A Discrete Hardy-Laptev-Weidl-Type Inequality and Associated Schrödinger-Type Operators

Although the classical Hardy inequality is valid only in the three- and higher dimensional case, Laptev and Weidl established a two-dimensional Hardy-type inequality for the magnetic gradient with an Aharonov-Bohm magnetic potential. Here we consider a discrete analogue, replacing the punctured plane with a radially exponential lattice. In addition to discrete Hardy and Sobolev inequalities, we study the spectral properties of two associated self-adjoint operators. In particular, it is shown that, for suitable potentials, the discrete Schrödingertype operator in the Aharonov-Bohm field has essential spectrum concentrated at 0, and the multiplicity of its lower spectrum satisfies a CLR-type inequality.Although the classical Hardy inequality is valid only in the three- and higher dimensional case, Laptev and Weidl established a two-dimensional Hardy-type inequality for the magnetic gradient with an Aharonov-Bohm magnetic potential. Here we consider a discrete analogue, replacing the punctured plane with a radially exponential lattice. In addition to discrete Hardy and Sobolev inequalities, we study the spectral properties of two associated self-adjoint operators. In particular, it is shown that, for suitable potentials, the discrete Schrödingertype operator in the Aharonov-Bohm field has essential spectrum concentrated at 0, and the multiplicity of its lower spectrum satisfies a CLR-type inequality

Sharp Estimates of the Embedding Constants for Besov Spaces

Sharp estimates are obtained for the rates of blow up of the norms of embeddings of Besov spaces in Lorentz spaces as the parameters approach critical values.Sharp estimates are obtained for the rates of blow up of the norms of embeddings of Besov spaces in Lorentz spaces as the parameters approach critical values

Sharp Estimates of the Embedding Constants for Besov Spaces bs p,q, 0 < p < 1

Sharp estimates are obtained for the rates of blow up of the norms of embeddings of Besov spaces bs p,q in Lorentz spaces as the parameters approach critical values. In [8] the case 1 _ p < 1 was investigated. The case 0 < p < 1 of the present paper requires different methods as the pointwise estimates established are different and the interpolation argument used in [8] is no longer available

Native knowledge of great lakes ecology: Climate changes to Odawa lands

Climate change has been observed for hundreds of years by the plant specialists of three Odawa Tribes in the Upper Great Lakes along Lake Michigan. Sleeping Bear Dunes National Lakeshore (SLBE) is the focus of two National Park Service (NPS) studies of Odawa Traditional Ecological Knowledge (TEK) of plants, ecosystems, and climate change. Data collected during these studies contributed to developing Plant Gathering Agreements between tribes and parks. This analysis derived from 95 ethnographic interviews conducted by University of Arizona (UofA) anthropologists in partnership with expert elders appointed by tribes. Odawa elders recognized in the park 288 plants and five habitats of traditional and contemporary concern. Tribal elders explained that 115 of these traditional plants and all five habitats are known from multigenerational eyewitness accounts to have been impacted by climate change. The TEK study thus represents what Odawa people know about the traditional environment and thus provides a foundation for more complex government-to government relationships between Odawa tribes and the NPS. These research findings are neither intended to test Native TEK nor the climate findings of Western science. It should however be pointed out that both are in general agreement about what has happened due to climate change and thus there is now a TEK data base for co-stewardship

High frequency of pathogenic non-founder germline mutations in BRCA1 and BRCA2 in families with breast and ovarian cancer in a founder population

