On the Jager-Kaul theorem concerning harmonic maps

In 1983, Jager and Kaul proved that the equator map u*(x) = (x/\x\,0) : B-n --> S-n is unstable for 3 less than or equal to n less than or equal to 6 and a minimizer for the energy functional E(u, B-n) = integral B-n \del u\(2) dx in the class H-1,H-2(B-n, S-n) with u = u* on partial derivative B-n when n greater than or equal to 7. In this paper, we give a new and elementary proof of this Jager-Kaul result. We also generalize the Jager-Kaul result to the case of p-harmonic maps.

Differential localization and regulation of death and decoy receptors for TNF-related apoptosis-inducing ligand (TRAIL) in human melanoma cells

Induction of apoptosis in cells by TNF-related apoptosis-inducing ligand (TRAIL), a member of the TNF family, is believed to be regulated by expression of two death-inducing and two inhibitory (decoy) receptors on the cell surface. In previous studies we found no correlation between expression of decoy receptors and susceptibility of human melanoma cells to TRAIL-induced apoptosis, In view of this, we studied the localization of the receptors in melanoma cells by confocal microscopy to better understand their function. We show that the death receptors TRAIL-R1 and R2 are located in the trans-Golgi network, whereas the inhibitory receptors TRAIL-R3 and -R4 are located in the nucleus. After exposure to TRAIL, TRAIL-R1 and -R2 are internalized into endosomes, whereas TRAIL-R3 and -R4 undergo relocation from the nucleus to the cytoplasm and cell membranes. This movement of decoy receptors was dependent on signals from TRAIL-R1 and -R2, as shown by blocking experiments with Abs to TRAIL-R1 and -R2, The location of TRAIL-R1, -R3, and -R4 in melanoma cells transfected with cDNA for these receptors was similar to that in nontransfected cells, Transfection of TRAIL-R3 and -R4 increased resistance of the melanoma lines to TRAIL-induced apoptosis even in melanoma lines that naturally expressed these receptors. These results indicate that abnormalities in decoy receptor location or function may contribute to sensitivity of melanoma to TRAIL-induced apoptosis and suggest that further studies are needed on the functional significance of their nuclear location and TRAIL-induced movement within cell.

A novel genetic locus for low renin hypertension: familial hyperaldosteronism type II maps to chromosome 7 (7p22)

Familial hyperaldosteronism type II (FH-II) is caused by adrenocortical hyperplasia or aldosteronoma or both and is frequently transmitted in an autosomal dominant fashion. Unlike FH type I (FI-I-I), which results from fusion of the CYP11B1 and CYP11B2 genes, hyperaldosteronism in FH-II is not glucocorticoid remediable. A large family with FH-II was used for a genome wide search and its members were evaluated by measuring the aldosterone:renin ratio. In those with an increased ratio, FH-II was confirmed by fludrocortisone suppression testing. After excluding most of the genome, genetic linkage was identified with a maximum two point lod score of 3.26 at theta =0, between FH-II in this family and the polymorphic markers D7S511, D7S517, and GATA24F03 on chromosome 7,a region that corresponds to cytogenetic band 7p22. This is the first identified locus for FH-II; its molecular elucidation may provide further insight into the aetiology of primary aldosteronism.

Disaggregation of polygons of surficial geology and soil maps using spatial modelling and legacy data

Examples from the Murray-Darling basin in Australia are used to illustrate different methods of disaggregation of reconnaissance-scale maps. One approach for disaggregation revolves around the de-convolution of the soil-landscape paradigm elaborated during a soil survey. The descriptions of soil ma units and block diagrams in a soil survey report detail soil-landscape relationships or soil toposequences that can be used to disaggregate map units into component landscape elements. Toposequences can be visualised on a computer by combining soil maps with digital elevation data. Expert knowledge or statistics can be used to implement the disaggregation. Use of a restructuring element and k-means clustering are illustrated. Another approach to disaggregation uses training areas to develop rules to extrapolate detailed mapping into other, larger areas where detailed mapping is unavailable. A two-level decision tree example is presented. At one level, the decision tree method is used to capture mapping rules from the training area; at another level, it is used to define the domain over which those rules can be extrapolated. (C) 2001 Elsevier Science B.V. All rights reserved.

