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The Dual Characteristic-Galerkin method (DCGM) is conservative, precise and experimentally positive. We present the method and prove convergence and $L^2$-stability in the case of Neumann boundary conditions. In a 2D numerical finite element setting (FEM), the method is compared to Primal Characteristic-Galerkin (PCGM), Streamline upwinding (SUPG), the Dual Discontinuous Galerkin method (DDG) and centered FEM without upwinding. DCGM is difficult to implement numerically but, in the numerical context of this note, it is far superior to all others.

Topic modeling is a widely used technique for revealing underlying thematic structures within textual data. However, existing models have certain limitations, particularly when dealing with short text datasets that lack co-occurring words. Moreover, these models often neglect sentence-level semantics, focusing primarily on token-level semantics. In this paper, we propose PromptTopic, a novel topic modeling approach that harnesses the advanced language understanding of large language models (LLMs) to address these challenges. It involves extracting topics at the sentence level from individual documents, then aggregating and condensing these topics into a predefined quantity, ultimately providing coherent topics for texts of varying lengths. This approach eliminates the need for manual parameter tuning and improves the quality of extracted topics. We benchmark PromptTopic against the state-of-the-art baselines on three vastly diverse datasets, establishing its proficiency in discovering meaningful topics. Furthermore, qualitative analysis showcases PromptTopic's ability to uncover relevant topics in multiple datasets.

Artificial Intelligence (AI)-driven defect inspection is pivotal in industrial manufacturing. Yet, many methods, tailored to specific pipelines, grapple with diverse product portfolios and evolving processes. Addressing this, we present the Incremental Unified Framework (IUF) that can reduce the feature conflict problem when continuously integrating new objects in the pipeline, making it advantageous in object-incremental learning scenarios. Employing a state-of-the-art transformer, we introduce Object-Aware Self-Attention (OASA) to delineate distinct semantic boundaries. Semantic Compression Loss (SCL) is integrated to optimize non-primary semantic space, enhancing network adaptability for novel objects. Additionally, we prioritize retaining the features of established objects during weight updates. Demonstrating prowess in both image and pixel-level defect inspection, our approach achieves state-of-the-art performance, proving indispensable for dynamic and scalable industrial inspections. Our code will be released at //github.com/jqtangust/IUF.

Quantum Internetworking is a recent field that promises numerous interesting applications, many of which require the distribution of entanglement between arbitrary pairs of users. This work deals with the problem of scheduling in an arbitrary entanglement swapping quantum network - often called first generation quantum network - in its general topology, multicommodity, loss-aware formulation. We introduce a linear algebraic framework that exploits quantum memory through the creation of intermediate entangled links. The framework is then employed to apply Lyapunov Drift Minimization (a standard technique in classical network science) to mathematically derive a natural class of scheduling policies for quantum networks minimizing the square norm of the user demand backlog. Moreover, an additional class of Max-Weight inspired policies is proposed and benchmarked, reducing significantly the computation cost at the price of a slight performance degradation. The policies are compared in terms of information availability, localization and overall network performance through an ad-hoc simulator that admits user-provided network topologies and scheduling policies in order to showcase the potential application of the provided tools to quantum network design.

Representing a polygon using a set of simple shapes has numerous applications in different use-case scenarios. We consider the problem of covering the interior of a rectilinear polygon with holes by a set of area-weighted, axis-aligned rectangles such that the total weight of the rectangles in the cover is minimized. Already the unit-weight case is known to be NP-hard and the general problem has, to the best of our knowledge, not been studied experimentally before. We show a new basic property of optimal solutions of the weighted problem. This allows us to speed up existing algorithms for the unit-weight case, obtain an improved ILP formulation for both the weighted and unweighted problem, and develop several approximation algorithms and heuristics for the weighted case. All our algorithms are evaluated in a large experimental study on 186 837 polygons combined with six cost functions, which provides evidence that our algorithms are both fast and yield close-to-optimal solutions in practice.

