We show that it is possible to locate the event horizon of a black hole (in arbitrary dimensions) by the zeros of certain Cartan invariants. This approach accounts for the recent results on the detection of stationary horizons using scalar polynomial curvature invariants, and improves upon them since the proposed method is computationally less expensive. As an application, we produce Cartan invariants that locate the event horizons for various exact four-dimensional and five-dimensional stationary, asymptotically flat (or (anti) de Sitter), black hole solutions and compare the Cartan invariants with the corresponding scalar curvature invariants that detect the event horizon.

We study pattern formation in a model of cyanobacteria motion recently proposed by Galante, Wisen, Bhaya and Levy. By taking a continuum limit of their model, we derive a novel fourth-order nonlinear parabolic PDE equation that governs the behaviour of the model. This PDE is

The following sentences at the end of section 2: "There is a fundamental difficulty with applying the alignment classification, as it may depend on solving degree five polynomials to determine the WANDs. The solutions to these polynomials may not be expressible in terms of algebraic functions, and instead require transcendental functions, which are often too complex to implement in practice. Thus, unlike the case in 4D, the ability to explicitly determine the WANDs is not guaranteed." should be replaced by: