Predicting the future trajectories of pedestrians is of increasing importance for many applications such as autonomous driving and social robots. Nevertheless, current trajectory prediction models suffer from limitations such as lack of diversity in candidate trajectories, poor accuracy, and instability. In this paper, we propose a novel Sequence Entropy Energy-based Model named SEEM, which consists of a generator network and an energy network. Within SEEM we optimize the sequence entropy by taking advantage of the local variational inference of f-divergence estimation to maximize the mutual information across the generator in order to cover all modes of the trajectory distribution, thereby ensuring SEEM achieves full diversity in candidate trajectory generation. Then, we introduce a probability distribution clipping mechanism to draw samples towards regions of high probability in the trajectory latent space, while our energy network determines which trajectory is most representative of the ground truth. This dual approach is our so-called all-then-one strategy. Finally, a zero-centered potential energy regularization is proposed to ensure stability and convergence of the training process. Through experiments on both synthetic and public benchmark datasets, SEEM is shown to substantially outperform the current state-of-the-art approaches in terms of diversity, accuracy and stability of pedestrian trajectory prediction.

Detecting self-organized coalitions from functional networks is one of the most important ways to uncover functional mechanisms in the brain. Determining these raises well-known technical challenges in terms of scale imbalance, outliers and hard-examples. In this article, we propose a novel self-adaptive skeleton approach to detect coalitions through an approximation method based on probabilistic mixture models. The nodes in the networks are characterized in terms of robust k -order complete subgraphs ( k -clique ) as essential substructures. The k -clique enumeration algorithm quickly enumerates all k -cliques in a parallel manner for a given network. Then, the cliques, from max -clique down to min -clique, of each order k , are hierarchically embedded into a probabilistic mixture model. They are self-adapted to the corresponding structure density of coalitions in the brain functional networks through different order k . All the cliques are merged and evolved into robust skeletons to sustain each unbalanced coalition by eliminating outliers and separating overlaps. We call this the k -CLIque Merging Evolution (CLIME) algorithm. The experimental results illustrate that the proposed approaches are robust to density variation and coalition mixture and can enable the effective detection of coalitions from real brain functional networks. There exist potential cognitive functional relations between the regions of interest in the coalitions revealed by our methods, which suggests the approach can be usefully applied in neuroscientific studies.

As one of the counting-based topological indices, the number of subtrees and its variations has received much attention in recent years. In this paper, using generating functions, we investigate and derive formulas for this index of hexagonal and phenylene chains. We also present graph-theoretical algorithms for enumerating subtrees of these two chains. Extremal values and graphs with respect to the subtree number among all hexagonal and phenylene chains with n hexagons are also determined. As an application, we briefly examine the subtree densities of these two chains.