Multi-Scale Attention with Dense Encoder for Handwritten Mathematical Expression Recognition

Handwritten mathematical expression recognition is a challenging problem due to the complicated two-dimensional structures, ambiguous handwriting input and variant scales of handwritten math symbols. To settle this problem, we utilize the attention based encoder-decoder model that recognizes mathematical expression images from two-dimensional layouts to one-dimensional LaTeX strings. We improve the encoder by employing densely connected convolutional networks as they can strengthen feature extraction and facilitate gradient propagation especially on a small training set. We also present a novel multi-scale attention model which is employed to deal with the recognition of math symbols in different scales and save the fine-grained details that will be dropped by pooling operations. Validated on the CROHME competition task, the proposed method significantly outperforms the state-of-the-art methods with an expression recognition accuracy of 52.8% on CROHME 2014 and 50.1% on CROHME 2016, by only using the official training dataset

B0→D0Dˉ0K0B^0 \to D^0 \bar D^0 K^0, B+→D0Dˉ0K+B^+ \to D^0 \bar D^0 K^+ and the scalar DDˉD \bar D bound state

We study the $B^0$ decay to $D^0 \bar D^0 K^0$ based on the chiral unitary model that generates the X(3720) resonance, and make predictions for the $D^0 \bar D^0$ invariant mass distribution. From the shape of the distribution, the existence of the resonance below threshold could be induced. We also predict the rate of production of the X(3720) resonance to the $D^0 \bar D^0$ mass distribution with no free parameters.Comment: 9 pages, 17 figure