Overfitting Bayesian mixture models with an unknown number of components

This paper proposes solutions to three issues pertaining to the estimation of finite mixture models with an unknown number of components: the non-identifiability induced by overfitting the number of components, the mixing limitations of standard Markov Chain Monte Carlo (MCMC) sampling techniques, and the related label switching problem. An overfitting approach is used to estimate the number of components in a finite mixture model via a Zmix algorithm. Zmix provides a bridge between multidimensional samplers and test based estimation methods, whereby priors are chosen to encourage extra groups to have weights approaching zero. MCMC sampling is made possible by the implementation of prior parallel tempering, an extension of parallel tempering. Zmix can accurately estimate the number of components, posterior parameter estimates and allocation probabilities given a sufficiently large sample size. The results will reflect uncertainty in the final model and will report the range of possible candidate models and their respective estimated probabilities from a single run. Label switching is resolved with a computationally light-weight method, Zswitch, developed for overfitted mixtures by exploiting the intuitiveness of allocation-based relabelling algorithms and the precision of label-invariant loss functions. Four simulation studies are included to illustrate Zmix and Zswitch, as well as three case studies from the literature. All methods are available as part of the R package Zmix, which can currently be applied to univariate Gaussian mixture models.

Differential expression profiling of components associated with exoskeletal hardening in crustaceans

Background: Exoskeletal hardening in crustaceans can be attributed to mineralization and sclerotization of the organic matrix. Glycoproteins have been implicated in the calcification process of many matrices. Sclerotization, on the other hand, is catalysed by phenoloxidases, which also play a role in melanization and the immunological response in arthropods. Custom cDNA microarrays from Portunus pelagicus were used to identify genes possibly associated with the activation pathways involved in these processes. Results: Two genes potentially involved in the recognition of glycosylation, the C-type lectin receptor and the mannose-binding protein, were found to display molt cycle-related differential expression profiles. C-type lectin receptor up-regulation was found to coincide with periods associated with new uncalcified cuticle formation, while the up-regulation of mannose-binding protein occurred only in the post-molt stage, during which calcification takes place, implicating both in the regulation of calcification. Genes presumed to be involved in the phenoloxidase activation pathway that facilitates sclerotization also displayed molt cycle-related differential expression profiles. Members of the serine protease superfamily, trypsin-like and chymotrypsin-like, were up-regulated in the intermolt stage when compared to post-molt, while trypsin-like was also up-regulated in pre-molt compared to ecdysis. Additionally, up-regulation in pre- and intermolt stages was observed by transcripts encoding other phenoloxidase activators including the putative antibacterial protein carcinin-like, and clotting protein precursor-like. Furthermore, hemocyanin, itself with phenoloxidase activity, displayed an identical expression pattern to that of the phenoloxidase activators, i.e. up-regulation in pre- and intermolt. Conclusion: Cuticle hardening in crustaceans is a complex process that is precisely timed to occur in the post-molt stage of the molt cycle. We have identified differential expression patterns of several genes that are believed to be involved in biomineralization and sclerotization and propose possible regulatory mechanisms for these processes based on their expression profiles, such as the potential involvement of C-type lectin receptors and mannose binding protein in the regulation of calcification.

Coupled substitution of niobium and silicon in potassium titanyl phosphate and arsenate (KTiOPO4 and KTiOAsO4. Synthesis and nonlinear optical properties of KTi1-xNbxOX1-xSixO4 (X = P, As)

Coupled substitution of Nb(V) and Si(IV) for Ti(IV) and P(V)/As(V) in KTiOP04 (KTP) and KTiOAsO4 (KTA) giving new series of nonlinear optical materials, KTi1-xNbxOX1-xSixO4 (X=P,As), has been investigated. Substitution up to x = 0.40 readily occurs, the members retaining the orthorhombic (Pna2(1)) structure of KTP. The second harmonic generation (SHG) property of the parent KTP and KTA is not adversely affected by the coupled substitution. SHG intensity of the powder samples of the X = P series shows a slight increase with x up to x = 0.15; for 0.15 < x less-than-or-equal-to 0.40, there is a decrease in SHG intensity as compared to that for KTP. A similar trend in SHG intensity is seen for the arsenic analogs.

