We investigate the disorder-driven phase transitions in bosonic fractional quantum Hall liquids at filling factors $f=1/2$ and $f=1$ in the lowest Landau level. We use the evolution of ground-state entanglement entropy, fidelity susceptibility, and Hall conductance with the increasing of disorder strength to identify the underlying phase transitions. The critical disorder strengths obtained from these different quantities are consistent with each other, validating the reliability of our numerical calculations based on exact diagonalization. At $f=1/2$, we observe a clear transition from the bosonic Laughlin state to a trivial insulating phase. At $f=1$, we identify a direct phase transition from the non-Abelian bosonic Moore-Read state to a trivial insulating phase, although some signs of a disorder-induced intermediate fractional quantum Hall phase were recently reported for the $f=5/2$ fermionic Moore-Read cousin.
We prove that any positive solution of the Yamabe equation on an asymptotically flat $n$-dimensional manifold of flatness order at least $frac{n-2}{2}$ and $nle 24$ must converge at infinity either to a fundamental solution of the Laplace operator on the Euclidean space or to a radial Fowler solution defined on the entire Euclidean space. The flatness order $frac{n-2}{2}$ is the minimal flatness order required to define ADM mass in general relativity; the dimension $24$ is the dividing dimension of the validity of compactness of solutions to the Yamabe problem. We also prove such alternatives for bounded solutions when $n>24$. We prove these results by establishing appropriate asymptotic behavior near an isolated singularity of solutions to the Yamabe equation when the metric has a flatness order of at least $frac{n-2}{2}$ at the singularity and $n<24$, also when $n>24$ and the solution grows no faster than the fundamental solution of the flat metric Laplacian at the singularity. These results extend earlier results of L. Caffarelli, B. Gidas and J. Spruck, also of N. Korevaar, R. Mazzeo, F. Pacard and R. Schoen, when the metric is conformally flat, and work of C.C. Chen and C. S. Lin when the scalar curvature is a non-constant function with appropriate flatness at the singular point, also work of F. Marques when the metric is not necessarily conformally flat but smooth, and the dimension of the manifold is three, four, or five, as well as recent similar results by the second and third authors in dimension six.
With the autonomy of aerial robots advances in recent years, autonomous drone racing has drawn increasing attention. In a professional pilot competition, a skilled operator always controls the drone to agilely avoid obstacles in aggressive attitudes, for reaching the destination as fast as possible. Autonomous flight like elite pilots requires planning in SE(3), whose non-triviality and complexity hindering a convincing solution in our community by now. To bridge this gap, this paper proposes an open-source baseline, which includes a high-performance SE(3) planner and a challenging simulation platform tailored for drone racing. We specify the SE(3) trajectory generation as a soft-penalty optimization problem, and speed up the solving process utilizing its underlying parallel structure. Moreover, to provide a testbed for challenging the planner, we develop delicate drone racing tracks which mimic real-world set-up and necessities planning in SE(3). Besides, we provide necessary system components such as common map interfaces and a baseline controller, to make our work plug-in-and-use. With our baseline, we hope to future foster the research of SE(3) planning and the competition of autonomous drone racing.
We propose a scheme comprising an array of anisotropic optical waveguides, embedded in a gas of cold atoms, which can be tuned from a Hermitian to an odd-PT -- symmetric configuration through the manipulation of control and assistant laser fields. We show that the system can be controlled by tuning intra -- and inter-cell coupling coefficients, enabling the creation of topologically distinct phases and linear topological edge states. The waveguide array, characterized by a quadrimer primitive cell, allows for implementing transitions between Hermitian and odd-PT -symmetric configurations, broken and unbroken PT -symmetric phases, topologically trivial and nontrivial phases, as well as transitions between linear and nonlinear regimes. The introduced scheme generalizes the Rice-Mele Hamiltonian for a nonlinear non-Hermitian quadrimer array featuring odd-PT symmetry and makes accessible unique phenomena and functionalities that emerge from the interplay of non-Hermiticity, topology, and nonlinearity. We also show that in the presence of nonlinearity the system sustains nonlinear topological edge states bifurcating from the linear topological edge states and the modes without linear limit. Each nonlinear mode represents a doublet of odd-PT -conjugate states. In the broken PT phase, the nonlinear edge states may be effectively stabilized when an additional absorption is introduced into the system.
Given the proliferation of wireless sensors and smart mobile devices, an explosive escalation of the volume of data is anticipated. However, restricted by their limited physical sizes and low manufacturing costs, these wireless devices tend to have limited computational capabilities and battery lives. To overcome this limitation, wireless devices may offload their computational tasks to the nearby computing nodes at the network edge in mobile edge computing (MEC). At the time of writing, the benefits of MEC systems have not been fully exploited, predominately because the computation offloading link is still far from perfect. In this article, we propose to enhance MEC systems by exploiting the emerging technique of reconfigurable intelligent surfaces (RIS), which are capable of `reconfiguring the wireless propagation environments, hence enhancing the offloading links. The benefits of RISs can be maximized by jointly optimizing both the RISs as well as the communications and computing resource allocations of MEC systems. Unfortunately, this joint optimization imposes new research challenges on the system design. Against this background, this article provides an overview of RIS-assisted MEC systems and highlights their four use cases as well as their design challenges and solutions. Finally, their performance is characterized with the aid of a specific case study, followed by a range of future research ideas.
