Averages Along the Primes: Improving and Sparse Bounds

Consider averages along the prime integers $\mathbb P$ given by \begin{equation*} \mathcal{A}_N f (x) = N ^{-1} \sum_{ p \in \mathbb P \;:\; p\leq N} (\log p) f (x-p). \end{equation*} These averages satisfy a uniform scale-free $\ell ^{p}$-improving estimate. For all $1< p < 2$, there is a constant $C_p$ so that for all integer $N$ and functions $f$ supported on $[0,N]$, there holds \begin{equation*} N ^{-1/p' }\lVert \mathcal{A}_N f\rVert_{\ell^{p'}} \leq C_p N ^{- 1/p} \lVert f\rVert_{\ell^p}. \end{equation*} The maximal function $\mathcal{A}^{\ast} f =\sup_{N} \lvert \mathcal{A}_N f \rvert$ satisfies $(p,p)$ sparse bounds for all $1< p < 2$. The latter are the natural variants of the scale-free bounds. As a corollary, $\mathcal{A}^{\ast}$ is bounded on $\ell ^{p} (w)$, for all weights $w$ in the Muckenhoupt $A_p$ class. No prior weighted inequalities for $\mathcal{A}^{\ast}$ were known.Comment: 13 page

Adiposity, fat-free mass and incident heart failure in 500 000 individuals

Background and aims: The independent role of body fat distribution and fat-free mass in heart failure (HF) risk is unclear. We investigated the role of different body composition compartments in risk of HF. Methods: Present analyses include 428 087 participants (mean age 55.9 years, 44% male) from the UK Biobank. Associations of long-term average levels of body composition measures with incident HF were determined using adjusted Cox proportional hazards regression models. Results: Over a median follow-up of 13.8 years, there were 10 455 first-ever incident HF events. Overall, HF risk was more strongly associated with central adiposity (waist circumference (WC) adjusted for body mass index (BMI); HR 1.38, 95% CI 1.32 to 1.45) than general adiposity (BMI adjusted for WC; HR 1.22, 95% CI 1.16 to 1.27). Although dual X-ray absorptiometry-derived body fat remained positively related to HF after adjustment for fat-free mass (HR 1.37, 95% CI 1.18 to 1.59), the association of fat-free mass with HF was substantially attenuated by fat mass (HR 1.12, 95% CI 1.01 to 1.26) while visceral fat (VAT) remained associated with HF independent of subcutaneous fat (HR 1.20, 95% CI 1.09 to 1.33). In analyses of HF subtypes, HF with preserved ejection fraction was independently associated with all fat measures (eg, VAT: HR 1.23, 95% CI 1.12 to 1.35; body fat: HR 1.36, 95% CI 1.17 to 1.57) while HF with reduced ejection fraction was not independently associated with fat measures (eg, VAT: HR 1.29, 95% CI 0.98 to 1.68; body fat: HR 1.29, 95% CI 0.80 to 2.07). Conclusions: This large-scale study shows that excess adiposity and fat mass are associated with higher HF risk while the association of fat-free mass with HF could be explained largely by its correlation with fat mass. The study also describes the independent relevance of body fat distribution to HF subtypes, suggesting different mechanisms may be driving their aetiopathogenesis

Adiposity, fat-free mass and incident heart failure in 500 000 individuals

Background and aims The independent role of body fat distribution and fat-free mass in heart failure (HF) risk is unclear. We investigated the role of different body composition compartments in risk of HF. Methods Present analyses include 428 087 participants (mean age 55.9 years, 44% male) from the UK Biobank. Associations of long-term average levels of body composition measures with incident HF were determined using adjusted Cox proportional hazards regression models. Results Over a median follow-up of 13.8 years, there were 10 455 first-ever incident HF events. Overall, HF risk was more strongly associated with central adiposity (waist circumference (WC) adjusted for body mass index (BMI); HR 1.38, 95% CI 1.32 to 1.45) than general adiposity (BMI adjusted for WC; HR 1.22, 95% CI 1.16 to 1.27). Although dual X-ray absorptiometry-derived body fat remained positively related to HF after adjustment for fat-free mass (HR 1.37, 95% CI 1.18 to 1.59), the association of fat-free mass with HF was substantially attenuated by fat mass (HR 1.12, 95% CI 1.01 to 1.26) while visceral fat (VAT) remained associated with HF independent of subcutaneous fat (HR 1.20, 95% CI 1.09 to 1.33). In analyses of HF subtypes, HF with preserved ejection fraction was independently associated with all fat measures (eg, VAT: HR 1.23, 95% CI 1.12 to 1.35; body fat: HR 1.36, 95% CI 1.17 to 1.57) while HF with reduced ejection fraction was not independently associated with fat measures (eg, VAT: HR 1.29, 95% CI 0.98 to 1.68; body fat: HR 1.29, 95% CI 0.80 to 2.07). Conclusions This large-scale study shows that excess adiposity and fat mass are associated with higher HF risk while the association of fat-free mass with HF could be explained largely by its correlation with fat mass. The study also describes the independent relevance of body fat distribution to HF subtypes, suggesting different mechanisms may be driving their aetiopathogenesis

