Nima Arkani-Hamed, Hugh Thomas, Jaroslav Trnka

We present new, fundamentally combinatorial and topological characterizations of the amplituhedron. Upon projecting external data through the amplituhedron, the resulting configuration of points has a specified (and maximal) generalized 'winding number'. Equivalently, the amplituhedron can be fully described in binary: canonical projections of the geometry down to one dimension have a specified (and maximal) number of 'sign flips' of the projected data. The locality and unitarity of scattering amplitudes are easily derived as elementary consequences of this binary code. Minimal winding defines a natural 'dual' of the amplituhedron. This picture gives us an avatar of the amplituhedron purely in the configuration space of points in vector space (momentum-twistor space in the physics), a new interpretation of the canonical amplituhedron form, and a direct bosonic understanding of the scattering super-amplitude in planar N = 4 SYM as a differential form on the space of physical kinematical data.

Julian Merten, Quim Llorens, Hans Winther

This work explores the ability of computer vision algorithms to characterise dark matter haloes formed in different models of structure formation. We produce surface mass density maps of the most massive haloes in a suite of eight numerical simulations, all based on the same initial conditions, but implementing different models of gravity. This suite includes a standard $\Lambda$CDM model, two variations of $f(R)$-gravity, two variations of Symmetron gravity and three Dvali, Gabadadze and Porrati (DGP) models. We use the publicly available WND-CHARM algorithm to extract 2919 image features from either the raw pixel intensities of the maps, or from a variety of image transformations including Fourier, Wavelet, Chebyshev and Edge transformations. After discarding the most degenerate models, we achieve more than 60% single-image classification success rate in distinguishing the four different models of gravity while using a simple weighted neighbour distance (WND) to define our classification metric. This number can be increased to more than 70% if additional information, such as a rough estimate of the halo mass, is included. We find that the classification success steeply declines when the noise level in the images is increased, but that this trend can be largely reduced by smoothing the noisy data. We find Zernike moments of the Fourier transformation of either the raw image or its Wavelet transformation to be the most descriptive feature, followed by the Gini coefficient of several transformations and the Haralick and Tamura textures of the raw pixel data eventually pre-processed by an Edge transformation. The proposed methodology is general and does not only apply to the characterisation of modified gravity models, but can be used to classify any set of models which show variations in the 2D morphology of their respective structure.