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

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

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

Tidal stirring and the origin of dwarf spheroidals in the Local Group

N-Body/SPH simulations are used to study the evolution of dwarf irregular galaxies (dIrrs) entering the dark matter halo of the Milky Way or M31 on plunging orbits. We propose a new dynamical mechanism driving the evolution of gas rich, rotationally supported dIrrs, mostly found at the outskirts of the Local Group (LG), into gas free, pressure supported dwarf spheroidals (dSphs) or dwarf ellipticals (dEs), observed to cluster around the two giant spirals. The initial model galaxies are exponential disks embedded in massive dark matter halos and reproduce nearby dIrrs. Repeated tidal shocks at the pericenter of their orbit partially strip their halo and disk and trigger dynamical instabilities that dramatically reshape their stellar component. After only 2-3 orbits low surface brightness (LSB) dIrrs are transformed into dSphs, while high surface brightness (HSB) dIrrs evolve into dEs. This evolutionary mechanism naturally leads to the morphology-density relation observed for LG dwarfs. Dwarfs surrounded by very dense dark matter halos, like the archetypical dIrr GR8, are turned into Draco or Ursa Minor, the faintest and most dark matter dominated among LG dSphs. If disks include a gaseous component, this is both tidally stripped and consumed in periodic bursts of star formation. The resulting star formation histories are in good qualitative agreement with those derived using HST color-magnitude diagrams for local dSphs.Comment: 5 pages, 5 figures, to appear on ApJL. Simulation images and movies can be found at the Local Group web page at http://pcblu.uni.mi.astro.it/~lucio/LG/LG.htm

Dramatic Shape Sensitivity of Directional Emission Patterns from Similarly Deformed Cylindrical Polymer Lasers

Recent experiments on similarly shaped polymer micro-cavity lasers show a dramatic difference in the far-field emission patterns. We show for different deformations of the ellipse, quadrupole and hexadecapole that the large differences in the far-field emission patterns is explained by the differing ray dynamics corresponding to each shape. Analyzing the differences in the appropriate phase space for ray motion, it is shown that the differing geometries of the unstable manifolds of periodic orbits are the decisive factors in determining the far-field pattern. Surprisingly, we find that strongly chaotic ray dynamics is compatible with highly directional emission in the far-field.Comment: 14 pages, 16 figures (eps), RevTeX 4, submitted to JOSA

Genetically predicted vegetable intake and cardiovascular diseases and risk factors: an investigation with Mendelian randomization

Background: The associations between vegetable intake and cardiovascular diseases have been demonstrated in observational studies, but less sufficiently in randomized trials. Mendelian randomization has been considered a promising alternative in causal inference. The separate effects of cooked and raw vegetable intake remain unclear. This study aimed to investigate the associations between cooked and raw vegetable intake with cardiovascular outcomes using MR. Methods: We identified 15 and 28 genetic variants statistically and biologically associated with cooked and raw vegetable intake, respectively, from previous genome-wide association studies, which were used as instrumental variables to estimate associations with coronary heart disease (CHD), stroke, heart failure (HF), and atrial fibrillation (AF). The independent effects of genetically predicted cooked and raw vegetable intake were examined using multivariable MR analysis. We performed one-sample and two-sample MR analyses and combined their results using meta-analysis. Bonferroni correction was applied for multiple comparisons. We performed two-sample MR analysis for cardiometabolic risk factors (serum lipids, blood pressure, body mass index, and glycemic traits) to explore the potential mechanisms. Results: In the MR meta-analysis of 1.2 million participants, we found null evidence for associations between genetically predicted cooked and raw vegetable intake with CHD, HF, or AF. Raw vegetable intake was nominally associated with stroke (odds ratio [95% confidence interval] 0.82 [0.69–0.98] per 1 daily serving increase, p = 0.03), but this association did not pass the corrected significance level. We found consistently null evidence for associations with serum lipids, blood pressure, body mass index, or glycemic traits. Conclusions: We found null evidence for associations between genetically predicted vegetable intake with CHD, AF, HF, or cardiometabolic risk factors in this MR study. Raw vegetable intake may reduce risk of stroke, but this warrants more research. True associations between vegetable intake and CVDs cannot be completely ruled out, and future investigations are required for causal inference in nutritional research

Physical distancing interventions and incidence of coronavirus disease 2019: natural experiment in 149 countries.

OBJECTIVE: To evaluate the association between physical distancing interventions and incidence of coronavirus disease 2019 (covid-19) globally. DESIGN: Natural experiment using interrupted time series analysis, with results synthesised using meta-analysis. SETTING: 149 countries or regions, with data on daily reported cases of covid-19 from the European Centre for Disease Prevention and Control and data on the physical distancing policies from the Oxford covid-19 Government Response Tracker. PARTICIPANTS: Individual countries or regions that implemented one of the five physical distancing interventions (closures of schools, workplaces, and public transport, restrictions on mass gatherings and public events, and restrictions on movement (lockdowns)) between 1 January and 30 May 2020. MAIN OUTCOME MEASURE: Incidence rate ratios (IRRs) of covid-19 before and after implementation of physical distancing interventions, estimated using data to 30 May 2020 or 30 days post-intervention, whichever occurred first. IRRs were synthesised across countries using random effects meta-analysis. RESULTS: On average, implementation of any physical distancing intervention was associated with an overall reduction in covid-19 incidence of 13% (IRR 0.87, 95% confidence interval 0.85 to 0.89; n=149 countries). Closure of public transport was not associated with any additional reduction in covid-19 incidence when the other four physical distancing interventions were in place (pooled IRR with and without public transport closure was 0.85, 0.82 to 0.88; n=72, and 0.87, 0.84 to 0.91; n=32, respectively). Data from 11 countries also suggested similar overall effectiveness (pooled IRR 0.85, 0.81 to 0.89) when school closures, workplace closures, and restrictions on mass gatherings were in place. In terms of sequence of interventions, earlier implementation of lockdown was associated with a larger reduction in covid-19 incidence (pooled IRR 0.86, 0.84 to 0.89; n=105) compared with a delayed implementation of lockdown after other physical distancing interventions were in place (pooled IRR 0.90, 0.87 to 0.94; n=41). CONCLUSIONS: Physical distancing interventions were associated with reductions in the incidence of covid-19 globally. No evidence was found of an additional effect of public transport closure when the other four physical distancing measures were in place. Earlier implementation of lockdown was associated with a larger reduction in the incidence of covid-19. These findings might support policy decisions as countries prepare to impose or lift physical distancing measures in current or future epidemic waves