Symmetric informationally complete positive operator valued measure and probability representation of quantum mechanics

Symmetric informationally complete positive operator valued measures (SIC-POVMs) are studied within the framework of the probability representation of quantum mechanics. A SIC-POVM is shown to be a special case of the probability representation. The problem of SIC-POVM existence is formulated in terms of symbols of operators associated with a star-product quantization scheme. We show that SIC-POVMs (if they do exist) must obey general rules of the star product, and, starting from this fact, we derive new relations on SIC-projectors. The case of qubits is considered in detail, in particular, the relation between the SIC probability representation and other probability representations is established, the connection with mutually unbiased bases is discussed, and comments to the Lie algebraic structure of SIC-POVMs are presented.Comment: 22 pages, 1 figure, LaTeX, partially presented at the Workshop "Nonlinearity and Coherence in Classical and Quantum Systems" held at the University "Federico II" in Naples, Italy on December 4, 2009 in honor of Prof. Margarita A. Man'ko in connection with her 70th birthday, minor misprints are corrected in the second versio

nIFTy Galaxy Cluster simulations VI: The dynamical imprint of substructure on gaseous cluster outskirts

Galaxy cluster outskirts mark the transition region from the mildly non-linear cosmic web to the highly non-linear, virialised, cluster interior. It is in this transition region that the intra-cluster medium (ICM) begins to influence the properties of accreting galaxies and groups, as ram pressure impacts a galaxy's cold gas content and subsequent star formation rate. Conversely, the thermodynamical properties of the ICM in this transition region should also feel the influence of accreting substructure (i.e. galaxies and groups), whose passage can drive shocks. In this paper, we use a suite of cosmological hydrodynamical zoom simulations of a single galaxy cluster, drawn from the nIFTy comparison project, to study how the dynamics of substructure accreted from the cosmic web influences the thermodynamical properties of the ICM in the cluster's outskirts. We demonstrate how features evident in radial profiles of the ICM (e.g. gas density and temperature) can be linked to strong shocks, transient and short-lived in nature, driven by the passage of substructure. The range of astrophysical codes and galaxy formation models in our comparison are broadly consistent in their predictions (e.g. agreeing when and where shocks occur, but differing in how strong shocks will be); this is as we would expect of a process driven by large-scale gravitational dynamics and strong, inefficiently radiating, shocks. This suggests that mapping such shock structures in the ICM in a cluster's outskirts (via e.g. radio synchrotron emission) could provide a complementary measure of its recent merger and accretion history

Gene Function Classification Using Bayesian Models with Hierarchy-Based Priors

We investigate the application of hierarchical classification schemes to the annotation of gene function based on several characteristics of protein sequences including phylogenic descriptors, sequence based attributes, and predicted secondary structure. We discuss three Bayesian models and compare their performance in terms of predictive accuracy. These models are the ordinary multinomial logit (MNL) model, a hierarchical model based on a set of nested MNL models, and a MNL model with a prior that introduces correlations between the parameters for classes that are nearby in the hierarchy. We also provide a new scheme for combining different sources of information. We use these models to predict the functional class of Open Reading Frames (ORFs) from the E. coli genome. The results from all three models show substantial improvement over previous methods, which were based on the C5 algorithm. The MNL model using a prior based on the hierarchy outperforms both the non-hierarchical MNL model and the nested MNL model. In contrast to previous attempts at combining these sources of information, our approach results in a higher accuracy rate when compared to models that use each data source alone. Together, these results show that gene function can be predicted with higher accuracy than previously achieved, using Bayesian models that incorporate suitable prior information

nIFTY galaxy cluster simulations - III. The similarity and diversity of galaxies and subhaloes

