Graviton Resonances in E+ E- -> MU+ MU- at Linear Colliders with Beamstrahlung and ISR Effects

Electromagnetic radiation emitted by the colliding beams is expected to play an important role at the next generation of high energy e^+ e^- linear collider(s). Focusing on the simplest process e+e- -> mu+ mu-, we show that radiative effects like initial state radiation (ISR) and beamstrahlung can lead to greatly-enhanced signals for resonant graviton modes of the Randall-Sundrum model.Comment: 20 pages Latex, 7 eps figure

OL\'E: Orthogonal Low-rank Embedding, A Plug and Play Geometric Loss for Deep Learning

Deep neural networks trained using a softmax layer at the top and the cross-entropy loss are ubiquitous tools for image classification. Yet, this does not naturally enforce intra-class similarity nor inter-class margin of the learned deep representations. To simultaneously achieve these two goals, different solutions have been proposed in the literature, such as the pairwise or triplet losses. However, such solutions carry the extra task of selecting pairs or triplets, and the extra computational burden of computing and learning for many combinations of them. In this paper, we propose a plug-and-play loss term for deep networks that explicitly reduces intra-class variance and enforces inter-class margin simultaneously, in a simple and elegant geometric manner. For each class, the deep features are collapsed into a learned linear subspace, or union of them, and inter-class subspaces are pushed to be as orthogonal as possible. Our proposed Orthogonal Low-rank Embedding (OL\'E) does not require carefully crafting pairs or triplets of samples for training, and works standalone as a classification loss, being the first reported deep metric learning framework of its kind. Because of the improved margin between features of different classes, the resulting deep networks generalize better, are more discriminative, and more robust. We demonstrate improved classification performance in general object recognition, plugging the proposed loss term into existing off-the-shelf architectures. In particular, we show the advantage of the proposed loss in the small data/model scenario, and we significantly advance the state-of-the-art on the Stanford STL-10 benchmark

Eriksson's numbers game and finite Coxeter groups

The numbers game is a one-player game played on a finite simple graph with certain ``amplitudes'' assigned to its edges and with an initial assignment of real numbers to its nodes. The moves of the game successively transform the numbers at the nodes using the amplitudes in a certain way. This game and its interactions with Coxeter/Weyl group theory and Lie theory have been studied by many authors. In particular, Eriksson connects certain geometric representations of Coxeter groups with games on graphs with certain real number amplitudes. Games played on such graphs are ``E-games.'' Here we investigate various finiteness aspects of E-game play: We extend Eriksson's work relating moves of the game to reduced decompositions of elements of a Coxeter group naturally associated to the game graph. We use Stembridge's theory of fully commutative Coxeter group elements to classify what we call here the ``adjacency-free'' initial positions for finite E-games. We characterize when the positive roots for certain geometric representations of finite Coxeter groups can be obtained from E-game play. Finally, we provide a new Dynkin diagram classification result of E-game graphs meeting a certain finiteness requirement.Comment: 18 page

Play, John E. Wells, Becky Burkes

MSU students John E. Wells and Becky Burkes are pictured practicing for the play The Dark of the Moon.https://scholarsjunction.msstate.edu/ua-photo-collection/3894/thumbnail.jp