The No-Triangle Hypothesis for N=8 Supergravity

We study the perturbative expansion of N=8 supergravity in four dimensions from the viewpoint of the ``no-triangle'' hypothesis, which states that one-loop graviton amplitudes in N=8 supergravity only contain scalar box integral functions. Our computations constitute a direct proof at six-points and support the no-triangle conjecture for seven-point amplitudes and beyond.Comment: 43page

Proof of the MHV vertex expansion for all tree amplitudes in N=4 SYM theory

We prove the MHV vertex expansion for all tree amplitudes of N=4 SYM theory. The proof uses a shift acting on all external momenta, and we show that every N^kMHV tree amplitude falls off as 1/z^k, or faster, for large z under this shift. The MHV vertex expansion allows us to derive compact and efficient generating functions for all N^kMHV tree amplitudes of the theory. We also derive an improved form of the anti-NMHV generating function. The proof leads to a curious set of sum rules for the diagrams of the MHV vertex expansion.Comment: 40 pages, 7 figure

Multigluon tree amplitudes with a pair of massive fermions

We consider the calculation of n-point multigluon tree amplitudes with a pair of massive fermions in QCD. We give the explicit transformation rules of this kind of massive fermion-pair amplitudes with respect to different reference momenta and check the correctness of them by SUSY Ward identities. Using these rules and onshell BCFW recursion relation, we calculate the analytic results of several n-point multigluon amplitudes.Comment: 15page

Solution to the Ward Identities for Superamplitudes

Supersymmetry and R-symmetry Ward identities relate on-shell amplitudes in a supersymmetric field theory. We solve these Ward identities for (Next-to)^K MHV amplitudes of the maximally supersymmetric N=4 and N=8 theories. The resulting superamplitude is written in a new, manifestly supersymmetric and R-invariant form: it is expressed as a sum of very simple SUSY and SU(N)_R-invariant Grassmann polynomials, each multiplied by a "basis amplitude". For (Next-to)^K MHV n-point superamplitudes the number of basis amplitudes is equal to the dimension of the irreducible representation of SU(n-4) corresponding to the rectangular Young diagram with N columns and K rows. The linearly independent amplitudes in this algebraic basis may still be functionally related by permutation of momenta. We show how cyclic and reflection symmetries can be used to obtain a smaller functional basis of color-ordered single-trace amplitudes in N=4 gauge theory. We also analyze the more significant reduction that occurs in N=8 supergravity because gravity amplitudes are not ordered. All results are valid at both tree and loop level.Comment: 29 pages, published versio

Recursive Calculation of One-Loop QCD Integral Coefficients

We present a new procedure using on-shell recursion to determine coefficients of integral functions appearing in one-loop scattering amplitudes of gauge theories, including QCD. With this procedure, coefficients of integrals, including bubbles and triangles, can be determined without resorting to integration. We give criteria for avoiding spurious singularities and boundary terms that would invalidate the recursion. As an example where the criteria are satisfied, we obtain all cut-constructible contributions to the one-loop n-gluon scattering amplitude, A_n^{oneloop}(...--+++...), with split-helicity from an N=1 chiral multiplet and from a complex scalar. Using the supersymmetric decomposition, these are ingredients in the construction of QCD amplitudes with the same helicities. This method requires prior knowledge of amplitudes with sufficiently large numbers of legs as input. In many cases, these are already known in compact forms from the unitarity method.Comment: 36 pages; v2 clarification added and typos fixed, v3 typos fixe

A super MHV vertex expansion for N=4 SYM theory

We present a supersymmetric generalization of the MHV vertex expansion for all tree amplitudes in N=4 SYM theory. In addition to the choice of a reference spinor, this super MHV vertex expansion also depends on four reference Grassmann parameters. We demonstrate that a significant fraction of diagrams in the expansion vanishes for a judicious choice of these Grassmann parameters, which simplifies the computation of amplitudes. Even pure-gluon amplitudes require fewer diagrams than in the ordinary MHV vertex expansion. We show that the super MHV vertex expansion arises from the recursion relation associated with a holomorphic all-line supershift. This is a supersymmetric generalization of the holomorphic all-line shift recently introduced in arXiv:0811.3624. We study the large-z behavior of generating functions under these all-line supershifts, and find that they generically provide 1/z^k falloff at (Next-to)^k MHV level. In the case of anti-MHV generating functions, we find that a careful choice of shift parameters guarantees a stronger 1/z^(k+4) falloff. These particular all-line supershifts may therefore play an important role in extending the super MHV vertex expansion to N=8 supergravity.Comment: 26 pages, 3 figures, v2: analytic expression for counting of super MHV vertex diagrams added; references adde

Classification of behaviour in housed dairy cows using an accelerometer-based activity monitoring system

