Part2Word: Learning Joint Embedding of Point Clouds and Text by Matching Parts to Words

It is important to learn joint embedding for 3D shapes and text in different shape understanding tasks, such as shape-text matching, retrieval, and shape captioning. Current multi-view based methods learn a mapping from multiple rendered views to text. However, these methods can not analyze 3D shapes well due to the self-occlusion and limitation of learning manifolds. To resolve this issue, we propose a method to learn joint embedding of point clouds and text by matching parts from shapes to words from sentences in a common space. Specifically, we first learn segmentation prior to segment point clouds into parts. Then, we map parts and words into an optimized space, where the parts and words can be matched with each other. In the optimized space, we represent a part by aggregating features of all points within the part, while representing each word with its context information, where we train our network to minimize the triplet ranking loss. Moreover, we also introduce cross-modal attention to capture the relationship of part-word in this matching procedure, which enhances joint embedding learning. Our experimental results outperform the state-of-the-art in multi-modal retrieval under the widely used benchmark

Approximation algorithms for the shortest total path length spanning tree problem

AbstractGiven an undirected graph with a nonnegative weight on each edge, the shortest total path length spanning tree problem is to find a spanning tree of the graph such that the total path length summed over all pairs of the vertices is minimized. In this paper, we present several approximation algorithms for this problem. Our algorithms achieve approximation ratios of 2, 15/8, and 3/2 in time O(n2+f(G)),O(n3), and O(n4) respectively, in which f(G) is the time complexity for computing all-pairs shortest paths of the input graph G and n is the number of vertices of G. Furthermore, we show that the approximation ratio of (4/3+ε) can be achieved in polynomial time for any constant ε>0

Crystal structure of 3-methyl-2-oxo-2H-chromen-7-yl propionate, C13H12O4

Abstract C13H12O4, triclinic, P1̄ (no. 2), a = 6.141(5) Å, b = 8.108(6) Å, c = 12.234(9) Å, α = 79.257(12)°, β = 76.820(12)°, γ = 74.687(11)°, V = 566.8(7) Å3, Z = 2, R gt(F) = 0.0515, wR ref(F 2) = 0.1575, T = 296(2) K