On a discrete version of Tanaka's theorem for maximal functions

In this paper we prove a discrete version of Tanaka's Theorem \cite{Ta} for the Hardy-Littlewood maximal operator in dimension $n=1$, both in the non-centered and centered cases. For the discrete non-centered maximal operator $\widetilde{M}$ we prove that, given a function $f: \mathbb{Z} \to \mathbb{R}$ of bounded variation, $$\textrm{Var}(\widetilde{M} f) \leq \textrm{Var}(f),$$ where $\textrm{Var}(f)$ represents the total variation of $f$. For the discrete centered maximal operator $M$ we prove that, given a function $f: \mathbb{Z} \to \mathbb{R}$ such that $f \in \ell^1(\mathbb{Z})$, $$\textrm{Var}(Mf) \leq C \|f\|_{\ell^1(\mathbb{Z})}.$$ This provides a positive solution to a question of Haj{\l}asz and Onninen \cite{HO} in the discrete one-dimensional case.Comment: V4 - Proof of Lemma 3 update

Adaptable Xerogel-Layered Amperometric Biosensor Platforms on Wire Electrodes for Clinically Relevant Measurements

Biosensing strategies that employ readily adaptable materials for different analytes, can be miniaturized into needle electrode form, and function in bodily fluids represent a significant step toward the development of clinically relevant in vitro and in vivo sensors. In this work, a general scheme for 1st generation amperometric biosensors involving layer-by-layer electrode modification with enzyme-doped xerogels, electrochemically-deposited polymer, and polyurethane semi-permeable membranes is shown to achieve these goals. With minor modifications to these materials, sensors representing potential point-of-care medical tools are demonstrated to be sensitive and selective for a number of conditions. The potential for bedside measurements or continuous monitoring of analytes may offer faster and more accurate clinical diagnoses for diseases such as diabetes (glucose), preeclampsia (uric acid), galactosemia (galactose), xanthinuria (xanthine), and sepsis (lactate). For the specific diagnostic application, the sensing schemes have been miniaturized to wire electrodes and/or demonstrated as functional in synthetic urine or blood serum. Signal enhancement through the incorporation of platinum nanoparticle film in the scheme offers additional design control within the sensing scheme. The presented sensing strategy has the potential to be applied to any disease that has a related biomolecule and corresponding oxidase enzyme and represents rare, adaptable, sensing capabilities

Halogen Bonding Interactions for Aromatic and Non-Aromatic Explosive Detection

Improved sensing strategies are needed for facile, accurate and rapid detection of aromatic and nonaromatic explosives. Density functional theory was used to evaluate the relative binding interaction energies between halogen-containing sensor model molecules and nitro-containing explosives. Interaction energies ranged from –18 to –14 kJ/mol and highly directional halogen bonding interactions were observed with bond distances ranging between 3.0 and 3.4 Å. In all geometry optimized structures, the sigma-hole of electropositive potential on the halogen aligned with a lone pair of electrons on the nitro-moiety of the explosive. The computational results predict that the strongest interactions will occur with iodine-based sensors as, of all the halogens studied, iodine is the largest, most polarizable halogen with the smallest electronegativity. Based on these promising proof-of-concept results, synthetically accessible sensors were designed using1, 4-dihalobenzene (X= Cl, Br and I) with and without tetra-fluoro electron withdrawing groups attached to the benzene ring. These sensing molecules were embedded onto single walled carbon nanotubes that were mechanically abraded onto interdigitated array electrodes and these were used to measure the responses to explosive model compounds cyclohexanone and dimethyl-dinitro-benzene in nitrogen gas. Amperometric current-time curves for selectors and control molecules, including concentration correlated signal enhancement, as well as response and recovery times, indicate selector responsiveness to these model compounds, with the largest response observed for iodo-substituted sensors

Role of Oxygen in Laser Induced Contamination at Diamond-Vacuum Interfaces

Many modern-day quantum science experiments rely on high-fidelity measurement of fluorescent signals emitted by the quantum system under study. A pernicious issue encountered when such experiments are conducted near a material interface in vacuum is "laser-induced contamination" (LIC): the gradual accretion of fluorescent contaminants on the surface where a laser is focused. Fluorescence from these contaminants can entirely drown out any signal from e.g. optically-probed color centers in the solid-state. Crucially, while LIC appears often in this context, it has not been systematically studied. In this work, we probe the onset and growth rate of LIC for a diamond nitrogen-vacancy center experiment in vacuum, and we correlate the contamination-induced fluorescence intensities to micron-scale physical build-up of contaminant on the diamond surface. Drawing upon similar phenomena previously studied in the space optics community, we use photo-catalyzed oxidation of contaminants as a mitigation strategy. We vary the residual oxygen pressure over 9 orders of magnitude and find that LIC growth is inhibited at near-atmospheric oxygen partial pressures, but the growth rate at lower oxygen pressure is non-monotonic. Finally, we discuss a model for the observed dependence of LIC growth rate on oxygen content and propose methods to extend in situ mitigation of LIC to a wider range of operating pressures.Comment: 22 pages, 10 figure

