Parametrizing arbitrary galaxy morphologies: potentials and pitfalls

A Review of Concentration, Diversity or Entropy Metrics in Economics, Finance, Ecology and Communication Science

We present broad-band photometry and provide a quantitative analysis of the structure of galaxies in the inner region of the Abell Cluster 2443 (z~0.1). The galaxy parameters have been derived by fitting a two-component model (Sersic r^{1/n} bulge and exponential disk) to a magnitude-limited sample. Using a new method of analysis which takes into account the effects of seeing on the structural parameters and considers the ellipticity as an active parameter, we avoid systematic errors arising from assumptions of circular symmetry. 76% of the sample galaxies were classified with these models, the rest were morphologically peculiar. For the spiral galaxies, the relation between n and B/D is consistent with the trend observed in nearby field galaxy samples. The Sersic index n (which can be considered as a concentration index) of the elliptical galaxies is correlated with the local surface density of the cluster. Monte Carlo simulations were used to check the reliability of the method and determine the magnitude selection criteria.

Motivated by the challenges of calculating the dynamical masses of late-type galaxies (LTGs) and the enormous amount of data from the Sloan Digital Sky Survey (SDSS), we calculate virial masses of a sample of approximately 126 000 LTGs from the sixteenth data release of the SDSS. The virial mass estimations were made considering Newtonian mechanics, virial equilibrium and velocity dispersion from stars and gas. The procedure gave as a result seven mass estimations for each galaxy. The calculated masses were calibrated using a sample of spiral galaxies with velocity rotation curves. Considering the results from the calibration, we find that the correlation between virial and dynamical (rotation curve) masses is stronger for high inclination values. Therefore, the calibration relies more on the available data for higher inclination angle galaxies. We also show that if we have a heterogeneous sample of galaxies one must take into consideration the size and colour of these galaxies by using the following variables: Sersic index n, concentration index, and colour of the stars. For relatively smaller and bluer LTGs, the gas velocity dispersion provides a more consistent mass calculation, while for LTGs that are relatively larger and redder the stellar velocity dispersion provides a better correlated mass calculation.

Mayall II = G1 is one of the most luminous globular clusters (GCs) known in M31. New deep, high-resolution observations with the Advanced Camera for Surveys on the Hubble Space Telescope are used to provide accurate photometric data to the smallest radii yet. In particular, we present the precise variation of ellipticity and position angle, and of surface brightness for the core of the object. Based on these accurate photometric data, we redetermine the structural parameters of G1 by fitting a single-mass isotropic King model. We derive a core radius, rc= 0.21 ± 0.01 arcsec (= 0.78 ± 0.04 pc), a tidal radius, rt= 21.8 ± 1.1 arcsec (= 80.7 ± 3.9 pc), and a concentration index c= log (rt/rc) = 2.01 ± 0.02. The central surface brightness is 13.510 mag arcsec−2. We also calculate the half-light radius, at rh= 1.73 ± 0.07 arcsec (= 6.5 ± 0.3 pc). The results show that, within 10 core radii, a King model fits the surface brightness distribution well. We find that this object falls in the same region of the MV versus log Rh diagram as ω Centauri, M54 and NGC 2419 in the Milky Way. All three of these objects have been claimed to be the stripped cores of now defunct dwarf galaxies. We discuss in detail whether GCs, stripped cores of dwarf spheroidals and normal dwarf galaxies form a continuous distribution in the MV versus log Rh plane, or if GCs and dwarf spheroidals constitute distinct classes of objects; we present arguments in favour of this latter view.

We propose a simple theoretical formula for describing the refractive indices in binary liquid mixtures containing salt ions. Our theory is based on the Clausius-Mossotti equation; it gives the refractive index of the mixture in terms of the refractive indices of the pure liquids and the polarizability of the ionic species, by properly accounting for the volume change upon mixing. The theoretical predictions are tested by extensive experimental measurements of the refractive indices for water-acetonitrile-salt systems for several liquid compositions, different salt species, and a range of salt concentrations. Excellent agreement is obtained in all cases, especially at low salt concentrations, with no fitting parameters. A simplified expression of the refractive index for low salt concentration is also given, which can be the theoretical basis for determination of salt concentration using refractive index measurements.

