Although sensory perception and neurobiology are traditionally investigated one modality at a time, real world behaviour and perception are driven by the integration of information from multiple sensory sources. Mounting evidence suggests that the neural underpinnings of multisensory integration extend into early sensory processing. This article examines the notion that neocortical operations a...

In this note we introduce a notion of essentially-Euclidean normed spaces (and convex bodies). Roughly speaking, an n-dimensional space is λ-essentially-Euclidean (with 0 < λ < 1) if it has a [λn]dimensional subspace which has further proportionally dimensional Euclidean subspaces of any proportion. We consider a space X1 = (Rn, ‖ · ‖1) with the property that if a space X2 = (Rn, ‖ · ‖2) is “no...

For f in L∞, the space of essentially bounded Lebesgue measurable functions on the unit circle, ∂D, the Toeplitz operator with symbol f is the operator Tf on the Hardy space H2 of the unit circle defined by Tfh = P (fh). Here P denotes the orthogonal projection in L2 with range H2. There are many fascinating problems about Toeplitz operators ([3], [6], [7] and [20]). In this paper we shall conc...

The Lake: Alice, Bertha, and Claudia live around Forest Lake, at some distance from each other. The ecosystem is sensitive, in particular to the solvent they have been using when painting their boats, and the lake is faring badly. Until recently, they had no way of knowing that the solvent would have this effect, but they just learned that it is in fact killing the fish in the lake, and that th...