In this paper, we prove that the self-dual morphological hierarchical structure computed on a n-D gray-level wellcomposed image u by the algorithm of G{\'e}raud et al. [1] is exactly the mathematical structure defined to be the tree of shape of u in Najman et al [2]. We recall that this algorithm is in quasi-linear time and thus considered to be optimal. The tree of shapes leads to many applications in mathematical morphology and in image processing like grain filtering, shapings, image segmentation, and so on.
We consider nonstationary multi-armed bandit problems where the model parameters of the arms change over time. We introduce the adaptive resetting bandit (ADR-bandit), which is a class of bandit algorithms that leverages adaptive windowing techniques from the data stream community. We first provide new guarantees on the quality of estimators resulting from adaptive windowing techniques, which are of independent interest in the data mining community. Furthermore, we conduct a finite-time analysis of ADR-bandit in two typical environments: an abrupt environment where changes occur instantaneously and a gradual environment where changes occur progressively. We demonstrate that ADR-bandit has nearly optimal performance when the abrupt or global changes occur in a coordinated manner that we call global changes. We demonstrate that forced exploration is unnecessary when we restrict the interest to the global changes. Unlike the existing nonstationary bandit algorithms, ADR-bandit has optimal performance in stationary environments as well as nonstationary environments with global changes. Our experiments show that the proposed algorithms outperform the existing approaches in synthetic and real-world environments.
There exists a gap in terms of the signals provided by pacemakers (i.e., intracardiac electrogram (EGM)) and the signals doctors use (i.e., 12-lead electrocardiogram (ECG)) to diagnose abnormal rhythms. Therefore, the former, even if remotely transmitted, are not sufficient for doctors to provide a precise diagnosis, let alone make a timely intervention. To close this gap and make a heuristic step towards real-time critical intervention in instant response to irregular and infrequent ventricular rhythms, we propose a new framework dubbed RT-RCG to automatically search for (1) efficient Deep Neural Network (DNN) structures and then (2)corresponding accelerators, to enable Real-Time and high-quality Reconstruction of ECG signals from EGM signals. Specifically, RT-RCG proposes a new DNN search space tailored for ECG reconstruction from EGM signals, and incorporates a differentiable acceleration search (DAS) engine to efficiently navigate over the large and discrete accelerator design space to generate optimized accelerators. Extensive experiments and ablation studies under various settings consistently validate the effectiveness of our RT-RCG. To the best of our knowledge, RT-RCG is the first to leverage neural architecture search (NAS) to simultaneously tackle both reconstruction efficacy and efficiency.
In this contribution we use an ensemble deep-learning method for combining the prediction of two individual one-stage detectors (i.e., YOLOv4 and Yolact) with the aim to detect artefacts in endoscopic images. This ensemble strategy enabled us to improve the robustness of the individual models without harming their real-time computation capabilities. We demonstrated the effectiveness of our approach by training and testing the two individual models and various ensemble configurations on the "Endoscopic Artifact Detection Challenge" dataset. Extensive experiments show the superiority, in terms of mean average precision, of the ensemble approach over the individual models and previous works in the state of the art.
3D detection based on surround-view camera system is a critical technique in autopilot. In this work, we present Polar Parametrization for 3D detection, which reformulates position parametrization, velocity decomposition, perception range, label assignment and loss function in polar coordinate system. Polar Parametrization establishes explicit associations between image patterns and prediction targets, exploiting the view symmetry of surround-view cameras as inductive bias to ease optimization and boost performance. Based on Polar Parametrization, we propose a surround-view 3D DEtection TRansformer, named PolarDETR. PolarDETR achieves promising performance-speed trade-off on different backbone configurations. Besides, PolarDETR ranks 1st on the leaderboard of nuScenes benchmark in terms of both 3D detection and 3D tracking at the submission time (Mar. 4th, 2022). Code will be released at \url{https://github.com/hustvl/PolarDETR}.
We propose a hybrid framework opPINN: physics-informed neural network (PINN) with operator learning for approximating the solution to the Fokker-Planck-Landau (FPL) equation. The opPINN framework is divided into two steps: Step 1 and Step 2. After the operator surrogate models are trained during Step 1, PINN can effectively approximate the solution to the FPL equation during Step 2 by using the pre-trained surrogate models. The operator surrogate models greatly reduce the computational cost and boost PINN by approximating the complex Landau collision integral in the FPL equation. The operator surrogate models can also be combined with the traditional numerical schemes. It provides a high efficiency in computational time when the number of velocity modes becomes larger. Using the opPINN framework, we provide the neural network solutions for the FPL equation under the various types of initial conditions, and interaction models in two and three dimensions. Furthermore, based on the theoretical properties of the FPL equation, we show that the approximated neural network solution converges to the a priori classical solution of the FPL equation as the pre-defined loss function is reduced.