Health record hiccups—5,526 real-world time series with change points labelled by crowdsourced visual inspection

Background: Large routinely collected data such as electronic health records (EHRs) are increasingly used in research, but the statistical methods and processes used to check such data for temporal data quality issues have not moved beyond manual, ad hoc production and visual inspection of graphs. With the prospect of EHR data being used for disease surveillance via automated pipelines and public-facing dashboards, automation of data quality checks will become increasingly valuable. Findings: We generated 5,526 time series from 8 different EHR datasets and engaged >2,000 citizen-science volunteers to label the locations of all suspicious-looking change points in the resulting graphs. Consensus labels were produced using density-based clustering with noise, with validation conducted using 956 images containing labels produced by an experienced data scientist. Parameter tuning was done against 670 images and performance calculated against 286 images, resulting in a final sensitivity of 80.4% (95% CI, 77.1%–83.3%), specificity of 99.8% (99.7%–99.8%), positive predictive value of 84.5% (81.4%–87.2%), and negative predictive value of 99.7% (99.6%–99.7%). In total, 12,745 change points were found within 3,687 of the time series. Conclusions: This large collection of labelled EHR time series can be used to validate automated methods for change point detection in real-world settings, encouraging the development of methods that can successfully be applied in practice. It is particularly valuable since change point detection methods are typically validated using synthetic data, so their performance in real-world settings cannot be assumed to be comparable. While the dataset focusses on EHRs and data quality, it should also be applicable in other fields

Averages over the Gaussian Primes: Goldbach's Conjecture and Improving Estimates

We prove versions of Goldbach conjectures for Gaussian Primes in arbitrary sectors. Fix an interval $\omega \subset \mathbb{T}$. There is an integer $N_\omega$, so that every odd integer $n$ with $\arg (n) \in \omega$ and $N(n)>N_\omega$, is a sum of three Gaussian primes $n=p_1+p_2+p_3$, with $\arg (p_j) \in \omega$, for $j=1,2,3$. A density version of the binary Goldbach conjecture is proved. Both follow from a High/Low decomposition of the Fourier transform of averages over Gaussian primes, defined as follows. Let $\Lambda(n)$ be the Von Mangoldt function for the Gaussian integers and consider the norm function $N:\mathbb Z[i]\rightarrow \mathbb Z^+$, $\alpha + i \beta \mapsto \alpha ^2 + \beta ^2$. Define the averages $$A_Nf(x)=\frac{1}{N}\sum_{N(n)<N}\Lambda(n)f(x-n).$$ Our decomposition also proves the $\ell ^p$ improving estimate $$\lVert A_N f \rVert _{\ell^{p'}}\ll N ^{1/p'- 1/p} \lVert f\rVert _{\ell^p}, \qquad 1<p\leq 2.$$Comment: 36 page

Health record hiccups—5,526 real-world time series with change points labelled by crowdsourced visual inspection

Background: Large routinely collected data such as electronic health records (EHRs) are increasingly used in research, but the statistical methods and processes used to check such data for temporal data quality issues have not moved beyond manual, ad hoc production and visual inspection of graphs. With the prospect of EHR data being used for disease surveillance via automated pipelines and public-facing dashboards, automation of data quality checks will become increasingly valuable. / Findings: We generated 5,526 time series from 8 different EHR datasets and engaged >2,000 citizen-science volunteers to label the locations of all suspicious-looking change points in the resulting graphs. Consensus labels were produced using density-based clustering with noise, with validation conducted using 956 images containing labels produced by an experienced data scientist. Parameter tuning was done against 670 images and performance calculated against 286 images, resulting in a final sensitivity of 80.4% (95% CI, 77.1%–83.3%), specificity of 99.8% (99.7%–99.8%), positive predictive value of 84.5% (81.4%–87.2%), and negative predictive value of 99.7% (99.6%–99.7%). In total, 12,745 change points were found within 3,687 of the time series. / Conclusions: This large collection of labelled EHR time series can be used to validate automated methods for change point detection in real-world settings, encouraging the development of methods that can successfully be applied in practice. It is particularly valuable since change point detection methods are typically validated using synthetic data, so their performance in real-world settings cannot be assumed to be comparable. While the dataset focusses on EHRs and data quality, it should also be applicable in other fields

