The dynamical system of iterated Cevian Tribbles

Ceva\u27s Theorem gives a necessary and sufficient condition for three lines through the vertices of a triangle to intersect at a single point. We investigate what happens when that condition is not met, which means the three lines form a triangle inside the original (called a Tribble), and the process is iterated. By Cantor\u27s Intersection Theorem, we know that the Tribbles will converge to a point within the initial triangle as long as the side lengths of the Tribbles go to zero. We consider different ways to iterate this process. We establish an nth term test for convergence when the Cevian ratios are deterministic sequences. We prove that when the Cevian ratios used to iterate are chosen at random, the Tribbles always converge. We initiate study on the distribution of limit points. With the aid of a simulation in MATLAB that produces graphical plots for the numerical estimations of Tribble limit points, we begin to visualize and describe the distribution of limit points

BHPR research: qualitative1. Complex reasoning determines patients' perception of outcome following foot surgery in rheumatoid arhtritis

Background: Foot surgery is common in patients with RA but research into surgical outcomes is limited and conceptually flawed as current outcome measures lack face validity: to date no one has asked patients what is important to them. This study aimed to determine which factors are important to patients when evaluating the success of foot surgery in RA Methods: Semi structured interviews of RA patients who had undergone foot surgery were conducted and transcribed verbatim. Thematic analysis of interviews was conducted to explore issues that were important to patients. Results: 11 RA patients (9 ♂, mean age 59, dis dur = 22yrs, mean of 3 yrs post op) with mixed experiences of foot surgery were interviewed. Patients interpreted outcome in respect to a multitude of factors, frequently positive change in one aspect contrasted with negative opinions about another. Overall, four major themes emerged. Function: Functional ability & participation in valued activities were very important to patients. Walking ability was a key concern but patients interpreted levels of activity in light of other aspects of their disease, reflecting on change in functional ability more than overall level. Positive feelings of improved mobility were often moderated by negative self perception ("I mean, I still walk like a waddling duck”). Appearance: Appearance was important to almost all patients but perhaps the most complex theme of all. Physical appearance, foot shape, and footwear were closely interlinked, yet patients saw these as distinct separate concepts. Patients need to legitimize these feelings was clear and they frequently entered into a defensive repertoire ("it's not cosmetic surgery; it's something that's more important than that, you know?”). Clinician opinion: Surgeons' post operative evaluation of the procedure was very influential. The impact of this appraisal continued to affect patients' lasting impression irrespective of how the outcome compared to their initial goals ("when he'd done it ... he said that hasn't worked as good as he'd wanted to ... but the pain has gone”). Pain: Whilst pain was important to almost all patients, it appeared to be less important than the other themes. Pain was predominately raised when it influenced other themes, such as function; many still felt the need to legitimize their foot pain in order for health professionals to take it seriously ("in the end I went to my GP because it had happened a few times and I went to an orthopaedic surgeon who was quite dismissive of it, it was like what are you complaining about”). Conclusions: Patients interpret the outcome of foot surgery using a multitude of interrelated factors, particularly functional ability, appearance and surgeons' appraisal of the procedure. While pain was often noted, this appeared less important than other factors in the overall outcome of the surgery. Future research into foot surgery should incorporate the complexity of how patients determine their outcome Disclosure statement: All authors have declared no conflicts of interes

The genetic architecture of the human cerebral cortex

The cerebral cortex underlies our complex cognitive capabilities, yet little is known about the specific genetic loci that influence human cortical structure. To identify genetic variants that affect cortical structure, we conducted a genome-wide association meta-analysis of brain magnetic resonance imaging data from 51,665 individuals. We analyzed the surface area and average thickness of the whole cortex and 34 regions with known functional specializations. We identified 199 significant loci and found significant enrichment for loci influencing total surface area within regulatory elements that are active during prenatal cortical development, supporting the radial unit hypothesis. Loci that affect regional surface area cluster near genes in Wnt signaling pathways, which influence progenitor expansion and areal identity. Variation in cortical structure is genetically correlated with cognitive function, Parkinson's disease, insomnia, depression, neuroticism, and attention deficit hyperactivity disorder

