Perturbative expansion of N<8 Supergravity

We characterise the one-loop amplitudes for N=6 and N=4 supergravity in four dimensions. For N=6 we find that the one-loop n-point amplitudes can be expanded in terms of scalar box and triangle functions only. This simplification is consistent with a loop momentum power count of n-3, which we would interpret as being n+4 for gravity with a further -7 from the N=6 superalgebra. For N=4 we find that the amplitude is consistent with a loop momentum power count of n, which we would interpret as being n+4 for gravity with a further -4 from the N=4 superalgebra. Specifically the N=4 amplitudes contain non-cut-constructible rational terms.Comment: 13 pages. v2 adds analytic expression for rational parts of 5-pt 1-loop N=4 SUGRA amplitude; v3 normalisations clarifie

Obtaining One-loop Gravity Amplitudes Using Spurious Singularities

The decomposition of a one-loop scattering amplitude into elementary functions with rational coefficients introduces spurious singularities which afflict individual coefficients but cancel in the complete amplitude. These cancellations create a web of interactions between the various terms. We explore the extent to which entire one-loop amplitudes can be determined from these relationships starting with a relatively small input of initial information, typically the coefficients of the scalar integral functions as these are readily determined. In the context of one-loop gravity amplitudes, of which relatively little is known, we find that some amplitudes with a small number of legs can be completely determined from their box coefficients. For increasing numbers of legs, ambiguities appear which can be determined from the physical singularity structure of the amplitude. We illustrate this with the four-point and N=1,4 five-point (super)gravity one-loop amplitudes.Comment: Minor corrections. Appendix adde

The n-point MHV one-loop Amplitude in N=4 Supergravity

We present an explicit formula for the n-point MHV one-loop amplitude in a N=4 supergravity theory. This formula is derived from the soft and collinear factorisations of the amplitude.Comment: 8 pages; v2 References added. Minor changes to tex

Constructing Gravity Amplitudes from Real Soft and Collinear Factorisation

Soft and collinear factorisations can be used to construct expressions for amplitudes in theories of gravity. We generalise the "half-soft" functions used previously to "soft-lifting" functions and use these to generate tree and one-loop amplitudes. In particular we construct expressions for MHV tree amplitudes and the rational terms in one-loop amplitudes in the specific context of N=4 supergravity. To completely determine the rational terms collinear factorisation must also be used. The rational terms for N=4 have a remarkable diagrammatic interpretation as arising from algebraic link diagrams.Comment: 18 pages, axodraw, Proof of eq. 4.3 adde

Analytic results for two-loop Yang-Mills

Recent Developments in computing very specific helicity amplitudes in two loop QCD are presented. The techniques focus upon the singular structure of the amplitude rather than on a diagramatic and integration approachComment: Talk presented at 13th International Symposium on Radiative Corrections, 24-29 September, 2017,St. Gilgen, Austria, 9 page

Large Area Crop Inventory Experiment (LACIE). User requirements

There are no author-identified significant results in this report

Methodology for urban rail and construction technology research and development planning

A series of transit system visits, organized by the American Public Transit Association (APTA), was conducted in which the system operators identified the most pressing development needs. These varied by property and were reformulated into a series of potential projects. To assist in the evaluation, a data base useful for estimating the present capital and operating costs of various transit system elements was generated from published data. An evaluation model was developed which considered the rate of deployment of the research and development project, potential benefits, development time and cost. An outline of an evaluation methodology that considered benefits other than capital and operating cost savings was also presented. During the course of the study, five candidate projects were selected for detailed investigation; (1) air comfort systems; (2) solid state auxiliary power conditioners; (3) door systems; (4) escalators; and (5) fare collection systems. Application of the evaluation model to these five examples showed the usefulness of modeling deployment rates and indicated a need to increase the scope of the model to quantitatively consider reliability impacts

Flux networks in metabolic graphs

A metabolic model can be represented as bipartite graph comprising linked reaction and metabolite nodes. Here it is shown how a network of conserved fluxes can be assigned to the edges of such a graph by combining the reaction fluxes with a conserved metabolite property such as molecular weight. A similar flux network can be constructed by combining the primal and dual solutions to the linear programming problem that typically arises in constraint-based modelling. Such constructions may help with the visualisation of flux distributions in complex metabolic networks. The analysis also explains the strong correlation observed between metabolite shadow prices (the dual linear programming variables) and conserved metabolite properties. The methods were applied to recent metabolic models for Escherichia coli, Saccharomyces cerevisiae, and Methanosarcina barkeri. Detailed results are reported for E. coli; similar results were found for the other organisms.Comment: 9 pages, 4 figures, RevTeX 4.0, supplementary data available (excel