Semidirect product decomposition of Coxeter groups

Let $(W,S)$ be a Coxeter system, let $S=I \dot{\cup} J$ be a partition of $S$ such that no element of $I$ is conjugate to an element of $J$, let $\widetilde{J}$ be the set of $W_I$-conjugates of elements of $J$ and let $\widetilde{W}$ be the subgroup of $W$ generated by $\widetilde{J}$. We show that $W=\widetilde{W} \rtimes W_I$ and that $(\widetilde{W},\widetilde{J})$ is a Coxeter system.Comment: 28 pages, one table. We have added some comments on parabolic subgroups, double cosets representatives, finite and affine Weyl groups, invariant theory, Solomon descent algebr

Mapping of the EQ-5D index from clinical outcome measures and demographic variables in patients with coronary heart disease.

RIGHTS : This article is licensed under the BioMed Central licence at http://www.biomedcentral.com/about/license which is similar to the 'Creative Commons Attribution Licence'. In brief you may : copy, distribute, and display the work; make derivative works; or make commercial use of the work - under the following conditions: the original author must be given credit; for any reuse or distribution, it must be made clear to others what the license terms of this work are.BACKGROUND: The EuroQoL 5D (EQ-5D) is a questionnaire that provides a measure of utility for cost-effectiveness analysis. The EQ-5D has been widely used in many patient groups, including those with coronary heart disease. Studies often require patients to complete many questionnaires and the EQ-5D may not be gathered. This study aimed to assess whether demographic and clinical outcome variables, including scores from a disease specific measure, the Seattle Angina Questionnaire (SAQ), could be used to predict, or map, the EQ-5D index value where it is not available. METHODS: Patient-level data from 5 studies of cardiac interventions were used. The data were split into two groups - approximately 60% of the data were used as an estimation dataset for building models, and 40% were used as a validation dataset. Forward ordinary least squares linear regression methods and measures of prediction error were used to build a model to map to the EQ-5D index. Age, sex, a proxy measure of disease stage, Canadian Cardiovascular Society (CCS) angina severity class, treadmill exercise time (ETT) and scales of the SAQ were examined. RESULTS: The exertional capacity (ECS), disease perception (DPS) and anginal frequency scales (AFS) of the SAQ were the strongest predictors of the EQ-5D index and gave the smallest root mean square errors. A final model was chosen with age, gender, disease stage and the ECS, DPS and AFS scales of the SAQ. ETT and CCS did not improve prediction in the presence of the SAQ scales. Bland-Altman agreement between predicted and observed EQ-5D index values was reasonable for values greater than 0.4, but below this level predicted values were higher than observed. The 95% limits of agreement were wide (-0.34, 0.33). CONCLUSIONS: Mapping of the EQ-5D index in cardiac patients from demographics and commonly measured cardiac outcome variables is possible; however, prediction for values of the EQ-5D index below 0.4 was not accurate. The newly designed 5-level version of the EQ-5D with its increased ability to discriminate health states may improve prediction of EQ-5D index values

A review of health utilities using the EQ-5D in studies of cardiovascular disease

