What is the difference between computational neuroscience, theoretical neuroscience, and neuroinformatics (if there is one)?

In particular, theoretical and computational neuroscience seem to be synonymous with each other. Neuroinformatics at least seems to deal somewhat more with solving things numerically and the usage and creation of algorithms and programs.

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I'm not much of a neuroscientist, but does all theoretical neuroscience involve computation? I assume at least all computational neuroscience does... – Nick Stauner Mar 13 '14 at 22:22
Computation as in at least manipulation of equations, yes. This Moldakarimov paper is an example that I think represents what a typical theoretical neuroscience paper looks like -- establish some equations, demonstrate fit of equations to data, etc. – potpie Mar 14 '14 at 15:38