EFFECTS OF BALANCING HAMSTRING AND QUADRICEPS MUSCLE TORQUE ON RUNNING TECHNIQUE

It has been suggested that balancing the isokinetic strength of quadriceps (Q) and hamstring (H) muscles can reduce hamstring injuries during running (Croisier et al 2008). The efficacy of this type of intervention has been previously explored. To further the knowledge of the H: Q relationship we have examined the intervention’s affect on running technique as presented here

One-Loop NMHV Amplitudes involving Gluinos and Scalars in N=4 Gauge Theory

We use Supersymmetric Ward Identities and quadruple cuts to generate n-pt NMHV amplitudes involving gluinos and adjoint scalars from purely gluonic amplitudes. We present a set of factors that can be used to generate one-loop NMHV amplitudes involving gluinos or adjoint scalars in N=4 Super Yang-Mills from the corresponding purely gluonic amplitude.Comment: 16 pages, JHEP versio

Generalized Unitarity and One-Loop Amplitudes in N=4 Super-Yang-Mills

One-loop amplitudes of gluons in N=4 gauge theory can be written as linear combinations of known scalar box integrals with coefficients that are rational functions. In this paper we show how to use generalized unitarity to basically read off the coefficients. The generalized unitarity cuts we use are quadruple cuts. These can be directly applied to the computation of four-mass scalar integral coefficients, and we explicitly present results in next-to-next-to-MHV amplitudes. For scalar box functions with at least one massless external leg we show that by doing the computation in signature (--++) the coefficients can also be obtained from quadruple cuts, which are not useful in Minkowski signature. As examples, we reproduce the coefficients of some one-, two-, and three-mass scalar box integrals of the seven-gluon next-to-MHV amplitude, and we compute several classes of three-mass and two-mass-hard coefficients of next-to-MHV amplitudes to all multiplicities.Comment: 36 pages, harvmac. 13 figures. v3: References added, typos fixed. Figure 4 added. New n-gluon example with internal fermions and scalars. v4: Footnotes 2, 4 and 6 added, acknowledgments added, minor correction

Coplanarity In Twistor Space Of N=4 Next-To-MHV One-Loop Amplitude Coefficients

Next-to-MHV one-loop amplitudes in N=4 gauge theory can be written as a linear combination of known multivalued functions, called scalar box functions, with coefficients that are rational functions. We consider the localization of these coefficients in twistor space and prove that all of them are localized on a plane. The proof is done by studying the action of differential operators that test coplanarity on the unitarity cuts of the amplitudes.Comment: 11 pages, harvmac, 2 figure

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

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

MHV Rules for Higgs Plus Multi-Gluon Amplitudes

We use tree-level perturbation theory to show how non-supersymmetric one-loop scattering amplitudes for a Higgs boson plus an arbitrary number of partons can be constructed, in the limit of a heavy top quark, from a generalization of the scalar graph approach of Cachazo, Svrcek and Witten. The Higgs boson couples to gluons through a top quark loop which generates, for large top mass, a dimension-5 operator H tr G^2. This effective interaction leads to amplitudes which cannot be described by the standard MHV rules; for example, amplitudes where all of the gluons have positive helicity. We split the effective interaction into the sum of two terms, one holomorphic (selfdual) and one anti-holomorphic (anti-selfdual). The holomorphic interactions give a new set of MHV vertices -- identical in form to those of pure gauge theory, except for momentum conservation -- that can be combined with pure gauge theory MHV vertices to produce a tower of amplitudes with more than two negative helicities. Similarly, the anti-holomorphic interactions give anti-MHV vertices that can be combined with pure gauge theory anti-MHV vertices to produce a tower of amplitudes with more than two positive helicities. A Higgs boson amplitude is the sum of one MHV-tower amplitude and one anti-MHV-tower amplitude. We present all MHV-tower amplitudes with up to four negative-helicity gluons and any number of positive-helicity gluons (NNMHV). These rules reproduce all of the available analytic formulae for Higgs + n-gluon scattering (n<=5) at tree level, in some cases yielding considerably shorter expressions.Comment: 34 pages, 8 figures; v2, references correcte

Unitarity Method with Spurious Pole

In unitarity cut method, compact input of on-shell tree level amplitudes is crucial to simplify calculations. Although BCFW on-shell recursion relation gives very compact tree level amplitudes, they usually contain spurious poles. In this paper, we present a method to deal with this issue and provide explicit simple algebraic functions for various coefficients in the presence of spurious poles. As an application, we present analytic result (not just rational term) for one-loop five gluon A(-++++) with scalar propagator for the first time.Comment: 49 pages; typos corrected, reference added; figures added, final version to appear in NP

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

Identification of animal movement patterns using tri-axial magnetometry

BackgroundAccelerometers are powerful sensors in many bio-logging devices, and are increasingly allowing researchers to investigate the performance, behaviour, energy expenditure and even state, of free-living animals. Another sensor commonly used in animal-attached loggers is the magnetometer, which has been primarily used in dead-reckoning or inertial measurement tags, but little outside that. We examine the potential of magnetometers for helping elucidate the behaviour of animals in a manner analogous to, but very different from, accelerometers. The particular responses of magnetometers to movement means that there are instances when they can resolve behaviours that are not easily perceived using accelerometers.MethodsWe calibrated the tri-axial magnetometer to rotations in each axis of movement and constructed 3-dimensional plots to inspect these stylised movements. Using the tri-axial data of Daily Diary tags, attached to individuals of number of animal species as they perform different behaviours, we used these 3-d plots to develop a framework with which tri-axial magnetometry data can be examined and introduce metrics that should help quantify movement and behaviour.ResultsTri-axial magnetometry data reveal patterns in movement at various scales of rotation that are not always evident in acceleration data. Some of these patterns may be obscure until visualised in 3D space as tri-axial spherical plots (m-spheres). A tag-fitted animal that rotates in heading while adopting a constant body attitude produces a ring of data around the pole of the m-sphere that we define as its Normal Operational Plane (NOP). Data that do not lie on this ring are created by postural rotations of the animal as it pitches and/or rolls. Consequently, stereotyped behaviours appear as specific trajectories on the sphere (m-prints), reflecting conserved sequences of postural changes (and/or angular velocities), which result from the precise relationship between body attitude and heading. This novel approach shows promise for helping researchers to identify and quantify behaviours in terms of animal body posture, including heading.ConclusionMagnetometer-based techniques and metrics can enhance our capacity to identify and examine animal behaviour, either as a technique used alone, or one that is complementary to tri-axial accelerometry