We use the Fourth Data Release of the Sloan Digital Sky Survey to investigate the relation between galaxy rest frame u-r colour, morphology, as described by the concentration and Sersic indices, and environmental density, for a sample of 79,553 galaxies at z < ~0.1. We split the samples according to density and luminosity and recover the expected bimodal distribution in the colour-morphology plane, shown especially clearly by this subsampling. We quantify the bimodality by a sum of two Gaussians on the colour and morphology axes and show that, for the red/early-type population both colour and morphology do not change significantly as a function of density. For the blue/late-type population, with increasing density the colour becomes redder but the morphology again does not change significantly. Both populations become monotonically redder and of earlier type with increasing luminosity. There is no significant qualitative difference between the behaviour of the two morphological measures. We supplement the morphological sample with 13,655 galaxies assigned Hubble types by an artificial neural network. We find, however, that the resulting distribution is less well described by two Gaussians. Therefore, there are either more than two significant morphological populations, physical processes not seen in colour space, or the Hubble type, particularly the different subtypes of spirals Sa-Sd, has an irreducible fuzziness when related to environmental density. For each of the three measures of morphology, on removing the density relation due to it, we recover a strong residual relation in colour. However, on similarly removing the colour-density relation there is no evidence for a residual relation due to morphology. [Abridged]

Aims. We report on a photometric study of a sample of 22 disk galaxies in the Hubble Deep Field South NICMOS parallel field. The redshift range of the galaxies is $z=0.5{-}2.6$. Methods. We use deep NICMOS J and H band and STIS open mode images, taken as part of the HDF-S project, to construct rest-frame B -profiles and $(U-V)$ color profiles of the galaxies. Before fitting isophotes, images are deconvolved with PSF. Derived surface brightness profiles are approximated by Sersic luminosity distribution. Results. Significantly large population of disks cannot be represented by an exponential disk, but this can be well done by Sersic law, if $n n does not vary significantly with redshift. Galactic sizes decrease with redshift as $r_{\rm e}(z)/r_{\rm e}(0) = 1-0.26z$. The rest frame $(U-V)$ color shows a clear decrease at $z\approx2$, concordantly with the understanding of more intense star formation at earlier epochs. Color gradients $\Delta(U-V)/\Delta r$ are small and roughly constant at $z 2$, dominantly positive gradients appear, possibly indicating centrally concentrated star-formation. On the basis of $(U-V)$ color and chemical evolution models, the disks observed at $z\sim 2.5$ have formed between $z=3.5{-}7$. Scale radii r e of the galaxies correlate with the scale surface brightnesses $\mu_{\rm e}$ for the sample. None of the studied parameters shows clear dependence on absolute B luminosity for the galaxies.

Response surface functions are often used as simple and inexpensive replacements for computationally expensive computer models that simulate the behavior of a complex system over some parameter space. Progressive response surfaces are built up incrementally as global information is added from new sample points added to the previous points in the parameter space. As the response surfaces are globally upgraded, indications of the convergence of the response surface approximation to the exact (fitted) function can be inferred. Sampling points can be incrementally added in a structured or unstructured fashion. Whatever the approach, it is usually desirable to sample the entire parameter space uniformly (at least in early stages of sampling). At later stages of sampling, depending on the nature of the quantity being resolved it may be desirable to continue sampling uniformly (progressive response surfaces), or to switch to a focusing/economizing strategy of preferentially sampling certain regions of the parameter space based on information gained in previous stages of sampling (adaptive response surfaces). Here we consider progressive response surfaces where a balanced representation of global response over the parameter space is desired. We use Kriging and Moving-Least-Squares methods to fit Halton quasi-Monte-Carlo data samples and interpolate over the parameter space. On 2-D test problems we use the response surfaces to compute various response measures and assess the accuracy/applicability of heuristic error estimates based on convergence behavior of the computed response quantities. Where applicable we apply Richardson Extrapolation for estimates of error and asymptotic convergence, and assess the accuracy of these estimates. We seek to develop a robust methodology for constructing progressive response surface approximations with reliable error estimates.

