Invariant Higher-Order Variational Problems II

Motivated by applications in computational anatomy, we consider a second-order problem in the calculus of variations on object manifolds that are acted upon by Lie groups of smooth invertible transformations. This problem leads to solution curves known as Riemannian cubics on object manifolds that are endowed with normal metrics. The prime examples of such object manifolds are the symmetric spaces. We characterize the class of cubics on object manifolds that can be lifted horizontally to cubics on the group of transformations. Conversely, we show that certain types of non-horizontal geodesic on the group of transformations project to cubics. Finally, we apply second-order Lagrange–Poincaré reduction to the problem of Riemannian cubics on the group of transformations. This leads to a reduced form of the equations that reveals the obstruction for the projection of a cubic on a transformation group to again be a cubic on its object manifold.     

Sulfur‐Bridged BODIPY DYEmers

Reactions of BODIPY monomers with sulfur nucleophiles and electrophiles result in the formation of new BODIPY dimers. Mono‐ and disulfur bridges are established, and the new dyestuff molecules were studied with respect to their structural, optical, and electrochemical properties. X‐ray diffraction analyses reveal individual angulated orientations of the BODIPY subunits in all cases. DFT calculations provide solution conformers of the DYEmers which deviate in a specific manner from the crystallographic results. Clear exciton‐like splittings are observed in the absorption spectra, with maxima at up to 628 nm, in combination with the expected weak fluorescence in polar solvents. A strong communication between the BODIPY subunits was detected by cyclic voltammetry, where two separated one‐electron oxidation and reduction waves with peak‐to‐peak potential differences of 120–400 mV are observed. The qualitative applicability of the exciton model by Kasha for the interpretation of the absorption spectral shape with respect to the conformational state, subunit orientation and distance, and conjugation through the different sulfur bridges, is discussed in detail for the new BODIPY derivatives. This work is part of our concept of DYEmers, where the covalent oligomerisation of BODIPY‐type dye molecules with close distances is leading to new functional dyes with predictable properties.     

Pressure effects on the alpha and alpha' relaxations in polymethylphenylsiloxane

In some polymers, in addition to the usual structural alpha relaxation, a slower alpha' relaxation is observed with a non-Arrhenius temperature dependence. In order to understand better the molecular origin of this alpha' relaxation in poly(methylphenylsiloxane) (PMPS) we have studied, for the first time, the pressure dependence of its relaxation time, together with the usual temperature dependence, by means of dynamic light scattering (DLS). For the same material the alpha relaxation was also studied by means of DLS and dielectric spectroscopy (DS) in broad temperature and pressure ranges. We find that the temperature dependence of both alpha and alpha' relaxation times, at all pressures studied, can be described by a double Vogel-Fulcher-Tammann (VFT) law. The pressure dependence of the characteristic temperatures Tg (glass transition temperature) and T0 (Vogel temperature) as well as the activation volumes for both alpha and alpha' processes are very similar, indicating, that both relaxation processes originate from similar local molecular dynamics. Additionally, for both alpha and alpha' relaxations the combined temperature and pressure dependences of the relaxation times can be described using a parameter Gamma=rhon/T with the same value of the exponent n.     

Alkylphenol retention indices

A novel type of retention indices for alkylphenols and related compounds are proposed. The alkylphenol retention indices (APRI) use para-substituted n-alkylphenols as reference series. APRI for para-n-alkylphenols are per definition equal to the number of carbon atoms in the alkyl substituent; the value for phenol is zero. Application of the APRI system with different types of derivatisation of the phenolic hydroxy group showed that the derivatisation has limited influence on these indices. Especially para-substituted alkylphenols gave APRI values that could be transferred with high accuracy from one type of derivative to another. By comparing results obtained with different gradients in temperature-programmed GC, it was also shown that APRI is less affected by chromatographic conditions than retention indices based on n-alkanes.     

On the interpretation of the 1100 cm(-1) Raman band in phospholipids and other alkyl-containing molecular entities

The long-standing issue on the interpretation of a Raman band at 1100 cm(-1) is discussed. By combining observations from studies on lipid bilayers, alkanes, and polyethylenes, one can now definitely assign this band to the presence of isolated gauche bonds. In addition, we discuss the use of an order parameter S(trans) in lipid bilayer structures.     

GLMMLasso: An Algorithm for High-Dimensional Generalized Linear Mixed Models Using ℓ1-Penalization

We propose an ?₁-penalized algorithm for fitting high-dimensional generalized linear mixed models (GLMMs). GLMMs can be viewed as an extension of generalized linear models for clustered observations. Our Lasso-type approach for GLMMs should be mainly used as variable screening method to reduce the number of variables below the sample size. We then suggest a refitting by maximum likelihood based on the selected variables only. This is an effective correction to overcome problems stemming from the variable screening procedure that are more severe with GLMMs than for generalized linear models. We illustrate the performance of our algorithm on simulated as well as on real data examples. Supplementary materials are available online and the algorithm is implemented in the R package glmmixedlasso.