Hidden Symmetries and Integrable Hierarchy of the N=4 Supersymmetric Yang-Mills Equations

We describe an infinite-dimensional algebra of hidden symmetries of N=4 supersymmetric Yang-Mills (SYM) theory. Our derivation is based on a generalization of the supertwistor correspondence. Using the latter, we construct an infinite sequence of flows on the solution space of the N=4 SYM equations. The dependence of the SYM fields on the parameters along the flows can be recovered by solving the equations of the hierarchy. We embed the N=4 SYM equations in the infinite system of the hierarchy equations and show that this SYM hierarchy is associated with an infinite set of graded symmetries recursively generated from supertranslations. Presumably, the existence of such nonlocal symmetries underlies the observed integrable structures in quantum N=4 SYM theory.Comment: 24 page

A Conformally Invariant Holographic Two-Point Function on the Berger Sphere

We apply our previous work on Green's functions for the four-dimensional quaternionic Taub-NUT manifold to obtain a scalar two-point function on the homogeneously squashed three-sphere (otherwise known as the Berger sphere), which lies at its conformal infinity. Using basic notions from conformal geometry and the theory of boundary value problems, in particular the Dirichlet-to-Robin operator, we establish that our two-point correlation function is conformally invariant and corresponds to a boundary operator of conformal dimension one. It is plausible that the methods we use could have more general applications in an AdS/CFT context.Comment: 1+49 pages, no figures. v2: Several typos correcte

Conformal geometry of the supercotangent and spinor bundles

We study the actions of local conformal vector fields X∈conf(M,g) on the spinor bundle of (M,g) and on its classical counterpart: the supercotangent bundle M of (M,g). We first deal with the classical framework and determine the Hamiltonian lift of conf(M,g) to M. We then perform the geometric quantization of the supercotangent bundle of (M,g), which constructs the spinor bundle as the quantum representation space. The Kosmann Lie derivative of spinors is btained by quantization of the comoment map. The quantum and classical actions of conf(M,g) turn, respectively, the space of differential operators acting on spinor densities and the space of their symbols into conf(M,g)-modules. They are filtered and admit a common associated graded module. In the conformally flat case, the latter helps us determine the conformal invariants of both conf(M,g)-modules, in particular the conformally odd powers of the Dirac operator.Peer reviewe

The Earth: Plasma Sources, Losses, and Transport Processes

This paper reviews the state of knowledge concerning the source of magnetospheric plasma at Earth. Source of plasma, its acceleration and transport throughout the system, its consequences on system dynamics, and its loss are all discussed. Both observational and modeling advances since the last time this subject was covered in detail (Hultqvist et al., Magnetospheric Plasma Sources and Losses, 1999) are addressed

Evaluating satellite-based pasture measurement for Australian dairy farmers

Australian dairy farms rely on grazing pastures as their primary and cheapest source of feed. Accurate and timely measurement of pasture biomass is integral for effective grazing management practice, however few Australian dairy farmers record pasture mass or growth rate objectively. A system using satellite images has been developed to measure pasture biomass at a paddock-scale in Australia. The concept was evaluated through an 18 farm pilot study over the spring growth period, July to November 2008. The study was evaluated in terms of technology fit with grazing management practice of participant farmers. Qualitative research methods, including semi-structured interviews and a group workshop, were used to ascertain participant views on issues such as timeliness, accuracy, and value proposition within the context of farming systems. In this paper we discuss preliminary findings from the study, focussing on the farmer attitudes to the use of satellite-based measurement and delivery of pasture biomass information. The findings suggest that a technology such as satellite pasture measurement has potential application in Australian dairy farm systems. However the provision of data alone does not guarantee successful technology uptake. Support structures must also be provided to help farmers interpret the information within the specific context of their farm system. These support structures may include use of private agronomists, producer groups, agriculture extension personnel, or associated software applications

Field validation of protocols developed to evaluate in-line mastitis detection systems

