Abstract:
AquaticHealth.net is an open-source aquatic biosecurity intelligence application. By combining automated data collection and human analysis, AquaticHealth.net provides fast and accurate disease outbreak detection and forecasts, accompanied with nuanced explanations. The system has been online and open to the public since 1 January 2010, it has over 200 registered expert users around the world, and it typically publishes about seven daily reports and two weekly disease alerts. We document the major trends in aquatic animal health that the system has detected over these two years, and conclude with some forecasts for the future.

Abstract:
MicroBooNE is an experiment designed to both probe neutrino physics phenomena and develop the LArTPC (Liquid Argon Time Projection Chamber) detector technology. The MicroBooNE experiment, which began taking data this year, is the first large LArTPC detector in the U.S. This experiment is the beginning of a path of detectors (both on the surface and underground) envisioned for the U.S. SBL (Short-BaseLine) and LBL (Long-BaseLine) programs. In order to interpret the data from the experiments on the surface, the impact of space charge effects must be simulated and calibrated. The space charge effect is the build-up of slow-moving positive ions in a detector due to, for instance, ionization from cosmic rays, leading to a distortion of the electric field within the detector. This effect leads to a displacement in the reconstructed position of signal ionization electrons in LArTPC detectors. The LArTPC utilized in the MicroBooNE experiment is expected to be modestly impacted from the space charge effect, with the electric field magnitude changing by roughly 5\% (at a drift field of 500 V/cm) in some locations within the TPC. We discuss the simulation of the space charge effect at MicroBooNE as well as calibration techniques that make use of a UV laser system and cosmic muon events. A successful calibration of the space charge effect is imperative both to the success of the MicroBooNE physics program as well as to the development of LArTPC technology for future experiments.

Abstract:
C Croke and B Kleiner have constructed an example of a CAT(0) group with more than one visual boundary. J Wilson has proven that this same group has uncountably many distinct boundaries. In this article we prove that the knot group of any connected sum of two non-trivial torus knots also has uncountably many distinct CAT(0) boundaries.

Abstract:
M. Bestvina has shown that for any given torsion-free CAT(0) group G, all of its boundaries are shape equivalent. He then posed the question of whether they satisfy the stronger condition of being cell-like equivalent. In this article we prove that the answer is "Yes" in the situation where the group in question splits as a direct product with infinite factors. We accomplish this by proving an interesting theorem in shape theory.

Abstract:
We prove that solutions to the Monge-Ampere inequality $$\det D^2u \geq 1$$ in $\mathbb{R}^n$ are strictly convex away from a singular set of Hausdorff $n-1$ dimensional measure zero. Furthermore, we show this is optimal by constructing solutions to $\det D^2u = 1$ with singular set of Hausdorff dimension as close as we like to $n-1$. As a consequence we obtain $W^{2,1}$ regularity for the Monge-Ampere equation with bounded right hand side and unique continuation for the Monge-Ampere equation with sufficiently regular right hand side.

Abstract:
We construct a counterexample to $W^{2,1}$ regularity for convex solutions to $$\det D^2u \leq 1, \quad u|_{\partial \Omega} = 0$$ in two dimensions. We also prove a result on the propagation of singularities in two dimensions that are logarithmically slower than Lipschitz. This generalizes a classical result of Alexandrov and is optimal by example.

Abstract:
It is well known that every word hyperbolic group has a well-defined visual boundary. An example of C. Croke and B. Kleiner shows that the same cannot be said for CAT(0) groups. All boundaries of a CAT(0) group are, however, shape equivalent, as observed by M. Bestvina and R. Geoghegan. Bestvina has asked if they also satisfy the stronger condition of being cell-like equivalent. This article describes a construction which will produce CAT(0) groups with multiple boundaries. These groups have very complicated boundaries in high dimensions. It is our hope that their study may provide insight into Bestvina's question.

Abstract:
We prove an interior $W^{2,1}$ estimate for singular solutions to the Monge-Ampere equation, and construct an example to show our results are optimal.