Competition of interactions and a new high-temperature phase of selenourea

The aggregation of molecules is usually associated with a specific type of interaction, which can be altered by thermodynamic conditions. Under normal conditions, the crystal structure of selenourea, SeC(NH₂)₂, phase α is trigonal, space group P3₁, Z = 27. Its large number of independent molecules (Z_α' = 9) can be associated with the formation of an NH...N hydrogen bond substituting one of 36 independent NH...Se hydrogen bonds, which prevail among intermolecular interactions. Phase α approximates the trigonal structure with a threefold smaller unit cell (Z = 9), which in turn approximates another still threefold smaller unit cell (Z = 3). The temperature-induced transformations of selenourea have been characterized by calorimetry and by performing 21 single-crystal X-ray diffraction structural determinations as a function of temperature. At 381.0 K, phase α undergoes a first-order displacive transition to phase γ, with space group P3₁21 and Z reduced to 9, when the NH...N bond is broken and an NH...Se bond is formed in its place. Previously, an analogous competition was observed between NH...N and NH...O hydrogen bonds in high-pressure phase III of urea. The lattice vectors along the (001) plane in low- and high-temperature phases of selenourea are related by a similarity rule, while the lattice dimensions along direction c are not affected. This similarity rule also applies to the structures of phase γ and hypothetical phase δ (Z = 3). The thermally controlled transition between enantiomorphic phases of selenourea contrasts with its high-pressure transition at 0.21 GPa to a centrosymmetric phase β, where both the NH...Se and NH...N bonds are present. The compression and heating reduce the number of independent molecules from Z' = 9 in phase α, to Z' = 2 in phase β and to Z' = 1.5 in phase γ.

BAYESIAN ALIGNMENT OF SIMILARITY SHAPES

We develop a Bayesian model for the alignment of two point configurations under the full similarity transformations of rotation, translation and scaling. Other work in this area has concentrated on rigid body transformations, where scale information is preserved, motivated by problems involving molecular data; this is known as form analysis. We concentrate on a Bayesian formulation for statistical shape analysis. We generalize the model introduced by Green and Mardia for the pairwise alignment of two unlabeled configurations to full similarity transformations by introducing a scaling factor to the model. The generalization is not straight-forward, since the model needs to be reformulated to give good performance when scaling is included. We illustrate our method on the alignment of rat growth profiles and a novel application to the alignment of protein domains. Here, scaling is applied to secondary structure elements when comparing protein folds; additionally, we find that one global scaling factor is not in general sufficient to model these data and, hence, we develop a model in which multiple scale factors can be included to handle different scalings of shape components.

Statistical analysis of relative pose information of subcortical nuclei: application on ADNI data

Many brain morphometry studies have been performed in order to characterize the brain atrophy pattern of Alzheimer's disease (AD). The earliest studies focused on the volume of particular brain structures, such as hippocampus and entorhinal cortex. Even though volumetry is a powerful, robust and intuitive technique that has yielded a wealth of findings, more complex shape descriptors have been used to perform statistical shape analysis of particular brain structures. However, in shape analysis studies of brain structures the information of the relative pose between neighbor structures is typically disregarded. This work presents a framework to analyse pose information including the following approaches: similarity transformations with either pseudo-Riemannian or left-invariant Riemannian metric, and centered transformations with a bi-invariant Riemannian metric. As an illustration, an analysis of covariance (ANCOVA) and a discrimination analysis were performed on Alzheimer's Disease Neuroimaging Initiative (ADNI) data.