Frequency Distributions Of Elements Research Articles

Distinguishing subsampled power laws from other heavy-tailed distributions.

Distinguishing power-law distributions from other heavy-tailed distributions is challenging, and this task is often further complicated by subsampling effects. In this work, we evaluate the performance of two commonly used methods for detecting power-law distributions-the maximum likelihood method of Clauset etal. and the extreme value method of Voitalov etal.-in distinguishing subsampled power laws from two other heavy-tailed distributions, the lognormal and the stretched exponential distributions. We focus on a random subsampling method commonly applied in network science and biological sciences. In this subsampling scheme, we are ultimately interested in the frequency distribution of elements with a certain number of constituent parts-for example, species with k individuals or nodes with k connections-and each part is selected to the subsample with an equal probability. We investigate how well the results obtained from low-subsampling-depth subsamples generalize to the original distribution. Our results show that the power-law exponent of the original distribution can be estimated fairly accurately from subsamples, but classifying the distribution correctly is more challenging. The maximum likelihood method falsely rejects the power-law hypothesis for a large fraction of subsamples from power-law distributions. While the extreme value method correctly recognizes subsampled power-law distributions with all tested subsampling depths, its capacity to distinguish power laws from the heavy-tailed alternatives is limited. However, these false positives tend to result not from the subsampling itself but from the estimators' inability to classify the original sample correctly. In fact, we show that the extreme value method can sometimes be expected to perform better on subsamples than on the original samples from the lognormal and the stretched exponential distributions, while the contrary is true for the main tests included in the maximum likelihood method.

Chemodynamical Simulations of the Milky Way Galaxy - Inhomogeneous Chemical Enrichment

AbstractThe predictions of our chemodynamical simulations from cosmological initial conditions are as follows: The disk formed Inside-out. Metallicity radial and vertical gradients exist, but no [α/Fe] radial gradient. Metallicity radial gradient is steeper at higher redshifts. The [α/Fe]-[Fe/H] relation is caused by the delayed enrichment of Type Ia supernovae (not with long lifetimes, but with the metallicity effect). The bulge formed through the assembly of small gas-rich galaxies at high redshifts. [α/Fe] is higher, [Mn/Fe] is lower, [(Na, Al)/Fe] are higher than the disk. Metallicity and [α/Fe] vertical gradients exist, which is caused by the increase of metal-rich and low [α/Fe] populations at lower latitudes. Bars may form later, which may show boxy and cylindrical rotation. Half of thick disk stars (kinetically selected) come from minor mergers. [α/Fe] is higher, and [Mn/Fe] is lower than the thin disk, but [(Na, Al, Cu, Zn)/Fe] are lower than the bulge. There are metallicity vertical, weak metallicity radial, and no [α/Fe] radial gradients. It would be interesting to compare the predictions with other models such as radial mixing, disk heating, and clumpy disks.For the solar neighborhood, the frequency distributions of elements from oxygen to zinc are in excellent agreement not only for the average values but also for the scatter. In chemodynamical simulations, chemical enrichment takes place inhomogeneously, and the scatter originates from a combination of various effects - mergers, migration, and in-situ. The inhomogeneous enrichment is important in reproducing observed nitrogen abundances, and also in understanding elemental abundance patterns of dwarf spheroidal galaxies and carbon-enhanced damped Lyman α systems.

Chemical composition of magmatic rocks in a certain region and its regional geochemical characteristics

Based on a review of the available petrological and petrochemical data on magmatic rocks in a certain region in China, the average chemical composition of them has been calculated, and the frequency distribution of elements in the rocks, the mineralization of rock bodies and the regional geochemical characteristics have been discussed. In response to temporal and spatial variations during the evolutionary process of magmatic activity, a systematic variation is obvious from this study in the chemical composition of magmatic rocks, the frequency distribution patterns of elements, the concentration levels of various elements and the calc-alkali index of the rocks as well as in the average atomic weight and average atomic valence. Particularly, different geochemical indicators have been established for mineralized and barren rock bodies, respectively. Crystallization-differentiation and post-magmatic metasomatism constitute the most important mechanism controlling mineralization.

