MHV Lagrangian for N=4 Super Yang-Mills

Here we formulate two field redefinitions for N=4 Super Yang-Mills in light cone superspace that generates only MHV vertices in the new Lagrangian. After careful consideration of the S-matrix equivalence theorem, we see that only the canonical transformation gives the MHV Lagrangian that would correspond to the CSW expansion. Being in superspace, it is easier to analyse the equivalence theorem at loop level. We calculate the on shell amplitude for 4pt $(\bar{\Lambda}\bar{{\rm A}}\Lambda {\rm A})$ MHV in the new lagrangian and show that it reproduces the previously known form. We also briefly discuss the relationship with the off-shell continuation prescription of CSW.Comment: 17 pages 4 figures, 2 sections and several references added typo correcte

Trace mineral concentrations and accretion rates in the empty body and body tissues of growing Fleckvieh (German Simmental) bulls

This research project aimed to generate basic data for specifying the trace mineral requirements of Fleckvieh (German Simmental) bulls. Hence, the concentrations of the trace minerals iron (Fe), zinc (Zn), copper (Cu), and manganese (Mn) in the empty-body and body tissue fractions of growing Fleckvieh bulls slaughtered at 120–780 kg live weight were determined. Results were used to calculate trace mineral accretion rates. Fe and Zn represented the largest shares in the animals' bodies. The Zn accretion increased, while Mn accretion steadily declined during cattle growth. Fe accretion attained a maximum at 400 kg live weight. Cu accretion declined until 600 kg live weight and then increased slightly afterwards. The provided data may be used to adjust the recommendations with respect to the trace mineral requirements of growing Fleckvieh bulls.</p

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

Loop amplitudes in gauge theories: modern analytic approaches

This article reviews on-shell methods for analytic computation of loop amplitudes, emphasizing techniques based on unitarity cuts. Unitarity techniques are formulated generally but have been especially useful for calculating one-loop amplitudes in massless theories such as Yang-Mills theory, QCD, and QED.Comment: 34 pages. Invited review for a special issue of Journal of Physics A devoted to "Scattering Amplitudes in Gauge Theories." v2: typesetting macro error fixe

On All-loop Integrands of Scattering Amplitudes in Planar N=4 SYM

We study the relationship between the momentum twistor MHV vertex expansion of planar amplitudes in N=4 super-Yang-Mills and the all-loop generalization of the BCFW recursion relations. We demonstrate explicitly in several examples that the MHV vertex expressions for tree-level amplitudes and loop integrands satisfy the recursion relations. Furthermore, we introduce a rewriting of the MHV expansion in terms of sums over non-crossing partitions and show that this cyclically invariant formula satisfies the recursion relations for all numbers of legs and all loop orders.Comment: 34 pages, 17 figures; v2: Minor improvements to exposition and discussion, updated references, typos fixe

Tree-Level Formalism

We review two novel techniques used to calculate tree-level scattering amplitudes efficiently: MHV diagrams, and on-shell recursion relations. For the MHV diagrams, we consider applications to tree-level amplitudes and focus in particular on the N=4 supersymmetric formulation. We also briefly describe the derivation of loop amplitudes using MHV diagrams. For the recursion relations, after presenting their general proof, we discuss several applications to massless theories with and without supersymmetry, to theories with massive particles, and to graviton amplitudes in General Relativity. This article is an invited review for a special issue of Journal of Physics A devoted to "Scattering Amplitudes in Gauge Theories".Comment: 40 pages, 8 figures, invited review for a special issue of Journal of Physics A devoted to "Scattering Amplitudes in Gauge Theories", R. Roiban(ed), M. Spradlin(ed), A. Volovich(ed); v2: minor corrections, references adde

Integrands for QCD rational terms and N=4 SYM from massive CSW rules

We use massive CSW rules to derive explicit compact expressions for integrands of rational terms in QCD with any number of external legs. Specifically, we present all-n integrands for the one-loop all-plus and one-minus gluon amplitudes in QCD. We extract the finite part of spurious external-bubble contributions systematically; this is crucial for the application of integrand-level CSW rules in theories without supersymmetry. Our approach yields integrands that are independent of the choice of CSW reference spinor even before integration. Furthermore, we present a recursive derivation of the recently proposed massive CSW-style vertex expansion for massive tree amplitudes and loop integrands on the Coulomb-branch of N=4 SYM. The derivation requires a careful study of boundary terms in all-line shift recursion relations, and provides a rigorous (albeit indirect) proof of the recently proposed construction of massive amplitudes from soft-limits of massless on-shell amplitudes. We show that the massive vertex expansion manifestly preserves all holomorphic and half of the anti-holomorphic supercharges, diagram-by-diagram, even off-shell.Comment: 30 pages, many figure

QTL mapping of improving forage maize starch degradability in European elite maize germplasm

Improving maize starch content is of great importance for both forage and grain yield. In this study, 13 starch degradability traits were analyzed including percentage of the seedling area, floury endosperm, hard endosperm of total grain area, percentage of the floury endosperm surface, and vitreousness ratio surface hard: floury endosperm surface, etc. We mapped quantitative trait loci (QTL) in a biparental population of 309 doubled haploid lines (DHL) based on field phenotyping at two locations. A genetic linkage map was constructed using 168 SSR (simple sequence repeat) markers, which covered 1508 cM of the maize genome, with an average distance of 9.0 cM. Close phenotypic and genotypic correlations were found for all traits, and were all statistically significant (P = 0.01) at two locations. Major QTL for more than two traits were detected, especially in two regions in bins 4.05-4.06 and 7.04-7.05, associated with 13 and 9 traits, respectively. This study contributes to marker assisted breeding and also to fine mapping candidate genes associated with maize starch degradability

Regeneration of myelin sheaths of normal length and thickness in the zebrafish CNS correlates with growth of axons in caliber

Demyelination is observed in numerous diseases of the central nervous system, including multiple sclerosis (MS). However, the endogenous regenerative process of remyelination can replace myelin lost in disease, and in various animal models. Unfortunately, the process of remyelination often fails, particularly with ageing. Even when remyelination occurs, it is characterised by the regeneration of myelin sheaths that are abnormally thin and short. This imperfect remyelination is likely to have implications for the restoration of normal circuit function and possibly the optimal metabolic support of axons. Here we describe a larval zebrafish model of demyelination and remyelination. We employ a drug-inducible cell ablation system with which we can consistently ablate 2/3rds of oligodendrocytes in the larval zebrafish spinal cord. This leads to a concomitant demyelination of 2/3rds of axons in the spinal cord, and an innate immune response over the same time period. We find restoration of the normal number of oligodendrocytes and robust remyelination approximately two weeks after induction of cell ablation, whereby myelinated axon number is restored to control levels. Remarkably, we find that myelin sheaths of normal length and thickness are regenerated during this time. Interestingly, we find that axons grow significantly in caliber during this period of remyelination. This suggests the possibility that the active growth of axons may stimulate the regeneration of myelin sheaths of normal dimensions