Few-shot Knowledge Graph (KG) completion is a focus of current research, where each task aims at querying unseen facts of a relation given its few-shot reference entity pairs. Recent attempts solve this problem by learning static representations of entities and references, ignoring their dynamic properties, i.e., entities may exhibit diverse roles within task relations, and references may make different contributions to queries. This work proposes an adaptive attentional network for few-shot KG completion by learning adaptive entity and reference representations. Specifically, entities are modeled by an adaptive neighbor encoder to discern their task-oriented roles, while references are modeled by an adaptive query-aware aggregator to differentiate their contributions. Through the attention mechanism, both entities and references can capture their fine-grained semantic meanings, and thus render more expressive representations. This will be more predictive for knowledge acquisition in the few-shot scenario. Evaluation in link prediction on two public datasets shows that our approach achieves new state-of-the-art results with different few-shot sizes.

Cold-start problems are long-standing challenges for practical recommendations. Most existing recommendation algorithms rely on extensive observed data and are brittle to recommendation scenarios with few interactions. This paper addresses such problems using few-shot learning and meta learning. Our approach is based on the insight that having a good generalization from a few examples relies on both a generic model initialization and an effective strategy for adapting this model to newly arising tasks. To accomplish this, we combine the scenario-specific learning with a model-agnostic sequential meta-learning and unify them into an integrated end-to-end framework, namely Scenario-specific Sequential Meta learner (or s^2 meta). By doing so, our meta-learner produces a generic initial model through aggregating contextual information from a variety of prediction tasks while effectively adapting to specific tasks by leveraging learning-to-learn knowledge. Extensive experiments on various real-world datasets demonstrate that our proposed model can achieve significant gains over the state-of-the-arts for cold-start problems in online recommendation. Deployment is at the Guess You Like session, the front page of the Mobile Taobao.

Text in natural images is of arbitrary orientations, requiring detection in terms of oriented bounding boxes. Normally, a multi-oriented text detector often involves two key tasks: 1) text presence detection, which is a classification problem disregarding text orientation; 2) oriented bounding box regression, which concerns about text orientation. Previous methods rely on shared features for both tasks, resulting in degraded performance due to the incompatibility of the two tasks. To address this issue, we propose to perform classification and regression on features of different characteristics, extracted by two network branches of different designs. Concretely, the regression branch extracts rotation-sensitive features by actively rotating the convolutional filters, while the classification branch extracts rotation-invariant features by pooling the rotation-sensitive features. The proposed method named Rotation-sensitive Regression Detector (RRD) achieves state-of-the-art performance on three oriented scene text benchmark datasets, including ICDAR 2015, MSRA-TD500, RCTW-17 and COCO-Text. Furthermore, RRD achieves a significant improvement on a ship collection dataset, demonstrating its generality on oriented object detection.

Multi-relation Question Answering is a challenging task, due to the requirement of elaborated analysis on questions and reasoning over multiple fact triples in knowledge base. In this paper, we present a novel model called Interpretable Reasoning Network that employs an interpretable, hop-by-hop reasoning process for question answering. The model dynamically decides which part of an input question should be analyzed at each hop; predicts a relation that corresponds to the current parsed results; utilizes the predicted relation to update the question representation and the state of the reasoning process; and then drives the next-hop reasoning. Experiments show that our model yields state-of-the-art results on two datasets. More interestingly, the model can offer traceable and observable intermediate predictions for reasoning analysis and failure diagnosis.

Image segmentation is considered to be one of the critical tasks in hyperspectral remote sensing image processing. Recently, convolutional neural network (CNN) has established itself as a powerful model in segmentation and classification by demonstrating excellent performances. The use of a graphical model such as a conditional random field (CRF) contributes further in capturing contextual information and thus improving the segmentation performance. In this paper, we propose a method to segment hyperspectral images by considering both spectral and spatial information via a combined framework consisting of CNN and CRF. We use multiple spectral cubes to learn deep features using CNN, and then formulate deep CRF with CNN-based unary and pairwise potential functions to effectively extract the semantic correlations between patches consisting of three-dimensional data cubes. Effective piecewise training is applied in order to avoid the computationally expensive iterative CRF inference. Furthermore, we introduce a deep deconvolution network that improves the segmentation masks. We also introduce a new dataset and experimented our proposed method on it along with several widely adopted benchmark datasets to evaluate the effectiveness of our method. By comparing our results with those from several state-of-the-art models, we show the promising potential of our method.