The projection body operator Π, which associates with every convex body in Euclidean space Rn its projection body, is a continuous valuation, it is invariant under translations and equivariant under rotations. It is also well known that Π maps the set of polytopes in Rn into itself. We show that Π is the only non-trivial operator with these properties. MSC 2000: 52B45, 52A20

Whole-body PET scanning for an oncology study produces a large number of transaxial images by data acquisition over multiple bed positions. The sagittal and coronal reformatted images are often used for better understanding of radioisotope distribution. We reduced the number of PET images by calculating projection images and evaluated the merit of additional data processing for the visualizatio...

We give a number of characterizations of bodies of constant width in arbitrary dimension. As an application, we describe a way to construct a body of constant width in dimension n, one of its (n − 1)dimensional projection being given. We give a number of examples, like a four-dimensional body of constant width whose 3D-projection is the classical Meissner’s body.

We explored the transformations accompanying the transmission of odor information from the first-order processing area, the antennal lobe, to the mushroom body, a higher-order integration center in the insect brain. Using Ca2+ imaging, we recorded activity in the dendrites of the projection neurons that connect the antennal lobe with the mushroom body. Next, we recorded the presynaptic terminal...

We explored the transformations accompanying the transmission of odor information from the first-order processing area, the antennal lobe, to the mushroom body, a higher-order integration center in the insect brain. Using Ca 2+ imaging, we recorded activity in the dendrites of the projection neurons that connect the antennal lobe with the mushroom body. Next, we recorded the presynaptic termina...

Odors evoke synchronized oscillations and slow temporal patterns in antennal lobe neurons and fast oscillations in the mushroom body local field potential (LFP) of the locust. What is the contribution of primary afferents in the generation of these dynamics? We addressed this question in two ways. First, we recorded odor-evoked afferent activity in both isolated antennae and intact preparations...