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The genuine entanglement of Dirac fields for an N-partite system is investigated in Schwarzschild spacetime and the analysis is carried out using the single-mode approximation. Due to the Hawking effect, quantum entanglement is divided into two parts physically accessible and inaccessible entanglement. We obtain a general analytic expression of genuine N-partite entanglement that includes all accessible and inaccessible entanglement in a Schwarzschild black hole. Unlike bosonic entanglement, the accessible N-partite entanglement of Dirac fields monotonically decreases to a nonzero value with the Hawking temperature. Interestingly, the inaccessible N-partite entanglement is a monotonic or non-monotonic function of the Hawking temperature, depending on the ratio between accessible and inaccessible modes, in contrast to bipartite or tripartite entanglement that is only a monotonic function of the Hawking temperature. Finally, we obtain two restrictive relationships for the quantum information of the black hole. This conclusion provides a new understanding of Hawking effect of the black hole., Comment: 14 pages, 1 figure

Motivated by recent experimental observations of opposite Chern numbers in $R$-type twisted MoTe$_2$ and WSe$_2$ homobilayers, we perform large-scale density-functional-theory (DFT) calculations with machine learning force fields to investigate moir\'e band topology from large to small twist angles in both materials. We find that the Chern numbers of the moir\'e frontier bands change sign as a function of twist angle, and this change is driven by the competition between moir\'{e} ferroelectricity and piezoelectricity. Our large-scale calculations, enabled by machine learning methods, reveal crucial insights into interactions across different scales in twisted bilayer systems. The interplay between atomic-level relaxation effects and moir\'e-scale electrostatic potential variation opens new avenues for the design of intertwined topological and correlated states, including the possibility of mimicking higher Landau-level physics in the absence of a magnetic field., Comment: 8 pages, 5 figures

We study the redistribution of the fermionic steering and the relation among fermionic Bell nonlocality, steering, and entanglement in the background of the Garfinkle-Horowitz-Strominger dilaton black hole. We analyze the meaning of the fermionic steering in terms of the Bell inequality in curved spacetime. We find that the fermionic steering, which is previously found to survive in the extreme dilaton black hole, cannot be considered to be nonlocal. We also find that the dilaton gravity can redistribute the fermionic steering, but cannot redistribute Bell nonlocality, which means that the physically inaccessible steering is also not nonlocal. Unlike the inaccessible entanglement, the inaccessible steering may increase non-monotonically with the dilaton. Furthermore, we obtain some monogamy relations between the fermionic steering and entanglement in dilaton spacetime. In addition, we show the difference between the fermionic and bosonic steering in curved spacetime., Comment: 21 pages, 4 figures

Incorporating both flexible and rigid components in robot designs offers a unique solution to the limitations of traditional rigid robotics by enabling both compliance and strength. This paper explores the challenges and solutions for controlling soft-rigid hybrid robots, particularly addressing the issue of self-contact. Conventional control methods prioritize precise state tracking, inadvertently increasing the system's overall stiffness, which is not always desirable in interactions with the environment or within the robot itself. To address this, we investigate the application of Control Barrier Functions (CBFs) and High Order CBFs to manage self-contact scenarios in serially connected soft-rigid hybrid robots. Through an analysis based on Piecewise Constant Curvature (PCC) kinematics, we establish CBFs within a classical control framework for self-contact dynamics. Our methodology is rigorously evaluated in both simulation environments and physical hardware systems. The findings demonstrate that our proposed control strategy effectively regulates self-contact in soft-rigid hybrid robotic systems, marking a significant advancement in the field of robotics., Comment: 6 pages, 6 figures, submitted to IEEE Robosoft 2024 Conference

As autonomous driving technology matures, end-to-end methodologies have emerged as a leading strategy, promising seamless integration from perception to control via deep learning. However, existing systems grapple with challenges such as unexpected open set environments and the complexity of black-box models. At the same time, the evolution of deep learning introduces larger, multimodal foundational models, offering multi-modal visual and textual understanding. In this paper, we harness these multimodal foundation models to enhance the robustness and adaptability of autonomous driving systems, enabling out-of-distribution, end-to-end, multimodal, and more explainable autonomy. Specifically, we present an approach to apply end-to-end open-set (any environment/scene) autonomous driving that is capable of providing driving decisions from representations queryable by image and text. To do so, we introduce a method to extract nuanced spatial (pixel/patch-aligned) features from transformers to enable the encapsulation of both spatial and semantic features. Our approach (i) demonstrates unparalleled results in diverse tests while achieving significantly greater robustness in out-of-distribution situations, and (ii) allows the incorporation of latent space simulation (via text) for improved training (data augmentation via text) and policy debugging. We encourage the reader to check our explainer video at https://www.youtube.com/watch?v=4n-DJf8vXxo&feature=youtu.be and to view the code and demos on our project webpage at https://drive-anywhere.github.io/., Comment: Project webpage: https://drive-anywhere.github.io Explainer video: https://www.youtube.com/watch?v=4n-DJf8vXxo&feature=youtu.be

