Fast ML estimation for the mixture of factor analyzers via an ECM algorithm

In this brief, we propose a fast expectation conditional maximization (ECM) algorithm for maximum-likelihood (ML) estimation of mixtures of factor analyzers (MFA). Unlike the existing expectation-maximization (EM) algorithms such as the EM in Ghahramani and Hinton, 1996, and the alternating ECM (AECM) in McLachlan and Peel, 2003, where the missing data contains component-indicator vectors as well as latent factors, the missing data in our ECM consists of component-indicator vectors only. The novelty of our algorithm is that closed-form expressions in all conditional maximization (CM) steps are obtained explicitly, instead of resorting to numerical optimization methods. As revealed by experiments, the convergence of our ECM is substantially faster than EM and AECM regardless of whether assessed by central processing unit (CPU) time or number of iterations. © 2008 IEEE.published_or_final_versio

Melting of newly formed mafic crust for the formation of Neoproterozoic I-type granite in the Hannan region, South China

Neoproterozoic magmatism in the Hannan region at the northwestern margin of the Yangtze Block is characterized by numerous felsic plutons associated with minor mafic-ultramafic intrusions. The felsic plutons are either adakitic or normal-arc granitic in composition. The adakitic plutons are ∼735 Ma in age and are interpreted as having formed by partial melting of a thickened lower mafic crust. Among the normal-arc-related felsic plutons, the Tianpinghe pluton is the largest and has a SHRIMP zircon U-Pb age of 762 ± 4 Ma, older than the adakitic plutons in the region. Rocks from the Tianpinghe pluton have relatively high SiO2 (67.1-70.1 wt%) and K2O+ Na 2O (7.8-8.6 wt%) and relatively low MgO (0.7-1.3 wt%) and Al 2O3 contents (14.5-15.6 wt%), with Al2O 3/(CaO + K2O + Na2O) (A/CNK) values ranging from 0.95 to 1.08. They have arc-affinity trace-element compositions that are characterized by enrichment of large-ion lithophile elements and depletion of high-field-strength elements (Nb, Ta), with strong positive Pb and negative Ti anomalies. They have a narrow range of εNd(t) values (+0.15 to - 1.76) and relatively high zircon eHf values (+0.6 to - 8.3). These geochemical features are typical of I-type granites. The rocks from the Tianpinghe pluton have relatively young single-stage and two-stage Hf model ages (1.01-1.31 and 1.31-2.01 Ga, respectively), suggesting that the pluton was generated by partial melting of newly formed basaltic rocks. On the basis of its arc-related geochemical affinity and its emplacement before voluminous adakitic magmatism but after mafic-ultramafic intrusions, the Tianpinghe pluton is considered to be Neoproterozoic arc granite formed during a period of crustal growth and reworking. Generation of the later adakitic plutons suggests that the crustal thickness increased to more than 50 km by mafic magma underplating. © 2009 by The University of Chicago. All rights reserved.published_or_final_versio

Neoproterozoic adakitic plutons and arc magmatism along the western margin of the Yangtze Block, South China

Neoproterozoic adakitic plutons that crop out along the western margin of the Yangtze Block (South China) from Kangding on the north to Panxi on the south provide constraints on the origin of the giant Jinningian magmatic event of South China. Representative plutons include the Xuelongbao (750 Ma), Datian (760 Ma), and Dajianshan intrusions. The latter two bodies consist mainly of granodiorite with relatively high SiO2 (51.0-73.4 wt%) and Mg#'s (0.36-0.55). They have fractionated rare earth element patterns, with (La/Yb)N ratios ranging from 2.6 to 101.8, and are characterized by high Sr (344-1018 ppm) and low Y (4.3-17.9 ppm), yielding Sr/Y ratios ranging from 27 to 111. On primitive mantle-normalized trace-element diagrams, these rocks show enrichment of large-ion lithophile elements and depletion of high-field-strength elements (Nb, Ta), with positive Zr-Hf and negative Ti anomalies, consistent with an arc-related setting. They have relatively constant initial whole-rock 87Sr/86Sr ratios (0.704308-0.705068) and εNd values (+0.66 to -0.92). From their geochemistry, these plutons are interpreted to have formed in an arc environment. The parental magmas were generated from partial melts of a subducted oceanic slab that were modified by interaction with the overlying mantle wedge. Therefore, we conclude that the western margin of the Yangtze Block was an active magmatic arc during the Neoproterozoic. © 2007 by The University of Chicago. All rights reserved.published_or_final_versio

