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In this paper we present extensions to the original adaptive paralleltempering algorithm. Two different approaches are presented. In the first onewe introduce state-dependent strategies using current information to perform aswap step. It encompasses a wide family of potential moves including thestandard one and Equi Energy type move, without any loss in tractability. Inthe second one, we introduce online adjustment of the number of temperatures.Numerical experiments demonstrate the effectiveness of the proposed method.

State dependent swap strategies and adaptive adjusting of number of temperatures in Parallel Tempering algorithms