Predicting the trajectories of pedestrians in crowded conditions is an important task for applications like autonomous navigation systems. Previous studies have tackled this problem using two strategies. They (1) infer all future steps recursively, or (2) predict potential destinations at once and interpolate intermediate to arrive there. However, these strategies often suffer from accumulated ...

In this paper, we define the directional edge escaping points set of function iteration under a given plane partition and then prove that upper bound Hausdorff dimension \(S(z)=a e^{z}+b e^{-z}\), where \(a, b\in \mathbb{C}\) \(|a|^{2}+|b|^{2}\neq 0\), is no more than 1.

Let X ⊂ R be a set that is definable in an o-minimal expansion of R. This paper shows that, in a suitable sense, there are very few rational points of X that do not lie on some connected semialgebraic subset of X of positive dimension. 2000 Mathematics Subject Classification: 11G99, 03C64