We investigate bounds on the dichromatic number of digraphs which avoid a fixed digraph as topological minor. For F , denote by mader ? ? ( ) smallest integer k such that every -dichromatic contains subdivision . As our first main result, we prove if is an orientation cycle then = v This settles conjecture Aboulker, Cohen, Havet, Lochet, Moura and Thomassé. also extend this result to more gener...

We examine two mechanisms that have been put forward to explain the selection of quasipatterns in single- and multifrequency forced Faraday wave experiments. Both mechanisms can be used to generate stable quasipatterns in a parametrically forced partial differential equation that shares some characteristics of the Faraday wave experiment. One mechanism, which is robust and works with single-fre...

What happens when investment grade bonds are downgraded to junk status? The received wisdom is that these fallen angels are sold by fixed income investors who, by regulation, are prohibited from investing substantial portions of their portfolios in speculative grade paper. We investigate insurance company sales of bonds that were downgraded to junk in order to document the extent of forced sell...