An algebraic approach to the scattering equations

We employ the so-called companion matrix method from computational algebraic geometry, tailored for zero-dimensional ideals, to study the scattering equations. The method renders the CHY-integrand of scattering amplitudes computable using simple linear algebra and is amenable to an algorithmic approach. Certain identities in the amplitudes as well as rationality of the final integrand become immediate in this formalism

Veterinary decision making in relation to metritis - a qualitative approach to understand the background for variation and bias in veterinary medical records

<p>Abstract</p> <p>Background</p> <p>Results of analyses based on veterinary records of animal disease may be prone to variation and bias, because data collection for these registers relies on different observers in different settings as well as different treatment criteria. Understanding the human influence on data collection and the decisions related to this process may help veterinary and agricultural scientists motivate observers (veterinarians and farmers) to work more systematically, which may improve data quality. This study investigates qualitative relations between two types of records: 1) 'diagnostic data' as recordings of metritis scores and 2) 'intervention data' as recordings of medical treatment for metritis and the potential influence on quality of the data.</p> <p>Methods</p> <p>The study is based on observations in veterinary dairy practice combined with semi-structured research interviews of veterinarians working within a herd health concept where metritis diagnosis was described in detail. The observations and interviews were analysed by qualitative research methods to describe differences in the veterinarians' perceptions of metritis diagnosis (scores) and their own decisions related to diagnosis, treatment, and recording.</p> <p>Results</p> <p>The analysis demonstrates how data quality can be affected during the diagnostic procedures, as interaction occurs between diagnostics and decisions about medical treatments. Important findings were when scores lacked consistency within and between observers (variation) and when scores were adjusted to the treatment decision already made by the veterinarian (bias). The study further demonstrates that veterinarians made their decisions at 3 different levels of focus (cow, farm, population). Data quality was influenced by the veterinarians' perceptions of collection procedures, decision making and their different motivations to collect data systematically.</p> <p>Conclusion</p> <p>Both variation and bias were introduced into the data because of veterinarians' different perceptions of and motivations for decision making. Acknowledgement of these findings by researchers, educational institutions and veterinarians in practice may stimulate an effort to improve the quality of field data, as well as raise awareness about the importance of including knowledge about human perceptions when interpreting studies based on field data. Both recognitions may increase the usefulness of both within-herd and between-herd epidemiological analyses.</p

Two-loop scattering amplitudes from ambitwistor strings: from genus two to the nodal Riemann sphere

We derive from ambitwistor strings new formulae for two-loop scattering amplitudes in supergravity and super-Yang-Mills theory, with any number of particles. We start by constructing a formula for the type II ambitwistor string amplitudes on a genus-two Riemann surface, and then study the localisation of the moduli space integration on a degenerate limit, where the genus-two surface turns into a Riemann sphere with two nodes. This leads to scattering amplitudes in supergravity, expressed in the formalism of the two-loop scattering equations. For super-Yang-Mills theory, we import `half' of the supergravity result, and determine the colour dependence by considering a current algebra on the nodal Riemann sphere, thereby completely specifying the two-loop analogue of the Parke-Taylor factor, including non-planar contributions. We also present in appendices explicit expressions for the Szego kernels and the partition functions for even spin structures, up to the relevant orders in the degeneration parameters, which may be useful for related investigations in conventional superstring theory.Comment: 66 pages plus appendices, 14 figures. v2: small changes, published version. v3: typos fixed in appendix