MNE: Magnetoencephalography (MEG) and Electroencephalography (EEG) in Python
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Numenta Platform for Intelligent Computing is an implementation of Hierarchical Temporal Memory (HTM), a theory of intelligence based strictly on the neuroscience of the neocortex.
For running psychology and neuroscience experiments
Machine learning for NeuroImaging in Python
Brian is a free, open source simulator for spiking neural networks.