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The notion of a holomorphic bundle and Hermitian-Yang-Mills connections is one that proved to be very fruitful in complex geometry. There are some natural generalizations of these notions in almost complex geometry such as those of pseudo-holomorphic and pseudo-Hermitian-Yang-Mills connections. In this talk, I will focus on a system of partial differential equations, the DT-instanton equations, whose solutions give a further generalization of the notion of a Hermitian-Yang-Mills connection in the setting of real 6 dimensional almost Hermitian manifolds. (Joint work with Gavin Ball)