Game-theoretic motion planners are a powerful tool for the control of interactive multi-agent robot systems. Indeed, contrary to predict-then-plan paradigms, game-theoretic planners do not ignore the interactive nature of the problem, and simultaneously predict the behaviour of other agents while considering change in one's policy. This, however, comes at the expense of computational complexity, especially as the number of agents considered grows. In fact, planning with more than a handful of agents can quickly become intractable, disqualifying game-theoretic planners as possible candidates for large scale planning. In this paper, we propose a planning algorithm enabling the use of game-theoretic planners in robot systems with a large number of agents. Our planner is based on the reality of locality of information and thus deploys local games with a selected subset of agents in a receding horizon fashion to plan collision avoiding trajectories. We propose five different principled schemes for selecting game participants and compare their collision avoidance performance. We observe that the use of Control Barrier Functions for priority ranking is a potent solution to the player selection problem for motion planning., Comment: to be published in IROS 2023 conference proceedings

Audio coding is an essential module in the real-time communication system. Neural audio codecs can compress audio samples with a low bitrate due to the strong modeling and generative capabilities of deep neural networks. To address the poor high-frequency expression and high computational cost and storage consumption, we proposed an integrated framework that utilizes a neural network to model wide-band components and adopts traditional signal processing to compress high-band components according to psychological hearing knowledge. Inspired by auditory perception theory, a perception-based loss function is designed to improve harmonic modeling. Besides, generative adversarial network (GAN) compression is proposed for the first time for neural audio codecs. Our method is superior to prior advanced neural codecs across subjective and objective metrics and allows real-time inference on desktop and mobile.

Diffusion models have risen as a promising approach to data-driven planning, and have demonstrated impressive robotic control, reinforcement learning, and video planning performance. Given an effective planner, an important question to consider is replanning -- when given plans should be regenerated due to both action execution error and external environment changes. Direct plan execution, without replanning, is problematic as errors from individual actions rapidly accumulate and environments are partially observable and stochastic. Simultaneously, replanning at each timestep incurs a substantial computational cost, and may prevent successful task execution, as different generated plans prevent consistent progress to any particular goal. In this paper, we explore how we may effectively replan with diffusion models. We propose a principled approach to determine when to replan, based on the diffusion model's estimated likelihood of existing generated plans. We further present an approach to replan existing trajectories to ensure that new plans follow the same goal state as the original trajectory, which may efficiently bootstrap off previously generated plans. We illustrate how a combination of our proposed additions significantly improves the performance of diffusion planners leading to 38\% gains over past diffusion planning approaches on Maze2D, and further enables the handling of stochastic and long-horizon robotic control tasks. Videos can be found on the anonymous website: \url{https://vis-www.cs.umass.edu/replandiffuser/}.

In the framework of nonrelativistic QCD (NRQCD) factorization, we compute both the polarized and the unpolarized decay widths for the processes $\eta_b(\chi_{bJ})\to J/\psi J/\psi$, accurate up to next-to-next-to-leading-order (NNLO) in $\alpha_s$. For the first time, we confirm that the NRQCD factorization does hold at NNLO for the process involving triple quarkonia. We find the radiative corrections are considerable. In particular for $\chi_{b2}$, both $\mathcal{O}(\alpha_s)$ and $\mathcal{O}(\alpha_s^2)$ corrections are sizable and negative, and can significantly reduce the leading order prediction. At NNLO, the branching fractions are $8.2\times 10^{-7}$, $6.2\times 10^{-6}$, $7.2\times 10^{-7}$ and $2.7\times 10^{-6}$ for $\eta_b$, $\chi_{b0}$, $\chi_{b1}$ and $\chi_{b2}$ decay, respectively. Our theoretical predictions are consistent with the upper limits measured by the {\tt Belle} Collaboration. Moreover, we investigate the dependence of the theoretical predictions on the ratio of the charm quark mass and the bottom quark mass. By fixing $m_b$ and varying $m_c$ from $1.25$ to $1.9$ GeV, we find the branching fraction can change a factor of $2$, $3$, and $6$ for $\eta_b$, $\chi_{b0}$, and $\chi_{b1}$, respectively. In the phenomenological analysis, with the integrate luminosity $\mathcal{L}=100\,{\rm fb}^{-1}$, we expect about $(5-10)\times 10^3$ $\eta_b(\chi_{bJ})\to J/\psi J/\psi\to \ell \bar{\ell}\ell \bar{\ell}$ events produced at the {\tt LHC}, thus it might be hopeful to search for these processes. On the other hand, there are less than $100$ $\eta_b(\chi_{bJ})\to J/\psi J/\psi$ signal events at the B factory, so it seems the experimental measurements on these channels are quite challenging based on current dataset., Comment: 17 pages, 3 figures, 4 tables; The affiliation and acknowledgement of the first author are updated

