Visualizing Clustering and Uncertainty Analysis with Multivariate Longitudinal Data.
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The structural evolution in a rapid cooling process of silver melt has been investigated at different scales by adopting several analysis methods. The results testify Ostwald’s rule of stages and Frank conjecture upon icosahedron with many specific details. In particular, the cluster-scale analysis by a recent developed method called LSCA (the Largest Standard Cluster Analysis) clarified the complex structural evolution occurred in crystallization: different kinds of local clusters (such as ico-like (ico is the abbreviation of icosahedron), ico-bcc like (bcc, body-centred cubic), bcc, bcc-like structures) in turn have their maximal numbers as temperature decreases. And in a rather wide temperature range the icosahedral short-range order (ISRO) demonstrates a saturated stage (where the amount of ico-like structures keeps stable) that breeds metastable bcc clusters. As the precursor of crystallization, after reaching the maximal number bcc clusters finally decrease, resulting in the final solid being a mixture mainly composed of fcc/hcp (face-centred cubic and hexagonal-closed packed) clusters and to a less degree, bcc clusters. This detailed geometric picture for crystallization of liquid metal is believed to be useful to improve the fundamental understanding of liquid–solid phase transition. - Highlights: • A comprehensive structural analysis is conducted focusing on crystallization. • The involved atoms in our analysis are more than 90% for all samples concerned. • A series of distinct intermediate states are found in crystallization of silver melt. • A novelty icosahedron-saturated state breeds the metastable bcc state.
We perform a three-dimensional multi-probe analysis of the rich galaxy cluster A1689, one of the most powerful known lenses on the sky, by combining improved weak-lensing data from new wide-field BVR{sub C}i′z′ Subaru/Suprime-Cam observations with strong-lensing, X-ray, and Sunyaev–Zel’dovich effect (SZE) data sets. We reconstruct the projected matter distribution from a joint weak-lensing analysis of two-dimensional shear and azimuthally integrated magnification constraints, the combination of which allows us to break the mass-sheet degeneracy. The resulting mass distribution reveals elongation with an axis ratio of ∼0.7 in projection, aligned well with the distributions of cluster galaxies and intracluster gas. When assuming a spherical halo, our full weak-lensing analysis yields a projected halo concentration of c{sub 200c}{sup 2D}=8.9±1.1 (c{sub vir}{sup 2D}∼11), consistent with and improved from earlier weak-lensing work. We find excellent consistency between independent weak and strong lensing in the region of overlap. In a parametric triaxial framework, we constrain the intrinsic structure and geometry of the matter and gas distributions, by combining weak/strong lensing and X-ray/SZE data with minimal geometric assumptions. We show that the data favor a triaxial geometry with minor–major axis ratio 0.39±0.15 and major axis closely aligned with the line of sight (22°±10°). We obtain a halo mass M{sub 200c}=(1.2±0.2)×10{sup 15} M{sub ⊙} h{sup −1} and a halo concentration c{sub 200c}=8.4±1.3, which overlaps with the ≳1σ tail of the predicted distribution. The shape of the gas is rounder than the underlying matter but quite elongated with minor–major axis ratio 0.60 ± 0.14. The gas mass fraction within 0.9 Mpc is 10{sub −2}{sup +3}%, a typical value for high-mass clusters. The thermal gas pressure contributes to ∼60% of the equilibrium pressure, indicating a significant level of non-thermal pressure support. When compared to Planck's hydrostatic mass estimate, our lensing measurements yield a spherical mass ratio of M{sub Planck}/M{sub GL}=0.70±0.15 and 0.58 ± 0.10 with and without corrections for lensing projection effects, respectively.
Standard forms of density-functional theory (DFT) have good suggestive power for many materials, but are not yet fully satisfactory for cluster, solid, and liquid forms of water. Current work has stressed the importance of DFT errors in describing dispersion, but we note that errors in other parts of the energy may also contribute. We obtain information about the nature of DFT errors by using a many-body separation of the total energy into its 1-body, 2-body, and beyond-2-body components to analyze the deficiencies of the popular PBE and BLYP approximations for the energetics of water clusters and ice structures. The errors of these approximations are computed by using accurate benchmark energies from the coupled-cluster technique of molecular quantum chemistry and from quantum Monte Carlo calculations. The systems studied are isomers of the water hexamer cluster, the crystal structures Ih, II, XV, and VIII of ice, and two clusters extracted from ice VIII. For the binding energies of these systems, we use the machine-learning technique of Gaussian Approximation Potentials to correct successively for 1-body and 2-body errors of the DFT approximations. We find that even after correction for these errors, substantial beyond-2-body errors remain. The characteristics of the 2-body and beyond-2-body errors of PBE are completely different from those of BLYP, but the errors of both approximations disfavor the close approach of non-hydrogen-bonded monomers. We note the possible relevance of our findings to the understanding of liquid water.