SARS-CoV-2-specific immune responses and clinical outcomes after COVID-19 vaccination in patients with immune-suppressive disease

Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) immune responses and infection outcomes were evaluated in 2,686 patients with varying immune-suppressive disease states after administration of two Coronavirus Disease 2019 (COVID-19) vaccines. Overall, 255 of 2,204 (12%) patients failed to develop anti-spike antibodies, with an additional 600 of 2,204 (27%) patients generating low levels (<380 AU ml−1). Vaccine failure rates were highest in ANCA-associated vasculitis on rituximab (21/29, 72%), hemodialysis on immunosuppressive therapy (6/30, 20%) and solid organ transplant recipients (20/81, 25% and 141/458, 31%). SARS-CoV-2-specific T cell responses were detected in 513 of 580 (88%) patients, with lower T cell magnitude or proportion in hemodialysis, allogeneic hematopoietic stem cell transplantation and liver transplant recipients (versus healthy controls). Humoral responses against Omicron (BA.1) were reduced, although cross-reactive T cell responses were sustained in all participants for whom these data were available. BNT162b2 was associated with higher antibody but lower cellular responses compared to ChAdOx1 nCoV-19 vaccination. We report 474 SARS-CoV-2 infection episodes, including 48 individuals with hospitalization or death from COVID-19. Decreased magnitude of both the serological and the T cell response was associated with severe COVID-19. Overall, we identified clinical phenotypes that may benefit from targeted COVID-19 therapeutic strategies

Testing a global standard for quantifying species recovery and assessing conservation impact.

Recognizing the imperative to evaluate species recovery and conservation impact, in 2012 the International Union for Conservation of Nature (IUCN) called for development of a "Green List of Species" (now the IUCN Green Status of Species). A draft Green Status framework for assessing species' progress toward recovery, published in 2018, proposed 2 separate but interlinked components: a standardized method (i.e., measurement against benchmarks of species' viability, functionality, and preimpact distribution) to determine current species recovery status (herein species recovery score) and application of that method to estimate past and potential future impacts of conservation based on 4 metrics (conservation legacy, conservation dependence, conservation gain, and recovery potential). We tested the framework with 181 species representing diverse taxa, life histories, biomes, and IUCN Red List categories (extinction risk). Based on the observed distribution of species' recovery scores, we propose the following species recovery categories: fully recovered, slightly depleted, moderately depleted, largely depleted, critically depleted, extinct in the wild, and indeterminate. Fifty-nine percent of tested species were considered largely or critically depleted. Although there was a negative relationship between extinction risk and species recovery score, variation was considerable. Some species in lower risk categories were assessed as farther from recovery than those at higher risk. This emphasizes that species recovery is conceptually different from extinction risk and reinforces the utility of the IUCN Green Status of Species to more fully understand species conservation status. Although extinction risk did not predict conservation legacy, conservation dependence, or conservation gain, it was positively correlated with recovery potential. Only 1.7% of tested species were categorized as zero across all 4 of these conservation impact metrics, indicating that conservation has, or will, play a role in improving or maintaining species status for the vast majority of these species. Based on our results, we devised an updated assessment framework that introduces the option of using a dynamic baseline to assess future impacts of conservation over the short term to avoid misleading results which were generated in a small number of cases, and redefines short term as 10 years to better align with conservation planning. These changes are reflected in the IUCN Green Status of Species Standard

Conversion Discriminative Analysis on Mild Cognitive Impairment Using Multiple Cortical Features from MR Images

