In strongly recurrent systems, such as the hippocampal CA3 region, the temporal compression mechanism (Skaggs et al., 1996) can ensure that in a neural word not only adjacent assemblies but also next-neighbor and more distant assemblies can be linked, as long as they consistently co-occur in the same theta cycles. These higher order connections, in turn, can provide a substrate for alternative routes in the evolution of neuronal trajectories and for combination of different assembly sequences, mechanisms necessary e.g., for solving detour and transitive inference problems (Dusek and Eichenbaum, 1997; Muller et al., 1996) and for higher-order associations in episodic memory (Polyn and Kahana, 2008). Thus, if the recall of a learned chain of fundamental assemblies a, b, c and d is blocked at c, the trajectory may jump to assembly d, i.e., to the second-order partner of assembly b (Gerstner and Kistler, 2002; Kiebel et al., 2009; Rabinovich et al., 2008a).
