Discovery of a New WZ Sagittae Type Cataclysmic Variable in the Kepler/K2 Data

We identify a new, bright transient in the Kepler/K2 Campaign 11 field. Its light curve rises over seven magnitudes in a day and then declines three magnitudes over a month before quickly fading another two magnitudes. The transient was still detectable at the end of the campaign. The light curve is consistent with a WZ~Sge type dwarf nova outburst. Early superhumps with a period of 82 minutes are seen in the first 10 days and suggest that this is the orbital period of the binary which is typical for the WZ~Sge class. Strong superhump oscillations develop ten days after peak brightness with periods ranging between 83 and 84 minutes. At 25 days after the peak brightness a bump in the light curve appears to signal a subtle rebrightening phase implying that this was an unusual type-A outburst. This is the only WZ~Sge type system observed by Kepler/K2 during an outburst. The early rise of this outburst is well-fit with a broken power law. In first 10 hours the system brightened linearly and then transitioned to a steep rise with a power law index of 4.8. Looking at archival Kepler/K2 data and new TESS observations, a linear rise in the first several hours at the initiation of a superoutburst appears to be common in SU~UMa stars.Comment: 11 pages, 14 figures, 2 tables, accepted to appear in the Monthly Notices of the Royal Astronomical Societ

A monkey-resistant lever switch for avoidance conditioning

Motivated by the question of how macromolecules assemble, the notion of an assembly tree of a graph is introduced. Given a graph G, the paper is concerned with enumerating the number of assembly trees of G, a problem that applies to the macromolecular assembly problem. Explicit formulas or generating functions are provided for the number of assembly trees of several families of graphs, in particular for what we call (H, φ)-graphs. In some natural special cases, we apply powerful recent results of Zeilberger and Apagodu on multivariate generating functions, and results of Wimp and Zeilberger, to deduce recurrence relations and very precise asymptotic formulas for the number of assembly trees of the complete bipartite graphs Kn,n and the complete tripartite graphs Kn,n,n. Future directions for reseach, as well as open questions, are suggested.