First cohomology for finite groups of Lie type: simple modules with small dominant weights

Let $k$ be an algebraically closed field of characteristic $p > 0$, and let $G$ be a simple, simply connected algebraic group defined over $\mathbb{F}_p$. Given $r \geq 1$, set $q=p^r$, and let $G(\mathbb{F}_q)$ be the corresponding finite Chevalley group. In this paper we investigate the structure of the first cohomology group $H^1(G(\mathbb{F}_q),L(\lambda))$ where $L(\lambda)$ is the simple $G$-module of highest weight $\lambda$. Under certain very mild conditions on $p$ and $q$, we are able to completely describe the first cohomology group when $\lambda$ is less than or equal to a fundamental dominant weight. In particular, in the cases we consider, we show that the first cohomology group has dimension at most one. Our calculations significantly extend, and provide new proofs for, earlier results of Cline, Parshall, Scott, and Jones, who considered the special case when $\lambda$ is a minimal nonzero dominant weight.Comment: 24 pages, 5 figures, 6 tables. Typos corrected and some proofs streamlined over previous versio

Three tools for managing vertigo in the frontline

Vertigo is a challenging symptom in general practice. With access to three tools – a focused history, eye examination and a management algorithm – a large proportion of vertiginous patients could be managed effectively by GPs. This practical guide seeks to increase the skills and confidence of frontline practitioners when managing vertigo

Second cohomology for finite groups of Lie type

Let $G$ be a simple, simply-connected algebraic group defined over $\mathbb{F}_p$. Given a power $q = p^r$ of $p$, let $G(\mathbb{F}_q) \subset G$ be the subgroup of $\mathbb{F}_q$-rational points. Let $L(\lambda)$ be the simple rational $G$-module of highest weight $\lambda$. In this paper we establish sufficient criteria for the restriction map in second cohomology $H^2(G,L(\lambda)) \rightarrow H^2(G(\mathbb{F}_q),L(\lambda))$ to be an isomorphism. In particular, the restriction map is an isomorphism under very mild conditions on $p$ and $q$ provided $\lambda$ is less than or equal to a fundamental dominant weight. Even when the restriction map is not an isomorphism, we are often able to describe $H^2(G(\mathbb{F}_q),L(\lambda))$ in terms of rational cohomology for $G$. We apply our techniques to compute $H^2(G(\mathbb{F}_q),L(\lambda))$ in a wide range of cases, and obtain new examples of nonzero second cohomology for finite groups of Lie type.Comment: 29 pages, GAP code included as an ancillary file. Rewritten to include the adjoint representation in types An, B2, and Cn. Corrections made to Theorem 3.1.3 and subsequent dependent results in Sections 3-4. Additional minor corrections and improvements also implemente

PaLM 2 Technical Report

We introduce PaLM 2, a new state-of-the-art language model that has better multilingual and reasoning capabilities and is more compute-efficient than its predecessor PaLM. PaLM 2 is a Transformer-based model trained using a mixture of objectives. Through extensive evaluations on English and multilingual language, and reasoning tasks, we demonstrate that PaLM 2 has significantly improved quality on downstream tasks across different model sizes, while simultaneously exhibiting faster and more efficient inference compared to PaLM. This improved efficiency enables broader deployment while also allowing the model to respond faster, for a more natural pace of interaction. PaLM 2 demonstrates robust reasoning capabilities exemplified by large improvements over PaLM on BIG-Bench and other reasoning tasks. PaLM 2 exhibits stable performance on a suite of responsible AI evaluations, and enables inference-time control over toxicity without additional overhead or impact on other capabilities. Overall, PaLM 2 achieves state-of-the-art performance across a diverse set of tasks and capabilities. When discussing the PaLM 2 family, it is important to distinguish between pre-trained models (of various sizes), fine-tuned variants of these models, and the user-facing products that use these models. In particular, user-facing products typically include additional pre- and post-processing steps. Additionally, the underlying models may evolve over time. Therefore, one should not expect the performance of user-facing products to exactly match the results reported in this report

Safety and efficacy of fluoxetine on functional outcome after acute stroke (AFFINITY): a randomised, double-blind, placebo-controlled trial

