Topic: Spectral sensitivity

Charles Bordenave revisits von Neumann and Goldstine's proposal to model numerical computing errors as probabilistic noise. This perspective helps explain large errors in computed eigenvalues of badly conditioned matrices. Toeplitz matrices provide a case study: they occur throughout mathematics, physics, and engineering, are highly sensitive to small perturbations, and possess a rich spectral theory that supports precise descriptions under random perturbations. The talk is based on joint work with Mireille Capitaine and François Chapon.

In many butterflies, the ancestral trichromatic insect colour vision, based on UV-, blue- and green-sensitive photoreceptors, is extended with red-sensitive cells. Physiological evidence for red receptors has been missing in nymphalid butterflies, although some species can discriminate red hues well. In eight species from genera Archaeoprepona, Argynnis, Charaxes, Danaus, Melitaea, Morpho, Heliconius and Speyeria, we found a novel class of green-sensitive photoreceptors that have hyperpolarizing responses to stimulation with red light. These green-positive, red-negative (G+R–) cells are alloca