Redressing the Silent Interim: Precautionary Action & Short Term Tests in Toxicological Risk Assessment

The author recommends that a stronger emphasis be placed on creating and implementing short-term tests that use iterative, conservative-based, tiered procedures in conjunction with a precautionary attitude during the interim phase of toxicological risk assessments

Lamplighters, Metabelian Groups, and Horocyclic Products of Trees

Bartholdi, Neuhauser and Woess proved that a family of metabelian groups including lamplighters have a striking geometric manifestation as 1-skeleta of horocyclic products of trees. The purpose of this article is to give an elementary account of this result, to widen the family addressed to include the infinite valence case (for instance $\mathbb{Z} \wr \mathbb{Z}$), and to make the translation between the algebraic and geometric descriptions explicit. In the rank-2 case, where the groups concerned include a celebrated example of Baumslag and Remeslennikov, we give the translation by means of a combinatorial `lamplighter description'. This elucidates our proof in the general case which proceeds by manipulating polynomials. Additionally, we show that the Cayley 2-complex of a suitable presentation of Baumslag and Remeslennikov's example is a horocyclic product of three trees

Exponentially distorted subgroups in wreath products

We exhibit exponentially distorted subgroups in $\mathbb{Z} \wr ( \mathbb{Z} \wr \mathbb{Z} )$ and $\mathbb{Z} \wr F_2$.Comment: 9 pages, no figure