Background Trials of fluoxetine for recovery after stroke report conflicting results. The Assessment oF FluoxetINe In sTroke recoverY (AFFINITY) trial aimed to show if daily oral fluoxetine for 6 months after stroke improves functional outcome in an ethnically diverse population. Methods AFFINITY was a randomised, parallel-group, double-blind, placebo-controlled trial done in 43 hospital stroke units in Australia (n=29), New Zealand (four), and Vietnam (ten). Eligible patients were adults (aged ≥18 years) with a clinical diagnosis of acute stroke in the previous 2–15 days, brain imaging consistent with ischaemic or haemorrhagic stroke, and a persisting neurological deficit that produced a modified Rankin Scale (mRS) score of 1 or more. Patients were randomly assigned 1:1 via a web-based system using a minimisation algorithm to once daily, oral fluoxetine 20 mg capsules or matching placebo for 6 months. Patients, carers, investigators, and outcome assessors were masked to the treatment allocation. The primary outcome was functional status, measured by the mRS, at 6 months. The primary analysis was an ordinal logistic regression of the mRS at 6 months, adjusted for minimisation variables. Primary and safety analyses were done according to the patient's treatment allocation. The trial is registered with the Australian New Zealand Clinical Trials Registry, ACTRN12611000774921. Findings Between Jan 11, 2013, and June 30, 2019, 1280 patients were recruited in Australia (n=532), New Zealand (n=42), and Vietnam (n=706), of whom 642 were randomly assigned to fluoxetine and 638 were randomly assigned to placebo. Mean duration of trial treatment was 167 days (SD 48·1). At 6 months, mRS data were available in 624 (97%) patients in the fluoxetine group and 632 (99%) in the placebo group. The distribution of mRS categories was similar in the fluoxetine and placebo groups (adjusted common odds ratio 0·94, 95% CI 0·76–1·15; p=0·53). Compared with patients in the placebo group, patients in the fluoxetine group had more falls (20 [3%] vs seven [1%]; p=0·018), bone fractures (19 [3%] vs six [1%]; p=0·014), and epileptic seizures (ten [2%] vs two [<1%]; p=0·038) at 6 months. Interpretation Oral fluoxetine 20 mg daily for 6 months after acute stroke did not improve functional outcome and increased the risk of falls, bone fractures, and epileptic seizures. These results do not support the use of fluoxetine to improve functional outcome after stroke

Orthodontia-implantology-prosthodontics in rare diseases: the oligodontia example

Among rare diseases, a fifth of them are associated with oral manifestations. The most frequent are: enamel dysplasia, cleft lip or palate and oligodontia. Beside the pathology, patients are eager of functional therapeutics which often needs prosthodontics. This oral rehabilitation aims to a better life quality. Teeth absence management in the case of oligodontia necessitates critical analysis of the supporting tissues: the periodontium and the underlying bone. Deciduous teeth with resorbed roots and hypoplasic permanent teeth are often observed. Thus, some questions arise: can we use them as abutments or can we restore them knowing that they present an anomaly in their position and are more fragile? How do we replace many teeth when bone is lacking (clefts, agenesis)? Can we implant on a missing tooth site or can we use autograft? What do we expect for periodontal healing? Adjacent teeth have often migrated, occlusion is unstable due to mixed dentition and patient’s disease. For example, in mandibular incisors agenesis cases, the remaining deciduous teeth are used when consultation happens at adolescence. This results in upper jaw incisors migration toward mandible and thus an anterior overbite. Orthodontic treatments will allow to recreate gap width and a normal occlusion in order to perform prosthodontics treatment in the best possible conditions. Giving the weak dental and periodontal supports, our attention will be focused on choosing the best option between tooth and implant supported prosthodontics. During the mixed dentition, orthodontic treatment and aesthetic rehabilitation have to be planed at the same time and to last until “definitive” implant and periodontal therapies are possible. In this article, we will present one oligodontia case report to illustrate a possible solution

Interaction orthodontie-implantologie et prothèse dans les maladies rares l’exemple des oligodonties

