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In recent years, the integration of prediction and planning through neural networks has received substantial attention. Despite extensive studies on it, there is a noticeable gap in understanding the operation of such models within a closed-loop planning setting. To bridge this gap, we propose a novel closed-loop planning framework compatible with neural networks engaged in joint prediction and planning. The framework contains two running modes, namely planning and safety monitoring, wherein the neural network performs Motion Prediction and Planning (MPP) and Conditional Motion Prediction (CMP) correspondingly without altering architecture. We evaluate the efficacy of our framework using the nuPlan dataset and its simulator, conducting closed-loop experiments across diverse scenarios. The results demonstrate that the proposed framework ensures the feasibility and local stability of the planning process while maintaining safety with CMP safety monitoring. Compared to other learning-based methods, our approach achieves substantial improvement., Comment: 7 pages,5 figures

BaNi$_2$As$_2$ is a nonmagnetic analogue of the iron pnictide superconductors, and in its tetragonal state exhibits an incommensurate charge-density-wave (IC-CDW) and a sizable elastoresistance. In this work, phonons in BaNi$_2$As$_2$ associated with the IC-CDW and uniform in-plane lattice distortions are investigated using high-resolution inelastic X-ray scattering. The in-plane transverse acoustic phonons reveal no softening at temperatures where the elastoresistance increases strongly, indicating the latter to be electronically driven. Systematic phonon measurements reveal the IC-CDW occurs in two stages upon cooling: underdamped phonons first soften to zero energy well above the IC-CDW ordering temperature, then the resulting quasielastic IC-CDW fluctuations gradually slow down and coalesce into the static IC-CDW order. A possible origin for our observations is the IC-CDW in tetragonal BaNi$_2$As$_2$ being uniaxial, which provides an additional Ising degree of freedom favorable for disordered IC-CDW modulations, and accounts for the elastoresistance through a weak coupling to the lattice., Comment: Supplemental Materials available upon request

In this paper, we consider the Cauchy problem for the generalized Camassa-Holm equation proposed by Hakkaev and Kirchev (2005) \cite{Hakkaev 2005}. We prove that the solution map of the generalized Camassa-Holm equation is not uniformly continuous on the initial data in Besov spaces. Our result include the present work (2020) \cite{Li 2020,Li 2020-1} on Camassa-Holm equation with $Q=1$ and extends the previous non-uniform continuity in Sobolev spaces (2015) \cite{Mi 2015} to Besov spaces. In addition, the non-uniform continuity in critical space $B_{2, 1}^{\frac{3}{2}}(\mathbb{R})$ is the first to be considered in our paper.