We examine subhaloes and galaxies residing in a simulated $\Lambda$ cold dark matter galaxy cluster ($M^{crit} _{200}$ = 1.1 × 10$^{15}$ $h^{−1}$ M$_\odot$) produced by hydrodynamical codes ranging from classic smooth particle hydrodynamics (SPH), newer SPH codes, adaptive and moving mesh codes. These codes use subgrid models to capture galaxy formation physics. We compare how well these codes reproduce the same subhaloes/galaxies in gravity-only, non-radiative hydrodynamics and $\textit{full feedback physics}$ runs by looking at the overall subhalo/galaxy distribution and on an individual object basis. We find that the subhalo population is reproduced to within $\lesssim$10 per cent for both dark matter only and non-radiative runs, with individual objects showing code-to-code scatter of $\lesssim$0.1 dex, although the gas in non-radiative simulations shows significant scatter. Including feedback physics significantly increases the diversity. Subhalo mass and $V_{max}$ distributions vary by ≈20 per cent. The galaxy populations also show striking code-to-code variations. Although the Tully–Fisher relation is similar in almost all codes, the number of galaxies with 10$^9$ $h^{−1}$ M$_\odot$ $\lesssim$ $M_∗$ $\lesssim$ 10$^{12}$ $h^{−1}$ M$_\odot$ can differ by a factor of 4. Individual galaxies show code-to-code scatter of ~0.5 dex in stellar mass. Moreover, systematic differences exist, with some codes producing galaxies 70 per cent smaller than others. The diversity partially arises from the inclusion/absence of active galactic nucleus feedback. Our results combined with our companion papers demonstrate that subgrid physics is not just subject to fine-tuning, but the complexity of building galaxies $\textit{in all environments}$ remains a challenge. We argue that even basic galaxy properties, such as stellar mass to halo mass, should be treated with errors bars of ~0.2–0.4 dex

nIFTY galaxy cluster simulations - III. The similarity and diversity of galaxies and subhaloes

We examine subhaloes and galaxies residing in a simulated $\Lambda$ cold dark matter galaxy cluster ($M^{crit} _{200}$ = 1.1 × 10$^{15}$ $h^{−1}$ M$_\odot$) produced by hydrodynamical codes ranging from classic smooth particle hydrodynamics (SPH), newer SPH codes, adaptive and moving mesh codes. These codes use subgrid models to capture galaxy formation physics. We compare how well these codes reproduce the same subhaloes/galaxies in gravity-only, non-radiative hydrodynamics and $\textit{full feedback physics}$ runs by looking at the overall subhalo/galaxy distribution and on an individual object basis. We find that the subhalo population is reproduced to within $\lesssim$10 per cent for both dark matter only and non-radiative runs, with individual objects showing code-to-code scatter of $\lesssim$0.1 dex, although the gas in non-radiative simulations shows significant scatter. Including feedback physics significantly increases the diversity. Subhalo mass and $V_{max}$ distributions vary by ≈20 per cent. The galaxy populations also show striking code-to-code variations. Although the Tully–Fisher relation is similar in almost all codes, the number of galaxies with 10$^9$ $h^{−1}$ M$_\odot$ $\lesssim$ $M_∗$ $\lesssim$ 10$^{12}$ $h^{−1}$ M$_\odot$ can differ by a factor of 4. Individual galaxies show code-to-code scatter of ~0.5 dex in stellar mass. Moreover, systematic differences exist, with some codes producing galaxies 70 per cent smaller than others. The diversity partially arises from the inclusion/absence of active galactic nucleus feedback. Our results combined with our companion papers demonstrate that subgrid physics is not just subject to fine-tuning, but the complexity of building galaxies $\textit{in all environments}$ remains a challenge. We argue that even basic galaxy properties, such as stellar mass to halo mass, should be treated with errors bars of ~0.2–0.4 dex

Tritium and 14 C background levels in pristine aquatic systems and their potential sources of variability

