The (exclusion) statistics of parafermions is used to study degeneracies of quasiholes over the paired (or in general clustered) quantum Hall states. Focus is on the Zk and su(3)k/u(1) 2 parafermions, which are used in the description of spin-polarized and spin-singled clustered quantum Hall states.

Symbolic perturbation by innnitely small values removes degeneracies in geometric algorithms and enables programmers to handle only generic cases: there are a few such cases, whereas there are an overwhelming number of degenerate cases. Current perturbation schemes have limitations, presented below. To overcome them, this paper proposes to use an-arithmetic, i.e. to represent in an explicit way...

Turing mechanisms can yield a large variety of patterns from noisy, homogenous initial conditions and have been proposed as patterning mechanism for many developmental processes. However, the molecular components that give rise to Turing patterns have remained elusive, and the small size of the parameter space that permits Turing patterns to emerge makes it difficult to explain how Turing patte...

Intervertebral disc (IVD) cells derived from degenerate tissue respond aberrantly to mechanical stimuli, potentially due to altered mechanotransduction pathways. Elucidation of the altered, or alternative, mechanotransduction pathways operating with degeneration could yield novel targets for the treatment of IVD disease. Our aim here was to investigate the involvement of RGD-recognising integri...

The structure of boundaries between degenerate and nondegenerate solutions of Ashtekar's canonical reformulation of Einstein's equations is studied. Several examples are given of such \phase boundaries" in which the metric is degenerate on one side of a null hypersurface and non-degenerate on the other side. These include portions of at space, Schwarzschild, and plane wave solutions joined to d...

We show that static electrovacuum black hole spacetimes containing an asymptotically flat spacelike hypersurface with compact interior and with both degenerate and non-degenerate components of the event horizon do not exist, under the supplementary hypothesis that all degenerate components of the event horizon have charges of the same sign. This extends previous uniqueness theorems of Simon and...

The structure of boundaries between degenerate and nondegenerate solutions of Ashtekar’s canonical reformulation of Einstein’s equations is studied. Several examples are given of such “phase boundaries” in which the metric is degenerate on one side of a null hypersurface and non-degenerate on the other side. These include portions of flat space, Schwarzschild, and plane wave solutions joined to...