Funding Information: This work was supported by State Research Program “Biomedicine for the public health (BIOMEDICINE)” project 5 “Personalised cancer diagnostics and treatment effectiveness evaluation”. Publisher Copyright: © 2018 The Author(s).Background: Pathogenic BRCA1 founder mutations (c.4035delA, c.5266dupC) contribute to 3.77% of all consecutive primary breast cancers and 9.9% of all consecutive primary ovarian cancers. Identifying germline pathogenic gene variants in patients with primary breast and ovarian cancer could significantly impact the medical management of patients. The aim of the study was to evaluate the rate of pathogenic mutations in the 26 breast and ovarian cancer susceptibility genes in patients who meet the criteria for BRCA1/2 testing and to compare the accuracy of different selection criteria for second-line testing in a founder population. Methods: Fifteen female probands and 1 male proband that met National Comprehensive Cancer Network (NCCN) criteria for BRCA1/2 testing were included in the study and underwent 26-gene panel testing. Fourteen probands had breast cancer, one proband had ovarian cancer, and one proband had both breast and ovarian cancer. In a 26-gene panel, the following breast and/or ovarian cancer susceptibility genes were included: ATM, BARD1, BLM, BRCA1, BRCA2, BRIP1, CDH1, CHEK2, EPCAM, FAM175A, MEN1, MLH1, MRE11A, MSH2, MSH6, MUTYH, NBN, PALB2, PMS2, PTEN, RAD50, RAD51C, RAD51D, STK11, TP53, and XRCC2. All patients previously tested negative for BRCA1 founder mutations. Results: In 44% (7 out of 16) of tested probands, pathogenic mutations were identified. Six probands carried pathogenic mutations in BRCA1, and one proband carried pathogenic mutations in BRCA2. In patients, a variant of uncertain significance was found in BRCA2, RAD50, MRE11A and CDH1. The Manchester scoring system showed a high accuracy (87.5%), high sensitivity (85.7%) and high specificity (88.9%) for the prediction of pathogenic non-founder BRCA1/2 mutations. Conclusion: A relatively high incidence of pathogenic non-founder BRCA1/2 mutations was observed in a founder population. The Manchester scoring system predicted the probability of non-founder pathogenic mutations with high accuracy.publishersversionPeer reviewe

Frequency drift in MR spectroscopy at 3T

Purpose: Heating of gradient coils and passive shim components is a common cause of instability in the B-0 field, especially when gradient intensive sequences are used. The aim of the study was to set a benchmark for typical drift encountered during MR spectroscopy (MRS) to assess the need for real-time field-frequency locking on MRI scanners by comparing field drift data from a large number of sites.Method: A standardized protocol was developed for 80 participating sites using 99 3T MR scanners from 3 major vendors. Phantom water signals were acquired before and after an EPI sequence. The protocol consisted of: minimal preparatory imaging; a short pre-fMRI PRESS; a ten-minute fMRI acquisition; and a long post-fMRI PRESS acquisition. Both pre- and post-fMRI PRESS were non-water suppressed. Real-time frequency stabilization/adjustment was switched off when appropriate. Sixty scanners repeated the protocol for a second dataset. In addition, a three-hour post-fMRI MRS acquisition was performed at one site to observe change of gradient temperature and drift rate. Spectral analysis was performed using MATLAB. Frequency drift in pre-fMRI PRESS data were compared with the first 5:20 minutes and the full 30:00 minutes of data after fMRI. Median (interquartile range) drifts were measured and showed in violin plot. Paired t-tests were performed to compare frequency drift pre- and post-fMRI. A simulated in vivo spectrum was generated using FID-A to visualize the effect of the observed frequency drifts. The simulated spectrum was convolved with the frequency trace for the most extreme cases. Impacts of frequency drifts on NAA and GABA were also simulated as a function of linear drift. Data from the repeated protocol were compared with the corresponding first dataset using Pearson's and intraclass correlation coefficients (ICC).Results: Of the data collected from 99 scanners, 4 were excluded due to various reasons. Thus, data from 95 scanners were ultimately analyzed. For the first 5:20 min (64 transients), median (interquartile range) drift was 0.44 (1.29) Hz before fMRI and 0.83 (1.29) Hz after. This increased to 3.15 (4.02) Hz for the full 30 min (360 transients) run. Average drift rates were 0.29 Hz/min before fMRI and 0.43 Hz/min after. Paired t-tests indicated that drift increased after fMRI, as expected (p &lt; 0.05). Simulated spectra convolved with the frequency drift showed that the intensity of the NAA singlet was reduced by up to 26%, 44 % and 18% for GE, Philips and Siemens scanners after fMRI, respectively. ICCs indicated good agreement between datasets acquired on separate days. The single site long acquisition showed drift rate was reduced to 0.03 Hz/min approximately three hours after fMRI.Discussion: This study analyzed frequency drift data from 95 3T MRI scanners. Median levels of drift were relatively low (5-min average under 1 Hz), but the most extreme cases suffered from higher levels of drift. The extent of drift varied across scanners which both linear and nonlinear drifts were observed.</p

Rare germline copy number variants (CNVs) and breast cancer risk.

