Split buildings of type F₄ in buildings of type E₆

A symplectic polarity of a building of type is a polarity whose fixed point structure is a building of type containing residues isomorphic to symplectic polar spaces (i.e., so-called split buildings of type ). In this paper, we show in a geometric way that every building of type contains, up to conjugacy, a unique class of symplectic polarities. We also show that the natural point-line geometry of each split building of type fully embedded in the natural point-line geometry of arises from a symplectic polarity

Protocol for a non-randomised feasibility study testing a primary care intervention to promote engagement in an online health community for adults with troublesome asthma

Introduction: In the UK, approximately 4.3 million adults have asthma, with one-third experiencing poor asthma control, affecting their quality of life, and increasing their healthcare use. Interventions promoting emotional/behavioural self-management can improve asthma control and reduce comorbidities and mortality. Integration of online peer support into primary care services to foster self-management is a novel strategy. We aim to co-design and evaluate an intervention for primary care clinicians to promote engagement with an asthma online health community (OHC). Our protocol describes a ‘survey leading to a trial’ design as part of a mixed-methods, non-randomised feasibility study to test the feasibility and acceptability of the intervention. Methods and analysis: Adults on the asthma registers of six London general practices (~3000 patients) will be invited to an online survey, via text messages. The survey will collect data on attitudes towards seeking online peer support, asthma control, anxiety, depression, quality of life, information on the network of people providing support with asthma and demographics. Regression analyses of the survey data will identify correlates/predictors of attitudes/receptiveness towards online peer support. Patients with troublesome asthma, who (in the survey) expressed interest in online peer support, will be invited to receive the intervention, aiming to reach a recruitment target of 50 patients. Intervention will involve a one-off, face-to-face consultation with a practice clinician to introduce online peer support, sign patients up to an established asthma OHC, and encourage OHC engagement. Outcome measures will be collected at baseline and 3 months post intervention and analysed with primary care and OHC engagement data. Recruitment, intervention uptake, retention, collection of outcomes, and OHC engagement will be assessed. Interviews with clinicians and patients will explore experiences of the intervention. Ethics and dissemination: Ethical approval was obtained from a National Health Service Research Ethics Committee (reference: 22/NE/0182). Written consent will be obtained before intervention receipt and interview participation. Findings will be shared via dissemination to general practices, conference presentations and peer-reviewed publications. Trial registration number: NCT05829265

Reducing Tumour Hypoxia via Oral Administration of Oxygen Nanobubbles

Hypoxia has been shown to be a key factor inhibiting the successful treatment of solid tumours. Existing strategies for reducing hypoxia, however, have shown limited efficacy and/or adverse side effects. The aim of this study was to investigate the potential for reducing tumour hypoxia using an orally delivered suspension of surfactant-stabilised oxygen nanobubbles. Experiments were carried out in a mouse xenograft tumour model for human pancreatic cancer (BxPc-3 cells in male SCID mice). A single dose of 100 μL of oxygen saturated water, oxygen nanobubbles or argon nanobubbles was administered via gavage. Animals were sacrificed 30 minutes post-treatment (3 per group) and expression of hypoxia-inducible-factor-1α (HIF1α) protein measured by real time quantitative polymerase chain reaction and Western blot analysis of the excised tumour tissue. Neither the oxygen saturated water nor argon nanobubbles produced a statistically significant change in HIF1α expression at the transcriptional level. In contrast, a reduction of 75% and 25% in the transcriptional and translational expression of HIF1α respectively (p<0.001) was found for the animals receiving the oxygen nanobubbles. This magnitude of reduction has been shown in previous studies to be commensurate with an improvement in outcome with both radiation and drug-based treatments. In addition, there was a significant reduction in the expression of vascular endothelial growth factor (VEGF) in this group and corresponding increase in the expression of arrest-defective protein 1 homolog A (ARD1A)

International Conference on Groups and Geometries

The book deals with fundamental structural aspects of algebraic and simple groups, Coxeter groups and the related geometries and buildings. All contributing authors are very active researchers in the topics related to the theme of the book. Some of the articles provide the latest developments in the subject; some provide an overview of the current status of some important problems in this area; some survey an area highlighting the current developments; and some provide an exposition of an area to collect problems and conjectures. It is hoped that these articles would be helpful to a beginner to start independent research on any of these topics, as well as to an expert to know some of the latest developments or to consider some problems for investigation

Group theory and computation

This book is a blend of recent developments in theoretical and computational aspects of group theory. It presents the state-of-the-art research topics in different aspects of group theory, namely, character theory, representation theory, integral group rings, the Monster simple group, computational algorithms and methods on finite groups, finite loops, periodic groups, Camina groups and generalizations, automorphisms and non-abelian tensor product of groups. Presenting a collection of invited articles by some of the leading and highly active researchers in the theory of finite groups and their representations and the Monster group, with a focus on computational aspects, this book is of particular interest to researchers in the area of group theory and related fields of mathematics

Group theory and computation

This book is a blend of recent developments in theoretical and computational aspects of group theory. It presents the state-of-the-art research topics in different aspects of group theory, namely, character theory, representation theory, integral group rings, the Monster simple group, computational algorithms and methods on finite groups, finite loops, periodic groups, Camina groups and generalizations, automorphisms and non-abelian tensor product of groups. Presenting a collection of invited articles by some of the leading and highly active researchers in the theory of finite groups and their representations and the Monster group, with a focus on computational aspects, this book is of particular interest to researchers in the area of group theory and related fields of mathematics