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This paper extends parts of the results from [17] for plane curves to the case of hypersurfaces in R n. Let M be a compact connected oriented n − 1 dimensional manifold without boundary like S 2 or the torus S 1 × S 1. Then shape space is either the manifold of submanifolds of R n of type M , or the orbifold of immersions from M to R n modulo the group of(More)
ii iii In nova fert animus mutatas dicere formas corpora; di, coeptis (nam vos mutastis et illas) adspirate meis primaque ab origine mundi ad mea perpetuum deducite tempora carmen! * The persistence of memory by Salvador Dali. Picture taken from Abstract. Many procedures in science, engineering and medicine produce data in the form of geometric shapes.(More)
Binding of radioactive thyroxine to proteins in the plasma of vertebrates was studied by electrophoresis followed by autoradiography. Albumin was found to be a thyroxine carrier in the blood of all studied fish, amphibians, reptiles, monotremes, marsupials, eutherians (placental mammals), and birds. Thyroxine binding to transthyretin was detected in the(More)
1. The major protein synthesized and secreted by the choroid plexus from mammals, birds, reptiles and probably amphibians is similar in subunit structure to transthyretin. 2. In mammals and birds the proportion of transthyretin mRNA is much higher in choroid plexus RNA than in liver RNA. No transthyretin mRNA is found in brain outside the choroid plexus. 3.(More)
The presence of transthyretin in mammals and birds, but not amphibia, suggested that transthyretin expression first appeared in stem reptiles. Therefore, transthyretin synthesis was studied in a lizard. Transthyretin synthesis in choroid plexus pieces from Tiliqua rugosa was demonstrated by incorporation of radiactive amino acids. Oligonucleotides(More)
Thyroxine binding to proteins in pig plasma during electrophoresis was observed in the albumin, but not in the prealbumin and post-albumin regions. Transthyretin could be identified in medium from in vitro pig choroid plexus incubations by size and number of subunits and a very high rate of synthesis and secretion. Its electrophoretic mobility was(More)
Among the proteins secreted by choroid plexus of vertebrates, one protein is much more abundant than all others. In mammals, birds, and reptiles this protein is transthyretin, a tetramer of identical 15-kDa subunits. In this study choroid plexus from frogs, tadpoles, and toads incubated in vitro were found to synthesize and secrete one predominant protein.(More)
We study Sobolev-type metrics of fractional order on the group of compactly supported diffeomorphisms Diffc(M), where M is a Riemannian manifold of bounded geometry. We prove that the geodesic distance, induced by the Riemannian metric, vanishes if the order s satisfies 0 ≤ s < 1 2. For M = R we show the vanishing of the geodesic distance also for s = 1 2 ,(More)
A number of mitochondrial DNA (mtDNA) deletions have been recently identified in the tissues of patients with mitochondrial diseases and in elderly individuals. To investigate the distribution of mutant mitochondrial genomes within any particular tissue, we have developed a sensitive method based on indirect in situ PCR. Our experiments have shown that the(More)
Let M be a compact connected oriented n−1 dimensional manifold without boundary. In this work, shape space is the orbifold of unparametrized immersions from M to R n. The results of [1], where mean curvature weighted metrics were studied, suggest to incorporate Gauß curvature weights in the definition of the metric. This leads us to study metrics on shape(More)