Iterative actions of normal operators

Let $A$ be a normal operator in a Hilbert space $\mathcal{H}$, and let $\mathcal{G} \subset \mathcal{H}$ be a countable set of vectors. We investigate the relations between $A$, $\mathcal{G}$ , and $L$ that makes the system of iterations $\{A^ng: g\in \mathcal{G},\;0\leq n< L(g)\}$ complete, Bessel, a basis, or a frame for $\mathcal{H}$. The problem is motivated by the dynamical sampling problem and is connected to several topics in functional analysis, including, frame theory and spectral theory. It also has relations to topics in applied harmonic analysis including, wavelet theory and time-frequency analysis.Comment: 14 pages, 0 figure

Variations on the Theme of Journe's Lemma

Journe's Lemma is a critical component of many questions related to the product ${BMO}$ theory of S.-Y. Chang and R. Fefferman. This article presents several different variants of the Lemma, some known, some implicit in the literature, and some new.Comment: 27 pages ; 17 references; To appear in Houston Journal of Mathematic

Prototype of a low-cost 3D breast ultrasound imaging system

This work describes a setup of the new acquisition system for 3D ultrasound images (i.e. B-mode) for breast tomography. Since premature and precise breast lesions diagnoses turn out in treatment more efficient and save lives, we are looking for a more precise, less painful exams and dose reduction for the patient. Therefore, a low cost scanner mechanism was built aiming to accommodate breasts under water while patient is laid down on a bed in which a robotic arm guides the ultrasound probe to acquire 2D images. Then 3D image is reconstructed using the 2D images due to render the mammary volume searching for lesions. The low cost scanner was built using a regular ultrasound machine, linear probe and major controls made by an Arduino Uno. We compared the acquired phantom images with gold standard images for mammary tissues diagnostics, i.e. Computerized Tomography and Magnetic Resonance Images. This study was evaluated using a paraffin-gel and mineral oil control phantom. Results show that the provided module is convicting enough to be used in local hospital as the next step of this study

Perception of nonnative tonal contrasts by Mandarin-English and English-Mandarin sequential bilinguals

This study examined the role of acquisition order and crosslinguistic similarity in influencing transfer at the initial stage of perceptually acquiring a tonal third language (L3). Perception of tones in Yoruba and Thai was tested in adult sequential bilinguals representing three different first (L1) and second language (L2) backgrounds: L1 Mandarin-L2 English (MEBs), L1 English-L2 Mandarin (EMBs), and L1 English-L2 intonational/non-tonal (EIBs). MEBs outperformed EMBs and EIBs in discriminating L3 tonal contrasts in both languages, while EMBs showed a small advantage over EIBs on Yoruba. All groups showed better overall discrimination in Thai than Yoruba, but group differences were more robust in Yoruba. MEBs’ and EMBs’ poor discrimination of certain L3 contrasts was further reflected in the L3 tones being perceived as similar to the same Mandarin tone; however, EIBs, with no knowledge of Mandarin, showed many of the same similarity judgments. These findings thus suggest that L1 tonal experience has a particularly facilitative effect in L3 tone perception, but there is also a facilitative effect of L2 tonal experience. Further, crosslinguistic perceptual similarity between L1/L2 and L3 tones, as well as acoustic similarity between different L3 tones, play a significant role at this early stage of L3 tone acquisition.Published versio

Coming of age in L3 initial stages transfer models: deriving developmental predictions and looking towards the future

Aims: Over the past decade in particular, formal linguistic work within L3 acquisition has concentrated on hypothesizing and empirically determining the source of transfer from previous languages—L1, L2 or both—in L3 grammatical representations. In view of the progressive concern with more advanced stages, we aim to show that focusing on L3 initial stages should be one continued priority of the field, even—or especially—if the field is ready to shift towards modeling L3 development and ultimate attainment. Approach: We argue that L3 learnability is significantly impacted by initial stages transfer, as such forms the basis of the initial L3 interlanguage. To illustrate our point, the insights from studies using initial and intermediary stages L3 data are discussed in light of developmental predictions that derive from the initial stages models. Conclusions: Despite a shared desire to understand the process of L3 acquisition in whole, inclusive of offering developmental L3 theories, we argue that the field does not yet have—although is ever closer to—the data basis needed to effectively do so. Originality: This article seeks to convince the readership for the need of conservatism in L3 acquisition theory building, whereby offering a framework on how and why we can most effectively build on the accumulated knowledge of the L3 initial stages in order to make significant, steady progress. Significance: The arguments exposed here are meant to provide an epistemological base for a tenable framework of formal approaches to L3 interlanguage development and, eventually, ultimate attainment

Pharmacogenomics of GLP-1 receptor agonists: a genome-wide analysis of observational data and large randomised controlled trials