Neuroimaging measurements derived from magnetic resonance imaging provide important information required for detecting changes related to the progression of mild cognitive impairment (MCI). Cortical features and changes play a crucial role in revealing unique anatomical patterns of brain regions, and further differentiate MCI patients from normal states. Four cortical features, namely, gray matter volume, cortical thickness, surface area, and mean curvature, were explored for discriminative analysis among three groups including the stable MCI (sMCI), the converted MCI (cMCI), and the normal control (NC) groups. In this study, 158 subjects (72 NC, 46 sMCI, and 40 cMCI) were selected from the Alzheimer's Disease Neuroimaging Initiative. A sparse-constrained regression model based on the l2-1-norm was introduced to reduce the feature dimensionality and retrieve essential features for the discrimination of the three groups by using a support vector machine (SVM). An optimized strategy of feature addition based on the weight of each feature was adopted for the SVM classifier in order to achieve the best classification performance. The baseline cortical features combined with the longitudinal measurements for 2 years of follow-up data yielded prominent classification results. In particular, the cortical thickness produced a classification with 98.84% accuracy, 97.5% sensitivity, and 100% specificity for the sMCI–cMCI comparison; 92.37% accuracy, 84.78% sensitivity, and 97.22% specificity for the cMCI–NC comparison; and 93.75% accuracy, 92.5% sensitivity, and 94.44% specificity for the sMCI–NC comparison. The best performances obtained by the SVM classifier using the essential features were 5–40% more than those using all of the retained features. The feasibility of the cortical features for the recognition of anatomical patterns was certified; thus, the proposed method has the potential to improve the clinical diagnosis of sub-types of MCI and predict the risk of its conversion to Alzheimer's disease

Safety and efficacy of the ChAdOx1 nCoV-19 vaccine (AZD1222) against SARS-CoV-2: an interim analysis of four randomised controlled trials in Brazil, South Africa, and the UK.

BACKGROUND: A safe and efficacious vaccine against severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), if deployed with high coverage, could contribute to the control of the COVID-19 pandemic. We evaluated the safety and efficacy of the ChAdOx1 nCoV-19 vaccine in a pooled interim analysis of four trials. METHODS: This analysis includes data from four ongoing blinded, randomised, controlled trials done across the UK, Brazil, and South Africa. Participants aged 18 years and older were randomly assigned (1:1) to ChAdOx1 nCoV-19 vaccine or control (meningococcal group A, C, W, and Y conjugate vaccine or saline). Participants in the ChAdOx1 nCoV-19 group received two doses containing 5 × 1010 viral particles (standard dose; SD/SD cohort); a subset in the UK trial received a half dose as their first dose (low dose) and a standard dose as their second dose (LD/SD cohort). The primary efficacy analysis included symptomatic COVID-19 in seronegative participants with a nucleic acid amplification test-positive swab more than 14 days after a second dose of vaccine. Participants were analysed according to treatment received, with data cutoff on Nov 4, 2020. Vaccine efficacy was calculated as 1 - relative risk derived from a robust Poisson regression model adjusted for age. Studies are registered at ISRCTN89951424 and ClinicalTrials.gov, NCT04324606, NCT04400838, and NCT04444674. FINDINGS: Between April 23 and Nov 4, 2020, 23 848 participants were enrolled and 11 636 participants (7548 in the UK, 4088 in Brazil) were included in the interim primary efficacy analysis. In participants who received two standard doses, vaccine efficacy was 62·1% (95% CI 41·0-75·7; 27 [0·6%] of 4440 in the ChAdOx1 nCoV-19 group vs71 [1·6%] of 4455 in the control group) and in participants who received a low dose followed by a standard dose, efficacy was 90·0% (67·4-97·0; three [0·2%] of 1367 vs 30 [2·2%] of 1374; pinteraction=0·010). Overall vaccine efficacy across both groups was 70·4% (95·8% CI 54·8-80·6; 30 [0·5%] of 5807 vs 101 [1·7%] of 5829). From 21 days after the first dose, there were ten cases hospitalised for COVID-19, all in the control arm; two were classified as severe COVID-19, including one death. There were 74 341 person-months of safety follow-up (median 3·4 months, IQR 1·3-4·8): 175 severe adverse events occurred in 168 participants, 84 events in the ChAdOx1 nCoV-19 group and 91 in the control group. Three events were classified as possibly related to a vaccine: one in the ChAdOx1 nCoV-19 group, one in the control group, and one in a participant who remains masked to group allocation. INTERPRETATION: ChAdOx1 nCoV-19 has an acceptable safety profile and has been found to be efficacious against symptomatic COVID-19 in this interim analysis of ongoing clinical trials. FUNDING: UK Research and Innovation, National Institutes for Health Research (NIHR), Coalition for Epidemic Preparedness Innovations, Bill & Melinda Gates Foundation, Lemann Foundation, Rede D'Or, Brava and Telles Foundation, NIHR Oxford Biomedical Research Centre, Thames Valley and South Midland's NIHR Clinical Research Network, and AstraZeneca