This paper studies safe driving interactions between Human-Driven Vehicles (HDVs) and Connected and Automated Vehicles (CAVs) in mixed traffic where the dynamics and control policies of HDVs are unknown and hard to predict. In order to address this challenge, we employ event-triggered Control Barrier Functions (CBFs) to estimate the HDV model online, construct data-driven and state-feedback safety controllers, and transform constrained optimal control problems for CAVs into a sequence of event-triggered quadratic programs. We show that we can ensure collision-free between HDVs and CAVs and demonstrate the robustness and flexibility of our framework on different types of human drivers in lane-changing scenarios while guaranteeing safety with human-in-the-loop interactions.

This paper studies safety and feasibility guarantees for systems with tight control bounds. It has been shown that stabilizing an affine control system while optimizing a quadratic cost and satisfying state and control constraints can be mapped to a sequence of Quadratic Programs (QPs) using Control Barrier Functions (CBF) and Control Lyapunov Functions (CLF). One of the main challenges in this method is that the QP could easily become infeasible under safety constraints of high relative degree, especially under tight control bounds. Recent work focused on deriving sufficient conditions for guaranteeing feasibility. The existing results are case-dependent. In this paper, we consider the general case. We define a feasibility constraint and propose a new type of CBF to enforce it. Our method guarantees the feasibility of the above mentioned QPs, while satisfying safety requirements. We demonstrate the proposed method on an Adaptive Cruise Control (ACC) problem for a heterogeneous platoon with tight control bounds, and compare our method to existing CBF-CLF approaches. The results show that our proposed approach can generate gradually transitioned control (without abrupt changes) with guaranteed feasibility and safety., Comment: 8 pages, 2 figures. arXiv admin note: text overlap with arXiv:2304.00372

This paper addresses the problem of safety-critical control for non-affine control systems. It has been shown that optimizing quadratic costs subject to state and control constraints can be sub-optimally reduced to a sequence of quadratic programs (QPs) by using Control Barrier Functions (CBFs). Our recently proposed High Order CBFs (HOCBFs) can accommodate constraints of arbitrary relative degree. The main challenges in this approach are that it requires affine control dynamics and the solution of the CBF-based QP is sub-optimal since it is solved point-wise. To address these challenges, we incorporate higher-order CBFs into neural ordinary differential equation-based learning models as differentiable CBFs to guarantee safety for non-affine control systems. The differentiable CBFs are trainable in terms of their parameters, and thus, they can address the conservativeness of CBFs such that the system state will not stay unnecessarily far away from safe set boundaries. Moreover, the imitation learning model is capable of learning complex and optimal control policies that are usually intractable online. We illustrate the effectiveness of the proposed framework on LiDAR-based autonomous driving and compare it with existing methods., Comment: 8 pages, accepted in IEEE CDC 2023

A series of recent experimental works on twisted MoTe$_2$ homobilayers have unveiled an abundance of exotic states in this system. Valley-polarized quantum anomalous Hall states have been identified at hole doping of $\nu = -1$, and the fractional quantum anomalous Hall effect is observed at $\nu = -2/3$ and $\nu = -3/5$. In this work, we investigate the electronic properties of AA-stacked twisted bilayer MoTe$_2$ at $\nu=-2$ by $k$-space Hartree-Fock calculations. We find that the phase diagram is qualitatively similar to the phase diagram of a Kane-Mele-Hubbard with staggered onsite potential. A noteworthy phase within the diagram is the antiferromagnetic Chern insulator, stabilized by the external electric field. We attribute the existence of this Chern insulator to an antiferromagnetic instability at a topological phase transition between the quantum spin hall phase and a band insulator phase. We highlight that the antiferromagnetic Chern insulator phase is most evident at a twist angle of approximately $4^\circ$. Our research proposes the potential of realizing a Chern insulator beyond $\nu=-1$, and contributes fresh perspectives on the interplay between band topology and electron-electron correlations in moir\'e superlattices.