RIGHTS : This article is licensed under the BioMed Central licence at http://www.biomedcentral.com/about/license which is similar to the 'Creative Commons Attribution Licence'. In brief you may : copy, distribute, and display the work; make derivative works; or make commercial use of the work - under the following conditions: the original author must be given credit; for any reuse or distribution, it must be made clear to others what the license terms of this work are.Abstract Background The EQ-5D has been extensively used to assess patient utility in trials of new treatments within the cardiovascular field. The aims of this study were to review evidence of the validity and reliability of the EQ-5D, and to summarise utility scores based on the use of the EQ-5D in clinical trials and in studies of patients with cardiovascular disease. Methods A structured literature search was conducted using keywords related to cardiovascular disease and EQ-5D. Original research studies of patients with cardiovascular disease that reported EQ-5D results and its measurement properties were included. Results Of 147 identified papers, 66 met the selection criteria, with 10 studies reporting evidence on validity or reliability and 60 reporting EQ-5D responses (VAS or self-classification). Mean EQ-5D index-based scores ranged from 0.24 (SD 0.39) to 0.90 (SD 0.16), while VAS scores ranged from 37 (SD 21) to 89 (no SD reported). Stratification of EQ-5D index scores by disease severity revealed that scores decreased from a mean of 0.78 (SD 0.18) to 0.51 (SD 0.21) for mild to severe disease in heart failure patients and from 0.80 (SD 0.05) to 0.45 (SD 0.22) for mild to severe disease in angina patients. Conclusions The published evidence generally supports the validity and reliability of the EQ-5D as an outcome measure within the cardiovascular area. This review provides utility estimates across a range of cardiovascular subgroups and treatments that may be useful for future modelling of utilities and QALYs in economic evaluations within the cardiovascular area.Published versio

Inferring energy-composition relationships with Bayesian optimization enhances exploration of inorganic materials

Computational exploration of the compositional spaces of materials can provide guidance for synthetic research and thus accelerate the discovery of novel materials. Most approaches employ high-throughput sampling and focus on reducing the time for energy evaluation for individual compositions, often at the cost of accuracy. Here, we present an alternative approach focusing on effective sampling of the compositional space. The learning algorithm PhaseBO optimizes the stoichiometry of the potential target material while improving the probability of and accelerating its discovery without compromising the accuracy of energy evaluation

Relationship between the EQ-5D index and measures of clinical outcomes in selected studies of cardiovascular interventions.

RIGHTS : This article is licensed under the BioMed Central licence at http://www.biomedcentral.com/about/license which is similar to the 'Creative Commons Attribution Licence'. In brief you may : copy, distribute, and display the work; make derivative works; or make commercial use of the work - under the following conditions: the original author must be given credit; for any reuse or distribution, it must be made clear to others what the license terms of this work are.BACKGROUND: The EuroQoL 5D (EQ-5D) has been widely used in studies of cardiac disease, but its measurement properties in this group are not well established. The study aimed to quantify the relationship between measures commonly used in studies of cardiac disease and the EQ-5D index across different levels of disease severity. METHODS: Patient-level data from 7 studies of cardiac interventions were used, which included randomised trials and observational studies. Relationships between the EQ-5D index and commonly used cardiac measures, Canadian Cardiovascular Society (CCS) angina severity class, treadmill exercise time (ETT) and scales of the Seattle Angina Questionnaire (SAQ) were examined. Mixed effects linear regression was used to assess these relationships, with the EQ-5D index as the response. RESULTS: Study sample sizes ranged from 68 to 2419. Mean baseline EQ-5D index ranged from 0.77 in patients at diagnosis (95% CI 0.75, 0.78) to 0.43 in patients with advanced disease (95% CI 0.39, 0.48) and differed significantly across studies (p < 0.001). There was evidence of a ceiling effect in patients at diagnosis. The minimum clinically important difference of a one minute increase in ETT was associated with a 0.019 (95% CI 0.014, 0.025) increase in EQ-5D index. One class increase in CCS was associated with a 0.11 (95% CI 0.09, 0.13) decrease in EQ-5D index. A 10 unit increase in SAQ scales was associated with increases between 0.04 and 0.07 in EQ-5D index (95% CIs 0.03, 0.05 and 0.05, 0.08). Tests of heterogeneity indicated the EQ-5D-covariate relationships were consistent across levels of disease severity for ETT and the treatment satisfaction scale of the SAQ, but heterogeneous for age, gender, CCS angina class and other scales of the SAQ. CONCLUSION: The EQ-5D index varies with coronary disease severity. The relationship between the EQ-5D index and an outcome measure used in cardiac intervention studies, ETT, was consistent across disease severity levels, but the relationship between demographic variables, CCS angina class and most of the SAQ scales and the EQ-5D index was heterogeneous for patients with different levels of coronary disease. Differences in the EQ-5D index associated with clinically important differences in cardiac measures can be quantified and vary between three important examples - angina class, ETT and SAQ