A theoretical analysis of the cluster-pair approximation (CPA) is presented based on the quasichemical theory of solutions. The sought single-ion hydration free energy of the proton includes an interfacial potential contribution by definition. It is shown, however, that the CPA involves an extra-thermodynamic assumption that does not guarantee uniform convergence to a bulk free energy value with increasing cluster size. A numerical test of the CPA is performed using the classical polarizable AMOEBA force field and supporting quantum chemical calculations. The enthalpy and free energy differences are computed for the kosmotropic Na{sup +}/F{sup −} ion pair in water clusters of size n = 5, 25, 105. Additional calculations are performed for the chaotropic Rb{sup +}/I{sup −} ion pair. A small shift in the proton hydration free energy and a larger shift in the hydration enthalpy, relative to the CPA values, are predicted based on the n = 105 simulations. The shifts arise from a combination of sequential hydration and interfacial potential effects. The AMOEBA and quantum chemical results suggest an electrochemical surface potential of water in the range −0.4 to −0.5 V. The physical content of single-ion free energies and implications for ion-water force field development are also discussed.
We present a joint shear-and-magnification weak-lensing analysis of a sample of 16 X-ray-regular and 4 high-magnification galaxy clusters at 0.19 ≲ z ≲ 0.69 selected from the Cluster Lensing And Supernova survey with Hubble (CLASH). Our analysis uses wide-field multi-color imaging, taken primarily with Suprime-Cam on the Subaru Telescope. From a stacked-shear-only analysis of the X-ray-selected subsample, we detect the ensemble-averaged lensing signal with a total signal-to-noise ratio of ≅ 25 in the radial range of 200-3500 kpc h {sup –1}, providing integrated constraints on the halo profile shape and concentration-mass relation. The stacked tangential-shear signal is well described by a family of standard density profiles predicted for dark-matter-dominated halos in gravitational equilibrium, namely, the Navarro-Frenk-White (NFW), truncated variants of NFW, and Einasto models. For the NFW model, we measure a mean concentration of c{sub 200c}=4.01{sub −0.32}{sup +0.35} at an effective halo mass of M{sub 200c}=1.34{sub −0.09}{sup +0.10}×10{sup 15} M{sub ⊙}. We show that this is in excellent agreement with Λ cold dark matter (ΛCDM) predictions when the CLASH X-ray selection function and projection effects are taken into account. The best-fit Einasto shape parameter is α{sub E}=0.191{sub −0.068}{sup +0.071}, which is consistent with the NFW-equivalent Einasto parameter of ∼0.18. We reconstruct projected mass density profiles of all CLASH clusters from a joint likelihood analysis of shear-and-magnification data and measure cluster masses at several characteristic radii assuming an NFW density profile. We also derive an ensemble-averaged total projected mass profile of the X-ray-selected subsample by stacking their individual mass profiles. The stacked total mass profile, constrained by the shear+magnification data, is shown to be consistent with our shear-based halo-model predictions, including the effects of surrounding large-scale structure as a two-halo term, establishing further consistency in the context of the ΛCDM model.
We use photometric and spectroscopic observations of the detached eclipsing binaries V40 and V41 in the globular cluster NGC 6362 to derive masses, radii, and luminosities of the component stars. The orbital periods of these systems are 5.30 and 17.89 days, respectively. The measured masses of the primary and secondary components (M{sub p}, M{sub s}) are (0.8337 ± 0.0063, 0.7947 ± 0.0048) M{sub ⊙} for V40 and (0.8215 ± 0.0058, 0.7280 ± 0.0047) M{sub ⊙} for V41. The measured radii (R{sub p}, R{sub s}) are (1.3253 ± 0.0075, 0.997 ± 0.013) R{sub ⊙} for V40 and (1.0739 ± 0.0048, 0.7307 ± 0.0046) R{sub ⊙} for V41. Based on the derived luminosities, we find that the distance modulus of the cluster is 14.74 ± 0.04 mag—in good agreement with 14.72 mag obtained from color–magnitude diagram (CMD) fitting. We compare the absolute parameters of component stars with theoretical isochrones in mass–radius and mass–luminosity diagrams. For assumed abundances [Fe/H] = −1.07, [α/Fe] = 0.4, and Y = 0.25 we find the most probable age of V40 to be 11.7 ± 0.2 Gyr, compatible with the age of the cluster derived from CMD fitting (12.5 ± 0.5 Gyr). V41 seems to be markedly younger than V40. If independently confirmed, this result will suggest that V41 belongs to the younger of the two stellar populations recently discovered in NGC 6362. The orbits of both systems are eccentric. Given the orbital period and age of V40, its orbit should have been tidally circularized some ∼7 Gyr ago. The observed eccentricity is most likely the result of a relatively recent close stellar encounter.
