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This paper presents the concepts behind the BrainScales (BSS) accelerated analog neuromorphic computing architecture. It describes the second-generation BrainScales-2 (BSS-2) version and its most recent in-silico realization, the HICANN-X Application Specific Integrated Circuit (ASIC), as it has been developed as part of the neuromorphic computing activities within the European Human Brain Project (HBP). While the first generation is implemented in an 180nm process, the second generation uses 65nm technology. This allows the integration of a digital plasticity processing unit, a highly-parallel micro processor specially built for the computational needs of learning in an accelerated analog neuromorphic systems. The presented architecture is based upon a continuous-time, analog, physical model implementation of neurons and synapses, resembling an analog neuromorphic accelerator attached to build-in digital compute cores. While the analog part emulates the spike-based dynamics of the neural network in continuous-time, the latter simulates biological processes happening on a slower time-scale, like structural and parameter changes. Compared to biological time-scales, the emulation is highly accelerated, i.e. all time-constants are several orders of magnitude smaller than in biology. Programmable ion channel emulation and inter-compartmental conductances allow the modeling of nonlinear dendrites, back-propagating action-potentials as well as NMDA and Calcium plateau potentials. To extend the usability of the analog accelerator, it also supports vector-matrix multiplication. Thereby, BSS-2 supports inference of deep convolutional networks as well as local-learning with complex ensembles of spiking neurons within the same substrate.