From Atiyah Classes to Homotopy Leibniz Algebras

A celebrated theorem of Kapranov states that the Atiyah class of the tangent bundle of a complex manifold $X$ makes $T_X[-1]$ into a Lie algebra object in $D^+(X)$, the bounded below derived category of coherent sheaves on $X$. Furthermore Kapranov proved that, for a K\"ahler manifold $X$, the Dolbeault resolution $\Omega^{\bullet-1}(T_X^{1,0})$ of $T_X[-1]$ is an $L_\infty$ algebra. In this paper, we prove that Kapranov's theorem holds in much wider generality for vector bundles over Lie pairs. Given a Lie pair $(L,A)$, i.e. a Lie algebroid $L$ together with a Lie subalgebroid $A$, we define the Atiyah class $\alpha_E$ of an $A$-module $E$ (relative to $L$) as the obstruction to the existence of an $A$-compatible $L$-connection on $E$. We prove that the Atiyah classes $\alpha_{L/A}$ and $\alpha_E$ respectively make $L/A[-1]$ and $E[-1]$ into a Lie algebra and a Lie algebra module in the bounded below derived category $D^+(\mathcal{A})$, where $\mathcal{A}$ is the abelian category of left $\mathcal{U}(A)$-modules and $\mathcal{U}(A)$ is the universal enveloping algebra of $A$. Moreover, we produce a homotopy Leibniz algebra and a homotopy Leibniz module stemming from the Atiyah classes of $L/A$ and $E$, and inducing the aforesaid Lie structures in $D^+(\mathcal{A})$.Comment: 36 page

Increased EZH2 expression in prostate cancer is associated with metastatic recurrence following external beam radiotherapy

Background Enhancer of zeste 2 (EZH2) promotes prostate cancer progression. We hypothesized that increased EZH2 expression is associated with postradiotherapy metastatic disease recurrence, and may promote radioresistance. Methods EZH2 expression was investigated using immunohistochemistry in diagnostic prostate biopsies of 113 prostate cancer patients treated with radiotherapy with curative intent. Associations between EZH2 expression in malignant and benign tissue in prostate biopsy cores and outcomes were investigated using univariate and multivariate Cox regression analyses. LNCaP and PC3 cell radiosensitivity was investigated using colony formation and γH2AX assays following UNC1999 chemical probe‐mediated EZH2 inhibition. Results While there was no significant association between EZH2 expression and biochemical recurrence following radiotherapy, univariate analysis revealed that prostate cancer cytoplasmic and total EZH2 expression were significantly associated with metastasis development postradiotherapy (P = 0.034 and P = 0.003, respectively). On multivariate analysis, the prostate cancer total EZH2 expression score remained statistically significant (P = 0.003), while cytoplasmic EZH2 expression did not reach statistical significance (P = 0.053). No association was observed between normal adjacent prostate EZH2 expression and biochemical recurrence or metastasis. LNCaP and PC3 cell treatment with UNC1999 reduced histone H3 lysine 27 tri‐methylation levels. Irradiation of LNCaP or PC3 cells with a single 2 Gy fraction with UNC1999‐mediated EZH2 inhibition resulted in a statistically significant, though modest, reduction in cell colony number for both cell lines. Increased γH2AX foci were observed 24 hours after ionizing irradiation in LNCaP cells, but not in PC3, following UNC1999‐mediated EZH2 inhibition vs controls. Conclusions Taken together, these results reveal that high pretreatment EZH2 expression in prostate cancer in diagnostic biopsies is associated with an increased risk of postradiotherapy metastatic disease recurrence, but EZH2 function may only at most play a modest role in promoting prostate cancer cell radioresistance

Scale-free static and dynamical correlations in melts of monodisperse and Flory-distributed homopolymers: A review of recent bond-fluctuation model studies

It has been assumed until very recently that all long-range correlations are screened in three-dimensional melts of linear homopolymers on distances beyond the correlation length $\xi$ characterizing the decay of the density fluctuations. Summarizing simulation results obtained by means of a variant of the bond-fluctuation model with finite monomer excluded volume interactions and topology violating local and global Monte Carlo moves, we show that due to an interplay of the chain connectivity and the incompressibility constraint, both static and dynamical correlations arise on distances $r \gg \xi$. These correlations are scale-free and, surprisingly, do not depend explicitly on the compressibility of the solution. Both monodisperse and (essentially) Flory-distributed equilibrium polymers are considered.Comment: 60 pages, 49 figure

