The NTCE half-hat function depicted as the difference of two sigmoids. A principal neuron (mitral cell Miin, dashed line) and a local inhibitory interneuron (periglomerular cell PG, dotted line) are both directly, sigmoidally activated by increasing input levels (abscissa; here depicted as odorant-receptor affinity and neglecting odorant concentration). The local interneuron exhibits greater sensitivity to this input (i.e., it is half-activated by a weaker degree of odorant-receptor affinity) while the principal neuron has a greater maximum output amplitude. While input levels in a chemical binding context can conflate ligand-receptor affinity and ligand concentration , this ambiguity can be resolved by global feedback mechanisms (see text). When the two neurons are driven by the same input and the local interneuron inhibits the principal neuron, the net output activity of the principal neuron can become nonmonotonic with respect to input level, exhibiting a half-hat function capable of mediating contrast enhancement (mitral cell Mout, solid line; see Methods). That is, with respect to the molecular receptive range of any glomerulus, the mitral cell output profile after NTCE (Miout) will exhibit a narrower selectivity for odorants than do its associated olfactory receptors (Miin). Inset: Traditional one-dimensional "Mexican hat" contrast enhancement function, typically modeled as the difference of two Gaussians or as the difference between two differences of sigmoids (see Methods).