Resonance-dominant optomechanical entanglement in open quantum systems

Motivated by entanglement protection, our work utilizes a resonance effect to enhance optomechanical entanglement in the coherent-state representation. We propose a filtering model to filter out the highly frequency-detuned coupling components between a thermal-mechanical mode and its surrounding heat baths within the weak-coupling limit. We reveal that continuous-variable entanglement protection involves the elimination of degrees of freedom associated with significant detuning components, thereby resisting decoherence. We construct a nonlinear Langevin equation of the filtering model and numerically show that the filtering model doubles the robustness of a stationary maximum optomechanical entanglement with respect to thermal noise and mechanical damping. Furthermore, we generalize these results to an optical cavity array with one oscillating end-mirror to investigate the long-distance optimal optomechanical entanglement transfer. Our study breaks new ground for applying the resonance effect to protect the quantum system from decoherence and advancing the possibilities for large-scale quantum information processing and quantum network construction.Comment: 19 pages, 7 figure

Safe Control for Nonlinear Systems under Faults and Attacks via Control Barrier Functions

Safety is one of the most important properties of control systems. Sensor faults and attacks and actuator failures may cause errors in the sensor measurements and system dynamics, which leads to erroneous control inputs and hence safety violations. In this paper, we improve the robustness against sensor faults and actuator failures by proposing a class of Fault-Tolerant Control Barrier Functions (FT-CBFs) for nonlinear systems. Our approach maintains a set of state estimators according to fault patterns and incorporates CBF-based linear constraints for each state estimator. We then propose a framework for joint safety and stability by integrating FT-CBFs with Control Lyapunov Functions. With a similar philosophy of utilizing redundancy, we proposed High order CBF-based approach to ensure safety when actuator failures occur. We propose a sum-of-squares (SOS) based approach to verify the feasibility of FT-CBFs for both sensor faults and actuator failures. We evaluate our approach via two case studies, namely, a wheeled mobile robot (WMR) system in the presence of a sensor attack and a Boeing 747 lateral control system under actuator failures.Comment: 15 pages, 5 figures, submitted to IEEE Transactions on Automatic Contro

Law of Balance and Stationary Distribution of Stochastic Gradient Descent

The stochastic gradient descent (SGD) algorithm is the algorithm we use to train neural networks. However, it remains poorly understood how the SGD navigates the highly nonlinear and degenerate loss landscape of a neural network. In this work, we prove that the minibatch noise of SGD regularizes the solution towards a balanced solution whenever the loss function contains a rescaling symmetry. Because the difference between a simple diffusion process and SGD dynamics is the most significant when symmetries are present, our theory implies that the loss function symmetries constitute an essential probe of how SGD works. We then apply this result to derive the stationary distribution of stochastic gradient flow for a diagonal linear network with arbitrary depth and width. The stationary distribution exhibits complicated nonlinear phenomena such as phase transitions, broken ergodicity, and fluctuation inversion. These phenomena are shown to exist uniquely in deep networks, implying a fundamental difference between deep and shallow models.Comment: Preprin

Assessing spatiotemporal predictability of LBSN : a case study of three Foursquare datasets

Location-based social networks (LBSN) have provided new possibilities for researchers to gain knowledge about human spatiotemporal behavior, and to make predictions about how people might behave through space and time in the future. An important requirement of successfully utilizing LBSN in these regards is a thorough understanding of the respective datasets, including their inherent potential as well as their limitations. Specifically, when it comes to predictions, we must know what we can actually expect from the data, and how we could maximize their usefulness. Yet, this knowledge is still largely lacking from the literature. Hence, this work explores one particular aspect which is the theoretical predictability of LBSN datasets. The uncovered predictability is represented with an interval. The lower bound of the interval corresponds to the amount of regular behaviors that can easily be anticipated, and represents the correct predication rate that any algorithm should be able to achieve. The upper bound corresponds to the amount of information that is contained in the dataset, and represents the maximum correct prediction rate that cannot be exceeded by any algorithms. Three Foursquare datasets from three American cities are studied as an example. It is found that, within our investigated datasets, the lower bound of predictability of the human spatiotemporal behavior is 27%, and the upper bound is 92%. Hence, the inherent potentials of the dataset for predicting human spatiotemporal behavior are clarified, and the revealed interval allows a realistic assessment of the quality of predictions and thus of associated algorithms. Additionally, in order to provide further insight into the practical use of the dataset, the relationship between the predictability and the check-in frequencies are investigated from three different perspectives. It was found that the individual perspective provides no significant correlations between the predictability and the check-in frequency. In contrast, the same two quantities are found to be negatively correlated from temporal and spatial perspectives. Our study further indicates that the heavily frequented contexts and some extraordinary geographic features such as airports could be good starting points for effective improvements of prediction algorithms. In general, this research provides novel knowledge regarding the nature of the LBSN dataset and practical insights for a more reasonable utilization of the dataset

Cooperative Perception for Safe Control of Autonomous Vehicles under LiDAR Spoofing Attacks

Autonomous vehicles rely on LiDAR sensors to detect obstacles such as pedestrians, other vehicles, and fixed infrastructures. LiDAR spoofing attacks have been demonstrated that either create erroneous obstacles or prevent detection of real obstacles, resulting in unsafe driving behaviors. In this paper, we propose an approach to detect and mitigate LiDAR spoofing attacks by leveraging LiDAR scan data from other neighboring vehicles. This approach exploits the fact that spoofing attacks can typically only be mounted on one vehicle at a time, and introduce additional points into the victim's scan that can be readily detected by comparison from other, non-modified scans. We develop a Fault Detection, Identification, and Isolation procedure that identifies non-existing obstacle, physical removal, and adversarial object attacks, while also estimating the actual locations of obstacles. We propose a control algorithm that guarantees that these estimated object locations are avoided. We validate our framework using a CARLA simulation study, in which we verify that our FDII algorithm correctly detects each attack pattern