Socioeconomic inequalities in the risk of infection with SARS-CoV-2 Delta and Omicron variants in United Kingdom, 2020-22

Objective: It is unknown whether SARS-CoV-2 exposure risks vary by socioeconomic deprivation within and across occupation sectors. We explored the risk of testing positive for Delta or Omicron variants, the predominantly dominant SARS-CoV-2 variants during our study period, within certain occupation sectors and deprivation groups in the UK. Methods and Analysis: We used the COVID-19 Infection Survey (CIS) to examine the risk of testing positive with SARS-CoV-2 across area-level deprivation and occupation sectors. We divided our cohort into Delta (02.07.2020–19.12.2021) and Omicron (20.12.2021–31.01.2022) cohorts as they were the predominantly dominant variants during our study period. Multivariable Poisson regression models were used to estimate adjusted incidence rate ratio (IRR) after adjusting for age, sex, ethnicity, comorbid conditions, urban/rural home address, household size, healthcare/client-facing job categories and calendar time. Results: There were 329,356 participants in the Delta cohort and 246,061 in the Omicron cohort. The crude incidence rate for Delta and Omicron cases were higher in the most deprived decile (Delta: 4.33 per 1000 person months; 95% CI: 4.09, 4.58; Omicron: 76.67; 71.60, 82.11) than in the least deprived decile (3.18; 3.05, 3.31; and 54.52; 51.93, 57.24, respectively); the corresponding adjusted IRRs were 1.37 (95% CI: 1.29, 1.47) and 1.34 (1.24, 1.46) during the Delta and Omicron period, respectively. The adjusted IRR for testing positive in the most deprived compared with the least deprived decile in the Delta cohort were 1.59 (1.25, 2.02) and 1.50 (1.19, 1.87) in healthcare and manufacturing or construction occupation sectors, respectively. Corresponding values in the Omicron cohort were 1.50 (1.15, 1.95) and 1.43 (1.09, 1.86) in healthcare and teaching and education sectors. The associations for the other employment sectors were not statistically significant or not tested due to small numbers. Conclusion: The risk of testing positive for SARS-CoV-2 in the Delta and Omicron cohorts was higher in the most deprived compared with the least deprived decile in healthcare, manufacturing or construction, and teaching and education sectors

Uses of Leisure

The book is a loose aggregate of Ben Cain’s practice from the past ten years or so, with thirty projects distributed according to a subjective categorization of work / leisure / rest. Throughout his career Ben Cain (b.1975 Leeds, lives and works in London and Zagreb) has worked with sculpture, installation, theatre, sound, performance, and publication. His practice deals with themes of work, labour, and artistic action. He has recurrently explored art’s ambiguous relationship to industry, commodification and immaterial labour, and is interested in how artworks might pose questions about what we think they are doing and, by implication, our role as viewers in their social and cultural production. The publication features an introduction by the artist & author David Price and writing by JJ Charlesworth (senior editor at ArtReview magazine), Bridget Crone (curator, writer and lecturer at Goldsmiths, the University of London), Emma Hoette (storyteller), Rose Lejeune (independent curator and researcher), Cuauhtémoc Medina (head curator at Museo Universitario Arte Contemporaneo) and Patrick Lacey. It is designed by the transdisciplinary graphic design collective Åbäke

Infrared thermography can detect previsual bacterial growth in a laboratory setting via metabolic heat detection

Aims Detection of bacterial contamination in healthcare and industry takes many hours if not days. Thermal imaging, the measurement of heat by an infrared camera, was investigated as a potential noninvasive method of detecting bacterial growth. Methods and Results Infrared thermography can detect the presence of Escherichia coli and Staphylococcus aureus on solid growth media by an increase in temperature before they are visually observable. A heat decrease is observed after treatment with ultraviolet light and heat increased after incubation with dinitrophenol. Conclusions Infrared thermography can detect early growth of bacteria before they are detectable by other microbiology-based method. The heat observed is due to the cells being viable and metabolically active, as cells killed with ultraviolet light exhibit reduced increase in temperature and treatment with dinitrophenol increases heat detected. Significance and Impact of the Study Infrared thermography detects bacterial growth without the need for specialized temperature control facilities. The method is statistically robust and can be undertaken in situ, thus is highly versatile. These data support the application of infrared thermography in a laboratory, clinical and industrial setting for vegetative bacteria, thus may become into an important methodology for the timely and straightforward detection of early-stage bacterial growth