Interpretation of geochemical soil surveys by block averaging

Abstract In many cases the spatial distribution patterns of elements in soils - especially where geochemical response is weak - is erratic and incoherent and poorly defines underlying mineralized zones; frequency distributions of elements are characteristically positively skewed. Geochemical soil survey data for Cu, Pb, and Zn from around the Key Anacon massive sulphide deposit in New Brunswick, Canada, are used to illustrate an interpretative technique useful in these situations. Calculation of mean element values of all samples within non-overlapping blocks eliminates random background noise and enhances significant spatial trends. Frequency curves of the block means tend to normality if the spatial distribution is random; the frequency curves emphasize the skewness or become polymodal if the spatial distribution is systematic. The only critical step in this simple interpretative procedure is the determination of the appropriate block size for the particular sample density relative to the areal size of the geochemical response to the target.

Frequency Distribution of Elements in Rensselaer Graywacke, Troy, New York

Frequency distributions of the major/minor oxides SiO 2 , Al 2 O 3 , Fe 2 O 3 , MgO, MnO, CaO, SrO, BaO, TiO 2 , Na 2 O, K 2 O and the trace elements Ni, V, Cu, Be, Y, Zr, La, Sc and Cr for 119 samples of Rensselaer Graywacke were tested against both normal and log normal distribution models. Based on chi square and moments, the distribution of SiO 2 , Al 2 O 3 , SrO, BaO, Na 2 O. and Sc were compared against the normal distribution model, whereas Fe 2 O 3 , MgO, MnO, CaO, TiO 2 , K 2 O, Ni, V, Cu, Be, Y, Zr, La, and Cr were converted to natural logarithms and their distributions tested against the expected log normal model. Most distributions fail to strictly follow either of the proposed hypothetical distributions; however, SiO 2 , BaO, and Na 2 O closely approximate the normal distribution, whereas Fe 2 O 3 , MgO, K 2 O, Y, Zr, and La are similar to the log normal model. If we accept the “Prior Knowledge Concept,” that is, based on previous information, state that the frequency distributions of elements approximately follow either the normal or log normal law, we may attribute discrepancies from the theorized distribution model to nonrandom sampling of a stratified population or to sampling of more than one population. Alternatively the samples may represent random samples from a non-normal parent population. The Rensselaer, Franciscan (Bailey and others, 1964) and “average” graywacke of Pettijohn (1963) when compared against the “average” arkose, lithic arenite, and quartzite of Pettijohn (1963), are enriched in A1 2 O 3 , total iron, and Na 2 O and have Na 2 O/K 2 O ratios of greater than unity, whereas the other sedimentary rock types have ratios less than 1.0. The present investigation agrees with earlier findings that graywackes have Na 2 O/K 2 O ratios of greater than unity; this appears to be a peculiarity of high-rank graywackes. The concentrations of trace elements Ni, V, Cu, and Cr in the Rensselaer are lower than the crustal abundance, whereas Y, Zr, La, and Sc are higher in concentration. Concentrations greater or less than ten times the crustal abundance, are not apparent. The Graywacke is enriched in La and Sc 60 and 26 times respectively over Pettijohn9s element range for sandstones (1963); all remaining trace elements are in favorable agreement. Hence, in chemistry the Rensselaer Gray-wacke appears to represent closely the composition of the “average” earth9s crust.

Frequency-distributions of elements in igneous rocks

A proposed geochemical law which states that “the concentration of an element in a specific igneous rock is lognormally distributed” is critically reviewed. It is shown 1. (a) that a lognormal law cannot apply even approximately to all the major constituents of a rock, 2. (b) that many minor elements will follow major constituents in failing to obey such a law. It is demonstrated that the dispersions of Ahrens's data for the minor elements of granite and diabase, and the extents which they exhibit an approximate lognormality, conform very largely with the known associations of the elements with other constituents of the two rock-types.