Algorithms should not know about begin and end run transitions, as these concepts become fuzzy if not entirely meaningless in an environment where multiple events are processed concurrently. In the vast majority of cases, anything done in Algorithm::beginRun can be migrated to Algorithm::start, and endRun -> stop.
I've hidden the compilation warnings that are triggered by Algorithm::sysBegin/EndRun, but have not touched the ones in GaudiAlg/Sequencer as I'm not sure what LHCb wants to do with those. Eliminate the the methods right now entirely? Hide the warnings?