Background: In the treatment of type 2 diabetes, GLP-1 receptor agonists lower blood glucose concentrations, body weight, and have cardiovascular benefits. The efficacy and side effects of GLP-1 receptor agonists vary between people. Human pharmacogenomic studies of this inter-individual variation can provide both biological insight into drug action and provide biomarkers to inform clinical decision making. We therefore aimed to identify genetic variants associated with glycaemic response to GLP-1 receptor agonist treatment. Methods: In this genome-wide analysis we included adults (aged ≥18 years) with type 2 diabetes treated with GLP-1 receptor agonists with baseline HbA1c of 7% or more (53 mmol/mol) from four prospective observational cohorts (DIRECT, PRIBA, PROMASTER, and GoDARTS) and two randomised clinical trials (HARMONY phase 3 and AWARD). The primary endpoint was HbA1c reduction at 6 months after starting GLP-1 receptor agonists. We evaluated variants in GLP1R, then did a genome-wide association study and gene-based burden tests. Findings: 4571 adults were included in our analysis, of these, 3339 (73%) were White European, 449 (10%) Hispanic, 312 (7%) American Indian or Alaskan Native, and 471 (10%) were other, and around 2140 (47%) of the participants were women. Variation in HbA1c reduction with GLP-1 receptor agonists treatment was associated with rs6923761G→A (Gly168Ser) in the GLP1R (0·08% [95% CI 0·04–0·12] or 0·9 mmol/mol lower reduction in HbA1c per serine, p=6·0 × 10−5) and low frequency variants in ARRB1 (optimal sequence kernel association test p=6·7 × 10−8), largely driven by rs140226575G→A (Thr370Met; 0·25% [SE 0·06] or 2·7 mmol/mol [SE 0·7] greater HbA1c reduction per methionine, p=5·2 × 10−6). A similar effect size for the ARRB1 Thr370Met was seen in Hispanic and American Indian or Alaska Native populations who have a higher frequency of this variant (6–11%) than in White European populations. Combining these two genes identified 4% of the population who had a 30% greater reduction in HbA1c than the 9% of the population with the worse response. Interpretation: This genome-wide pharmacogenomic study of GLP-1 receptor agonists provides novel biological and clinical insights. Clinically, when genotype is routinely available at the point of prescribing, individuals with ARRB1 variants might benefit from earlier initiation of GLP-1 receptor agonists. Funding: Innovative Medicines Initiative and the Wellcome Trus

Whole-genome sequencing reveals host factors underlying critical COVID-19

Critical COVID-19 is caused by immune-mediated inflammatory lung injury. Host genetic variation influences the development of illness requiring critical care1 or hospitalization2–4 after infection with SARS-CoV-2. The GenOMICC (Genetics of Mortality in Critical Care) study enables the comparison of genomes from individuals who are critically ill with those of population controls to find underlying disease mechanisms. Here we use whole-genome sequencing in 7,491 critically ill individuals compared with 48,400 controls to discover and replicate 23 independent variants that significantly predispose to critical COVID-19. We identify 16 new independent associations, including variants within genes that are involved in interferon signalling (IL10RB and PLSCR1), leucocyte differentiation (BCL11A) and blood-type antigen secretor status (FUT2). Using transcriptome-wide association and colocalization to infer the effect of gene expression on disease severity, we find evidence that implicates multiple genes—including reduced expression of a membrane flippase (ATP11A), and increased expression of a mucin (MUC1)—in critical disease. Mendelian randomization provides evidence in support of causal roles for myeloid cell adhesion molecules (SELE, ICAM5 and CD209) and the coagulation factor F8, all of which are potentially druggable targets. Our results are broadly consistent with a multi-component model of COVID-19 pathophysiology, in which at least two distinct mechanisms can predispose to life-threatening disease: failure to control viral replication; or an enhanced tendency towards pulmonary inflammation and intravascular coagulation. We show that comparison between cases of critical illness and population controls is highly efficient for the detection of therapeutically relevant mechanisms of disease

Genetic mechanisms of critical illness in COVID-19.

Host-mediated lung inflammation is present1, and drives mortality2, in the critical illness caused by coronavirus disease 2019 (COVID-19). Host genetic variants associated with critical illness may identify mechanistic targets for therapeutic development3. Here we report the results of the GenOMICC (Genetics Of Mortality In Critical Care) genome-wide association study in 2,244 critically ill patients with COVID-19 from 208 UK intensive care units. We have identified and replicated the following new genome-wide significant associations: on chromosome 12q24.13 (rs10735079, P = 1.65 × 10-8) in a gene cluster that encodes antiviral restriction enzyme activators (OAS1, OAS2 and OAS3); on chromosome 19p13.2 (rs74956615, P = 2.3 × 10-8) near the gene that encodes tyrosine kinase 2 (TYK2); on chromosome 19p13.3 (rs2109069, P = 3.98 ×  10-12) within the gene that encodes dipeptidyl peptidase 9 (DPP9); and on chromosome 21q22.1 (rs2236757, P = 4.99 × 10-8) in the interferon receptor gene IFNAR2. We identified potential targets for repurposing of licensed medications: using Mendelian randomization, we found evidence that low expression of IFNAR2, or high expression of TYK2, are associated with life-threatening disease; and transcriptome-wide association in lung tissue revealed that high expression of the monocyte-macrophage chemotactic receptor CCR2 is associated with severe COVID-19. Our results identify robust genetic signals relating to key host antiviral defence mechanisms and mediators of inflammatory organ damage in COVID-19. Both mechanisms may be amenable to targeted treatment with existing drugs. However, large-scale randomized clinical trials will be essential before any change to clinical practice