Background Advances in bio-telemetry technology have made it possible to automatically monitor and classify behavioural activities in many animals, including domesticated species such as dairy cows. Automated behavioural classification has the potential to improve health and welfare monitoring processes as part of a Precision Livestock Farming approach. Recent studies have used accelerometers and pedometers to classify behavioural activities in dairy cows, but such approaches often cannot discriminate accurately between biologically important behaviours such as feeding, lying and standing or transition events between lying and standing. In this study we develop a decision-tree algorithm that uses tri-axial accelerometer data from a neck-mounted sensor to both classify biologically important behaviour in dairy cows and to detect transition events between lying and standing. Results Data were collected from six dairy cows that were monitored continuously for 36 h. Direct visual observations of each cow were used to validate the algorithm. Results show that the decision-tree algorithm is able to accurately classify three types of biologically relevant behaviours: lying (77.42 % sensitivity, 98.63 % precision), standing (88.00 % sensitivity, 55.00 % precision), and feeding (98.78 % sensitivity, 93.10 % precision). Transitions between standing and lying were also detected accurately with an average sensitivity of 96.45 % and an average precision of 87.50 %. The sensitivity and precision of the decision-tree algorithm matches the performance of more computationally intensive algorithms such as hidden Markov models and support vector machines. Conclusions Biologically important behavioural activities in housed dairy cows can be classified accurately using a simple decision-tree algorithm applied to data collected from a neck-mounted tri-axial accelerometer. The algorithm could form part of a real-time behavioural monitoring system in order to automatically detect dairy cow health and welfare status

Molecular Phylogenetic Evaluation of Classification and Scenarios of Character Evolution in Calcareous Sponges (Porifera, Class Calcarea)

Calcareous sponges (Phylum Porifera, Class Calcarea) are known to be taxonomically difficult. Previous molecular studies have revealed many discrepancies between classically recognized taxa and the observed relationships at the order, family and genus levels; these inconsistencies question underlying hypotheses regarding the evolution of certain morphological characters. Therefore, we extended the available taxa and character set by sequencing the complete small subunit (SSU) rDNA and the almost complete large subunit (LSU) rDNA of additional key species and complemented this dataset by substantially increasing the length of available LSU sequences. Phylogenetic analyses provided new hypotheses about the relationships of Calcarea and about the evolution of certain morphological characters. We tested our phylogeny against competing phylogenetic hypotheses presented by previous classification systems. Our data reject the current order-level classification by again finding non-monophyletic Leucosolenida, Clathrinida and Murrayonida. In the subclass Calcinea, we recovered a clade that includes all species with a cortex, which is largely consistent with the previously proposed order Leucettida. Other orders that had been rejected in the current system were not found, but could not be rejected in our tests either. We found several additional families and genera polyphyletic: the families Leucascidae and Leucaltidae and the genus Leucetta in Calcinea, and in Calcaronea the family Amphoriscidae and the genus Ute. Our phylogeny also provided support for the vaguely suspected close relationship of several members of Grantiidae with giantortical diactines to members of Heteropiidae. Similarly, our analyses revealed several unexpected affinities, such as a sister group relationship between Leucettusa (Leucaltidae) and Leucettidae and between Leucascandra (Jenkinidae) and Sycon carteri (Sycettidae). According to our results, the taxonomy of Calcarea is in desperate need of a thorough revision, which cannot be achieved by considering morphology alone or relying on a taxon sampling based on the current classification below the subclass level

Identification of Behaviour in Freely Moving Dogs (Canis familiaris) Using Inertial Sensors

Monitoring and describing the physical movements and body postures of animals is one of the most fundamental tasks of ethology. The more precise the observations are the more sophisticated the interpretations can be about the biology of a certain individual or species. Animal-borne data loggers have recently contributed much to the collection of motion-data from individuals, however, the problem of translating these measurements to distinct behavioural categories to create an ethogram is not overcome yet. The objective of the present study was to develop a “behaviour tracker”: a system composed of a multiple sensor data-logger device (with a tri-axial accelerometer and a tri-axial gyroscope) and a supervised learning algorithm as means of automated identification of the behaviour of freely moving dogs. We collected parallel sensor measurements and video recordings of each of our subjects (Belgian Malinois, N=12; Labrador Retrievers, N=12) that were guided through a predetermined series of standard activities. Seven behavioural categories (lay, sit, stand, walk, trot, gallop, canter) were pre-defined and each video recording was tagged accordingly. Evaluation of the measurements was performed by support vector machine (SVM) classification. During the analysis we used different combinations of independent measurements for training and validation (belonging to the same or different individuals or using different training data size) to determine the robustness of the application. We reached an overall accuracy of above 90% perfect identification of all the defined seven categories of behaviour when both training and validation data belonged to the same individual, and over 80% perfect recognition rate using a generalized training data set of multiple subjects. Our results indicate that the present method provides a good model for an easily applicable, fast, automatic behaviour classification system that can be trained with arbitrary motion patterns and potentially be applied to a wide range of species and situations