene) (PEDOT) is an organic conducting polymer that has been the focus of significant research over the last decade, in both energy and biological applications. Most commonly, PEDOT is doped by the artificial polymer polystyrene sulfonate due to the excellent electrical characteristics yielded by this pairing. The biopolymer dextran sulphate (DS) has been recently reported as a promising alternative to PEDOT:PSS for biological application, having electrical properties rivaling PEDOT:PSS, complimented by the potential bioactivity of the polysaccharide. In this work we compared chemical and electrochemical polymerisations of PEDOT:DS in terms of their impact on the electrical, morphological and biological properties of the resultant PEDOT:DS films. Post-growth cyclic voltammograms and UV-Vis analyses revealed comparable redox behaviour and absorbance profiles for the two synthesis approaches. Despite good intrinsic conductivity of particles, the addition of chemically produced PEDOT:DS did not markedly enhance the bulk conductivity of aqueous solutions due to the lack of interconnectivity between adjacent PEDOT:DS particles at achievable concentrations. Scanning electron microscopy revealed significantly greater roughness in films cast from chemically produced PEDOT:DS compared to electropolymerised samples, attributable to the formation of solution phase nanoparticles prior to casting. In cell studies with the L929 cell line, electrochemical polymerisation of PEDOT:DS afforded better integrity of resultant films for surface seeding, whilst chemically polymerised PEDOT:DS appeared to localised at the proliferating cells, suggesting possible applications in drug delivery.

Let ‖x‖ denote the distance of x from the nearest integer. In 1948 H. Heilbronn proved [5] that for ε>0 and N>c1(ε) the inequality

holds for any real α. This result has since been generalised in many different directions, and we consider here extensions of the type: For ε>0, N>c2{ε, s) and a quadratic formQ(x1,…, xs) there exist integersn1,…,nsnot all zero with |n1|,…,|ns≦N and with

The authors sharpen a result of Baker and Harman (1995), showing that [x, x + x0.525] contains prime numbers for large x. An important step in the proof is the application of a theorem of Watt (1995) on a mean value containing the fourth power of the zeta function. 2000 Mathematical Subject Classification: 11N05.

Let $a_n$ be an increasing sequence of positive reals with $a_n \rightarrow \infty$ as $n \rightarrow \infty$. Necessary and sufficient conditions are obtained for each of the sequences $[\alpha a_n], [\alpha^{a_n}], [{a_n}^{\alpha}]$ to take on infinitely many prime values for almost all $\alpha > \beta$. For example, the sequence $[\alpha a_n]$ is infinitely often prime for almost all $\alpha > 0$ if and only if there is a subsequence of the $a_n$, say $b_n$, with $b_{n+1} > b_n + 1$ and with the series $\sum 1/{b_n}$ divergent. Asymptotic formulae are obtained when the sequences considered are lacunary. An earlier result of the author reduces the problem to estimating the measure of overlaps of certain sets, and sieve methods are used to obtain the correct order upper bounds.

1991 Mathematics Subject Classification: primary 11N05; secondary 11K99, 11N36.

The problem concerning the distribution of the fractional parts of the sequence ank (k an integer exceeding one) was first considered by Hardy and Littlewood [6] and Weyl [20] earlier this century. This work was developed, with the focus on small fractional parts of the sequence, by Vinogradov [17], Heilbronn [13] and Danicic [2] (see [1]). Recently Heath-Brown [12] has improved the unlocalized versions of these results for k ≥ 6 (a slightly stronger result than Heath-Brown's for K = 8 is given on page 24 of [8]. The method mentioned there can, after some numerical calculation, improve Heath-Brown's result for 8 ≤ k ≤ 20, but still stronger results have recently been obtained by Dr. T. D. Wooley). The cognate problem regarding the sequence apk, where p denotes a prime, has also received some attention. In this situation even the case k = 1 proves to be difficult (see [9] and [14]). The first results in this field were given by Vinogradov (see Chapter 11 of [19] for the case k = 1, [18] for k ≥ 2). For k = 2 the best result to date has been supplied by Ghosh [5], and for ≥, by Harman (Theorem 3 in [9], building on the work in [7] and [8]). In this paper we shall improve the known results for 2 ≤ k ≤ 12. For larger k, Theorem 3 in [8] is more efficient. The theorem we prove is as follows.

Let {α} denote the fractional part of the real number α. Write χ(x, y) = 1 for {x} < y and χ(x, y) = 0 otherwise. A real sequence (xn) is uniformly distributed (mod 1) if

It is a consequence of (1·1) that DN = o(N),

Where

is the discrepancy of the sequence (xn).

Materials problems have always been a significant cause of wire bond failures in microelectronics. However, modern VLSI materials, processing, and packaging methods combined often result in new or masked versions of old failure mechanisms. This paper describes the classical Au-Al intermetallic compound problem as described by a new two-dimensional finite element diffusion model and demonstrates that diffusion in poor welds is more rapid than in bulk couples. Failures resulting from modern bonding material couples (e.g., Cu-Au, Al-Ag, etc.) can result in bond failures superficially resembling Au-Al type failures. Failures resulting from bonds made to contaminated gold electroplated films are described, and a new failure model resulting from hydrogen in these films is shown.

Let p be an odd prime. We write g(p) for the least positive integer z such that

We denote by ∥…∥ the distance to the nearest integer. Let ε be an arbitrary positive number. Danicic(6) showed that for N > c1(s, ε) and a quadratic form Q(x1, …, xs) there exist integers n1, …, ns with

having