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.

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.

Unitary R-matrices for topological quantum computing

The main problem with current approaches to quantum computing is the difficulty of establishing and maintaining entanglement. A Topological Quantum Computer (TQC) aims to overcome this by using different physical processes that are topological in nature and which are less susceptible to disturbance by the environment. In a (2+1)-dimensional system, pseudoparticles called anyons have statistics that fall somewhere between bosons and fermions. The exchange of two anyons, an effect called braiding from knot theory, can occur in two different ways. The quantum states corresponding to the two elementary braids constitute a two-state system allowing the definition of a computational basis. Quantum gates can be built up from patterns of braids and for quantum computing it is essential that the operator describing the braiding-the R-matrix-be described by a unitary operator. The physics of anyonic systems is governed by quantum groups, in particular the quasi-triangular Hopf algebras obtained from finite groups by the application of the Drinfeld quantum double construction. Their representation theory has been described in detail by Gould and Tsohantjis, and in this review article we relate the work of Gould to TQC schemes, particularly that of Kauffman.

Topological charge and angular momentum of light beams carrying optical vortices

We analyze the properties of light beams carrying phase singularities, or optical vortices. The transformations of topological charge during free-space propagation of a light wave, which is a combination of a Gaussian beam and a multiple charged optical vortex within a Gaussian envelope, are studied both in theory and experiment. We revise the existing knowledge about topological charge conservation, and demonstrate possible scenarios where additional vortices appear or annihilate during free propagation of such a combined beam. Coaxial interference of optical vortices is also analyzed, and the general rule for angular-momentum density distribution in a combined beam is established. We show that, in spite of any variation in the number of vortices in a combined beam, the total angular momentum is constant during the propagation. [S1050-2947(97)09910-1].

Topological methods for some boundary value problems

We establish existence of solutions for a finite difference approximation to y = f(x, y, y ') on [0, 1], subject to nonlinear two-point Sturm-Liouville boundary conditions of the form g(i)(y(i),y ' (i)) = 0, i = 0, 1, assuming S satisfies one-sided growth bounds with respect to y '. (C) 2001 Elsevier Science Ltd. All rights reserved.

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.