We look at the behavior under state splitting of distinct kinds of properties regarding monochromatic paths on edge colored digraphs. These are absorbance and independence as well as the existence of kernels, semikernels, quasikernels and Grundy functions, all of them defined in terms of monochromatic paths.

We derive tight bounds on the expected weights of several combinatorial optimization problems for random point sets of size n distributed among the leaves of a balanced hierarchically separated tree. We consider monochromatic and bichromatic versions of the minimum matching, minimum spanning tree, and traveling salesman problems. We also present tight concentration results for the monochromatic...

If perturbing two genes together has a stronger or weaker effect than expected, they are said to genetically interact. Genetic interactions are important because they help map gene function, and functionally related genes have similar genetic interaction patterns. Mapping quantitative (positive and negative) genetic interactions on a global scale has recently become possible. This data clearly ...