This paper reports on a field validation of previously developed protocols for evaluating the performance of in-line mastitis-detection systems. The protocols outlined 2 requirements of these systems: (1) to detect cows with clinical mastitis (CM) promptly and accurately to enable timely and appropriate treatment and (2) to identify cows with high somatic cell count (SCC) to manage bulk milk SCC levels. Gold standard measures, evaluation tests, performance measures, and performance targets were proposed. The current study validated the protocols on commercial dairy farms with automated in-line mastitis-detection systems using both electrical conductivity (EC) and SCC sensor systems that both monitor at whole-udder level. The protocol for requirement 1 was applied on 3 commercial farms. For requirement 2, the protocol was applied on 6 farms; 3 of them had low bulk milk SCC (128 × 103cells/mL) and were the same farms as used for field evaluation of requirement 1. Three farms with high bulk milk SCC (270 × 103 cells/mL) were additionally enrolled. The field evaluation methodology and results were presented at a workshop including representation from 7 international suppliers of in-line mastitis-detection systems. Feedback was sought on the acceptance of standardized performance evaluation protocols and recommended refinements to the protocols. Although the methodology for requirement 1 was relatively labor intensive and required organizational skills over an extended period, no major issues were encountered during the field validation of both protocols. The validation, thus, proved the protocols to be practical. Also, no changes to the data collection process were recommended by the technology supplier representatives. However, 4 recommendations were made to refine the protocols: inclusion of an additional analysis that ignores small (low-density) clot observations in the definition of CM, extension of the time window from 4 to 5 milkings for timely alerts for CM, setting a maximum number of 10 milkings for the time window to detect a CM episode, and presentation of sensitivity for a larger range of false alerts per 1,000 milkings replacing minimum performance targets. The recommended refinements are discussed with suggested changes to the original protocols. The information presented is intended to inform further debate toward achieving international agreement on standard protocols to evaluate performance of in-line mastitis-detection systems

What is Q-Curvature?

The original publication can be found at www.springerlink.comBranson’s Q-curvature is now recognized as a fundamental quantity in conformal geometry. We outline its construction and present its basic properties.S.-Y. Alice Chang, Michael Eastwood, Bent Ørsted and Paul C. Yan

Designing future dairy systems for New Zealand using reflexive interactive design

Globally, agricultural systems are facing unprecedented challenges. The problems are of systemic nature and will require transformational changes and systemic redesign. In this study, we investigated the redesign of dairy systems in New Zealand, due to their large economic, social and environmental influence nationally. We did not set the boundaries of the ‘dairy systems’ from the outset, letting this definition be part of the design process. We applied ‘Reflexive Interactive Design’ (RIO), an approach aimed at structurally addressing complex trade-offs and contributing, by process and design, to change towards sustainable development and integral sustainability (i.e. in all relevant dimensions of sustainability). A detailed system analysis was conducted, followed by two rounds of structured design focused on four main stakeholders (‘actors') identified as part of the RIO process: the farmers, the citizens, the consumers, and the dairy cows. Our study established design goals related to enhancing the wellbeing of humans and animals, enhancing environmental performance, economics and resilience of dairy systems and reconnecting dairy farming with the rest of society. The process took us beyond the boundaries of a dairy farm and identified the territorial level as the object of design, arriving at a design concept we have called the ‘Agro-ecological Park’. The name was chosen to convey an analogy with ‘Eco-industrial Parks’. Operating as a multifunctional network, the Park has the goal of delivering multiple benefits for its members, and multiple goods and services for the rest of society. The coordinated network articulates linkages between farmers and many other businesses and people in the territory. The individual dairy farm is redesigned to be a node in that network rather than operating as an isolated entity. That way, much of the weight for the increased complexity and multifunctionality now demanded of farming can be carried by the network instead of the individual farmer. These preliminary design ideas, and the reasoning behind them, should encourage new perspectives on the complex problems facing NZ dairy farming, and agriculture globally, in the upcoming decades.</p