Identifying Mixtures of Mixtures Using Bayesian Estimation

The use of a finite mixture of normal distributions in model-based clustering allows us to capture non-Gaussian data clusters. However, identifying the clusters from the normal components is challenging and in general either achieved by imposing constraints on the model or by using post-processing procedures. Within the Bayesian framework, we propose a different approach based on sparse finite mixtures to achieve identifiability. We specify a hierarchical prior, where the hyperparameters are carefully selected such that they are reflective of the cluster structure aimed at. In addition, this prior allows us to estimate the model using standard MCMC sampling methods. In combination with a post-processing approach which resolves the label switching issue and results in an identified model, our approach allows us to simultaneously (1) determine the number of clusters, (2) flexibly approximate the cluster distributions in a semiparametric way using finite mixtures of normals and (3) identify cluster-specific parameters and classify observations. The proposed approach is illustrated in two simulation studies and on benchmark datasets. Supplementary materials for this article are available online.     

Surprising photochemical reactivity and visible light-driven energy transfer in heterodimetallic complexes

The bis(bidentate) phosphine cis,trans,cis-1,2,3,4-tetrakis(diphenylphosphino)cyclobutane (dppcb) has been used for the synthesis of a series of novel heterodimetallic complexes starting from [Ru(bpy)(2)(dppcb)]X(2) (1; X = PF(6), SbF(6)), so-called dyads, showing surprising photochemical reactivity. They consist of [Ru(bpy)(2)](2+)"antenna" sites absorbing light combined with reactive square-planar metal centres. Thus, irradiating [Ru(bpy)(2)(dppcb)MCl(2)]X(2) (M = Pt, 2; Pd, 3; X = PF(6), SbF(6)) dissolved in CH(3)CN with visible light, produces the unique heterodimetallic compounds [Ru(bpy)(CH(3)CN)(2)(dppcb)MCl(2)]X(2) (M = Pt, 7; Pd, 8; X = PF(6), SbF(6)). In an analogous reaction the separable diastereoisomers (ΔΛ/ΛΔ)- and (ΔΔ/ΛΛ)-[Ru(bpy)(2)(dppcb)Os(bpy)(2)](PF(6))(4) (5/6) lead to [Ru(bpy)(CH(3)CN)(2)(dppcb)Os(bpy)(2)](PF(6))(4) (9), where only the RuP(2)N(4) moiety of 5/6 is photochemically reactive. By contrast, in the case of [Ru(bpy)(2)(dppcb)NiCl(2)]X(2) (4; X = PF(6), SbF(6)) no clean photoreaction is observed. Interestingly, this difference in photochemical behaviour is completely in line with the related photophysical parameters, where 2, 3, and 5/6, but not 4, show long-lived excited states at ambient temperature necessary for this type of photoreaction. Furthermore, the photochemical as well as the photophysical properties of 2-4 are also in accordance with their single crystal X-ray structures presented in this work. It seems likely that differences in "steric pressure" play a major role for these properties. The unique complexes 7-9 are also fully characterized by single-crystal X-ray structure analyses, clearly showing that the stretching vibration modes of the ligand CH(3)CN, present only in 7-9, cannot be directly influenced by "steric pressure". This has dramatic consequences for their photophysical parameters. The trans-[Ru(bpy)(CH(3)CN)(2)](2+) chromophore of 9 acts as efficient "antenna" for visible light-driven energy transfer to the Os-centred "trap" site, resulting in k(en) ≥ 2 × 10(9) s(-1) for the energy transfer. Since electron transfer is made possible by the use of this intervening energy transfer, in dyads like 2-4 highly reactive M(0) species (M = Pt, Pd, Ni) could be generated. These species are not stable in water and M(II) hydride intermediates are usually formed, further reacting with H(+) to give H(2). Thus, derivatives of 3, namely [M(bpy)(2)(dppcb)Pd(bpy)](PF(6))(4) (M = Os, Ru) dissolved in 1:1 (v/v) H(2)O-CH(3)CN produce H(2) during photolysis with visible light.     

Divergent reaction pathways of a cationic intermediate: rearrangement and cyclization of 2-substituted furyl and benzofuryl enones catalyzed by iridium(III)

In contrast to 2-substituted pyrrole enones, furyl and benzofuryl enones do not undergo the Nazarov electrocyclization. Instead, these furyl and benzofuryl enones exhibit unusual rearrangement sequences in the presence of catalytic amounts of [IrBr(CO)(DIM)((R)-(+)-BINAP)](SbF(6))(2) (1; DIM = diethylisopropylidene malonate) and AgSbF(6) (1:1). A 1,2-H shift followed by intramolecular Friedel-Crafts alkylation leads to synthetically valuable cyclohexanones with furanylic quaternary centers. The electrophilicity of 1 is essential for this rearrangement.     

Polytypism in the lithium-aluminum layered double hydroxides: the [LiAl2(OH)6]+ layer as a structural synthon

The [LiAl(2)(OH)(6)](+) layer obtained from gibbsite-Al(OH)(3) belongs to the layer group symmetry P-312/m. This layer satisfies the defining characteristics of a synthon in that it predicts all the polymorphic modifications of the layered double hydroxides of Li and Al. The various possible ways of stacking these layers can be derived by the systematic elimination of the principal symmetry elements comprising the layer group. This approach yields the complete universe of possible structures. When the 3 axis of the layer is conserved in the stacking, the resultant crystal adopts the structure of the 1H, 2H, or 3R polytypes (H, hexagonal; R, rhombohedral). When the 3 axis is destroyed and the 2/m axis is retained, the crystal adopts monoclinic symmetry and crystallizes in the structures of the 1M(1) or 1M(2) (M, monoclinic) polytypes; the two polytypes differ only in their translational component. Experimentally, gibbsite-based precursors yield the 2H polytype, and bayerite-based precursors yield the 1M polytype. Faulted structures incorporating differently oriented 1M(1) motifs or a mixture of 1M(1) and 1M(2) motifs are also obtained. These stacking faults result in cation disorder along the c axis and produce signature effects on the line shapes of select reflections in the powder X-ray diffraction patterns. This symmetry-guided approach is general and can be extended to other classes of layered solids.     

Electronic structure and magnetic, electrical and optical properties of ferromagnetic Heusler alloys

Measurements of the electrical resistivity and the Hall effect of the Heusler alloys NiMnSb, PtMnSb, CoMnSb, AuMnSb, CuMnSb and PtMnSn are reported. The anomalous Hall effect is analyzed in terms of the contributions from skew scattering and side jump. The spin polarization of the charge carriers is proportional to the magnetization. This is an indication that the electronic structure as a function of the temperature is best described by a local band model, with complete spin polarization of charge carriers parallel to the local magnetization at all temperatures. The spin disorder resistivity of NiMnSb is calculated with the local band model. The magneto-optical Kerr effect of PtMnSb is enhanced by the plasma resonance of the charge carriers.     

Ideals in ortholattices, Bell inequalities, and simultaneously definite properties

The notion of quasiboolean algebras (Bell and Clifton, 1995) is compared with related notions of semiprime ideals, commutator ideals, partial compatibility, joint distributions of observables, and Bell inequalities on orthomodular lattices. Some consequences of characterizations of simultaneously definite properties are derived.     

Extensions of partially ordered partial abelian monoids

The notion of a partially ordered partial abelian monoid is introduced and extensions of partially ordered abelian monoids by partially ordered abelian groups are studied. Conditions for the extensions to exist are found. The cases when both the above mentioned structures have the Riesz decomposition property, or are lattice ordered, are treated. Some applications to effect algebras and MV-algebras are shown.