Cluster adjacency properties of scattering amplitudes

We conjecture a new set of analytic relations for scattering amplitudes in planar N=4 super Yang-Mills theory. They generalise the Steinmann relations and are expressed in terms of the cluster algebras associated to Gr(4,n). In terms of the symbol, they dictate which letters can appear consecutively. We study heptagon amplitudes and integrals in detail and present symbols for previously unknown integrals at two and three loops which support our conjecture.Comment: 6 pages, 3 figures. Symbols of integrals presented in four ancillary files, as detailed in README.tx

Cluster adjacency beyond MHV

We explore further the notion of cluster adjacency, focussing on non-MHV amplitudes. We extend the notion of adjacency to the BCFW decomposition of tree-level amplitudes. Adjacency controls the appearance of poles, both physical and spurious, in individual BCFW terms. We then discuss how this notion of adjacency is connected to the adjacency already observed at the level of symbols of scattering amplitudes which controls the appearance of branch cut singularities. Poles and symbols become intertwined by cluster adjacency and we discuss the relation of this property to the $\bar{Q}$-equation which imposes constraints on the derivatives of the transcendental functions appearing in loop amplitudes.Comment: 51 pages, 25 figures, 4 table

A Symbol of Uniqueness: The Cluster Bootstrap for the 3-Loop MHV Heptagon

Seven-particle scattering amplitudes in planar super-Yang-Mills theory are believed to belong to a special class of generalised polylogarithm functions called heptagon functions. These are functions with physical branch cuts whose symbols may be written in terms of the 42 cluster A-coordinates on Gr(4,7). Motivated by the success of the hexagon bootstrap programme for constructing six-particle amplitudes we initiate the systematic study of the symbols of heptagon functions. We find that there is exactly one such symbol of weight six which satisfies the MHV last-entry condition and is finite in the $7 \parallel 6$ collinear limit. This unique symbol is both dihedral and parity-symmetric, and remarkably its collinear limit is exactly the symbol of the three-loop six-particle MHV amplitude, although none of these properties were assumed a priori. It must therefore be the symbol of the three-loop seven-particle MHV amplitude. The simplicity of its construction suggests that the n-gon bootstrap may be surprisingly powerful for n>6.Comment: 30 pages, 3 ancillary files, v3: minor corrections, including a typo in (33

STOVL aircraft simulation for integrated flight and propulsion control research

The United States is in the initial stages of committing to a national program to develop a supersonic short takeoff and vertical landing (STOVL) aircraft. The goal of the propulsion community in this effort is to have the enabling propulsion technologies for this type aircraft in place to permit a low risk decision regarding the initiation of a research STOVL supersonic attack/fighter aircraft in the late mid-90's. This technology will effectively integrate, enhance, and extend the supersonic cruise, STOVL and fighter/attack programs to enable U.S. industry to develop a revolutionary supersonic short takeoff and vertical landing fighter/attack aircraft in the post-ATF period. A joint NASA Lewis and NASA Ames research program, with the objective of developing and validating technology for integrated-flight propulsion control design methodologies for short takeoff and vertical landing (STOVL) aircraft, was planned and is underway. This program, the NASA Supersonic STOVL Integrated Flight-Propulsion Controls Program, is a major element of the overall NASA-Lewis Supersonic STOVL Propulsion Technology Program. It uses an integrated approach to develop an integrated program to achieve integrated flight-propulsion control technology. Essential elements of the integrated controls research program are realtime simulations of the integrated aircraft and propulsion systems which will be used in integrated control concept development and evaluations. This paper describes pertinent parts of the research program leading up to the related realtime simulation development and remarks on the simulation structure to accommodate propulsion system hardware drop-in for real system evaluation

Review of AdS/CFT Integrability, Chapter V.2: Dual Superconformal Symmetry

Scattering amplitudes in planar $${\mathcal{N}=4}$$ super Yang-Mills theory reveal a remarkable symmetry structure. In addition to the superconformal symmetry of the Lagrangian of the theory, the planar amplitudes exhibit a dual superconformal symmetry. The presence of this additional symmetry imposes strong restrictions on the amplitudes and is connected to a duality relating scattering amplitudes to Wilson loops defined on polygonal light-like contours. The combination of the superconformal and dual superconformal symmetries gives rise to a Yangian, an algebraic structure which is known to be related to the appearance of integrability in other regimes of the theory. We discuss two dual formulations of the symmetry and address the classification of its invariant

The role of leading twist operators in the Regge and Lorentzian OPE limits

We study two kinematical limits, the Regge limit and the Lorentzian OPE limit, of the four-point function of the stress-tensor multiplet in Super Yang-Mills at weak coupling. We explain how both kinematical limits are controlled by the leading twist operators. We use the known expression of the four-point function up to three loops, to extract the pomeron residue at next-to-leading order. Using this data and the known form of pomeron spin up to next-to-leading order, we predict the behaviour of the four-point function in the Regge limit at higher loops. Specifically, we determine the leading log behaviour at any loop order and the next-to-leading log at four loops. Finally, we check the consistency of our results with conformal Regge theory. This leads us to predict the behaviour around $J=1$ of the OPE coefficient of the spin $J$ leading twist operator in the OPE of two chiral primary operators.Comment: 22+14 page

NICEly does it: economic analysis within evidence-based clinical practice guidelines

There is increasing professional and policy interest in the role of clinical guidelines for promoting effective and efficient health care. The NHS Health Technology Assessment Programme identified an urgent need, when such guidelines are produced, to develop a framework and methods for incorporating the best evidence of effectiveness, taking into account information on cost-effectiveness. This paper describes the development of recent evidence-based guidelines, for use in primary care, which were the result of recent work by the North of England Guidelines Development Group. Their specific aim was to incorporate economic analysis into the guideline process and treatment recommendations. The introduction of economic data raised some methodological issues, specifically: in providing valid and generalisable cost estimates; in the grading of cost ‘evidence’; in finding a presentation helpful to clinicians. The approach used was to help clinicians aggregate the various attributes of treatment to make good treatment recommendations, rather than interpret cost-effectiveness ratios. In none of the guideline areas was there adequate information to estimate a cost per quality-adjusted-life-year. In the light of this research, future areas of work are identified and some recommendations are made for the forthcoming National Institute for Clinical Excellence.evidence-based medicine, economic evaluation, clinical guidelines, NICE

QCD Pressure and the Trace Anomaly

Exact relations between the QCD thermal pressure and the trace anomaly are derived. These are used, first, to prove the equivalence of the thermodynamic and the hydrodynamic pressure in equilibrium in the presence of the trace anomaly, closing a gap in previous arguments. Second, in the temporal axial gauge a formula is derived which expresses the thermal pressure in terms of a Dyson-resummed two-point function. This overcomes the infrared problems encountered in the conventional perturbation-theory approach.Comment: 9 pages plain te

The transformation of Moiloa's Reserve in the Western Transvaal: politics, production and resistance in a rural setting, 1919 - 1986

Paper presented at the Wits History Workshop: Structure and Experience in the Making of Apartheid, 6-10 February, 199

The Enhanced Reading Opportunities Study: Early Impact and Implementation Findings

This report presents early findings from a demonstration and random assignment evaluation of two supplemental literacy programs that aim to improve the reading comprehension skills and school performance of struggling ninth-grade readers. On average, the programs produced a positive, statistically significant impact on reading comprehension among students