Geochronology and geochemistry of the c. 80 Ma Rutog granitic pluton, northwestern Tibet: Implications for the tectonic evolution of the Lhasa Terrane

The Rutog granitic pluton lies in the Gangdese magmatic arc in the westernmost part of the Lhasa Terrane, NW Tibet, and has SHRIMP zircon U-Pb ages of c. 80 Ma. The pluton consists of granodiorite and monzogranite with SiO2 ranging from 62 to 72 wt% and Al2 O3 from 15 to 17 wt%. The rocks contain 2.33-4.93 wt% K2O and 3.42-5.52 wt% Na2O and have Na2O/K2O ratios of 0.74-2.00. Their chondrite-normalized rare earth element (REE) patterns are enriched in LREE ((La/Yb)n = 15 to 26) and do not show significant Eu anomalies (αEu = 0.68-1.15). On a primitive mantle-normalized trace element diagram, the rocks are rich in large ion lithophile elements (LILE) and poor in high field strength elements (HFSE), HREE and Y. Their Sr/Y ratios range from 15 to 78 with an average of 30. The rocks have constant initial 87Sr/86Sr ratios (0.7045 to 0.7049) and slightly positive εNd(t) values (+0.1 to +2.3), similar to I-type granites generated in an arc setting. The geochemistry of the Rutog pluton is best explained by partial melting of a thickened continental crust, triggered by underplating of basaltic magmas in a mantle wedge. The formation of the Rutog pluton suggests flat subduction of the Neo-Tethyan oceanic lithosphere from the south. Crustal thickening may have occurred in the Late Cretaceous prior to the India-Asia collision. © Cambridge University Press 2008.published_or_final_versio

Bayesian linear mixed models with polygenic effects

We considered Bayesian estimation of polygenic effects, in particular heritability in relation to a class of linear mixed models implemented in R. Our approach is applicable to both family-based and population-based studies in human genetics with which a genetic relationship matrix can be derived either from family structure or genome-wide data. Using a simulated and a real data, we demonstrate our implementation of the models in the generic statistical software systems JAGS and Stan as well as several R packages. In doing so, we have not only provided facilities in R linking standalone programs such as GCTA and other packages in R but also addressed some technical issues in the analysis. Our experience with a host of general and special software systems will facilitate investigation into more complex models for both human and nonhuman genetics

Elemental and Sr-Nd-Pb isotopic geochemistry of Mesozoic mafic intrusions in southern Fujian Province, SE China: Implications for lithospheric mantle evolution