The Origin, Early Evolution and Predictability of Solar Eruptions

Coronal mass ejections (CMEs) were discovered in the early 1970s when space-borne coronagraphs revealed that eruptions of plasma are ejected from the Sun. Today, it is known that the Sun produces eruptive flares, filament eruptions, coronal mass ejections and failed eruptions; all thought to be due to a release of energy stored in the coronal magnetic field during its drastic reconfiguration. This review discusses the observations and physical mechanisms behind this eruptive activity, with a view to making an assessment of the current capability of forecasting these events for space weather risk and impact mitigation. Whilst a wealth of observations exist, and detailed models have been developed, there still exists a need to draw these approaches together. In particular more realistic models are encouraged in order to asses the full range of complexity of the solar atmosphere and the criteria for which an eruption is formed. From the observational side, a more detailed understanding of the role of photospheric flows and reconnection is needed in order to identify the evolutionary path that ultimately means a magnetic structure will erupt

Reporting guideline for the early stage clinical evaluation of decision support systems driven by artificial intelligence: DECIDE-AI

A growing number of artificial intelligence (AI)-based clinical decision support systems are showing promising performance in preclinical, in silico, evaluation, but few have yet demonstrated real benefit to patient care. Early stage clinical evaluation is important to assess an AI system’s actual clinical performance at small scale, ensure its safety, evaluate the human factors surrounding its use, and pave the way to further large scale trials. However, the reporting of these early studies remains inadequate. The present statement provides a multistakeholder, consensus-based reporting guideline for the Developmental and Exploratory Clinical Investigations of DEcision support systems driven by Artificial Intelligence (DECIDE-AI). We conducted a two round, modified Delphi process to collect and analyse expert opinion on the reporting of early clinical evaluation of AI systems. Experts were recruited from 20 predefined stakeholder categories. The final composition and wording of the guideline was determined at a virtual consensus meeting. The checklist and the Explanation & Elaboration (E&E) sections were refined based on feedback from a qualitative evaluation process. 123 experts participated in the first round of Delphi, 138 in the second, 16 in the consensus meeting, and 16 in the qualitative evaluation. The DECIDE-AI reporting guideline comprises 17 AI specific reporting items (made of 28 subitems) and 10 generic reporting items, with an E&E paragraph provided for each. Through consultation and consensus with a range of stakeholders, we have developed a guideline comprising key items that should be reported in early stage clinical studies of AI-based decision support systems in healthcare. By providing an actionable checklist of minimal reporting items, the DECIDE-AI guideline will facilitate the appraisal of these studies and replicability of their findings

Reducing the environmental impact of surgery on a global scale: systematic review and co-prioritization with healthcare workers in 132 countries

Background Healthcare cannot achieve net-zero carbon without addressing operating theatres. The aim of this study was to prioritize feasible interventions to reduce the environmental impact of operating theatres. Methods This study adopted a four-phase Delphi consensus co-prioritization methodology. In phase 1, a systematic review of published interventions and global consultation of perioperative healthcare professionals were used to longlist interventions. In phase 2, iterative thematic analysis consolidated comparable interventions into a shortlist. In phase 3, the shortlist was co-prioritized based on patient and clinician views on acceptability, feasibility, and safety. In phase 4, ranked lists of interventions were presented by their relevance to high-income countries and low–middle-income countries. Results In phase 1, 43 interventions were identified, which had low uptake in practice according to 3042 professionals globally. In phase 2, a shortlist of 15 intervention domains was generated. In phase 3, interventions were deemed acceptable for more than 90 per cent of patients except for reducing general anaesthesia (84 per cent) and re-sterilization of ‘single-use’ consumables (86 per cent). In phase 4, the top three shortlisted interventions for high-income countries were: introducing recycling; reducing use of anaesthetic gases; and appropriate clinical waste processing. In phase 4, the top three shortlisted interventions for low–middle-income countries were: introducing reusable surgical devices; reducing use of consumables; and reducing the use of general anaesthesia. Conclusion This is a step toward environmentally sustainable operating environments with actionable interventions applicable to both high– and low–middle–income countries