In this work, a Gaussian process regression(GPR) model incorporated with given physical information in partial differential equations(PDEs) is developed: physics-assisted Gaussian processes(PAGP). The targets of this model can be divided into two types of problem: finding solutions or discovering unknown coefficients of given PDEs with initial and boundary conditions. We introduce three different models: continuous time, discrete time and hybrid models. The given physical information is integrated into Gaussian process model through our designed GP loss functions. Three types of loss function are provided in this paper based on two different approaches to train the standard GP model. The first part of the paper introduces the continuous time model which treats temporal domain the same as spatial domain. The unknown coefficients in given PDEs can be jointly learned with GP hyper-parameters by minimizing the designed loss function. In the discrete time models, we first choose a time discretization scheme to discretize the temporal domain. Then the PAGP model is applied at each time step together with the scheme to approximate PDE solutions at given test points of final time. To discover unknown coefficients in this setting, observations at two specific time are needed and a mixed mean square error function is constructed to obtain the optimal coefficients. In the last part, a novel hybrid model combining the continuous and discrete time models is presented. It merges the flexibility of continuous time model and the accuracy of the discrete time model. The performance of choosing different models with different GP loss functions is also discussed. The effectiveness of the proposed PAGP methods is illustrated in our numerical section.
With the rapid increase in the integration of renewable energy generation and the wide adoption of various electric appliances, power grids are now faced with more and more challenges. One prominent challenge is to implement efficient anomaly detection for different types of anomalous behaviors within power grids. These anomalous behaviors might be induced by unusual consumption patterns of the users, faulty grid infrastructures, outages, external cyberattacks, or energy fraud. Identifying such anomalies is of critical importance for the reliable and efficient operation of modern power grids. Various methods have been proposed for anomaly detection on power grid time-series data. This paper presents a short survey of the recent advances in anomaly detection for power grid time-series data. Specifically, we first outline current research challenges in the power grid anomaly detection domain and further review the major anomaly detection approaches. Finally, we conclude the survey by identifying the potential directions for future research.
Vehicle routing problems (VRPs) can be divided into two major categories: offline VRPs, which consider a given set of trip requests to be served, and online VRPs, which consider requests as they arrive in real-time. Based on discussions with public transit agencies, we identify a real-world problem that is not addressed by existing formulations: booking trips with flexible pickup windows (e.g., 3 hours) in advance (e.g., the day before) and confirming tight pickup windows (e.g., 30 minutes) at the time of booking. Such a service model is often required in paratransit service settings, where passengers typically book trips for the next day over the phone. To address this gap between offline and online problems, we introduce a novel formulation, the offline vehicle routing problem with online bookings. This problem is very challenging computationally since it faces the complexity of considering large sets of requests -- similar to offline VRPs -- but must abide by strict constraints on running time -- similar to online VRPs. To solve this problem, we propose a novel computational approach, which combines an anytime algorithm with a learning-based policy for real-time decisions. Based on a paratransit dataset obtained from the public transit agency of Chattanooga, TN, we demonstrate that our novel formulation and computational approach lead to significantly better outcomes in this setting than existing algorithms.
In this paper, we consider the age of information (AoI) of a discrete time status updating system, focusing on finding the stationary AoI distribution assuming that the Ber/G/1/1 queue is used. Following the standard queueing theory, we show that by invoking a two-dimensional state vector which tracks the AoI and packet age in system simultaneously, the stationary AoI distribution can be derived by analyzing the steady state of the constituted two-dimensional stochastic process. We give the general formula of the AoI distribution and calculate the explicit expression when the service time is also geometrically distributed. The discrete and continuous AoI are compared, we depict the mean of discrete AoI and that of continuous time AoI for system with M/M/1/1 queue. Although the stationary AoI distribution of some continuous time single-server system has been determined before, in this paper, we shall prove that the standard queueing theory is still appliable to analyze the discrete AoI, which is even stronger than the proposed methods handling the continuous AoI.