Understanding the brain requires identifying the principles by which it computes information. Besides beneficial for a rapidly aging society, where brain diseases are assimilated to epidemics, this would revolutionize computer science. In fact, steady improvements of silicon technology for the past 40 years, which enabled e.g. consumer electronics, the Internet, and genome sequencing, slowed down. Searching for novel future computing paradigms is thus imperative. Our teams, expert in Neurobiology (UA) & Neuroinformatics (TUG), join forces and combine experiments & theory to search for the principles of brain computing. We start from key discoveries: (1) neurons process information electrically and in concert with other cells, as assemblies. (2) neurons and synapses are intrinsically unreliable, operating non-deterministically. This forces us to rethink how computations are organized in the brain, validating or extending an earlier theory of stochastic computation, proposed by TUG. Both biological and artificial neuronal networks will be studied, in a "dialogue" between electrophysiological experiments and theory. Novel microelectrodes and (opto)genetics will be employed for "reading" and "writing" neuronal signals, while numerical simulations will aid the development of a new theory. Searching for the biophysical mechanisms of assembly formation and plasticity will be our objective, with impact for neuroscience, neuroprosthetics, and novel computing paradigms.