An integrality theorem of Grosshans over arbitrary base ring

We revisit a theorem of Grosshans and show that it holds over arbitrary commutative base ring $k$. One considers a split reductive group scheme $G$ acting on a $k$-algebra $A$ and leaving invariant a subalgebra $R$. If $R^U=A^U$ then the conclusion is that $A$ is integral over $R$.Comment: 5 pages; final versio

Superoxide Dismutase 1 in Health and Disease: How a Frontline Antioxidant Becomes Neurotoxic.

Cu/Zn superoxide dismutase (SOD1) is a frontline antioxidant enzyme catalysing superoxide breakdown and is important for most forms of eukaryotic life. The evolution of aerobic respiration by mitochondria increased cellular production of superoxide, resulting in an increased reliance upon SOD1. Consistent with the importance of SOD1 for cellular health, many human diseases of the central nervous system involve perturbations in SOD1 biology. But far from providing a simple demonstration of how disease arises from SOD1 loss-of-function, attempts to elucidate pathways by which atypical SOD1 biology leads to neurodegeneration have revealed unexpectedly complex molecular characteristics delineating healthy, functional SOD1 protein from that which likely contributes to central nervous system disease. This review summarises current understanding of SOD1 biology from SOD1 genetics through to protein function and stability

The homotopy type of the loops on (n−1)(n-1)-connected (2n+1)(2n+1)-manifolds

For $n\geq 2$ we compute the homotopy groups of $(n-1)$-connected closed manifolds of dimension $(2n+1)$. Away from the finite set of primes dividing the order of the torsion subgroup in homology, the $p$-local homotopy groups of $M$ are determined by the rank of the free Abelian part of the homology. Moreover, we show that these $p$-local homotopy groups can be expressed as a direct sum of $p$-local homotopy groups of spheres. The integral homotopy type of the loop space is also computed and shown to depend only on the rank of the free Abelian part and the torsion subgroup.Comment: Trends in Algebraic Topology and Related Topics, Trends Math., Birkhauser/Springer, 2018. arXiv admin note: text overlap with arXiv:1510.0519

The Pure Virtual Braid Group Is Quadratic

If an augmented algebra K over Q is filtered by powers of its augmentation ideal I, the associated graded algebra grK need not in general be quadratic: although it is generated in degree 1, its relations may not be generated by homogeneous relations of degree 2. In this paper we give a sufficient criterion (called the PVH Criterion) for grK to be quadratic. When K is the group algebra of a group G, quadraticity is known to be equivalent to the existence of a (not necessarily homomorphic) universal finite type invariant for G. Thus the PVH Criterion also implies the existence of such a universal finite type invariant for the group G. We apply the PVH Criterion to the group algebra of the pure virtual braid group (also known as the quasi-triangular group), and show that the corresponding associated graded algebra is quadratic, and hence that these groups have a (not necessarily homomorphic) universal finite type invariant.Comment: 53 pages, 15 figures. Some clarifications added and inaccuracies corrected, reflecting suggestions made by the referee of the published version of the pape

Novel use of tranexamic acid to reduce the need for Nasal Packing in Epistaxis (NoPac) randomised controlled trial: research protocol.

INTRODUCTION: Patients presenting to emergency departments (EDs) with epistaxis uncontrolled by subsequent simple first aid measures or application of topical vasoconstrictors will typically undergo anterior nasal packing. Packing is effective, but can be extremely painful and unpleasant and patients usually need hospital admission. Tranexamic acid (TXA) is a cheap, safe, readily available antifibrinolytic agent known to be beneficial in a variety of clinical settings where uncontrolled bleeding may be a problem. Anecdotal evidence suggests that topical TXA may be of value in persistent epistaxis; however, further evaluation is required. METHODS AND ANALYSIS: This is a multicentre, double-blind, parallel group, randomised, controlled trial comparing the use of topical intranasal TXA with indistinguishable placebo in adults presenting to UK EDs with persistent atraumatic epistaxis. Follow-up is at 1 week by structured telephone review. The primary outcome measure is the subsequent need for anterior nasal packing in the ED. Key secondary outcomes include the need for hospital admission, blood transfusion and/or further treatment for epistaxis during the index ED attendance. Recruiting 450 patients will provide 90% power to demonstrate an absolute reduction in packing rate from 95% to 85%. An improvement of this magnitude would be of significant benefit to patients and healthcare providers and justify a change to standard practice. Given the low cost of TXA and its short administration time, a full economic evaluation is not being undertaken. ETHICS AND DISSEMINATION: The study has been approved by the South West-Bristol Research Ethics Committee (reference 17/SW/0010). We aim to publish the findings in a high impact, international peer-reviewed journal. Results will also be shared with the Hereditary Haemorrhagic Telangiectasia foundation and telangiectasia UK for dissemination through appropriate related forums. TRIAL REGISTRATION NUMBER: ISRCTN34153772 and EudraCT No: 2016-001530-10