Safety and efficacy of the ChAdOx1 nCoV-19 vaccine (AZD1222) against SARS-CoV-2: an interim analysis of four randomised controlled trials in Brazil, South Africa, and the UK

Background A safe and efficacious vaccine against severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), if deployed with high coverage, could contribute to the control of the COVID-19 pandemic. We evaluated the safety and efficacy of the ChAdOx1 nCoV-19 vaccine in a pooled interim analysis of four trials. Methods This analysis includes data from four ongoing blinded, randomised, controlled trials done across the UK, Brazil, and South Africa. Participants aged 18 years and older were randomly assigned (1:1) to ChAdOx1 nCoV-19 vaccine or control (meningococcal group A, C, W, and Y conjugate vaccine or saline). Participants in the ChAdOx1 nCoV-19 group received two doses containing 5 × 1010 viral particles (standard dose; SD/SD cohort); a subset in the UK trial received a half dose as their first dose (low dose) and a standard dose as their second dose (LD/SD cohort). The primary efficacy analysis included symptomatic COVID-19 in seronegative participants with a nucleic acid amplification test-positive swab more than 14 days after a second dose of vaccine. Participants were analysed according to treatment received, with data cutoff on Nov 4, 2020. Vaccine efficacy was calculated as 1 - relative risk derived from a robust Poisson regression model adjusted for age. Studies are registered at ISRCTN89951424 and ClinicalTrials.gov, NCT04324606, NCT04400838, and NCT04444674. Findings Between April 23 and Nov 4, 2020, 23 848 participants were enrolled and 11 636 participants (7548 in the UK, 4088 in Brazil) were included in the interim primary efficacy analysis. In participants who received two standard doses, vaccine efficacy was 62·1% (95% CI 41·0–75·7; 27 [0·6%] of 4440 in the ChAdOx1 nCoV-19 group vs71 [1·6%] of 4455 in the control group) and in participants who received a low dose followed by a standard dose, efficacy was 90·0% (67·4–97·0; three [0·2%] of 1367 vs 30 [2·2%] of 1374; pinteraction=0·010). Overall vaccine efficacy across both groups was 70·4% (95·8% CI 54·8–80·6; 30 [0·5%] of 5807 vs 101 [1·7%] of 5829). From 21 days after the first dose, there were ten cases hospitalised for COVID-19, all in the control arm; two were classified as severe COVID-19, including one death. There were 74 341 person-months of safety follow-up (median 3·4 months, IQR 1·3–4·8): 175 severe adverse events occurred in 168 participants, 84 events in the ChAdOx1 nCoV-19 group and 91 in the control group. Three events were classified as possibly related to a vaccine: one in the ChAdOx1 nCoV-19 group, one in the control group, and one in a participant who remains masked to group allocation. Interpretation ChAdOx1 nCoV-19 has an acceptable safety profile and has been found to be efficacious against symptomatic COVID-19 in this interim analysis of ongoing clinical trials