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The consequences for the brane cosmological evolution of energy exchange between the brane and the bulk are analyzed. A rich variety of brane cosmologies is obtained, depending on the precise mechanism of energy transfer, the equation of state of brane-matter and the spatial topology. An accelerating era is generically a feature of the solutions. (Prepared for 36th International Symposium Ahrenshoop on the Theory of Elementary Particles: Recent Developments in String M Theory and Field Theory, Wernsdorf, Germany, 26-30 Aug 2003.)

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