We study the conditions to have supersymmetric D-branes on general N = 1 backgrounds with Ramond-Ramond fluxes. These conditions can be written in terms of the two pure spinors associated to the SU (3) × SU (3) structure on T M ⊕ T ⋆ M , and can be split into two parts each involving a different pure spinor. The first involves the integrable pure spinor and requires the D-brane to wrap a generalised complex submanifold with respect to the generalised complex structure associated to it. The second contains the non-integrable pure spinor and is related to the stability of the brane. The two conditions can be rephrased as a generalised calibration condition for the brane. The results preserve the generalised mirror symmetry relating the type IIA and IIB backgrounds considered, giving further evidence for this duality.

Using the embedding tensor formalism we give the general conditions for the existence of N = 1 vacua in spontaneously broken N = 2 supergravities. Our results confirm the necessity of having both electrically and magnetically charged multiplets in the spectrum, but also show that no further constraints on the special Kähler geometry of the vector multiplets arise. The quaternionic field space of the hypermultiplets must have two commuting isometries, and as an example we discuss the special quaternionic-Kähler geometries which appear in the low-energy limit of type II string theories. For these cases we find the general solution for stable Minkowski and AdS N = 1 vacua, and determine the charges in terms of the holomorphic prepotentials. We find that the string theory realisation of the N = 1 Minkowski vacua requires the presence of non-geometric fluxes, whereas they are not needed for the AdS vacua. We also argue that our results should hold in the presence of spacetime and worldsheet instanton corrections.

We derive a general form of first-order flow equations for extremal and nonextremal, static, spherically symmetric black holes in theories with massless scalars and vectors coupled to gravity. By rewriting the action as a sum of squaresà la Bogomol'nyi, we identify the function governing the first-order gradient flow, the 'generalised superpotential', which reduces to the 'fake superpotential' for non-supersymmetric extremal black holes and to the central charge for supersymmetric black holes. For theories whose scalar manifold is a symmetric space after a timelike dimensional reduction, we present the condition for the existence of a generalised superpotential. We provide examples to illustrate the formalism in four and five spacetime dimensions.

The shape and appearance of the spine on lateral dual x-ray absorptiometry scans were statistically modeled. To measure vertebral shape accurately, rapidly, and automatically with a computer, this trained model was matched to findings on previously unseen scans. The technique obtained entire shape information, was faster than manual analysis, and was as accurate as human observers in the measurement of vertebral shape.