Visible Light Photo-oxidation of Model Pollutants Using CaCu3Ti4O12: An Experimental and Theoretical Study of Optical Properties, Electronic Structure, and Selectivity

[Image: see text] Charge transfer between metal ions occupying distinct crystallographic sublattices in an ordered material is a strategy to confer visible light absorption on complex oxides to generate potentially catalytically active electron and hole charge carriers. CaCu(3)Ti(4)O(12) has distinct octahedral Ti(4+) and square planar Cu(2+) sites and is thus a candidate material for this approach. The sol−gel synthesis of high surface area CaCu(3)Ti(4)O(12) and investigation of its optical absorption and photocatalytic reactivity with model pollutants are reported. Two gaps of 2.21 and 1.39 eV are observed in the visible region. These absorptions are explained by LSDA+U electronic structure calculations, including electron correlation on the Cu sites, as arising from transitions from a Cu-hybridized O 2p-derived valence band to localized empty states on Cu (attributed to the isolation of CuO(4) units within the structure of CaCu(3)Ti(4)O(12)) and to a Ti-based conduction band. The resulting charge carriers produce selective visible light photodegradation of 4-chlorophenol (monitored by mass spectrometry) by Pt-loaded CaCu(3)Ti(4)O(12) which is attributed to the chemical nature of the photogenerated charge carriers and has a quantum yield comparable with commercial visible light photocatalysts

Conformational control of structure and guest uptake by a tripeptide-based porous material

Chemical processes often rely on the selective sorting and transformation of molecules according to their size, shape and chemical functionality. For example, porous materials such as zeolites achieve the required selectivity through the constrained pore dimensions of a single structure.1 In contrast, proteins function by navigating between multiple metastable structures using bond rotations of the polypeptide,2,3 where each structure lies in one of the minima of a conformational energy landscape and can be selected according to the chemistry of the molecules interacting with the protein.3 Here we show that rotation about covalent bonds in a peptide linker can change a flexible metal-organic framework (MOF) to afford nine distinct crystal structures, revealing a conformational energy landscape characterised by multiple structural minima. The uptake of small molecule guests by the MOF can be chemically triggered by inducing peptide conformational change. This change transforms the material from a minimum on the landscape that is inactive for guest sorption to an active one. Chemical control of the conformation of a flexible organic linker offers a route to modify the pore geometry and internal surface chemistry and thus the function of open-framework materials

Element selection for functional materials discovery by integrated machine learning of atomic contributions to properties

At the high level, the fundamental differences between materials originate from the unique nature of the constituent chemical elements. Before specific differences emerge according to the precise ratios of elements (composition) in a given crystal structure (phase), the material can be represented by its phase field defined simply as the set of the constituent chemical elements. Classification of the materials at the level of their phase fields can accelerate materials discovery by selecting the elemental combinations that are likely to produce desirable functional properties in synthetically accessible materials. Here, we demonstrate that classification of the materials phase field with respect to the maximum expected value of a target functional property can be combined with the ranking of the materials synthetic accessibility. This end-to-end machine learning approach (PhaseSelect) first derives the atomic characteristics from the compositional environments in all computationally and experimentally explored materials and then employs these characteristics to classify the phase field by their merit. PhaseSelect can quantify the materials potential at the level of the periodic table, which we demonstrate with significant accuracy for three avenues of materials applications: high-temperature superconducting, high-temperature magnetic and targetted energy band gap materials

Computationally Assisted Identification of Functional Inorganic Materials

Modules of Desire Using computational methods to design materials with specific properties has found some limited success. Dyer et al. (p. 847 , published online 11 April) have devised a method, based on extended module materials assembly, that combines chemical intuition and ab initio calculations starting from fragments or modules of structure types that show the desired functionality. The method was tested by identifying materials suitable for a solid oxide fuel cell cathode. </jats:p