Variable Selection in Varying-Coefficient Models Using P-Splines

In this article, we consider nonparametric smoothing and variable selection in varying-coefficient models. Varying-coefficient models are commonly used for analyzing the time-dependent effects of covariates on responses measured repeatedly (such as longitudinal data). We present the P-spline estimator in this context and show its estimation consistency for a diverging number of knots (or B-spline basis functions). The combination of P-splines with nonnegative garrote (which is a variable selection method) leads to good estimation and variable selection. Moreover, we consider APSO (additive P-spline selection operator), which combines a P-spline penalty with a regularization penalty, and show its estimation and variable selection consistency. The methods are illustrated with a simulation study and real-data examples. The proofs of the theoretical results as well as one of the real-data examples are provided in the online supplementary materials.     

Selective Carbanion–Pyridine Coordination of a Reactive P,N Ligand to RhI

Ligands with reactive carbon sites in the periphery of a metal center have emerged as a powerful approach for metal–ligand bond activation. These reactive carbon sites are commonly generated by deprotonation strategies. Carbon–silicon bond cleavage is a potential alternative to access such constructs. Herein, the monodesilylation of bis-silyl-substituted P,N scaffold PN^Si2 in the coordination sphere of [Rh^I(Cl)(CO)( PN^Si2 )] ( 1 ) with sodium azide is disclosed. This affords a unique dinucleating anionic κ²-C,N-κ¹-P ligand with a carbanionic methine carbon atom directly bound to rhodium as part of a four-membered Rh-N-C-C rhodacycle. This dimer undergoes meta-pyridine C−H activation facilitated by weak bases, which leads to a desymmetrization of the system and provides a σ,π-bridging 3-pyridyl fragment bound to Rh^I. The facile Si−C cleavage strategy may pave the way to studying the reactivity and functionalization of a variety of κ²-C,N-coordinated pyridine scaffolds for selective transformations.     

24- and 26-membered macrocyclic diorganotin(IV) bis-dithiocarbamate complexes with N,N'-disubstituted 1,3- and 1,4-bis(aminomethyl)benzene and 1,1'-bis(aminomethyl)ferrocene as spacer groups

The potassium bis-dithiocarbamate (bis-dtc) salts of 1,3-bis(benzylaminomethyl)benzene (1,3-Bn-ambdtc), 1,3-bis(iso-butylaminomethyl)benzene (1,3-(i)Bu-ambdtc), 1,4-bis(benzylaminomethyl)benzene (1,4-Bn-ambdtc), and 1,4-bis(iso-butylaminomethyl)benzene (1,4-(i)Bu-ambdtc) were reacted with three different diorganotin dichlorides (R2SnCl2 with R = Me, (n)Bu, and Ph) in 1:1 stoichiometric ratios to give the corresponding diorganotin bis-dithiocarbamates. Additionally, the dimethyltin bis-dithiocarbamate of 1,1'-bis(benzylaminomethyl)ferrocene (1,1'-Bn-amfdtc) was prepared. The resulting complexes have been characterized as far as possible by elemental analysis, FAB(+) mass spectrometry, IR and NMR ((1)H, (13)C, and (119)Sn) spectroscopy, and single-crystal X-ray diffraction, showing that the tin complexes are dinuclear 24- and 26-membered macrocyclic species of composition [{R2Sn(bis-dtc)}2]. As shown by (119)Sn NMR spectroscopy, the tin centers are hexa-coordinated in all cases; however, two different coordination environments are possible, as detected by single-crystal X-ray diffraction. In the dimethyltin derivatives of 1,3-Bn-ambdtc, 1,3-(i)Bu-ambdtc, 1,4-Bn-ambdtc, and 1,1'-Bn-amfdtc and the di-n-butyltin derivative of 1,3-(i)Bu-ambdtc, the metal atoms are embedded in skewed-trapezoidal-bipyramidal coordination polyhedra with asymmetrically coordinating trans-oriented dtc groups. In contrast, in the diphenyltin derivative 1,3-(i)Bu-ambdtc, the metal centers have distorted octahedral coordination with symmetrically coordinating cis-oriented dtc functions. Thus, for the complexes derived from 1,3-Bn/(i)Bu-ambdtc, two different macrocyclic structures were observed. In the dimethyl- and di-n-butyltin derivatives, the bridging bis-dtc ligands adopt U-shaped conformations, while in the case of the diphenyltin derivative, the conformation is L-shaped. Furthermore, two different macrocyclic ring conformations can occur, which differ in the spatial orientation of the substituents attached to the nitrogen atoms (Bn or (i)Bu). The dimethyltin derivatives of 1,4-Bn-ambdtc and 1,1'-Bn-amfdtc have cavities, in which aromatic rings are accommodated in the solid state.     

