Integration and differentiation of afferent signals are fundamental to certain kinematic and dynamic operations in the brain. The recent demonstrations of both integral (Poon et al., NeuroReport, 10:2261, 1999) and differential (Poon et al., Neurosci. Lett. 284:5, 2000) computations in the mammalian respiratory central pattern generator (RCPG) provide a useful model of such brain calculus. In particular, the differentiator-like adaptations of the Hering-Breuer (HB) vagal reflex of the RCPG have been experimentally linked to parallel neural pathways (Siniaia et al., J. Physiol. 523:479, 2000) that conform to the classic dual-process model of nonassociative learning—with habituation in the primary central pathway for vagal proprioceptive feedback and desensitization in a secondary, pontine pathway with a tonic input. This neural differentiator structure is supported by the recent demonstration of synaptic short-term depression (STD) in the vagal and pontine pathways (Siniaia et al., SFN 2000, 2001 Meetings) ...