Shape change along geodesics with application to cleft lip surgery

Continuous shape change is represented as curves in the shape space. A method for checking the closeness of these curves to a geodesic is presented. Three large databases of short human motions are considered and shown to be well approximated by geodesics. The motions are thus approximated by two shapes on the geodesic and the rate of progress along the path. An analysis of facial motion data taken from a study of subjects with cleft lip or cleft palate is presented that allows the motion to be considered independently from the static shape. Inferential methods for assessing the change in motion are presented. The construction of predicted animated motions is discussed

Structure and dynamics invan der Waals complexes of aromatic molecules

Much work has been done to investigate the properties of van der Waals complexes of aromatic molecules. An area of interest is the relationship between the structure and dynamics of these systems. In particular, the fate of vibrational energy injected into the complex is examined in order to help understand the effect of structure on the observed dynamics. The experiments described involve time resolved fluorescence measurements using the technique of time-correlated single-photon counting. Van der Waals complexes are prepared in a pulsed supersonic jet, and vibrational levels are excited by a tunable laser. Fluorescence is collected at specific emission wavelengths to observe any time evolution of the emission spectrum. In addition, the polarization dependence of fluorescence allows measurement of rotational constants, thus providing structural information. Complexes studied involve perylene, xanthione, and 2,5-diphenylfuran (PPF) as host molecules. Perylene complexes are observed to undergo both singlet-singlet and singlet-triplet coupling upon vibrational excitation, and complexes with alkyl halide guest species undergo vibrationally induced conformational exchange. PPF and perylene complexes with argon and methane are the subject of studies to investigate the effects of vibrational and electronic coupling on the migration of energy from the mode excited to the vibrational predissociation channel. Xanthione complexes with linear, branched, and cyclic alkanes show strong singlet-triplet coupling, the rates of which are found to depend on the structure of the alkane. Structural measurements on PPF complexes with argon, methane, and n-alkanes indicate that time resolved techniques can be used in combination with semi-empirical calculations to assign structures of van der Waals complexes

The Karcher mean of a class of symmetric distributions on the circle

We derive unique Karcher means for symmetric probability distributions on the unit circle, under the conditions that: (i) the distributions have differentiable density functions and (ii) the distributions are concentrated at the symmetry points.

Laser desorption jet-cooling of organic-molecules - cooling characteristics and detection sensitivity

Contains fulltext : 99059.pdf (publisher's version ) (Open Access