Funder: CIHRGermline copy number variants (CNVs) are pervasive in the human genome but potential disease associations with rare CNVs have not been comprehensively assessed in large datasets. We analysed rare CNVs in genes and non-coding regions for 86,788 breast cancer cases and 76,122 controls of European ancestry with genome-wide array data. Gene burden tests detected the strongest association for deletions in BRCA1 (P = 3.7E-18). Nine other genes were associated with a p-value < 0.01 including known susceptibility genes CHEK2 (P = 0.0008), ATM (P = 0.002) and BRCA2 (P = 0.008). Outside the known genes we detected associations with p-values < 0.001 for either overall or subtype-specific breast cancer at nine deletion regions and four duplication regions. Three of the deletion regions were in established common susceptibility loci. To the best of our knowledge, this is the first genome-wide analysis of rare CNVs in a large breast cancer case-control dataset. We detected associations with exonic deletions in established breast cancer susceptibility genes. We also detected suggestive associations with non-coding CNVs in known and novel loci with large effects sizes. Larger sample sizes will be required to reach robust levels of statistical significance

Civil society leadership in the struggle for AIDS treatment in South Africa and Uganda

Includes abstract.Includes bibliographical references.This thesis is an attempt to theorise and operationalise empirically the notion of ‘civil society leadership’ in Sub-Saharan Africa. ‘AIDS leadership,’ which is associated with the intergovernmental institutions charged with coordinating the global response to HIV/AIDS, is both under-theorised and highly context-specific. In this study I therefore opt for an inclusive framework that draws on a range of approaches, including the literature on ‘leadership’, institutions, social movements and the ‘network’ perspective on civil society mobilisation. This framework is employed in rich and detailed empirical descriptions (‘thick description’) of civil society mobilisation around AIDS, including contentious AIDS activism, in the key case studies of South Africa and Uganda. South Africa and Uganda are widely considered key examples of poor and good leadership (from national political leaders) respectively, while the Treatment Action Campaign (TAC) and The AIDS Support Organisation (TASO) are both seen as highly effective civil society movements. These descriptions emphasise ‘transnational networks of influence’ in which civil society leaders participated (and at times actively constructed) in order to mobilise both symbolic and material resources aimed at exerting influence at the transnational, national and local levels

Intravenous alteplase for stroke with unknown time of onset guided by advanced imaging: systematic review and meta-analysis of individual patient data

