We define the decomposition property for partial actions of discrete groups on C⁎-algebras. Decomposable systems appear naturally in practice, and many commonly occurring can be decomposed into with property. For instance, any action a finite group is an iterated extension decomposable systems. Partial are always globalizable amenable, regardless acting group, their globalization explicitly des...

Let g(x) be a fixed non-constant complex polynomial. It was conjectured by Schinzel that if g(h(x)) has boundedly many terms, then h(x) ∈ C[x] must also have boundedly many terms. Solving an older conjecture raised by Rényi and by Erdös, Schinzel had proved this in the special cases g(x) = x; however that method does not extend to the general case. Here we prove the full Schinzel’s conjecture (...

We examine maximum spanning tree-based methods for learning the structure of tree Conditional Random Fields (CRFs) P (Y|X ). We use edge weights which take advantage of local inputs X and thus scale to large problems. For a general class of edge weights, we give a negative learnability result. However, we demonstrate that two members of the class–local Conditional Mutual Information and Decompo...