Is the List of Incomplete Open Cubes Complete?

Variations of Incomplete Open Cubes is the major project by the twentieth-century conceptual artist Sol LeWitt. In this paper we interpret the enumerative component of the project as embeddings of graphs. This formulation permits use of an algorithm to check the completeness of the list of the structures produced by the artist. Our conclusion is that the artist found the correct number of structures (that is, 122), but that his list contains a mistake in the presentation of a pair of incomplete cubes, a discovery that appears not to have been noted before.     

Improved method for roadside barrier length of need modeling using real-world trajectories

The 2011 AASHTO Roadside Design Guide (RDG) contains perhaps the most widely used procedure for choosing an appropriate length of need (LON) for roadside barriers. However, this procedure has several limitations. The procedure uses a highly simplified model of vehicle departure, and the procedure does not allow designers to specify an explicit level of protection. A new procedure for choosing LON that addresses these limitations is presented in this paper. This new procedure is based on recent, real-world road departure trajectories and uses this departure data in a more realistic way. The new procedure also allows LON to be specified for a precisely known level of protection – a level which can be based on number of crashes, injury outcomes or even estimated crash cost – while still remaining straightforward and quick to use like the 2011 RDG procedure.