Are Few Bins Enough: Testing Histogram Distributions by Clement Canonne (ECCC). Testing whether a distribution is uniform is a very important, well studied and almost completely understood problem. A generalization of this question is whether a distribution on the set {1,…,n} is a k-histogram, that is, whether the distribution can be represented as a piece-wise constant function over at most k contiguous intervals. This very important generalization has been much less understood and huge gap between the upper and lower bound for the query complexity existed. In this paper the gap has been almost closed by improving both the upper and lower bounds.

Testing Properties of Functions on Finite Groups by Kenta Oono and Yuichi Yoshida (arXiv). Testing algebraic properties of functions have taken a central place in property testing right from the time of its inception.  Different kinds of functions have been studied in literature. In this paper the authors study the functions that map elements of a finite group to square matrices over the complex field with Frobenius norm 1. In this paper various properties of these functions are proved to be testable.  Some of the properties considered in this paper are important from the point of view of representation theory. This is the first paper making the connection between property testing and representation theory. With representation theory taking a prominent role in computer science lately, this paper is expected to be the first of a long list of related results to follow.