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Autonomous driving on water surfaces plays an essential role in executing hazardous and time-consuming missions, such as maritime surveillance, survivors rescue, environmental monitoring, hydrography mapping and waste cleaning. This work presents WaterScenes, the first multi-task 4D radar-camera fusion dataset for autonomous driving on water surfaces. Equipped with a 4D radar and a monocular camera, our Unmanned Surface Vehicle (USV) proffers all-weather solutions for discerning object-related information, including color, shape, texture, range, velocity, azimuth, and elevation. Focusing on typical static and dynamic objects on water surfaces, we label the camera images and radar point clouds at pixel-level and point-level, respectively. In addition to basic perception tasks, such as object detection, instance segmentation and semantic segmentation, we also provide annotations for free-space segmentation and waterline segmentation. Leveraging the multi-task and multi-modal data, we conduct benchmark experiments on the uni-modality of radar and camera, as well as the fused modalities. Experimental results demonstrate that 4D radar-camera fusion can considerably improve the accuracy and robustness of perception on water surfaces, especially in adverse lighting and weather conditions. WaterScenes dataset is public on https://waterscenes.github.io., Comment: Accepted by IEEE Transactions on Intelligent Transportation Systems

Solar filament eruptions, flares and coronal mass ejections (CMEs) are manifestations of drastic release of energy in the magnetic field, which are related to many eruptive phenomena from the Earth magnetosphere to black hole accretion disks. With the availability of high-resolution magnetograms on the solar surface, observational data-based modelling is a promising way to quantitatively study the underlying physical mechanisms behind observations. By incorporating thermal conduction and radiation losses in the energy equation, we develop a new data-driven radiative magnetohydrodynamic (MHD) model, which has the capability to capture the thermodynamic evolution compared to our previous zero-\b{eta} model. Our numerical results reproduce major observational characteristics of the X1.0 flare on 2021 October 28 in NOAA active region (AR) 12887, including the morphology of the eruption, kinematic of flare ribbons, extreme-ultraviolet (EUV) radiations, and two components of the EUV waves predicted by the magnetic stretching model, i.e., a fast-mode shock wave and a slower apparent wave due to successive stretching of magnetic field lines. Moreover, some intriguing phenomena are revealed in the simulation. We find that flare ribbons separate initially and ultimately stop at the outer stationary quasi-separatrix layers (QSLs). Such outer QSLs correspond to the border of the filament channel and determine the final positions of flare ribbons, which can be used to predict the size and the lifetime of a flare before it occurs. In addition, the side view of the synthesized EUV and white-light images exhibit typical three-part structures of CMEs, where the bright leading front is roughly cospatial with the non-wave component of the EUV wave, reinforcing the magnetic stretching model for the slow component of EUV waves., Comment: 46 pages, 15 figures, accepted for publication in The Astrophysical Journal Supplement

We prove that the knot Floer complex of a fibered knot detects whether the monodromy of its fibration is right-veering. In particular, this leads to a purely knot Floer-theoretic characterization of tight contact structures, by the work of Honda, Kazez, and Matic. Our proof makes use of the relationship between the Heegaard Floer homology of mapping tori and the symplectic Floer homology of area-preserving surface diffeomorphisms. We describe applications of this work to Dehn surgeries and taut foliations., Comment: 30 pages, 4 figures; v2: accepted version

We prove that if $K$ is a nontrivial null-homotopic knot in a closed oriented $3$--manfiold $Y$ such that $Y-K$ does not have an $S^1\times S^2$ summand, then the zero surgery on $K$ does not have an $S^1\times S^2$ summand. This generalizes a result of Hom and Lidman, who proved the case when $Y$ is an irreducible rational homology sphere., Comment: 9 pages

If $K$ is a fibered knot in a closed, oriented $3$--manifold $Y$ with fiber $F$, and $\widehat{HFK}(Y,K,[F], g(F)-1;\mathbb Z/2\mathbb Z)$ has rank $r$, then the monodromy of $K$ is freely isotopic to a diffeomorphism with at most $r-1$ fixed points. This generalizes earlier work of Baldwin--Hu--Sivek and Ni. We also clarify a misleading formula in Cotton-Clay's computation of the symplectic Floer homology of mapping classes of surfaces., Comment: 9 pages

Using an argument of Baldwin--Hu--Sivek, we prove that if $K$ is a hyperbolic fibered knot with fiber $F$ in a closed, oriented $3$--manifold $Y$, and $\widehat{HFK}(Y,K,[F], g(F)-1)$ has rank $1$, then the monodromy of $K$ is freely isotopic to a pseudo-Anosov map with no fixed points. In particular, this shows that the monodromy of a hyperbolic L-space knot is freely isotopic to a map with no fixed points., Comment: 9 pages, 1 figure

A slope $\frac pq$ is called a characterizing slope for a given knot $K_0\subset S^3$ if whenever the $\frac pq$--surgery on a knot $K\subset S^3$ is homeomorphic to the $\frac pq$--surgery on $K_0$ via an orientation preserving homeomorphism, then $K=K_0$. In a previous paper, we showed that, outside a certain finite set of slopes, only the negative integers could possibly be non-characterizing slopes for the torus knot $T_{5,2}$. Applying recent work of Baldwin--Hu--Sivek, we improve our result by showing that a nontrivial slope $\frac pq$ is a characterizing slope for $T_{5,2}$ if $\frac pq>-1$ and $\frac pq\notin \{0,1, \pm\frac12,\pm\frac13\}$. In particular, every nontrivial L-space slope of $T_{5,2}$ is characterizing for $T_{5,2}$. As a consequence, if a nontrivial $\frac pq$-surgery on a non-torus knot in $S^3$ yields a manifold of finite fundamental group, then $|p|>9$., Comment: 7 pages, 2 figures