On the weak-hash metric for boundedly finite integer-valued measures

It is known that the space of boundedly finite integer-valued measures on a complete separable metric space becomes itself a complete separable metric space when endowed with the weak-hash metric. It is also known that convergence under this topology can be characterised in a way that is similar to the weak convergence of totally finite measures. However, the original proofs of these two fundamental results assume that a certain term is monotonic, which is not the case as we give a counterexample. We manage to clarify these original proofs by addressing specifically the parts that rely on this assumption and finding alternative arguments.Comment: Minor typos corrected, Bulletin of the Australian Mathematical Society, 201

Finite Noncommutative Chern-Simons with a Wilson Line and the Quantum Hall Effect

We present a finite dimensional matrix model associated to the noncommutative Chern-Simons theory, obtained by inserting a Wilson line. For a specific choice of the representation of the Wilson line the model is equivalent to the minimal modification of the matrix model which is compatible with finite dimensional matrices, and was introduced previously to study droplets of quantum Hall fluid. For other representations we obtain generalizations corresponding to regularized U(n) Chern-Simons theoris, representing multilayered quantum Hall fluids.Comment: LaTeX, 16 pages, no figures, references adde

Hybrid marked point processes: characterisation, existence and uniqueness

We introduce a class of hybrid marked point processes, which encompasses and extends continuous-time Markov chains and Hawkes processes. While this flexible class amalgamates such existing processes, it also contains novel processes with complex dynamics. These processes are defined implicitly via their intensity and are endowed with a state process that interacts with past-dependent events. The key example we entertain is an extension of a Hawkes process, a state-dependent Hawkes process interacting with its state process. We show the existence and uniqueness of hybrid marked point processes under general assumptions, extending the results of Massouli\'e (1998) on interacting point processes.Comment: v6: introduction updated with reference to application of state-dependent Hawkes processe

Advocacy, Politics, & Philanthropy

Over the course of our history, Atlantic has made some big bets designed to help solve major social issues. Needless to say, our 11-year, $70 million initiative to reform America's immigration system certainly ranks among the biggest of such bets. Among the factors leading to our decision to take on this challenging work was our deep concern that millions of immigrants to the United States have been without access to basic rights accorded by law or common practice to the majority of Americans. As a result of a broken immigration system, far too many individuals and families have been left vulnerable to a wide range of discrimination and abuse in the workplace, in housing and in healthcare settings, among others. Undocumented immigrants increasingly face growing social marginalization and hostility from those whose ancestors arrived on our shores in earlier times. At the time we started this work, as far back as 2004, we also firmly believed there was a willingness at the federal level and in the United States Congress to find a workable solution