Abstract Cretaceous mafic dykes in Fujian province, SE China provide an opportunity to examine the nature of their mantle source and the secular evolution of the Mesozoic lithospheric mantle beneath SE China. The mafic rocks have SiO2 ranging from 47.42 to 55.40 wt %, Al2O3 from 14.0 wt % to 20.4 wt %, CaO from 4.09 to 11.7 wt % and total alkaline (K2O+Na2O) from 2.15 wt % to 6.59 wt %. Two types are recognized based on their REE and primitive mantle-normalized trace element patterns. Type-A is the dominant Mesozoic mafic rock type in SE China and is characterized by enrichment of light rare earth elements (LREE) ((La/Yb)n = 2.85-19.0) and arc-like trace element geochemistry. Type-P has relatively flat REE patterns ((La/Yb)n = 1.68-3.43) and primitive mantle-like trace element patterns except for enrichment of Rb, Ba and Pb. Type-A samples show EMII signatures on the Sr-Nd isotopic diagram, whereas type-P rocks have high initial 143Nd/144Nd ratios (0.5126-0.5128) relative to the type-A rocks (143Nd/144Nd = 0.5124-0.5127). The type-A rocks have 207Pb/204Pb ranging from 15.47 to 15.67 and 206Pb/204Pb from 18.26 to 18.52. All the type-A rocks show a negative correlation between 143Nd/144Nd and 206Pb/204Pb ratios and a positive relationship between 87Sr/86 Sr and206Pb/204Pb ratios, indicating mixing of a depleted mantle source and an EMII component. Geochemical modelling shows that the parental magmas were formed by 5-15 % partial melting of a spinel lherzolite, and contaminated by less than 1 % melt derived from subducted sediment. The type-P magmas were derived from a mantle source unmodified by subduction components. The wide distribution of type-A dykes in SE China suggests that subduction-modified lithospheric mantle was extensive beneath the Cathaysia Block. Geochemical differences between Mesozoic and Cenozoic mafic rocks indicate that lithospheric thinning beneath SE China occurred in two episodes: firstly by heterogeneous modification by subducted components in early Mesozoic times, and later by chemical-mechanical erosion related to convective upwelling of the asthenosphere during Cenozoic times. © 2007 Cambridge University Press.published_or_final_versio

Comparison of depth-averaged concentration and bed load flux sediment transport models of dam-break flow

This paper presents numerical simulations of dam-break flow over a movable bed. Two different mathematical models were compared: a fully coupled formulation of shallow water equations with erosion and deposition terms (a depth-averaged concentration flux model), and shallow water equations with a fully coupled Exner equation (a bed load flux model). Both models were discretized using the cell-centered finite volume method, and a second-order Godunov-type scheme was used to solve the equations. The numerical flux was calculated using a Harten, Lax, and van Leer approximate Riemann solver with the contact wave restored (HLLC). A novel slope source term treatment that considers the density change was introduced to the depth-averaged concentration flux model to obtain higher-order accuracy. A source term that accounts for the sediment flux was added to the bed load flux model to reflect the influence of sediment movement on the momentum of the water. In a one-dimensional test case, a sensitivity study on different model parameters was carried out. For the depth-averaged concentration flux model, Manning's coefficient and sediment porosity values showed an almost linear relationship with the bottom change, and for the bed load flux model, the sediment porosity was identified as the most sensitive parameter. The capabilities and limitations of both model concepts are demonstrated in a benchmark experimental test case dealing with dam-break flow over variable bed topography

Settlement prediction methods considering creep

2004-2005 > Academic research: refereed > Publication in refereed journalVersion of RecordPublishe

Wave propagation speeds and source term influences in single and integral porosity shallow water equations

In urban flood modeling, so-called porosity shallow water equations (PSWEs), which conceptually account for unresolved structures, e.g., buildings, are a promising approach to addressing high CPU times associated with state-of-the-art explicit numerical methods. The PSWE can be formulated with a single porosity term, referred to as the single porosity shallow water model (SP model), which accounts for both the reduced storage in the cell and the reduced conveyance, or with two porosity terms: one accounting for the reduced storage in the cell and another accounting for the reduced conveyance. The latter form is referred to as an integral or anisotropic porosity shallow water model (AP model). The aim of this study was to analyze the differences in wave propagation speeds of the SP model and the AP model and the implications of numerical model results. First, augmented Roe-type solutions were used to assess the influence of the source terms appearing in both models. It is shown that different source terms have different influences on the stability of the models. Second, four computational test cases were presented and the numerical models were compared. It is observed in the eigenvalue-based analysis as well as in the computational test cases that the models converge if the conveyance porosity in the AP model is close to the storage porosity. If the porosity values differ significantly, the AP model yields different wave propagation speeds and numerical fluxes from those of the BP model. In this study, the ratio between the conveyance and storage porosities was determined to be the most significant parameter

Neoproterozoic Mafic-Ultramafic Intrusions from the Fanjingshan Region, South China: Implications for Subduction-Related Magmatism in the Jiangnan Fold Belt

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