The Graph Curvature Calculator and the curvatures of cubic graphs

We classify all cubic graphs with either non-negative Ollivier-Ricci curvature or non-negative Bakry-\'Emery curvature everywhere. We show in both curvature notions that the non-negatively curved graphs are the prism graphs and the M\"obius ladders. We also highlight an online tool for calculating the curvature of graphs under several variants of these curvature notions that we use in the classification. As a consequence of the classification result we show, that non-negatively curved cubic expanders do not exist

Context-aware Human Motion Prediction

The problem of predicting human motion given a sequence of past observations is at the core of many applications in robotics and computer vision. Current state-of-the-art formulate this problem as a sequence-to-sequence task, in which a historical of 3D skeletons feeds a Recurrent Neural Network (RNN) that predicts future movements, typically in the order of 1 to 2 seconds. However, one aspect that has been obviated so far, is the fact that human motion is inherently driven by interactions with objects and/or other humans in the environment. In this paper, we explore this scenario using a novel context-aware motion prediction architecture. We use a semantic-graph model where the nodes parameterize the human and objects in the scene and the edges their mutual interactions. These interactions are iteratively learned through a graph attention layer, fed with the past observations, which now include both object and human body motions. Once this semantic graph is learned, we inject it to a standard RNN to predict future movements of the human/s and object/s. We consider two variants of our architecture, either freezing the contextual interactions in the future of updating them. A thorough evaluation in the "Whole-Body Human Motion Database" shows that in both cases, our context-aware networks clearly outperform baselines in which the context information is not considered.Comment: Accepted at CVPR2