arXiv subjects
Publications and source records attributed to Qiuyu Ren.
We note an adjunction inequality in $k\overline{\mathbb{CP}^2}$ for the $s$-version of the $Sq^1$-refinement of Rasmussen's $s$-invariant. This does not hold for general spatial refinements of $s$-invariants.
Autonomous target tracking with quadrotors has wide applications in many scenarios, such as cinematographic follow-up shooting or suspect chasing. Target motion prediction is necessary when designing the tracking planner. However, the widely used constant velocity or constant rotation assumption can not fully capture the dynamics of the target. The tracker may fail when the target happens to move aggressively, such as sudden turn or deceleration. In this paper, we propose an intention-aware planner by additionally considering the intention of the target to enhance safety and robustness in aerial tracking applications. Firstly, a designated intention prediction method is proposed, which combines a user-defined potential assessment function and a state observation function. A reachable region is generated to specifically evaluate the turning intentions. Then we design an intention-driven hybrid A* method to predict the future possible positions for the target. Finally, an intention-aware optimization approach is designed to generate a spatial-temporal optimal trajectory, allowing the tracker to perceive unexpected situations from the target. Benchmark comparisons and real-world experiments are conducted to validate the performance of our method.
We determine the quantum filtration structure of the Lee homology of all torus links. In particular, this determines the $s$-invariant of a torus link equipped with any orientation. In the special case $T(n,n)$, our result confirms a conjecture of Pardon, as well as a conjecture of Manolescu-Marengon-Sarkar-Willis which establishes an adjunction-type inequality of the $s$-invariant for cobordisms in $k\overline{\mathbb{CP}^2}$. We also give a few applications of this adjunction inequality.
Extending a proposal of Defant and Kravitz [Discrete Mathematics, \textbf{1}, 347 (2024)], we define Hitomezashi patterns and loops on a torus and provide several structural results for such loops. For a given pattern, our main theorems give optimal residual information regarding the Hitomezashi loop length, loop count, as well as possible homology classes of such loops. Special attention is paid to toroidal Hitomezashi patterns that are symmetric with respect to the diagonal $x = y$, where we establish a novel connection between Hitomezashi and knot theory.
We prove a recent conjecture of Manolescu-Willis which states that the $s$-invariant of a knot in $\mathbb{RP}^3$ (as defined by them) gives a lower bound on its null-homologous slice genus in the unit disk bundle of $TS^2$. We also conjecture a lower bound in the more general case where the slice surface is not necessarily null-homologous, and give its proof in some special cases.
We provide a shorter proof to Defant and Kravitz's theorem (arXiv:2201.03461, Theorem 1.2) on the length of Hitomezashi loops modulo 8.
We prove the convergence of the spectrum of the generator of the kinetic Brownian motion to the spectrum of the base Laplacian for closed Riemannian manifolds. This generalizes recent work of Kolb--Weich--Wolf [arXiv:2011.06434] on constant curvature surfaces and of Ren--Tao [arXiv:2208.13111] on locally symmetric spaces. As an application, we prove a conjecture of Baudoin--Tardif [arXiv:1604.06813] on the optimal convergence rate to the equilibrium.
We prove the strong convergence of the spectrum of the kinetic Brownian motion to the spectrum of base Laplacian for a large class of compact locally Riemannian homogeneous spaces, in particular all compact locally symmetric spaces. This generalizes recent work of Kolb--Weich--Wolf [arXiv:2011.06434] on constant curvature surfaces.
Existing public person Re-Identification~(ReID) datasets are small in modern terms because of labeling difficulty. Although unlabeled surveillance video is abundant and relatively easy to obtain, it is unclear how to leverage these footage to learn meaningful ReID representations. In particular, most existing unsupervised and domain adaptation ReID methods utilize only the public datasets in their experiments, with labels removed. In addition, due to small data sizes, these methods usually rely on fine tuning by the unlabeled training data in the testing domain to achieve good performance. Inspired by the recent progress of large-scale self-supervised image classification using contrastive learning, we propose to learn ReID representation from large-scale unlabeled surveillance video alone. Assisted by off-the-shelf pedestrian detection tools, we apply the contrastive loss at both the image and the tracklet levels. Together with a principal component analysis step using camera labels freely available, our evaluation using a large-scale unlabeled dataset shows far superior performance among unsupervised methods that do not use any training data in the testing domain. Furthermore, the accuracy improves with the data size and therefore our method has great potential with even larger and more diversified datasets.
We say two $δ$-tubes (dimension $δ\times\cdots\timesδ\times1$) in $\mathbb{R}^n$ are essentially distinct if the measure of their intersection is smaller than a half of a single $δ$-tube. For a collection of essentially distinct $δ$-tubes, we give the asymptotically sharp lower bound for the measure of their union. Then we characterize all sharp examples. We will give a new measurement of convexity based on the X-ray transform.