A connection between the maximum displacements of rogue waves and the dynamics of poles in the complex plane.

Rogue waves of evolution systems are displacements which are localized in both space and time. The locations of the points of maximum displacements of the wave profiles may correlate with the trajectories of the poles of the exact solutions from the perspective of complex variables through analytic continuation. More precisely, the location of the maximum height of the rogue wave in laboratory coordinates (real space and time) is conjectured to be equal to the real part of the pole of the exact solution, if the spatial coordinate is allowed to be complex. This feature can be verified readily for the Peregrine breather (lowest order rogue wave) of the nonlinear Schrödinger equation. This connection is further demonstrated numerically here for more complicated scenarios, namely the second order rogue wave of the Boussinesq equation (for bidirectional long waves in shallow water), an asymmetric second order rogue wave for the nonlinear Schrödinger equation (as evolution system for slowly varying wave packets), and a symmetric second order rogue wave of coupled Schrödinger systems. Furthermore, the maximum displacements in physical space occur at a time instant where the trajectories of the poles in the complex plane reverse directions. This property is conjectured to hold for many other systems, and will help to determine the maximum amplitudes of rogue waves.

Mutational screening of the Wilms's tumour gene, WT1, in males with genital abnormalities.

Several lines of evidence suggest that the Wilms's tumour susceptibility gene, WT1, has an important role in genital as well as kidney development. WT1 is expressed in developing kidney and genital tissues. Furthermore, mutations in WT1 have been detected in patients with the Denys-Drash syndrome (DDS), which is characterised by nephropathy, genital abnormalities, and Wilms's tumour. It is possible that WT1 mutations may cause genital abnormalities in the absence of kidney dysfunction. We tested this hypothesis by screening the WT1 gene for mutation in 12 46,XY patients with various forms of genital abnormality. Using single strand conformation polymorphism (SSCP) we did not detect any WT1 mutations in these patients. However, in addition to the 12 patients, three DDS patients were also analysed using SSCP, and in all three cases heterozygous WT1 mutations were found which would be predicted to disrupt the DNA binding activity of WT1 protein. These results support the notion that DDS results from a dominant WT1 mutation. However, WT1 mutations are unlikely to be a common cause of male genital abnormalities when these are not associated with kidney abnormalities.