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Higher order finite difference Weighted Essentially Non-Oscillatory (WENO) schemes for conservation laws represent a technology that has been reasonably consolidated. They are extremely popular because, when applied to multidimensional problems, they offer high order accuracy at a fraction of the cost of finite volume WENO or DG schemes. They come in two flavors. There is the classical finite difference WENO (FD-WENO) method (Shu and Osher, J. Comput. Phys., 83 (1989) 32-78). However, in recent years there is also an alternative finite difference WENO (AFD-WENO) method which has recently been formalized into a very useful general-purpose algorithm for conservation laws (Balsara et al., Efficient Alternative Finite Difference WENO Schemes for Hyperbolic Conservation Laws, submitted to CAMC (2023)). However, the FD-WENO algorithm has only very recently been formulated for hyperbolic systems with non-conservative products (Balsara et al., Efficient Finite Difference WENO Scheme for Hyperbolic Systems with Non-Conservative Products, to appear CAMC (2023)). In this paper we show that there are substantial advantages in obtaining an AFD-WENO algorithm for hyperbolic systems with non-conservative products. Such an algorithm is documented in this paper. We present an AFD-WENO formulation in fluctuation form that is carefully engineered to retrieve the flux form when that is warranted and nevertheless extends to non-conservative products. The method is flexible because it allows any Riemann solver to be used. The formulation we arrive at is such that when non-conservative products are absent it reverts exactly to the formulation in the second citation above which is in exact flux conservation form. The ability to transition to a precise conservation form when non-conservative products are absent ensures, via the Lax-Wendroff theorem, that shock locations will be exactly ...

Most models for weakly supervised video anomaly detection (WS-VAD) rely on multiple instance learning, aiming to distinguish normal and abnormal snippets without specifying the type of anomaly. The ambiguous nature of anomaly definitions across contexts introduces bias in detecting abnormal and normal snippets within the abnormal bag. Taking the first step to show the model why it is anomalous, a novel framework is proposed to guide the learning of suspected anomalies from event prompts. Given a textual prompt dictionary of potential anomaly events and the captions generated from anomaly videos, the semantic anomaly similarity between them could be calculated to identify the suspected anomalous events for each video snippet. It enables a new multi-prompt learning process to constrain the visual-semantic features across all videos, as well as provides a new way to label pseudo anomalies for self-training. To demonstrate effectiveness, comprehensive experiments and detailed ablation studies are conducted on four datasets, namely XD-Violence, UCF-Crime, TAD, and ShanghaiTech. Our proposed model outperforms most state-of-the-art methods in terms of AP or AUC (82.6\%, 87.7\%, 93.1\%, and 97.4\%). Furthermore, it shows promising performance in open-set and cross-dataset cases.

We introduce a conceptual model for highlights to support data analysis and storytelling in the domain of Business Intelligence, via the automated extraction, representation, and exploitation of highlights revealing key facts that are hidden in the data with which a data analyst works. The model builds on the concepts of Holistic and Elementary Highlights, along with their context, constituents and interrelationships, whose synergy can identify internal properties, patterns and key facts in a dataset being analyzed.

Deep neural networks (DNN) are increasingly being used to learn controllers due to their excellent approximation capabilities. However, their black-box nature poses significant challenges to closed-loop stability guarantees and performance analysis. In this paper, we introduce a structured DNN-based controller for the trajectory tracking control of Lagrangian systems using backing techniques. By properly designing neural network structures, the proposed controller can ensure closed-loop stability for any compatible neural network parameters. In addition, improved control performance can be achieved by further optimizing neural network parameters. Besides, we provide explicit upper bounds on tracking errors in terms of controller parameters, which allows us to achieve the desired tracking performance by properly selecting the controller parameters. Furthermore, when system models are unknown, we propose an improved Lagrangian neural network (LNN) structure to learn the system dynamics and design the controller. We show that in the presence of model approximation errors and external disturbances, the closed-loop stability and tracking control performance can still be guaranteed. The effectiveness of the proposed approach is demonstrated through simulations.

This paper addresses the escalating challenge of redundant data transmission in networks. The surge in traffic has strained backhaul links and backbone networks, prompting the exploration of caching solutions at the edge router. Existing work primarily relies on Markov Decision Processes (MDP) for caching issues, assuming fixed-time interval decisions; however, real-world scenarios involve random request arrivals, and despite the critical role of various file characteristics in determining an optimal caching policy, none of the related existing work considers all these file characteristics in forming a caching policy. In this paper, first, we formulate the caching problem using a semi-Markov Decision Process (SMDP) to accommodate the continuous-time nature of real-world scenarios allowing for caching decisions at random times upon file requests. Then, we propose a double deep Q-learning-based caching approach that comprehensively accounts for file features such as lifetime, size, and importance. Simulation results demonstrate the superior performance of our approach compared to a recent Deep Reinforcement Learning-based method. Furthermore, we extend our work to include a Transfer Learning (TL) approach to account for changes in file request rates in the SMDP framework. The proposed TL approach exhibits fast convergence, even in scenarios with increased differences in request rates between source and target domains, presenting a promising solution to the dynamic challenges of caching in real-world environments.

