the mined positive neighbor objects.

3D Amino Acid Pose Estimation
-----------------------------

After we obtained the proposal for an amino acid, we further estimated its pose by locating its forming atoms in 3D space. The Stacked hourglass Network [@pose_hg] is widely used to handle the human pose estimation task. In this work, a 3D stacked hourglass network, named as poseNet, is proposed to regress 3D coordinates of each atom in amino acids. The network stacks multiple ($H$) hourglass structures sequentially. Each hourglass has $R_b$ residual blocks and provides feature volumes with different semantic resolutions. Importantly, auxiliary losses were applied to the intermediate feature volumes for learning robust features.

For an amino acid with $N$ atoms, poseNet produces $H$ estimated heatmaps with $N$ channels. The Mean Squared Error loss is adopted: $$\begin{aligned}
\begin{split}
      L_{pose} = \sum_{h}^{H} \sum_{n}^{N} \parallel y_h^*(n) - y_h(n) \parallel_{2}^{2},
\end{split}    \end{aligned}$$ where $y_h^*$ denotes the predicted heatmap by the $h$-th stack, $n$ denotes the $n$-th atom, and $y_h$ is the ground-truth heatmap with the $N \times 8 $ locations labeled as 1. For each atom, the $2^3$ neighborhood locations are labeled as 1.

Monte Carlo Tree Search for Threading {#sec:threading}
-------------------------------------

### Main Chain Threading Problem 

Given the predicted 