A stable smooth map f : N → M is called k-realizable if its composition with the inclusion ⊂ × ℝk C0-approximable by embeddings; and a k-prem same C∞-approximable embeddings, or, equivalently, lifts vertically to embedding ↪ ℝk. It obvious that k-prem, then it k-realizable. We refute so-called “prem conjecture” converse holds. Namely, for each n = 4k+3 ≥ 15 there exists immersion Sn ↬ ℝ2n−7 3-r...

We construct an area preserving map from the cube to the unit sphere S, both centered at the origin. More precisely, each face Fi of the cube is first projected to a curved square Si of the same area, and then each Si is projected onto the sphere by inverse Lambert azimuthal equal area projection, with respect to the points situated at the intersection of the coordinate axes with S. This map is...

To determine surface-view connectivity patterns of area 18, separate injections of up to six anatomical tracers were delivered to various rostrocaudal locations of area 18 in six normal cats. Subsequently, cortex was separated from subcortical structures, manually flattened, and cut parallel to the surface. Results reveal that ipsilateral cortical connections of area 18 with three regions of co...

Generation of gamma rhythms in reciprocally connected areas of cortex produces synchronous neuronal firing, although little is known about the consequences of gamma rhythms when generated in nonreciprocally connected regions. This nonreciprocity exists in hippocampus, where gamma rhythms are generated in area CA3 in vitro and in vivo and nonreciprocally projected to area CA1 by the Schaffer col...