Reduced-dimensional CsPbBr$_3$ nanoplatelets (NPLs) are promising candidates for color-saturated blue emitters, yet their electroluminescence performance is hampered by non-radiative recombination, which is associated with bromine vacancies. Here, we show that a post-synthetic treatment of CsPbBr$_3$ NPLs with GdBr$_3$-dimethylformamide (DMF) can effectively eliminate defects while preserving the color. According to a combined experimental and theoretical study, Gd$^{3+}$ ions are less reactive with NPLs as a result of compact interaction between them and DMF, and this stable Gd$^{3+}$-DMF solvation structure makes Brions more available and allows them to move more freely. Consequently, defects are rapidly passivated and photoluminescence quantum yield increases dramatically (from 35 to ~100%), while the surface ligand density and emission color remain unchanged. The result is a remarkable electroluminescence efficiency of 2.4% (at 464 nm), one of the highest in pure blue perovskite NPL light-emitting diodes. It is noteworthy that the conductive NPL film shows a high photoluminescence quantum yield of 80%, demonstrating NPLs' significant electroluminescence potential with further device structure design.

Quantum transport and localization are fundamental concepts in condensed matter physics. It is commonly believed that in one-dimensional systems, the existence of mobility edges is highly dependent on disorder. Recently, there has been a debate over the existence of an exact mobility edge in a modulated mosaic model without quenched disorder, the so-called mosaic Wannier-Stark lattice. Here, we experimentally implement such disorder-free mosaic photonic lattices using a silicon photonics platform. By creating a synthetic electric field, we could observe energy-dependent coexistence of both extended and localized states in a finite number of waveguides. The Wannier-Stark ladder emerges when the resulting potential is strong enough, and can be directly probed by exciting different spatial modes of the lattice. Our studies provide the experimental proof of coexisting sets of strongly localized and conducting (though weakly localized) states in finite-sized mosaic Wannier-Stark lattices, which hold the potential to encode high-dimensional quantum resources with compact and robust structures.

The mobility edge (ME) is a crucial concept in understanding localization physics, marking the critical transition between extended and localized states in the energy spectrum. Anderson localization scaling theory predicts the absence of ME in lower dimensional systems. Hence, the search for exact MEs, particularly for single particles in lower dimensions, has recently garnered significant interest in both theoretical and experimental studies, resulting in notable progress. However, several open questions remain, including the possibility of a single system exhibiting multiple MEs and the continual existence of extended states, even within the strong disorder domain. Here, we provide experimental evidence to address these questions by utilizing a quasiperiodic mosaic lattice with meticulously designed nanophotonic circuits. Our observations demonstrate the coexistence of both extended and localized states in lattices with broken duality symmetry and varying modulation periods. By single site injection and scanning the disorder level, we could approximately probe the ME of the modulated lattice. These results corroborate recent theoretical predictions, introduce a new avenue for investigating ME physics, and offer inspiration for further exploration of ME physics in the quantum regime using hybrid integrated photonic devices.

We propose a successive one-sided Hodrick-Prescott (SOHP) filter from multiple time scale decomposition perspective to derive trend estimate for a time series. The idea is to apply the one-sided HP (OHP) filter recursively on the updated cyclical component to extract the trend residual on multiple time scales, thereby to improve the trend estimate. To address the issue of optimization with a moving horizon as that of the SOHP filter, we present an incremental HP filtering algorithm, which greatly simplifies the involved inverse matrix operation and reduces the computational demand of the basic HP filtering. Actually, the new algorithm also applies effectively to other HP-type filters, especially for large-size or expanding data scenario. Numerical examples on real economic data show the better performance of the SOHP filter in comparison with other known HP-type filters.

We address the problem of controlling Connected and Automated Vehicles (CAVs) in conflict areas of a traffic network subject to hard safety constraints. It has been shown that such problems can be solved through a combination of tractable optimal control problems and Control Barrier Functions (CBFs) that guarantee the satisfaction of all constraints. These solutions can be reduced to a sequence of Quadratic Programs (QPs) which are efficiently solved on line over discrete time steps. However, guaranteeing the feasibility of the CBF-based QP method within each discretized time interval requires the careful selection of time steps which need to be sufficiently small. This creates computational requirements and communication rates between agents which may hinder the controller's application to real CAVs. In this paper, we overcome this limitation by adopting an event-triggered approach for CAVs in a conflict area such that the next QP is triggered by properly defined events with a safety guarantee. We present a laboratory-scale test bed we have developed to emulate merging roadways using mobile robots as CAVs which can be used to demonstrate how the event-triggered scheme is computationally efficient and can handle measurement uncertainties and noise compared to time-driven control while guaranteeing safety., Comment: arXiv admin note: substantial text overlap with arXiv:2203.12089, arXiv:2209.13053