The increasing demand for automatic high-level image understanding, particularly in detecting abstract concepts (AC) within images, underscores the necessity for innovative and more interpretable approaches. These approaches need to harmonize traditional deep vision methods with the nuanced, context-dependent knowledge humans employ to interpret images at intricate semantic levels. In this work, we leverage situated perceptual knowledge of cultural images to enhance performance and interpretability in AC image classification. We automatically extract perceptual semantic units from images, which we then model and integrate into the ARTstract Knowledge Graph (AKG). This resource captures situated perceptual semantics gleaned from over 14,000 cultural images labeled with ACs. Additionally, we enhance the AKG with high-level linguistic frames. We compute KG embeddings and experiment with relative representations and hybrid approaches that fuse these embeddings with visual transformer embeddings. Finally, for interpretability, we conduct posthoc qualitative analyses by examining model similarities with training instances. Our results show that our hybrid KGE-ViT methods outperform existing techniques in AC image classification. The posthoc interpretability analyses reveal the visual transformer's proficiency in capturing pixel-level visual attributes, contrasting with our method's efficacy in representing more abstract and semantic scene elements. We demonstrate the synergy and complementarity between KGE embeddings' situated perceptual knowledge and deep visual model's sensory-perceptual understanding for AC image classification. This work suggests a strong potential of neuro-symbolic methods for knowledge integration and robust image representation for use in downstream intricate visual comprehension tasks. All the materials and code are available online.

Deep neural networks have been shown to provide accurate function approximations in high dimensions. However, fitting network parameters requires informative training data that are often challenging to collect in science and engineering applications. This work proposes Neural Galerkin schemes based on deep learning that generate training data with active learning for numerically solving high-dimensional partial differential equations. Neural Galerkin schemes build on the Dirac-Frenkel variational principle to train networks by minimizing the residual sequentially over time, which enables adaptively collecting new training data in a self-informed manner that is guided by the dynamics described by the partial differential equations. This is in contrast to other machine learning methods that aim to fit network parameters globally in time without taking into account training data acquisition. Our finding is that the active form of gathering training data of the proposed Neural Galerkin schemes is key for numerically realizing the expressive power of networks in high dimensions. Numerical experiments demonstrate that Neural Galerkin schemes have the potential to enable simulating phenomena and processes with many variables for which traditional and other deep-learning-based solvers fail, especially when features of the solutions evolve locally such as in high-dimensional wave propagation problems and interacting particle systems described by Fokker-Planck and kinetic equations.

Graphs are important data representations for describing objects and their relationships, which appear in a wide diversity of real-world scenarios. As one of a critical problem in this area, graph generation considers learning the distributions of given graphs and generating more novel graphs. Owing to their wide range of applications, generative models for graphs, which have a rich history, however, are traditionally hand-crafted and only capable of modeling a few statistical properties of graphs. Recent advances in deep generative models for graph generation is an important step towards improving the fidelity of generated graphs and paves the way for new kinds of applications. This article provides an extensive overview of the literature in the field of deep generative models for graph generation. Firstly, the formal definition of deep generative models for the graph generation and the preliminary knowledge are provided. Secondly, taxonomies of deep generative models for both unconditional and conditional graph generation are proposed respectively; the existing works of each are compared and analyzed. After that, an overview of the evaluation metrics in this specific domain is provided. Finally, the applications that deep graph generation enables are summarized and five promising future research directions are highlighted.

Vast amount of data generated from networks of sensors, wearables, and the Internet of Things (IoT) devices underscores the need for advanced modeling techniques that leverage the spatio-temporal structure of decentralized data due to the need for edge computation and licensing (data access) issues. While federated learning (FL) has emerged as a framework for model training without requiring direct data sharing and exchange, effectively modeling the complex spatio-temporal dependencies to improve forecasting capabilities still remains an open problem. On the other hand, state-of-the-art spatio-temporal forecasting models assume unfettered access to the data, neglecting constraints on data sharing. To bridge this gap, we propose a federated spatio-temporal model -- Cross-Node Federated Graph Neural Network (CNFGNN) -- which explicitly encodes the underlying graph structure using graph neural network (GNN)-based architecture under the constraint of cross-node federated learning, which requires that data in a network of nodes is generated locally on each node and remains decentralized. CNFGNN operates by disentangling the temporal dynamics modeling on devices and spatial dynamics on the server, utilizing alternating optimization to reduce the communication cost, facilitating computations on the edge devices. Experiments on the traffic flow forecasting task show that CNFGNN achieves the best forecasting performance in both transductive and inductive learning settings with no extra computation cost on edge devices, while incurring modest communication cost.

Detecting carried objects is one of the requirements for developing systems to reason about activities involving people and objects. We present an approach to detect carried objects from a single video frame with a novel method that incorporates features from multiple scales. Initially, a foreground mask in a video frame is segmented into multi-scale superpixels. Then the human-like regions in the segmented area are identified by matching a set of extracted features from superpixels against learned features in a codebook. A carried object probability map is generated using the complement of the matching probabilities of superpixels to human-like regions and background information. A group of superpixels with high carried object probability and strong edge support is then merged to obtain the shape of the carried object. We applied our method to two challenging datasets, and results show that our method is competitive with or better than the state-of-the-art.