As in a symmetric space of noncompact type, one can associate to an oriented geodesic segment in a Euclidean building a vector valued length in the Euclidean Weyl chamber ∆euc. In addition to the metric length it contains information on the direction of the segment. We study in this paper restrictions on the ∆euc-valued side lengths of polygons in Euclidean buildings. The main result is that fo...

Advances in microscopy and sample preparation have led to the first ever mapping of individual neurons in the whole mouse brain.

We present a method for solving the wormlike chain model for semiflexible polymers to any desired accuracy over the entire range of polymer lengths. Our results are in excellent agreement with recent computer simulations and reproduce important qualitatively interesting features observed in simulations of polymers of intermediate lengths. We also make a number of predictions that can be tested ...