Emerging pharmacotherapy of tinnitus

Tinnitus, the perception of sound in the absence of an auditory stimulus, is perceived by about 1 in 10 adults, and for at least 1 in 100, tinnitus severely affects their quality of life. Because tinnitus is frequently associated with irritability, agitation, stress, insomnia, anxiety and depression, the social and economic burdens of tinnitus can be enormous. No curative treatments are available. However, tinnitus symptoms can be alleviated to some extent. The most widespread management therapies consist of auditory stimulation and cognitive behavioral treatment, aiming at improving habituation and coping strategies. Available clinical trials vary in methodological rigor and have been performed for a considerable number of different drugs. None of the investigated drugs have demonstrated providing replicable long-term reduction of tinnitus impact in the majority of patients in excess of placebo effects. Accordingly, there are no FDA or European Medicines Agency approved drugs for the treatment of tinnitus. However, in spite of the lack of evidence, a large variety of different compounds are prescribed off-label. Therefore, more effective pharmacotherapies for this huge and still growing market are desperately needed and even a drug that produces only a small but significant effect would have an enormous therapeutic impact. This review describes current and emerging pharmacotherapies with current difficulties and limitations. In addition, it provides an estimate of the tinnitus market. Finally, it describes recent advances in the tinnitus field which may help overcome obstacles faced in the pharmacological treatment of tinnitus. These include incomplete knowledge of tinnitus pathophysiology, lack of well-established animal models, heterogeneity of different forms of tinnitus, difficulties in tinnitus assessment and outcome measurement and variability in clinical trial methodology. © 2009 Informa UK Ltd.Fil: Langguth, Berthold. Universitat Regensburg; AlemaniaFil: Salvi, Richard. State University of New York; Estados UnidosFil: Elgoyhen, Ana Belen. Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto de Investigaciones en Ingeniería Genética y Biología Molecular "Dr. Héctor N. Torres"; Argentin

On the non-abelian Brumer-Stark conjecture and the equivariant Iwasawa main conjecture

We show that for an odd prime p, the p-primary parts of refinements of the (imprimitive) non-abelian Brumer and Brumer-Stark conjectures are implied by the equivariant Iwasawa main conjecture (EIMC) for totally real fields. Crucially, this result does not depend on the vanishing of the relevant Iwasawa mu-invariant. In combination with the authors' previous work on the EIMC, this leads to unconditional proofs of the non-abelian Brumer and Brumer-Stark conjectures in many new cases.Comment: 33 pages; to appear in Mathematische Zeitschrift; v3 many minor updates including new title; v2 some cohomological arguments simplified; v1 is a revised version of the second half of arXiv:1408.4934v

The relationship between sensory sensitivity and autistic traits in the general population.

Individuals with Autism Spectrum Disorders (ASDs) tend to have sensory processing difficulties (Baranek et al. in J Child Psychol Psychiatry 47:591–601, 2006). These difficulties include over- and under-responsiveness to sensory stimuli, and problems modulating sensory input (Ben-Sasson et al. in J Autism Dev Disorders 39:1–11, 2009). As those with ASD exist at the extreme end of a continuum of autistic traits that is also evident in the general population, we investigated the link between ASD and sensory sensitivity in the general population by administering two questionnaires online to 212 adult participants. Results showed a highly significant positive correlation (r = .775, p < .001) between number of autistic traits and the frequency of sensory processing problems. These data suggest a strong link between sensory processing and autistic traits in the general population, which in turn potentially implicates sensory processing problems in social interaction difficulties

The XMM cluster survey: Testing chameleon gravity using the profiles of clusters

The chameleon gravity model postulates the existence of a scalar field that couples with matter to mediate a fifth force. If it exists, this fifth force would influence the hot X-ray emitting gas filling the potential wells of galaxy clusters. However, it would not influence the clusters weak lensing signal. Therefore, by comparing X-ray and weak lensing profiles, one can place upper limits on the strength of a fifth force. This technique has been attempted before using a single, nearby cluster (Coma, z = 0.02). Here we apply the technique to the stacked profiles of 58 clusters at higher redshifts (0.1 R0| R0| on cosmological scales. We hope to improve this constraint in future by extending the study to hundreds of clusters using data from the Dark Energy Survey