A Simple Geometric Representative for μ\mu of a Point

For $SU(2)$ (or $SO(3)$) Donaldson theory on a 4-manifold $X$, we construct a simple geometric representative for $\mu$ of a point. Let $p$ be a generic point in $X$. Then the set $\{ [A] | F_A^-(p)$ is reducible $\}$, with coefficient -1/4 and appropriate orientation, is our desired geometric representative.Comment: Updated 2018 to published version. 8 pages, AmS-TeX, no figure

Quaternionic Monopoles

We present the simplest non-abelian version of Seiberg-Witten theory: Quaternionic monopoles. These monopoles are associated with Spin^h(4)-structures on 4-manifolds and form finite-dimensional moduli spaces. On a Kahler surface the quaternionic monopole equations decouple and lead to the projective vortex equation for holomorphic pairs. This vortex equation comes from a moment map and gives rise to a new complex-geometric stability concept. The moduli spaces of quaternionic monopoles on Kahler surfaces have two closed subspaces, both naturally isomorphic with moduli spaces of canonically stable holomorphic pairs. These components intersect along Donaldsons instanton space and can be compactified with Seiberg-Witten moduli spaces. This should provide a link between the two corresponding theories. Notes: To appear in CMP The revised version contains more details concerning the Uhlenbeck compactfication of the moduli space of quaternionic monopoles, and possible applications are discussed. Attention ! Due to an ununderstandable mistake, the duke server had replaced all the symbols "=" by "=3D" in the tex-file of the revised version we sent on February, the 2-nd. The command "\def{\ad}" had also been damaged !Comment: LaTeX, 35 page

Uncovering Bugs in Distributed Storage Systems during Testing (not in Production!)

Testing distributed systems is challenging due to multiple sources of nondeterminism. Conventional testing techniques, such as unit, integration and stress testing, are ineffective in preventing serious but subtle bugs from reaching production. Formal techniques, such as TLA+, can only verify high-level specifications of systems at the level of logic-based models, and fall short of checking the actual executable code. In this paper, we present a new methodology for testing distributed systems. Our approach applies advanced systematic testing techniques to thoroughly check that the executable code adheres to its high-level specifications, which significantly improves coverage of important system behaviors. Our methodology has been applied to three distributed storage systems in the Microsoft Azure cloud computing platform. In the process, numerous bugs were identified, reproduced, confirmed and fixed. These bugs required a subtle combination of concurrency and failures, making them extremely difficult to find with conventional testing techniques. An important advantage of our approach is that a bug is uncovered in a small setting and witnessed by a full system trace, which dramatically increases the productivity of debugging

Multilayer microwave windows for wideband gyro-amplifiers

This paper presents the design and measurement of a HE11 mode multilayer window for a W-band gyro-amplifier. The window acts to seal the vacuum inside the amplifier whilst coupling out microwave power with minimal reflection and absorption. The Gaussian-like HE11 mode is used in order to achieve the lowest reflection through the window. Operating over 90-100 GHz the simulated reflection of this window is better than -30 dB. The design, simulation and microwave measurement of the window is presented

Khovanov homology is an unknot-detector

We prove that a knot is the unknot if and only if its reduced Khovanov cohomology has rank 1. The proof has two steps. We show first that there is a spectral sequence beginning with the reduced Khovanov cohomology and abutting to a knot homology defined using singular instantons. We then show that the latter homology is isomorphic to the instanton Floer homology of the sutured knot complement: an invariant that is already known to detect the unknot.Comment: 124 pages, 13 figure

Engineering a static verification tool for GPU kernels

We report on practical experiences over the last 2.5 years related to the engineering of GPUVerify, a static verification tool for OpenCL and CUDA GPU kernels, plotting the progress of GPUVerify from a prototype to a fully functional and relatively efficient analysis tool. Our hope is that this experience report will serve the verification community by helping to inform future tooling efforts. © 2014 Springer International Publishing

Let's Twist Again: N=2 Super Yang Mills Theory Coupled To Matter

We give the twisted version of N=2 Super Yang Mills theory coupled to matter, including quantum fields, supersymmetry transformations, action and algebraic structure. We show that the whole action, coupled to matter, can be written as the variation of a nilpotent operator, modulo field equations. An extended Slavnov-Taylor identity, collecting gauge symmetry and supersymmetry, is written, which allows to define the web of algebraic constraints, in view of the algebraic renormalization and of the extension of the non-renormalization theorems holding for N=2 SYM theory without matter.Comment: 28 pages, final version to be published on CQ

SCOTT AND THE LOGS: DESIGN AND DATA CAPTURE IN A PREPARATORY ONLINE PACKAGE FOR CHILDREN UNDERGOING GA FOR DENTAL PROCEDURES

This National Institute of Health Research project aims to test if children scheduled for anaesthesia benefit from an interactive online package. The project deals with the design and data capture (logs) of a prototype (alpha) online interactive cartoon created to answer the research question: “Will internet delivered information help children cope better with anaesthesia?” Following modification of the alpha package the resultant beta package will be compared to two control groups: standard care procedures and a non-medical computer game. An international academic audience provided positive feedback on the package design and data capture. The animation package sets an example of good practice in design for other similar healthcare scenarios