The Grassmannian formulation of $mathcal{N}=4$ super Yang-Mills theory expresses tree-level scattering amplitudes as linear combinations of residues from certain contour integrals. BCFW bridge decompositions using adjacent transpositions simplify the
evaluation of individual residues, but orientation information is lost in the process. We present a straightforward algorithm to compute relative orientations between the resulting coordinate charts, and we show how to generalize the technique for charts corresponding to sequences of any not-necessarily-adjacent transpositions. As applications of these results, we demonstrate the existence of a signed boundary operator that manifestly squares to zero and prove via our algorithm that any residues appearing in the tree amplitude sum are decorated with appropriate signs so all non-local poles cancel exactly, not just mod 2 as in previous works.
The charge form factor of $^$4He has been extracted in the range 29 fm$^{-2}$ $le Q^2 le 77$ fm$^{-2}$ from elastic electron scattering, detecting $^4$He nuclei and electrons in coincidence with the High Resolution Spectrometers of the Hall A Facilit
y of Jefferson Lab. The results are in qualitative agreement with realistic meson-nucleon theoretical calculations. The data have uncovered a second diffraction minimum, which was predicted in the $Q^2$ range of this experiment, and rule out conclusively long-standing predictions of dimensional scaling of high-energy amplitudes using quark counting.
In this paper, we discuss the work on comets of Caroline Herschel, the first female comet-hunter. After leaving Bath for the environs of Windsor Castle and eventually Slough, she discovered at least eight comets, five of which were reported in the Ph
ilosophical Transactions of the Royal Society. We consider her public image, astronomers perceptions of her contributions, and the style of her astronomical drawings that changed with the technological developments in astronomical illustration.