Redox‐Active‐Ligand‐Mediated Formation of an Acyclic Trinuclear Ruthenium Complex with Bridging Nitrido Ligands

Coordination of a redox‐active pyridine aminophenol ligand to Ru^II followed by aerobic oxidation generates two diamagnetic Ru^III species [ 1 a (cis) and 1 b (trans)] with ligand‐centered radicals. The reaction of 1 a / 1 b with excess NaN₃ under inert atmosphere resulted in the formation of a rare bis(nitrido)‐bridged trinuclear ruthenium complex with two nonlinear asymmetrical Ru‐N‐Ru fragments. The spontaneous reduction of the ligand centered radical in the parent 1 a / 1 b supports the oxidation of a nitride (N^3?) to half an equivalent of N₂. The trinuclear omplex is reactive toward TEMPO‐H, tin hydrides, thiols, and dihydrogen.     

Velocimetry microsensors driven by linearly polarized optical tweezers

We report on a new type of single-point velocimetry microsensor that can be positioned in microfluidic devices by use of optical tweezers. The flag-shaped microsensor is readily made by a low-cost two-photon polymerization technique. At rest the linearly polarized optical tweezer traps the microsensor at the focal point, and the flag-plate gets aligned in the polarization direction. Under a fluid flow, the plate rotates to an equilibrium angle that is used to measure the fluid velocity with a micrometer-size spatial resolution. Experimental results are in good agreement with theoretical calculations of optical and hydrodynamic torques on such a flag-shaped microsensor.     

Capturing the Genesis of an Active Fischer–Tropsch Synthesis Catalyst with Operando X‐ray Nanospectroscopy

A state‐of‐the‐art operando spectroscopic technique is applied to Co/TiO₂ catalysts, which account for nearly half of the world's transportation fuels produced by Fischer–Tropsch catalysis. This allows determination of, at a spatial resolution of approximately 50 nm, the interdependence of formed hydrocarbon species in the inorganic catalyst. Observed trends show intra‐ and interparticular heterogeneities previously believed not to occur in particles under 200 μm. These heterogeneities are strongly dependent on changes in H₂/CO ratio, but also on changes thereby induced on the Co and Ti valence states. We have captured the genesis of an active FTS particle over its propagation to steady‐state operation, in which microgradients lead to the gradual saturation of the Co/TiO₂ catalyst surface with long chain hydrocarbons (i.e., organic film formation).     

Smoothing and preservation of irregularities using local linear fitting

For nonparametric estimation of a smooth regression function, local linear fitting is a widely-used method. The goal of this paper is to briefly review how to use this method when the unknown curve possibly has some irregularities, such as jumps or peaks, at unknown locations. It is then explained how the same basic method can be used when estimating unsmooth probability densities and conditional variance functions. This research was supported by GOA/07/04-project of the Research Fund KULeuven. Support from the IAP research network nr. P6/03 of the Federal Science Policy, Belgium, is also acknowledged.     

[Bis­(di­phenyl­phosphino)­methane][1,3-bis­(di­phenyl­phosphino)­propane]­platinum(II) dibromide

The asymmetric unit of the title compound, [Pt(C₂₅H₂₂P₂)(C₂₇H₂₆P₂)]Br₂ or [Pt(dppm)(dppp)]Br₂, where dppm is bis­(di­phenyl­phosphino)­methane and dppp is 1,3-bis­(di­phenyl­phosphino)­propane, consists of a discrete [Pt(dppm)(dppp)]²⁺ cation and two Br⁻ anions at van der Waals distances. This is the first reported platinum(II) complex containing both dppm and dppp ligands. Noticeable features are that the coordination of platinum by the differing dppm and dppp ligands produces a distorted coordination geometry with differing ligand bite angles (and to a lesser extent bond distances), and that the strain induced by the formation of the four-membered dppm chelate ring has a marked effect upon the bond angles at the P atoms of this ligand.