This paper proposes a systematic solution that uses an unmanned aerial vehicle (UAV) to aggressively and safely track an agile target. The solution properly handles the challenging situations where the intent of the target and the dense environments are unknown to the UAV. Our work is divided into two parts: target motion prediction and tracking trajectory planning. The target motion prediction method utilizes target observations to reliably predict the future motion of the target considering dynamic constraints. The tracking trajectory planner follows the traditional hierarchical workflow.A target informed kinodynamic searching method is adopted as the front-end, which heuristically searches for a safe tracking trajectory. The back-end optimizer then refines it into a spatial-temporal optimal and collision-free trajectory. The proposed solution is integrated into an onboard quadrotor system. We fully test the system in challenging real-world tracking missions.Moreover, benchmark comparisons validate that the proposed method surpasses the cutting-edge methods on time efficiency and tracking effectiveness.
Knowledge distillation (KD) has enabled remarkable progress in model compression and knowledge transfer. However, KD requires a large volume of original data or their representation statistics that are not usually available in practice. Data-free KD has recently been proposed to resolve this problem, wherein teacher and student models are fed by a synthetic sample generator trained from the teacher. Nonetheless, existing data-free KD methods rely on fine-tuning of weights to balance multiple losses, and ignore the diversity of generated samples, resulting in limited accuracy and robustness. To overcome this challenge, we propose robustness and diversity seeking data-free KD (RDSKD) in this paper. The generator loss function is crafted to produce samples with high authenticity, class diversity, and inter-sample diversity. Without real data, the objectives of seeking high sample authenticity and class diversity often conflict with each other, causing frequent loss fluctuations. We mitigate this by exponentially penalizing loss increments. With MNIST, CIFAR-10, and SVHN datasets, our experiments show that RDSKD achieves higher accuracy with more robustness over different hyperparameter settings, compared to other data-free KD methods such as DAFL, MSKD, ZSKD, and DeepInversion.
Agile satellites are the new generation of Earth observation satellites (EOSs) with stronger attitude maneuvering capability. Since optical remote sensing instruments equipped on satellites cannot see through the cloud, the cloud coverage has a significant influence on the satellite observation missions. We are the first to address multiple agile EOSs scheduling problem under cloud coverage uncertainty where the objective aims to maximize the entire observation profit. The chance constraint programming model is adopted to describe the uncertainty initially, and the observation profit under cloud coverage uncertainty is then calculated via sample approximation method. Subsequently, an improved simulated annealing based heuristic combining a fast insertion strategy is proposed for large-scale observation missions. The experimental results show that the improved simulated annealing heuristic outperforms other algorithms for the multiple AEOSs scheduling problem under cloud coverage uncertainty, which verifies the efficiency and effectiveness of the proposed algorithm.
In this paper we use a time-evolving graph which consists of a sequence of graph snapshots over time to model many real-world networks. We study the path classification problem in a time-evolving graph, which has many applications in real-world scenarios, for example, predicting path failure in a telecommunication network and predicting path congestion in a traffic network in the near future. In order to capture the temporal dependency and graph structure dynamics, we design a novel deep neural network named Long Short-Term Memory R-GCN (LRGCN). LRGCN considers temporal dependency between time-adjacent graph snapshots as a special relation with memory, and uses relational GCN to jointly process both intra-time and inter-time relations. We also propose a new path representation method named self-attentive path embedding (SAPE), to embed paths of arbitrary length into fixed-length vectors. Through experiments on a real-world telecommunication network and a traffic network in California, we demonstrate the superiority of LRGCN to other competing methods in path failure prediction, and prove the effectiveness of SAPE on path representation.
The Earth observation satellites (EOSs) are specially designed to collect images according to user requirements. The agile EOSs (AEOS), with stronger attitude maneuverability, greatly improve the observation capability, while increasing the complexity in scheduling. We address a multiple AEOSs scheduling with multiple observations for the first time}, where the objective function aims to maximize the entire observation profit over a fixed horizon. The profit attained by multiple observations for each target is nonlinear to the number of observations. We model the multiple AEOSs scheduling as a specific interval scheduling problem with each satellite orbit respected as machine. Then A column generation based framework is developed to solve this problem, in which we deal with the pricing problems with a label-setting algorithm. Extensive simulations are conducted on the basis of a Chinas AEOS constellation, and the results indicate the optimality gap is less than 3% on average, which validates the performance of the scheduling solution obtained by the proposed framework. We also compare the framework in the conventional EOS scheduling.