Two-dimensional spin systems in PECVD-grown diamond with tunable density and long coherence for enhanced quantum sensing and simulation

Systems of spins engineered with tunable density and reduced dimensionality enable a number of advancements in quantum sensing and simulation. Defects in diamond, such as nitrogen-vacancy (NV) centers and substitutional nitrogen (P1 centers), are particularly promising solid-state platforms to explore. However, the ability to controllably create coherent, two-dimensional spin systems and characterize their properties, such as density, depth confinement, and coherence is an outstanding materials challenge. We present a refined approach to engineer dense ($\gtrsim$1 ppm$\cdot$nm), 2D nitrogen and NV layers in diamond using delta-doping during plasma-enhanced chemical vapor deposition (PECVD) epitaxial growth. We employ both traditional materials techniques, e.g. secondary ion mass spectrometry (SIMS), alongside NV spin decoherence-based measurements to characterize the density and dimensionality of the P1 and NV layers. We find P1 densities of 5-10 ppm$\cdot$nm, NV densities between 1 and 3.5 ppm$\cdot$nm tuned via electron irradiation dosage, and depth confinement of the spin layer down to 1.6 nm. We also observe high (up to 42$\%$) conversion of P1 to NV centers and reproducibly long NV coherence times, dominated by dipolar interactions with the engineered P1 and NV spin baths

Diamond Surface Functionalization via Visible Light-Driven C-H Activation for Nanoscale Quantum Sensing

Nitrogen-vacancy centers in diamond are a promising platform for nanoscale nuclear magnetic resonance sensing. Despite significant progress towards using NV centers to detect and localize nuclear spins down to the single spin level, NV-based spectroscopy of individual, intact, arbitrary target molecules remains elusive. NV molecular sensing requires that target molecules are immobilized within a few nanometers of NV centers with long spin coherence time. The inert nature of diamond typically requires harsh functionalization techniques such as thermal annealing or plasma processing, limiting the scope of functional groups that can be attached to the surface. Solution-phase chemical methods can be more readily generalized to install diverse functional groups, but they have not been widely explored for single-crystal diamond surfaces. Moreover, realizing shallow NV centers with long spin coherence times requires highly ordered single-crystal surfaces, and solution-phase functionalization has not yet been shown to be compatible with such demanding conditions. In this work, we report a versatile strategy to directly functionalize C-H bonds on single-crystal diamond surfaces under ambient conditions using visible light. This functionalization method is compatible with charge stable NV centers within 10 nm of the surface with spin coherence times comparable to the state of the art. As a proof of principle, we use shallow ensembles of NV centers to detect nuclear spins from functional groups attached to the surface. Our approach to surface functionalization based on visible light-driven C-H bond activation opens the door to deploying NV centers as a broad tool for chemical sensing and single-molecule spectroscopy

Genomic Convergence among ERRα, PROX1, and BMAL1 in the Control of Metabolic Clock Outputs

Metabolic homeostasis and circadian rhythms are closely intertwined biological processes. Nuclear receptors, as sensors of hormonal and nutrient status, are actively implicated in maintaining this physiological relationship. Although the orphan nuclear receptor estrogen-related receptor α (ERRα, NR3B1) plays a central role in the control of energy metabolism and its expression is known to be cyclic in the liver, its role in temporal control of metabolic networks is unknown. Here we report that ERRα directly regulates all major components of the molecular clock. ERRα-null mice also display deregulated locomotor activity rhythms and circadian period lengths under free-running conditions, as well as altered circulating diurnal bile acid and lipid profiles. In addition, the ERRα-null mice exhibit time-dependent hypoglycemia and hypoinsulinemia, suggesting a role for ERRα in modulating insulin sensitivity and glucose handling during the 24-hour light/dark cycle. We also provide evidence that the newly identified ERRα corepressor PROX1 is implicated in rhythmic control of metabolic outputs. To help uncover the molecular basis of these phenotypes, we performed genome-wide location analyses of binding events by ERRα, PROX1, and BMAL1, an integral component of the molecular clock. These studies revealed the existence of transcriptional regulatory loops among ERRα, PROX1, and BMAL1, as well as extensive overlaps in their target genes, implicating these three factors in the control of clock and metabolic gene networks in the liver. Genomic convergence of ERRα, PROX1, and BMAL1 transcriptional activity thus identified a novel node in the molecular circuitry controlling the daily timing of metabolic processes

Implementation of corticosteroids in treating COVID-19 in the ISARIC WHO Clinical Characterisation Protocol UK:prospective observational cohort study