Using a 20% sample of Medicare claims data (2010–2019, N &amp;gt; 4 million), we examined the association between spatial social polarization (SSP) and Alzheimer’s Disease and Related Dementias (ADRD) prevalence and incidence. SSP was measured using the Index of Concentration at the Extremes (ICE) across five domains: race, income, education, language proficiency, and homeownership. Logistic regression models were used to estimate the association between neighborhood SSP and incident ADRD, adjusting for age, race, socioeconomic status, and comorbidities. Significant racial disparities were observed in ADRD prevalence and incidence in 2019, with rates notably higher among Black and Hispanic populations at 8% and 3.5%, respectively. Despite a yearly decrease in incidence rates, significant associations were found between higher risks in ADRD and neighborhood-level SSP in race, income, and education, though the association with SSP in primarily spoken language was not significant. These findings suggest that neighborhood SSP is associated with ADRD prevalence and incidence, with stronger associations observed for race, income, and education domains. Further investigation into the role of spatial social polarization in ADRD disparities may help identify potential intervention targets for reducing neighborhood-driven inequities in cognitive health.

We suggest that elliptical galaxies, as stellar systems in a stage of quasi-equilibrium, may have a specific entropy. We use the Sersic law to describe the light profile. The specific entropy (the Boltzmann–Gibbs definition) is then calculated assuming that the galaxy behaves as a spherical, isotropic, one-component system. We predict a relation between the three parameters of the Sersic law linked to the specific entropy, defining a surface in the parameter space, an ‘entropic plane’. We have analysed a sample of simulated merging elliptical galaxies (virtual) and a sample of galaxies belonging to the Coma Cluster (real). Both virtual and realgalaxies are: 1) located in their own ‘entropic plane‘ and 2) in this plane, they are located on a straight line, indicating constant entropy: another physical property A careful examination of the value of the specific entropy indicates a very small increase in the specific entropy with the generation after merging (virtual sample). Although one cannot distinguish between various generations for real galaxies, the distribution of specific entropy in this sample is very similar to that in the virtual sample.

BackgroundThe existence of socio-economic inequalities in child mortality is well documented. African cities grow faster than cities in most other regions of the world; and inequalities in African cities are thought to be particularly large. Revealing health-related inequalities is essential in order for governments to be able to act against them. This study aimed to systematically compare inequalities in child mortality across 10 major African cities (Cairo, Lagos, Kinshasa, Luanda, Abidjan, Dar es Salaam, Nairobi, Dakar, Addis Ababa, Accra), and to investigate trends in such inequalities over time.MethodsData from two rounds of demographic and health surveys (DHS) were used for this study (if available): one from around the year 2000 and one from between 2007 and 2011. Child mortality rates within cities were calculated by population wealth quintiles. Inequality in child mortality was assessed by computing two measures of relative inequality (the rate ratio and the concentration index) and two measures of absolute inequality (the difference and the Erreyger’s index).ResultsMean child mortality rates ranged from about 39 deaths per 1,000 live births in Cairo (2008) to about 107 deaths per 1,000 live births in Dar es Salaam (2010). Significant inequalities were found in Kinshasa, Luanda, Abidjan, and Addis Ababa in the most recent survey. The difference between the poorest quintile and the richest quintile was as much as 108 deaths per 1,000 live births (95% confidence interval 55 to 166) in Abidjan in 2011–2012. When comparing inequalities across cities or over time, confidence intervals of all measures almost always overlap. Nevertheless, inequalities appear to have increased in Abidjan, while they appear to have decreased in Cairo, Lagos, Dar es Salaam, Nairobi and Dakar.ConclusionsConsiderable inequalities exist in almost all cities but the level of inequalities and their development over time appear to differ across cities. This implies that inequalities are amenable to policy interventions and that it is worth investigating why inequalities are higher in one city than in another. However, larger samples are needed in order to improve the certainty of our results. Currently available data samples from DHS are too small to reliably quantify the level of inequalities within cities.