Background: Patients who have had a stroke with unknown time of onset have been previously excluded from thrombolysis. We aimed to establish whether intravenous alteplase is safe and effective in such patients when salvageable tissue has been identified with imaging biomarkers. Methods: We did a systematic review and meta-analysis of individual patient data for trials published before Sept 21, 2020. Randomised trials of intravenous alteplase versus standard of care or placebo in adults with stroke with unknown time of onset with perfusion-diffusion MRI, perfusion CT, or MRI with diffusion weighted imaging-fluid attenuated inversion recovery (DWI-FLAIR) mismatch were eligible. The primary outcome was favourable functional outcome (score of 0–1 on the modified Rankin Scale [mRS]) at 90 days indicating no disability using an unconditional mixed-effect logistic-regression model fitted to estimate the treatment effect. Secondary outcomes were mRS shift towards a better functional outcome and independent outcome (mRS 0–2) at 90 days. Safety outcomes included death, severe disability or death (mRS score 4–6), and symptomatic intracranial haemorrhage. This study is registered with PROSPERO, CRD42020166903. Findings: Of 249 identified abstracts, four trials met our eligibility criteria for inclusion: WAKE-UP, EXTEND, THAWS, and ECASS-4. The four trials provided individual patient data for 843 individuals, of whom 429 (51%) were assigned to alteplase and 414 (49%) to placebo or standard care. A favourable outcome occurred in 199 (47%) of 420 patients with alteplase and in 160 (39%) of 409 patients among controls (adjusted odds ratio [OR] 1·49 [95% CI 1·10–2·03]; p=0·011), with low heterogeneity across studies (I2=27%). Alteplase was associated with a significant shift towards better functional outcome (adjusted common OR 1·38 [95% CI 1·05–1·80]; p=0·019), and a higher odds of independent outcome (adjusted OR 1·50 [1·06–2·12]; p=0·022). In the alteplase group, 90 (21%) patients were severely disabled or died (mRS score 4–6), compared with 102 (25%) patients in the control group (adjusted OR 0·76 [0·52–1·11]; p=0·15). 27 (6%) patients died in the alteplase group and 14 (3%) patients died among controls (adjusted OR 2·06 [1·03–4·09]; p=0·040). The prevalence of symptomatic intracranial haemorrhage was higher in the alteplase group than among controls (11 [3%] vs two [&lt;1%], adjusted OR 5·58 [1·22–25·50]; p=0·024). Interpretation: In patients who have had a stroke with unknown time of onset with a DWI-FLAIR or perfusion mismatch, intravenous alteplase resulted in better functional outcome at 90 days than placebo or standard care. A net benefit was observed for all functional outcomes despite an increased risk of symptomatic intracranial haemorrhage. Although there were more deaths with alteplase than placebo, there were fewer cases of severe disability or death. Funding: None

Basic science232. Certolizumab pegol prevents pro-inflammatory alterations in endothelial cell function

Background: Cardiovascular disease is a major comorbidity of rheumatoid arthritis (RA) and a leading cause of death. Chronic systemic inflammation involving tumour necrosis factor alpha (TNF) could contribute to endothelial activation and atherogenesis. A number of anti-TNF therapies are in current use for the treatment of RA, including certolizumab pegol (CZP), (Cimzia ®; UCB, Belgium). Anti-TNF therapy has been associated with reduced clinical cardiovascular disease risk and ameliorated vascular function in RA patients. However, the specific effects of TNF inhibitors on endothelial cell function are largely unknown. Our aim was to investigate the mechanisms underpinning CZP effects on TNF-activated human endothelial cells. Methods: Human aortic endothelial cells (HAoECs) were cultured in vitro and exposed to a) TNF alone, b) TNF plus CZP, or c) neither agent. Microarray analysis was used to examine the transcriptional profile of cells treated for 6 hrs and quantitative polymerase chain reaction (qPCR) analysed gene expression at 1, 3, 6 and 24 hrs. NF-κB localization and IκB degradation were investigated using immunocytochemistry, high content analysis and western blotting. Flow cytometry was conducted to detect microparticle release from HAoECs. Results: Transcriptional profiling revealed that while TNF alone had strong effects on endothelial gene expression, TNF and CZP in combination produced a global gene expression pattern similar to untreated control. The two most highly up-regulated genes in response to TNF treatment were adhesion molecules E-selectin and VCAM-1 (q 0.2 compared to control; p > 0.05 compared to TNF alone). The NF-κB pathway was confirmed as a downstream target of TNF-induced HAoEC activation, via nuclear translocation of NF-κB and degradation of IκB, effects which were abolished by treatment with CZP. In addition, flow cytometry detected an increased production of endothelial microparticles in TNF-activated HAoECs, which was prevented by treatment with CZP. Conclusions: We have found at a cellular level that a clinically available TNF inhibitor, CZP reduces the expression of adhesion molecule expression, and prevents TNF-induced activation of the NF-κB pathway. Furthermore, CZP prevents the production of microparticles by activated endothelial cells. This could be central to the prevention of inflammatory environments underlying these conditions and measurement of microparticles has potential as a novel prognostic marker for future cardiovascular events in this patient group. Disclosure statement: Y.A. received a research grant from UCB. I.B. received a research grant from UCB. S.H. received a research grant from UCB. All other authors have declared no conflicts of interes