Identification of trail pheromone compounds from the labial glands of the stingless bee Geotrigona mombuca

Foragers of several species of stingless bees deposit pheromone spots in the vegetation to guide recruited nestmates to a rich food source. Recent studies have shown that Trigona and Scaptotrigona workers secrete these pheromones from their labial glands. An earlier report stated that species within the genus Geotrigona use citral from their mandibular glands for scent marking. Since convincing experimental proof for this conjecture is lacking, we studied the glandular origin of the trail pheromone of Geotrigona mombuca. In field bioassays, newly recruited bees were diverted by artificial scent trails that branched off from the natural scent trail deposited by their nestmates only when they were baited with extracts from the foragers` labial glands. Compounds extracted from the mandibular glands, however, did not release trail following behavior. This demonstrates that the trail pheromone of G. mombuca is produced in the labial glands, as in Trigona and Scaptotrigona. Furthermore, in chemical analyses citral was identified exclusively in the foragers` mandibular glands, which disproves its supposed role as a trail pheromone. The labial glands contained a series of terpene- and wax type esters, with farnesyl butanoate as major constituent. We, therefore, postulate that the trail pheromone of G. mombuca is composed of a blend of esters.

TRAIL expression by activated human CD4(+)V alpha 24NKT cells induces in vitro and in vivo apoptosis of human acute myeloid leukema cells

Human V alpha 24NKT cells are activated by alpha -galactosylceramide (alpha -GalCer)-pulsed dendritic cells in a CD1d-dependent and a T-cell receptor-mediated manner. Here, we demonstrate that CD4(+)V alpha 24NKT cells derived from a patient with acute myeloid leukemia (AML) M4 are phenotypically similar to those of healthy donors and, in common with those derived from healthy donors, express tumor necrosis factor-related apoptosis-inducing ligand (TRAIL) when the cells are activated by alpha -GalCer-pulsed dendritic cells but not prior to activation. We also show that myeloid that human activated CD4(+)V alpha 24NKT cells induced apoptosis of human leukemia cells in vivo. This is the first evidence that activated V alpha 24NKT cells express TRAIL and that TRAIL causes apoptosis of monocytic leukemia cells from patients with AML M4 in vitro and in vivo. Adoptive immune therapy with activated V alpha 24NKT cells, or other strategies to increase activated V alpha 24NKT cells in vivo, may be of benefit to patients with AML M4.

Riddling and invariance for discontinuous maps preserving Lebesgue measure

In this paper we use the mixture of topological and measure-theoretic dynamical approaches to consider riddling of invariant sets for some discontinuous maps of compact regions of the plane that preserve two-dimensional Lebesgue measure. We consider maps that are piecewise continuous and with invertible except on a closed zero measure set. We show that riddling is an invariant property that can be used to characterize invariant sets, and prove results that give a non-trivial decomposion of what we call partially riddled invariant sets into smaller invariant sets. For a particular example, a piecewise isometry that arises in signal processing (the overflow oscillation map), we present evidence that the closure of the set of trajectories that accumulate on the discontinuity is fully riddled. This supports a conjecture that there are typically an infinite number of periodic orbits for this system.

Multiple maps and activity-dependent representational plasticity in the anterior Wulst of the adult barn owl (Tyto alba)

In the present study we addressed the issue of somatosensory representation and plasticity in a nonmammalian species, the barn owl. Multiunit mapping techniques were used to examine the representation of the specialized receptor surface of the claw in the anterior Wulst. We found dual somatotopic mirror image representations of the skin surface of the contralateral claw. In addition, we examined both representations 2 weeks after denervation of the distal skin surface of a single digit. In both representations, the denervated digital representation became responsive to stimulation of the adjacent, mutually functional, digit. The mutability and multiple representations indicates that the Wulst provides the owl with sensory processing capabilities analogous to those in mammals.

Pseudo-randomness of round-off errors in discretized linear maps on the plane

We analyze the sequences of round-off errors of the orbits of a discretized planar rotation, from a probabilistic angle. It was shown [Bosio & Vivaldi, 2000] that for a dense set of parameters, the discretized map can be embedded into an expanding p-adic dynamical system, which serves as a source of deterministic randomness. For each parameter value, these systems can generate infinitely many distinct pseudo-random sequences over a finite alphabet, whose average period is conjectured to grow exponentially with the bit-length of the initial condition (the seed). We study some properties of these symbolic sequences, deriving a central limit theorem for the deviations between round-off and exact orbits, and obtain bounds concerning repetitions of words. We also explore some asymptotic problems computationally, verifying, among other things, that the occurrence of words of a given length is consistent with that of an abstract Bernoulli sequence.