BACKGROUND: Dexamethasone was the first intervention proven to reduce mortality in patients with COVID-19 being treated in hospital. We aimed to evaluate the adoption of corticosteroids in the treatment of COVID-19 in the UK after the RECOVERY trial publication on June 16, 2020, and to identify discrepancies in care. METHODS: We did an audit of clinical implementation of corticosteroids in a prospective, observational, cohort study in 237 UK acute care hospitals between March 16, 2020, and April 14, 2021, restricted to patients aged 18 years or older with proven or high likelihood of COVID-19, who received supplementary oxygen. The primary outcome was administration of dexamethasone, prednisolone, hydrocortisone, or methylprednisolone. This study is registered with ISRCTN, ISRCTN66726260. FINDINGS: Between June 17, 2020, and April 14, 2021, 47 795 (75·2%) of 63 525 of patients on supplementary oxygen received corticosteroids, higher among patients requiring critical care than in those who received ward care (11 185 [86·6%] of 12 909 vs 36 415 [72·4%] of 50 278). Patients 50 years or older were significantly less likely to receive corticosteroids than those younger than 50 years (adjusted odds ratio 0·79 [95% CI 0·70–0·89], p=0·0001, for 70–79 years; 0·52 [0·46–0·58], p80 years), independent of patient demographics and illness severity. 84 (54·2%) of 155 pregnant women received corticosteroids. Rates of corticosteroid administration increased from 27·5% in the week before June 16, 2020, to 75–80% in January, 2021. INTERPRETATION: Implementation of corticosteroids into clinical practice in the UK for patients with COVID-19 has been successful, but not universal. Patients older than 70 years, independent of illness severity, chronic neurological disease, and dementia, were less likely to receive corticosteroids than those who were younger, as were pregnant women. This could reflect appropriate clinical decision making, but the possibility of inequitable access to life-saving care should be considered. FUNDING: UK National Institute for Health Research and UK Medical Research Council

Adjunctive rifampicin for Staphylococcus aureus bacteraemia (ARREST): a multicentre, randomised, double-blind, placebo-controlled trial.

BACKGROUND: Staphylococcus aureus bacteraemia is a common cause of severe community-acquired and hospital-acquired infection worldwide. We tested the hypothesis that adjunctive rifampicin would reduce bacteriologically confirmed treatment failure or disease recurrence, or death, by enhancing early S aureus killing, sterilising infected foci and blood faster, and reducing risks of dissemination and metastatic infection. METHODS: In this multicentre, randomised, double-blind, placebo-controlled trial, adults (≥18 years) with S aureus bacteraemia who had received ≤96 h of active antibiotic therapy were recruited from 29 UK hospitals. Patients were randomly assigned (1:1) via a computer-generated sequential randomisation list to receive 2 weeks of adjunctive rifampicin (600 mg or 900 mg per day according to weight, oral or intravenous) versus identical placebo, together with standard antibiotic therapy. Randomisation was stratified by centre. Patients, investigators, and those caring for the patients were masked to group allocation. The primary outcome was time to bacteriologically confirmed treatment failure or disease recurrence, or death (all-cause), from randomisation to 12 weeks, adjudicated by an independent review committee masked to the treatment. Analysis was intention to treat. This trial was registered, number ISRCTN37666216, and is closed to new participants. FINDINGS: Between Dec 10, 2012, and Oct 25, 2016, 758 eligible participants were randomly assigned: 370 to rifampicin and 388 to placebo. 485 (64%) participants had community-acquired S aureus infections, and 132 (17%) had nosocomial S aureus infections. 47 (6%) had meticillin-resistant infections. 301 (40%) participants had an initial deep infection focus. Standard antibiotics were given for 29 (IQR 18-45) days; 619 (82%) participants received flucloxacillin. By week 12, 62 (17%) of participants who received rifampicin versus 71 (18%) who received placebo experienced treatment failure or disease recurrence, or died (absolute risk difference -1·4%, 95% CI -7·0 to 4·3; hazard ratio 0·96, 0·68-1·35, p=0·81). From randomisation to 12 weeks, no evidence of differences in serious (p=0·17) or grade 3-4 (p=0·36) adverse events were observed; however, 63 (17%) participants in the rifampicin group versus 39 (10%) in the placebo group had antibiotic or trial drug-modifying adverse events (p=0·004), and 24 (6%) versus six (2%) had drug interactions (p=0·0005). INTERPRETATION: Adjunctive rifampicin provided no overall benefit over standard antibiotic therapy in adults with S aureus bacteraemia. FUNDING: UK National Institute for Health Research Health Technology Assessment

A prenylated dsRNA sensor protects against severe COVID-19

Inherited genetic factors can influence the severity of COVID-19, but the molecular explanation underpinning a genetic association is often unclear. Intracellular antiviral defenses can inhibit the replication of viruses and reduce disease severity. To better understand the antiviral defenses relevant to COVID-19, we used interferon-stimulated gene (ISG) expression screening to reveal that OAS1, through RNase L, potently inhibits SARS-CoV-2. We show that a common splice-acceptor SNP (Rs10774671) governs whether people express prenylated OAS1 isoforms that are membrane-associated and sense specific regions of SARS-CoV-2 RNAs, or only express cytosolic, nonprenylated OAS1 that does not efficiently detect SARS-CoV-2. Importantly, in hospitalized patients, expression of prenylated OAS1 was associated with protection from severe COVID-19, suggesting this antiviral defense is a major component of a protective antiviral response