C Aquatic systems Background levels Global fallout Regional scale a b s t r a c t Tritium and 14 C are currently the two main radionuclides discharged by nuclear industry. Tritium integrates into and closely follows the water cycle and, as shown recently the carbon cycle, as does 14 C (Eyrolle-Boyer et al., 2014a, b). As a result, these two elements persist in both terrestrial and aquatic environments according to the recycling rates of organic matter. Although on average the organically bound tritium (OBT) activity of sediments in pristine rivers does not significantly differ today (2007 e2012) from the mean tritiated water (HTO) content on record for rainwater (2.4 ± 0.6 Bq/L and 1.6 ± 0.4 Bq/L, respectively), regional differences are expected depending on the biomass inventories affected by atmospheric global fallout from nuclear testing and the recycling rate of organic matter within watersheds. The results obtained between 2007 and 2012 for 14 C show that the levels varied between 94.5 ± 1.5 and 234 ± 2.7 Bq/kg of C for the sediments in French rivers and across a slightly higher range of 199 ± 1.3 to 238 ± 3.1 Bq/kg of C for fish. This variation is most probably due to preferential uptake of some organic carbon compounds by fish restraining 14 C dilution with refractory organic carbon and/or with old carbonates both depleted in 14 C. Overall, most of these ranges of values are below the mean baseline value for the terrestrial environment (232.0 ± 1.8 Bq/kg of C in 2012, Roussel-Debet, 2014a) in relation to dilution by the carbonates and/or fossil organic carbon present in aquatic systems. This emphasises yet again the value of establishing regional baseline value ranges for these two radionuclides in order to account for palaeoclimatic and lithological variations. Besides, our results obtained from sedimentary archive investigation have confirmed the delayed contamination of aquatic sediments by tritium from the past nuclear tests atmospheric fallout, as recently demonstrated from data chronicles (Eyrolle-Boyer et al., 2014a,b). Thus Sedimentary archives can be successfully used to reconstruct past 14 C and OBT levels. Additionally, sediment repositories potentially represent significant storages of OBT that may account for in case of further remobilisation. We finally show that floods can significantly affect the OBT and 14 C levels within suspended particles or sediments depending on the origin of particles reinforcing the need to acquire baseline value range at a regional scale

nIFTy galaxy cluster simulations – V. Investigation of the cluster infall region

We examine the properties of the galaxies and dark matter haloes residing in the cluster infall region surrounding the simulated $\Lambda$ cold dark matter galaxy cluster studied by Elahi et al. at $z$ = 0. The 1.1 × 10$^{15}$ $h^{−1}$ M$_\odot$ galaxy cluster has been simulated with eight different hydrodynamical codes containing a variety of hydrodynamic solvers and sub-grid schemes. All models completed a dark-matter-only, non-radiative and full-physics run from the same initial conditions. The simulations contain dark matter and gas with mass resolution $m_\text{DM}$ = 9.01 × 10$^8$ $h^{−1}$ M$_\odot$ and $m_\text{gas}$ = 1.9 × 10$^8$ $h^{−1}$ M$_\odot$, respectively. We find that the synthetic cluster is surrounded by clear filamentary structures that contain ~60 per cent of haloes in the infall region with mass ~10$^{12.5}$–10$^{14}$ $h^{−1}$ M$_\odot$, including 2–3 group-sized haloes (>10$^{13}$ $h^{−1}$ M$_\odot$). However, we find that only ~10 per cent of objects in the infall region are sub-haloes residing in haloes, which may suggest that there is not much ongoing pre-processing occurring in the infall region at $z$ = 0. By examining the baryonic content contained within the haloes, we also show that the code-to-code scatter in stellar fraction across all halo masses is typically ~2 orders of magnitude between the two most extreme cases, and this is predominantly due to the differences in sub-grid schemes and calibration procedures that each model uses. Models that do not include active galactic nucleus feedback typically produce too high stellar fractions compared to observations by at least ~1 order of magnitude.The authors would like the acknowledge the Centre for High Performance Computing in Rosebank, Cape Town, for financial support and for hosting the ‘Comparison Cape Town’ workshop in 2016, July. The authors would further like to acknowledge the support of the International Centre for Radio Astronomy Research (ICRAR) node at the University of Western Australia (UWA) in hosting the precursor workshop ‘Perth Simulated Cluster Comparison’ in 2015, March; the financial support of the UWA Research Collaboration Award 2014 and 2015 schemes; the financial support of the ARC Centre of Excellence for All Sky Astrophysics (CAASTRO) CE110001020 and ARC Discovery Projects DP130100117 and DP140100198. We would also like to thank the Instituto de Fisica Teorica (IFT-UAM/CSIC in Madrid) for its support, via the Centro de Excelencia Severo Ochoa Program under Grant No. SEV- 2012-0249, during the three-week workshop ‘nIFTy Cosmology’ in 2014, where the foundation for the whole comparison project was established. JA acknowledges support from a post-graduate award from STFC. PJE is supported by the SSimPL programme and the Sydney Institute for Astronomy (SIfA) and Australian Research Council (ARC) grants DP130100117 and DP140100198. AK is supported by the Ministerio de Econom´ıa y Competitividad (MINECO) in Spain through grant AYA2012-31101 as well as the ConsoliderIngenio 2010 Programme of the Spanish Ministerio de Ciencia e Innovacion (MICINN) under grant MultiDark CSD2009-00064. ´ He also acknowledges support from the ARC grant DP140100198. He further thanks Noonday Underground for surface noise. STK acknowledges support from STFC through grant ST/L000768/1. CP acknowledges the support of the ARC through Future Fellowship FT130100041 and Discovery Project DP140100198. WC and CP acknowledge the support of ARC DP130100117. GY and FS acknowledge support from MINECO (Spain) through the grant AYA 2012-31101. GY thanks also the Red Espanola de Supercomputa- ˜ cion for granting the computing time in the Marenostrum Supercomputer at BSC, where all the MUSIC simulations have been performed. AMB is supported by the DFG Research Unit 1254 ‘Magnetisation of interstellar and intergalactic media’ and by the DFG Cluster of Excellence ‘Universe’. GM acknowledge support from the PRIN-MIUR 2012 Grant ‘The Evolution of Cosmic Baryons’ funded by the Italian Minister of University and Research, by the PRIN-INAF 2012 Grant ‘Multi-scale Simulations of Cosmic Structures’, by the INFN INDARK Grant and by the ‘Consorzio per la Fisica di Trieste’. IGM acknowledges support from an STFC Advanced Fellowship. EP acknowledges support by the ERC grant ‘The Emergence of Structure During the Epoch of Reionization’

