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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 ...

Deep learning techniques have demonstrated great potential for accurately estimating brain age by analyzing Magnetic Resonance Imaging (MRI) data from healthy individuals. However, current methods for brain age estimation often directly utilize whole input images, overlooking two important considerations: 1) the heterogeneous nature of brain aging, where different brain regions may degenerate at different rates, and 2) the existence of age-independent redundancies in brain structure. To overcome these limitations, we propose a Dual Graph Attention based Disentanglement Multi-instance Learning (DGA-DMIL) framework for improving brain age estimation. Specifically, the 3D MRI data, treated as a bag of instances, is fed into a 2D convolutional neural network backbone, to capture the unique aging patterns in MRI. A dual graph attention aggregator is then proposed to learn the backbone features by exploiting the intra- and inter-instance relationships. Furthermore, a disentanglement branch is introduced to separate age-related features from age-independent structural representations to ameliorate the interference of redundant information on age prediction. To verify the effectiveness of the proposed framework, we evaluate it on two datasets, UK Biobank and ADNI, containing a total of 35,388 healthy individuals. Our proposed model demonstrates exceptional accuracy in estimating brain age, achieving a remarkable mean absolute error of 2.12 years in the UK Biobank. The results establish our approach as state-of-the-art compared to other competing brain age estimation models. In addition, the instance contribution scores identify the varied importance of brain areas for aging prediction, which provides deeper insights into the understanding of brain aging.

Controlled execution of dynamic motions in quadrupedal robots, especially those with articulated soft bodies, presents a unique set of challenges that traditional methods struggle to address efficiently. In this study, we tackle these issues by relying on a simple yet effective two-stage learning framework to generate dynamic motions for quadrupedal robots. First, a gradient-free evolution strategy is employed to discover simply represented control policies, eliminating the need for a predefined reference motion. Then, we refine these policies using deep reinforcement learning. Our approach enables the acquisition of complex motions like pronking and back-flipping, effectively from scratch. Additionally, our method simplifies the traditionally labour-intensive task of reward shaping, boosting the efficiency of the learning process. Importantly, our framework proves particularly effective for articulated soft quadrupeds, whose inherent compliance and adaptability make them ideal for dynamic tasks but also introduce unique control challenges.

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.

Recent advancements have underscored the impact of deep learning techniques on multivariate time series forecasting (MTSF). Generally, these techniques are bifurcated into two categories: Channel-independence and Channel-mixing approaches. Although Channel-independence methods typically yield better results, Channel-mixing could theoretically offer improvements by leveraging inter-variable correlations. Nonetheless, we argue that the integration of uncorrelated information in channel-mixing methods could curtail the potential enhancement in MTSF model performance. To substantiate this claim, we introduce the Cross-variable Decorrelation Aware feature Modeling (CDAM) for Channel-mixing approaches, aiming to refine Channel-mixing by minimizing redundant information between channels while enhancing relevant mutual information. Furthermore, we introduce the Temporal correlation Aware Modeling (TAM) to exploit temporal correlations, a step beyond conventional single-step forecasting methods. This strategy maximizes the mutual information between adjacent sub-sequences of both the forecasted and target series. Combining CDAM and TAM, our novel framework significantly surpasses existing models, including those previously considered state-of-the-art, in comprehensive tests.

Reassembly tasks play a fundamental role in many fields and multiple approaches exist to solve specific reassembly problems. In this context, we posit that a general unified model can effectively address them all, irrespective of the input data type (images, 3D, etc.). We introduce DiffAssemble, a Graph Neural Network (GNN)-based architecture that learns to solve reassembly tasks using a diffusion model formulation. Our method treats the elements of a set, whether pieces of 2D patch or 3D object fragments, as nodes of a spatial graph. Training is performed by introducing noise into the position and rotation of the elements and iteratively denoising them to reconstruct the coherent initial pose. DiffAssemble achieves state-of-the-art (SOTA) results in most 2D and 3D reassembly tasks and is the first learning-based approach that solves 2D puzzles for both rotation and translation. Furthermore, we highlight its remarkable reduction in run-time, performing 11 times faster than the quickest optimization-based method for puzzle solving. Code available at //github.com/IIT-PAVIS/DiffAssemble

Although Large Language Models (LLMs) have made significant progress in code generation, they still struggle with code generation tasks in specific scenarios. These scenarios usually necessitate the adaptation of LLMs to fulfill specific needs, but the limited training data available in practice leads to poor code generation performance. How to effectively adapt LLMs to new scenarios with fewer training samples is a major challenge for current code generation. In this paper, we propose a novel adaptation approach named SEED, which stands for Sample-Efficient adaptation with Error-Driven learning for code generation. SEED leverages the errors made by LLMs as learning opportunities, using error revision to overcome its own shortcomings, thus achieving efficient learning. Specifically, SEED involves identifying error code generated by LLMs, employing Self-revise for code revision, optimizing the model with revised code, and iteratively adapting the process for continuous improvement. Experimental results show that, compared to traditional fine-tuning approaches, SEED achieves superior performance with fewer training samples, showing a relative improvement of 27.2%-325.0% in Pass@1. We also validate the effectiveness of Self-revise, which generates revised code that optimizes the model more efficiently compared to the code samples from datasets. Moreover, SEED consistently demonstrates strong performance across various LLMs, underscoring its generalizability.

We revisit the well-known Gilbert-Varshamov (GV) bound for constrained systems. In 1991, Kolesnik and Krachkovsky showed that GV bound can be determined via the solution of some optimization problem. Later, Marcus and Roth (1992) modified the optimization problem and improved the GV bound in many instances. In this work, we provide explicit numerical procedures to solve these two optimization problems and hence, compute the bounds. We then show the procedures can be further simplified when we plot the respective curves. In the case where the graph presentation comprise a single state, we provide explicit formulas for both bounds.

Video captioning is a challenging task that requires a deep understanding of visual scenes. State-of-the-art methods generate captions using either scene-level or object-level information but without explicitly modeling object interactions. Thus, they often fail to make visually grounded predictions, and are sensitive to spurious correlations. In this paper, we propose a novel spatio-temporal graph model for video captioning that exploits object interactions in space and time. Our model builds interpretable links and is able to provide explicit visual grounding. To avoid unstable performance caused by the variable number of objects, we further propose an object-aware knowledge distillation mechanism, in which local object information is used to regularize global scene features. We demonstrate the efficacy of our approach through extensive experiments on two benchmarks, showing our approach yields competitive performance with interpretable predictions.