The compartment structures of the antennal lobe in the ant, Aphaenogaster smythiesi japonica

Pheromones are important cues for social insects such as ants. As a first step in elucidation of pheromonal information processing mechanisms in the myrmicine ant, we investigated the morphological structure of the antennal lobe. Using autofluorescence imaging, labeling of neuronal filamentous actin, and reduced silver impregnation staining, the antennal lobe was found to consist of five compartments that, each received input from a different antennal sensory tract. Two major tracts of projection neurons, the medial and lateral antenno-cerebral tract (m-and l-ACT), originated from a different region of the antennal lobe. The m-ACT originated from the posterior part of the antennal lobe whereas the l-ACT originated from the anterior part. These results demonstrate a spatial segregation of function within the antennal lobe

Bounds on the k-dimension of Products of Special Posets

Trotter conjectured that dimP×Q≥dimP+dimQ−2 for all posets P and Q. To shed light on this, we study the k-dimension of products of finite orders. For k ∈ o(ln n), the value 2dimk(P)−dimk(P×P) is unbounded when P is an n-element antichain, and 2dim2(mP)−dim2(mP×mP) is unbounded when P is a fixed poset with unique maximum and minimum. For products of the “standard” orders S m and S n of dimensions m and n, dimk(Sm×Sn)=m+n−min{2,k−2} . For higher-order products of “standard” orders, dim2(∏ti=1Sni)=∑ni if each n i  ≥ t.Hertz FoundationUnited States. Dept. of Defense (National Defense Science and Engineering Program)United States. National Security Agency (Award H98230-06-1-0065)United States. National Security Agency (Award H98230-10-1-0363