Isolated photon and photon+jet production at NNLO QCD accuracy and the ratio R13/8γR_{13/8}^\gamma

We discuss different approaches to photon isolation in fixed-order calculations and present a new next-to-next-to-leading order (NNLO) QCD calculation of $R_{13/8}^\gamma$, the ratio of the inclusive isolated photon cross section at 8 TeV and 13 TeV, differential in the photon transverse momentum, which was recently measured by the ATLAS collaboration.Comment: 4 pages, 1 figure. Contribution to the 2019 QCD session of the 54th Rencontres de Morion

COMPUTATIONALLY TRACTABLE STOCHASTIC INTEGER PROGRAMMING MODELS FOR AIR TRAFFIC FLOW MANAGEMENT

A primary objective of Air Traffic Flow Management (ATFM) is to ensure the orderly flow of aircraft through airspace, while minimizing the impact of delays and congestion on airspace users. A fundamental challenge of ATFM is the vulnerability of the airspace to changes in weather, which can lower the capacities of different regions of airspace. Considering this uncertainty along with the size of the airspace system, we arrive at a very complex problem. The development of efficient algorithms to solve ATFM problems is an important and active area of research. Responding to predictions of bad weather requires the solution of resource allocation problems that assign a combination of ground delay and route adjustments to many flights. Since there is much uncertainty associated with weather predictions, stochastic models are necessary. We address some of these problems using integer programming (IP). In general, IP models can be difficult to solve. However, if "strong" IP formulations can be found, then problems can be solved quickly by state of the art IP solvers. We start by describing a multi-period stochastic integer program for the single airport stochastic dynamic ground holding problem. We then show that the linear programming relaxation yields integer optimal solutions. This is a fairly unusual property for IP formulations that can significantly reduce the complexity of the corresponding problems. The proof is achieved by defining a new class of matrices with the Monge property and showing that the formulation presented belongs to this class. To further improve computation times, we develop alternative compact formulations. These formulations are extended to show that they can also be used to model different concepts of equity and fairness as well as efficiency. We explore simple rationing methods and other heuristics for these problems both to provide fast solution times, but also because these methods can embody inherent notions of fairness. The initial models address problems that seek to restrict flow into a single airport. These are extended to problems where stochastic weather affects en route traffic. Strong formulations and efficient solutions are obtained for these problems as well