Quantifying and assessing changes in biological diversity are central aspects of many ecological studies, yet accurate methods of estimating biological diversity from sampling data have been elusive. Hill numbers, or the effective number of species, are increasingly used to characterize the taxonomic, phylogenetic, or functional diversity of an assemblage. However, empirical estimates of Hill numbers, including species richness, tend to be an increasing function of sampling effort and, thus, tend to increase with sample completeness. Integrated curves based on sampling theory that smoothly link rarefaction (interpolation) and prediction (extrapolation) standardize samples on the basis of sample size or sample completeness and facilitate the comparison of biodiversity data. Here we extended previous rarefaction and extrapolation models for species richness (Hill number q D , where q = 0) to measures of taxon diversity incorporating relative abundance (i.e., for any Hill number q D , q &gt; 0) and present a unified approach for both individual‐based (abundance) data and sample‐based (incidence) data. Using this unified sampling framework, we derive both theoretical formulas and analytic estimators for seamless rarefaction and extrapolation based on Hill numbers. Detailed examples are provided for the first three Hill numbers: q = 0 (species richness), q = 1 (the exponential of Shannon's entropy index), and q = 2 (the inverse of Simpson's concentration index). We developed a bootstrap method for constructing confidence intervals around Hill numbers, facilitating the comparison of multiple assemblages of both rarefied and extrapolated samples. The proposed estimators are accurate for both rarefaction and short‐range extrapolation. For long‐range extrapolation, the performance of the estimators depends on both the value of q and on the extrapolation range. We tested our methods on simulated data generated from species abundance models and on data from large species inventories. We also illustrate the formulas and estimators using empirical data sets from biodiversity surveys of temperate forest spiders and tropical ants.

Worldwide countries are recognising the need for and significance of universal health coverage (UHC); however, health inequality continues to persist. This study evaluates the status and equity of residents’ demand for and utilisation of health services and expenditure by considering the three components of universal health coverage, urban-rural differences, and different income groups. Sample data from China’s Fifth Health Service Survey were analysed and the ‘five levels of income classification’ were used to classify people into income groups. This study used descriptive analysis and concentration index and concentration curve for equity evaluation. Statistically significant differences were found in the demand and utilisation of health services between urban and rural residents. Rural residents’ demand and utilisation of health services decreased with an increase in income and their health expenditure was higher than that of urban residents. Compared with middle- and high-income rural residents, middle- and lower-income rural residents faced higher hospitalisation expenses; and, compared with urban residents, equity in rural residents’ demand and utilisation of health services, and annual health and hospitalisation expenditures, were poorer. Thus, equity of health service utilisation and expenditure for urban and rural residents with different incomes remain problematic, requiring improved access and health policies.

We use a sample of ∼200 000 galaxies drawn from the Sloan Digital Sky Survey (SDSS) with 0.01 &amp;lt; z &amp;lt; 0.3 and −23 &amp;lt; M 0.1r &amp;lt; −16 to study how clustering depends on properties such as stellar mass (M*), colour (g−r), 4000-Å break strength (D4000), concentration index (C), and stellar surface mass density (μ*). Our measurements of wp(rp) as a function of the r-band luminosity are in excellent agreement with the previous two-degree Field Galaxy Redshift Survey and SDSS analyses. We compute wp(rp) as a function of stellar mass and we find that more-massive galaxies cluster more strongly than less-massive galaxies, with the difference increasing above the characteristic stellar mass M* of the Schechter mass function. We then divide our sample according to colour, 4000-Å break strength, concentration and surface density. As expected, galaxies with redder colours, larger 4000-Å break strengths, higher concentrations and larger surface mass densities cluster more strongly. The clustering differences are largest on small scales and for low-mass galaxies. At fixed stellar mass, the dependences of clustering on colour and 4000-Å break strength are similar. Different results are obtained when galaxies are split by concentration or surface density. The dependence of wp(rp) on g−r and D4000 extends out to physical scales that are significantly larger than those of individual dark matter haloes (&amp;gt;5 h−1 Mpc). This large-scale clustering dependence is not seen for the parameters C or μ*. On small scales (&amp;lt;1 h−1 Mpc), the amplitude of the correlation function is constant for ‘young’ galaxies with 1.1 &amp;lt; D4000 &amp;lt; 1.5 and a steeply rising function of age for ‘older’ galaxies with D4000 &amp;gt; 1.5. In contrast, the dependence of the amplitude of wp(rp) on concentration on scales less than 1 h−1 Mpc is strongest for disc-dominated galaxies with C &amp;lt; 2.6. This demonstrates that different processes are required to explain environmental trends in the structure and in the star formation history of galaxies.

New spatial econometric techniques and applications in regional science