Effect of Substitution of Ca on Thermal Expansion of Cordierite (Mg2Al4Si5O18)

The effect of substitution of calcium on the anisotropic axial thermal expansion of cordierite was investigated by using a high-temperature X-ray diffraction technique. The compositions were prepared by the sol–gel route. In the Mg2-xCax-Al4Si5O18 system, single-phase cordierite can be prepared for x up to 0.5. Thermal expansion anisotropy (αa–αc) of cordierites reduces progressively by the substitution of increasing amounts of Ca for Mg.

Bridgehead substitution of 1-methoxybicyclo[2.2.2]oct 5-en-2-one derivatives: towards the synthesis of (±)-allo-cedrol [khusiol]1

Preparation of the key intermediates, 11 and 21, required for the synthesis of (+/-)-allo-cedrol (khusiol) is reported by a novel methodology involving the substitution at the bridgehead position of 1-methoxybicyclo[2.2.2]oct-5-en-2-one derivatives

Effect of substitution of Y on the structural, magnetic, and thermal properties of hexagonal DyMnO3 single crystals

We investigate the structural, magnetic, and specific heat behavior of the hexagonal manganite Dy0.5Y0.5MnO3 in order to understand the effect of dilution of Dy magnetism with nonmagnetic yttrium. In this compound, the triangular Mn lattice orders antiferromagnetic at T-N(Mn) approximate to 68 K observed experimentally in the derivative of magnetic susceptibility as well as in specific heat. In addition, a low-temperature peak at T-N(Dy) similar to 3 K is observed in specific heat which is attributed to rare earth order. The T-N(Mn) increases by 9 K compared to that of hexagonal (h) DyMnO3 while T-N(Dy) is unchanged. A change in slope of thermal evolution of lattice parameters is observed to occur at temperature close to T-N(Mn). This hints at strong magnetoelastic coupling in this geometric multiferroic. In magnetization measurements, steplike features are observed when the magnetic field is applied along the c axis which shift to higher fields with temperature and vanish completely above 40 K. The presence of different magnetic phases at low temperature and strong magnetoelastic effects can lead to such field-induced transitions which resemble metamagnetic transitions. This indicates the possibility of strong field-induced effects in dielectric properties of this material, which is unexplored to date.

Substitution of chromium for univalent copper in superconducting Pb2Sr2(Ca,Y)Cu3O8+delta

Following considerations of geometry and the similarity between chromate and carbonate groups in terms of size and charge, we have investigated the possibility of replacing the two-coordinate Cu-I in superconducting lead cuprates of the general formula Pb2Sr2(Ca, Y)CU3O8 by Cr. A high-resolution electron microscopy study coupled with energy dispersive X-ray analysis on small crystals of the title phases suggests that between 10 and 15% of the Cu-I can be replaced by Cr. While from the present structural study using HRTEM and Rietveld refinement of X-ray powder data we are unable to precisely obtain the oxidation state and oxygen coordination of Cr, we suggest in analogy with Cr substitution in other similar cuprates that in the title phases (CuO2)-O-I rods are partially replaced by tetrahedral CrO42- groups. Infrared spectroscopy supports the presence of CrO42- groups. The phases Pb1.75Sr2Ca0.2Y0.8O8+delta and Pb1.75Sr2Ca0.2Y0.8CCu2.85Cr0.15O8+delta are superconducting as-prepared, but the substitution of Cr for Cu-I results in a decrease of the Te as well as the superconducting volume fraction. (C) 1996 Academic Press, lnc.