Inferring the values and uncertainties of cosmological parameters in a cosmology model is of paramount importance for modern cosmic observations. In this paper, we use the simulation-based inference (SBI) approach to estimate cosmological constraints from a simplified galaxy cluster observation analysis. Using data generated from the Quijote simulation suite and analytical models, we train a machine learning algorithm to learn the probability function between cosmological parameters and the possible galaxy cluster observables. The posterior distribution of the cosmological parameters at a given observation is then obtained by sampling the predictions from the trained algorithm. Our results show that the SBI method can successfully recover the truth values of the cosmological parameters within the 2σ limit for this simplified galaxy cluster analysis, and acquires similar posterior constraints obtained with a likelihood-based Markov Chain Monte Carlo method, the current state-of the-art method used in similar cosmological studies.
We present the first joint analysis of cluster abundances and auto or cross-correlations of three cosmic tracer fields: galaxy density, weak gravitational lensing shear, and cluster density split by optical richness. From a joint analysis (4×2pt+N) of cluster abundances, three cluster cross-correlations, and the auto correlations of the galaxy density measured from the first year data of the Dark Energy Survey, we obtain Ωm=0.305-0.038+0.055 and σ8=0.783-0.054+0.064. This result is consistent with constraints from the DES-Y1 galaxy clustering and weak lensing two-point correlation functions for the flat νΛCDM model. Consequently, we combine cluster abundances and all two-point correlations from across all three cosmic tracer fields (6×2pt+N) and find improved constraints on cosmological parameters as well as on the cluster observable-mass scaling relation. This analysis is an important advance in both optical cluster cosmology and multiprobe analyses of upcoming wide imaging surveys.
BACKGROUND: Despite great progress in reducing environmental lead (Pb) levels, many children in the United States are still being exposed. OBJECTIVE: Our aim was to develop a generalizable approach for systematically identifying, verifying, and analyzing locations with high prevalence of children’s elevated blood Pb levels (EBLLs) and to assess available Pb models/indices as surrogates, using a Michigan case study. METHODS: We obtained ~1:9 million BLL test results of children <6 years of age in Michigan from 2006–2016; we then evaluated them for data representativeness by comparing two percentage EBLL (%EBLL) rates (number of children tested with EBLL divided by both number of children tested and total population). We analyzed %EBLLs across census tracts over three time periods and between two EBLL reference values (≥5 vs. ≥10 μg/dL) to evaluate consistency. Locations with high %EBLLs were identified by a top 20 percentile method and a Getis-Ord Gi* geospatial cluster “hotspot” analysis. For the locations identified, we analyzed convergences with three available Pb exposure models/indices based on old housing and sociodemographics. RESULTS: Analyses of 2014–2016 %EBLL data identified 11 Michigan locations via cluster analysis and 80 additional locations via the top 20 percentile method and their associated census tracts. Data representativeness and consistency were supported by a 0.93 correlation coefficient between the two EBLL rates over 11 y, and a Kappa score of ~0:8 of %EBLL hotspots across the time periods (2014–2016) and reference values. Many EBLL hotspot locations converge with current Pb exposure models/indices; others diverge, suggesting additional Pb sources for targeted interventions. DISCUSSION: This analysis confirmed known Pb hotspot locations and revealed new ones at a finer geographic resolution than previously available, using advanced geospatial statistical methods and mapping/visualization. It also assessed the utility of surrogates in the absence of blood Pb data. This approach could be applied to other states to inform Pb mitigation and prevention efforts. https://doi.org/10.1289/EHP9705
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In this work, we present a strong lensing analysis of four massive galaxy clusters imaged with the Hubble Space Telescope in the Reionization Lensing Cluster Survey. We use a light-traces-mass technique to uncover sets of multiple images and constrain the mass distribution of the clusters. These mass models are the first published for Abell S295 and MACS J0159.8-0849 and are improvements over previous models for Abell 697 and MACS J0025.4-1222. Our analysis for MACS J0025.4-1222 and Abell S295 shows a bimodal mass distribution supporting the merger scenarios proposed for these clusters. The updated model for MACS J0025.4-1222 suggests a substantially smaller critical area than previously estimated. For MACS J0159.8-0849 and Abell 697, we find a single peak and relatively regular morphology revealing fairly relaxed clusters. Despite being less prominent lenses, three of these clusters seem to have lensing strengths, i.e., cumulative area above certain magnification, similar to those of the Hubble Frontier Fields clusters (e.g., A(μ > 5) ~ 1–3 arcmin 2 , A(μ > 10) ~ 0.5–1.5 arcmin 2 ), which in part can be attributed to their merging configurations. We make our lens models publicly available through the Mikulski Archive for Space Telescopes. Finally, using Gemini-N/GMOS spectroscopic observations, we detect a single emission line from a high-redshift J 125 ≃ 25.7 galaxy candidate lensed by Abell 697. While we cannot rule out a lower-redshift solution, we interpret the line as Lyα at z = 5.800 ± 0.001, in agreement with its photometric redshift and dropout nature. Within this scenario, we measure a Lyα rest-frame equivalent width of 52 ± 22 Å and an observed Gaussian width of 117 ± 15 km s -1 .