We present the details of a powerful new technique used in an exact calculation of the contribution of 6 sixth-order vertex graphs to the anomalous magnetic moment of the electron. By introducing four-dimensional spherical coordinates, the momentum-space integrals can be evaluated directly. The angular integrations areperformed using some simple properties of the Gegenbauer polynomials. For these graphs, the remaining convergent radial integrands are simple rational functions which are readily integrated. The divergent integrals are treated separately to extract all terms which do not vanish in the infrared and ultraviolet limits. The actual processing of the many terms involved was done using the algebraic

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The Bethe-Salpeter equation is solved numerically for a <£ 3 theory in the ladder approximation up to the second inelastic threshold. Below the first inelastic threshold, the results agree with previous work. Between the first and second inelastic thresholds, it is found that there are coupling strengths which cause unitarity (Elastic) to be violated.

In this paper, we describe Bridges, a new HPC resource that will integrate advanced memory technologies with a uniquely flexible, user-focused, data-centric environment to empower new research communities, bring desktop convenience to HPC, connect to campuses, and drive complex workflows. Bridges will differ from traditional HPC systems and support new communities through extensive interactivity, gateways (convenient web interfaces that hide complex functionality and ease access to HPC resources) and tools for gateway building, persistent databases and web servers, high-productivity programming languages, and virtualization. Bridges will feature three tiers of processing nodes having 128GB, 3TB, and 12TB of hardware-enabled coherent shared memory per node to support memory-intensive applications and ease of use, together with persistent database and web nodes and nodes for logins, data transfer, and system management. State-of-the-art Intel ® Xeon ® CPUs and NVIDIA Tesla GPUs will power Bridges' compute nodes. Multiple filesystems will provide optimal handling for different data needs: a high-performance, parallel, shared filesystem, node-local filesystems, and memory filesystems. Bridges' nodes and parallel filesystem will be interconnected by the Intel Omni-Path Fabric, configured in a topology developed by PSC to be optimal for the anticipated data-centric workload. Bridges will be a resource on XSEDE, the NSF Extreme Science and Engineering Discovery Environment, and will interoperate with other advanced cyberinfrastructure resources. Through a pilot project with Temple University, Bridges will develop infrastructure and processes for campus bridging, consisting of offloading jobs at periods of unusually high load to the other site and facilitating cross-site data management. Education, training, and outreach activities will raise awareness of Bridges and data-intensive science across K-12 and university communities, industry, and the general public.