Potentially inappropriate medication in older participants of the Berlin Aging Study II (BASE-II) - Sex differences and associations with morbidity and medication use

INTRODUCTION: Multimorbidity in advanced age and the need for drug treatment may lead to polypharmacy, while pharmacokinetic and pharmacodynamic changes may increase the risk of adverse drug events (ADEs). OBJECTIVE: The aim of this study was to determine the proportion of subjects using potentially inappropriate medication (PIM) in a cohort of older and predominantly healthy adults in relation to polypharmacy and morbidity. METHODS: Cross-sectional data were available from 1,382 study participants (median age 69 years, IQR 67-71, 51.3% females) of the Berlin Aging Study II (BASE-II). PIM was classified according to the EU(7)-PIM and German PRISCUS (representing a subset of the former) list. Polypharmacy was defined as the concomitant use of at least five drugs. A morbidity index (MI) largely based on the Charlson Index was applied to evaluate the morbidity burden. RESULTS: Overall, 24.1% of the participants were affected by polypharmacy. On average, men used 2 (IQR 1-4) and women 3 drugs (IQR 1-5). According to PRISCUS and EU(7)-PIM, 5.9% and 22.6% of participants received at least one PIM, while use was significantly more prevalent in females (25.5%) compared to males (19.6%) considering EU(7)-PIM (p = 0.01). In addition, morbidity in males receiving PIM according to EU(7)-PIM was higher (median MI 1, IQR 1-3) compared to males without PIM use (median MI 1, IQR 0-2, p<0.001). CONCLUSION: PIM use occurred more frequently in women than in men, while it was associated with higher morbidity in males. As expected, EU(7)-PIM identifies more subjects as PIM users than the PRISCUS list but further studies are needed to investigate the differential impact of both lists on ADEs and outcome. KEY POINTS: We found PIM use to be associated with a higher number of regular medications and with increased morbidity. Additionally, we detected a higher prevalence of PIM use in females compared to males, suggesting that women and people needing intensive drug treatment are patient groups, who are particularly affected by PIM use