In most of the Western world, age-related macular degeneration (AMD) remains the largest single cause of severe visual impairment, and its prevalence continues to increase. It is considered to be aâ€¦ (More)

We study 3-dimensional Ricci solitons which project via a semi-conformal mapping to a surface. We reformulate the equations in terms of parameters of the map; this enables us to give an ansatz forâ€¦ (More)

We construct new complex-valued harmonic morphisms from Euclidean spaces from functions which are holomorphic with respect to Hermitian structures. In particular, we give the first global examples ofâ€¦ (More)

We construct large families of harmonic morphisms which are holomorphic with respect to Hermitian structures by nding heierarchies of Weierstrass-type representations. This enables us to nd newâ€¦ (More)

We show that all harmonic morphisms from 3-dimensional Minkowski space with values in a surface have a Weierstrass representation involving the complex numbers or the hyperbolic numbers depending onâ€¦ (More)

Equivalences between conformal foliations on Euclidean 3-space, Hermitian structures on Euclid-ean 4-space, shear-free ray congruences on Minkowski 4-space, and holomorphic foliations on complexâ€¦ (More)

We describe the relationship between complex-valued harmonic morphisms from Minkowski 4-space and the shear-free ray congruences of mathematical physics. Then we show how a horizontally conformalâ€¦ (More)

A shear-free ray congruence (SFR) on Minkowsi space is a family of null geodesics that fill our a region of space-time, with the property that Lie transport along each geodesic, of vectors in theâ€¦ (More)

The widespread use of generalized linear models in case-control genetic studies has helped identify many disease-associated risk factors typically defined as DNA variants, or single nucleotideâ€¦ (More)