Effect of co-substitution of Mn and Al on thermoelectric properties of chromium disilicide

CrSi2 was earlier reported to be an interesting thermoelectric material for high temperature applications because of its high oxidation resistance and good mechanical properties. In order to enhance its figure of merit, Mn at Cr site and Al at Si site were substituted into CrSi2. Our results indicate that Cr1-x Mn (x) Si2-x Al (x) solid solutions exhibit significantly lower thermal conductivity and a higher figure of merit than CrSi2.

Growth of Phases and Diffusion of Components in the W-Pt System

Growth kinetics, phase boundary compositions, interdiffusion coefficients and the relative mobilities of the components are determined in the W-Pt system. The measured phase boundary compositions for the gamma phase are found to be different from the reported phase diagram. The interdiffusion coefficient and the activation energy decrease in the Pt(W) solid solution with increasing W content. An estimation of the parabolic growth constants and average interdiffusion coefficients in the gamma phase indicates that the diffusion process should be explained based on the estimation of diffusion parameters, which otherwise could lead to a wrong conclusion. The estimation of the relative mobilities of the components in the gamma phase indicates that Pt has a much higher diffusion rate than W. This is explained with the help of the crystal structure and the possible point defects present on different sublattices.

Basic studies on the role of components of Bacillus megaterium as flotation biocollectors in sulphide mineral separation

Studies were carried out to assess the utility of the cellular and extracellular constituents of Bacillus megaterium for the flotation of sphalerite and galena minerals. Based on the flotation results on the individual minerals, it was observed that sphalerite was preferentially floated compared to galena. A maximum selectivity index (SI) value of 11.7 was achieved in the presence of the soluble fraction of the thermolysed cells, which was higher than that obtained with the intact cells (SI of 6.5) and the insoluble fraction of the thermolysed cells (SI of 9.6). The results of the various enzymatic treatment tests revealed that extracellular DNA played a vital role in the selective flotation of sphalerite. A noteworthy finding was that the single-stranded DNA (ssDNA) had a higher biocollector capacity vis-A -vis the double-stranded DNA (dsDNA), leading to better flotation efficiency. About 95 % recovery of sphalerite could be achieved from the mineral mixture by the combined addition of the ssDNA with the non-DNA components of the bacterial cells, resulting in a maximum SI of 19.1. Calcium and phosphate components of the nutrient media were found to be essential for better selectivity of separation of sphalerite. The mechanisms of microbe-mineral interaction are discussed.

Diffusion of components via different modes during growth of the A15-V(3)Gaphase

Based on an interdiffusion study using an incremental diffusion couple in the V-Ga binary system, we have shown that V diffuses via the lattice, whereas Ga does so via grain boundaries, for the growth of the V3Ga phase. We estimate the contributions from the two different mechanisms, which are usually difficult to delineate in an interdiffusion study. Available tracer diffusion studies and the atomic arrangement in the crystal structure have been considered for a discussion on the diffusion mechanisms.

Evolution of texture and its influence on the failure of components in some aluminium alloys

This paper describes the evolution of crystallographic texture in three of the most important high strength aluminium alloys, viz., AA2219, AA7075 and AFNOR7020 in the cold rolled and artificially aged condition. Bulk texture results were obtained by plotting pole figures from X-ray diffraction results followed by Orientation Distribution Function (ODF) analysis and micro-textures were measured using EBSD. The results indicate that the deformation texture components Cu, Bs and S, which were also present in the starting materials, strengthen with increase in amount of deformation. On the other hand, recrystallization texture components Goss and Cube weaken. The Bs component is stronger in the deformation texture. This is attributed to the shear banding. In-service applications indicate that the as-processed AFNOR7020 alloy fails more frequently compared to the other high strength Al alloys used in the aerospace industry. Detailed study of deformation texture revealed that strong Brass (Bs) component could be associated to shear banding, which in turn could explain the frequent failures in AFNOR7020 alloy. The alloying elements in this alloy that could possibly influence the stacking fault energy of the material could be accounted for the strong Bs component in the texture.