Pour au moins un cinquième des maladies rares, des manifestations bucco-dentaires variées sont associées telles, les plus fréquemment diagnostiquées : les dysplasies amélaires, les séquelles de fente, les oligodonties. Au-delà de la maladie elle-même, les patients sont souvent demandeurs d’une réhabilitation dentaire fonctionnelle et souvent prothétique pour assurer une qualité de vie dentaire compatible avec leur vie quotidienne. La prise en charge des édentements observés dans le cadre d’oligodontie implique une analyse critique de la qualité du support dentaire et parodontal sous-jacent. Il est fréquemment observé des dents permanentes hypoplasiques et des persistances de dents temporaires rhizalysées. Comment alors s’en servir au mieux comme appui ou les restaurer dès lors qu’elles reposent dans un support fragile ou sont mal positionnées ? Comment remplacer une ou plusieurs dents quand l’os est en quantité moindre (fente avéolopalatine, agénésies) ? Peut-on implanter sur un site d’agénésie ou en zone de greffe autologue ? ,4 quelles difficultés parodontales doit-on s’attendre ? Très souvent, les dents collatérales se sont déplacées, le schéma occlusal est instable de par la phase de denture mixte mais aussi induit parla maladie. Ainsi, lorsque manquent les incisives mandibulaires, les dents déciduales sont-elles souvent bien usées lorsque le patient jeune adulte vient consulter et qu’il est objectivé cliniquement une égression des incisives maxillaires et un recouvrement important. Dès lors, il semble nécessaire d’avoir recours à l’orthodontie pour recréer les espaces et rétablir un schéma occlusal cohérent avec les attentes prothétiques. Faut-il enfin privilégier les solutions prothétiques implanto-portées ou dentoportées quand souvent à la fois les supports dentaires et parodontaux disposent d’une faible valeur intrinsèque et extrinsèque ? La nécessité de corréler le traitement orthodontique et la réponse prothétique esthétique est souvent concomitante à la phase de denture mixte jusqu’au moment où la thérapeutique implantaire et parodontale définitive seront possibles. Nous développerons quelques éléments de réponse illustrés à travers un cas d’oligodontie

Twelve-Month Outcomes of the AFFINITY Trial of Fluoxetine for Functional Recovery After Acute Stroke: AFFINITY Trial Steering Committee on Behalf of the AFFINITY Trial Collaboration

Background and Purpose: The AFFINITY trial (Assessment of Fluoxetine in Stroke Recovery) reported that oral fluoxetine 20 mg daily for 6 months after acute stroke did not improve functional outcome and increased the risk of falls, bone fractures, and seizures. After trial medication was ceased at 6 months, survivors were followed to 12 months post-randomization. This preplanned secondary analysis aimed to determine any sustained or delayed effects of fluoxetine at 12 months post-randomization. Methods: AFFINITY was a randomized, parallel-group, double-blind, placebo-controlled trial in adults (n=1280) with a clinical diagnosis of stroke in the previous 2 to 15 days and persisting neurological deficit who were recruited at 43 hospital stroke units in Australia (n=29), New Zealand (4), and Vietnam (10) between 2013 and 2019. Participants were randomized to oral fluoxetine 20 mg once daily (n=642) or matching placebo (n=638) for 6 months and followed until 12 months after randomization. The primary outcome was function, measured by the modified Rankin Scale, at 6 months. Secondary outcomes for these analyses included measures of the modified Rankin Scale, mood, cognition, overall health status, fatigue, health-related quality of life, and safety at 12 months. Results: Adherence to trial medication was for a mean 167 (SD 48) days and similar between randomized groups. At 12 months, the distribution of modified Rankin Scale categories was similar in the fluoxetine and placebo groups (adjusted common odds ratio, 0.93 [95% CI, 0.76–1.14]; P =0.46). Compared with placebo, patients allocated fluoxetine had fewer recurrent ischemic strokes (14 [2.18%] versus 29 [4.55%]; P =0.02), and no longer had significantly more falls (27 [4.21%] versus 15 [2.35%]; P =0.08), bone fractures (23 [3.58%] versus 11 [1.72%]; P =0.05), or seizures (11 [1.71%] versus 8 [1.25%]; P =0.64) at 12 months. Conclusions: Fluoxetine 20 mg daily for 6 months after acute stroke had no delayed or sustained effect on functional outcome, falls, bone fractures, or seizures at 12 months poststroke. The lower rate of recurrent ischemic stroke in the fluoxetine group is most likely a chance finding. REGISTRATION: URL: http://www.anzctr.org.au/ ; Unique identifier: ACTRN12611000774921