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This manuscript addresses the local well-posedness theories for the dynamics of non-isentropic compressible Euler equations in a physical vacuum. We establish the Hadamard-style local well-posedness within suitable weighted Sobolev spaces, demonstrating existence, uniqueness, and continuous dependence on initial data. Additionally, we provide a priori energy estimates and continuation criteria. These results are applicable to the low-regularity solutions, in the sense that, the pointwise regularities of the free boundaries and the velocity fields restricted to them could merely be $C^{1.5+}$ and $C^{1+}$, respectively. This is the first well-posedness result for the full compressible Euler equations in a physical vacuum for space dimensions not restricted to one. The approach is based on the framework of Eulerian coordinates., Comment: All comments are welcome!

Defense hardening can effectively enhance the resilience of distribution networks against extreme weather disasters. Currently, most existing hardening strategies focus on reducing load shedding. However, for electricity-hydrogen distribution networks (EHDNs), the leakage risk of hydrogen should be controlled to avoid severe incidents such as explosions. To this end, this paper proposes an optimal hardening strategy for EHDNs under extreme weather, aiming to minimize load shedding while limiting the leakage risk of hydrogen pipelines. Specifically, modified failure uncertainty models for power lines and hydrogen pipelines are developed. These models characterize not only the effect of hardening, referred to as decision-dependent uncertainties (DDUs), but also the influence of disaster intensity correlations on failure probability distributions. Subsequently, a hardening decision framework is established, based on the two-stage distributionally robust optimization incorporating a hydrogen leakage chance constraint (HLCC). To enhance the computational efficiency of HLCC under discrete DDUs, an efficient second-order-cone transformation is introduced. Moreover, to address the intractable inverse of the second-order moment under DDUs, lifted variables are adopted to refine the main-cross moments. These reformulate the hardening problem as a two-stage mixed-integer second-order-cone programming, and finally solved by the column-and-constraint generation algorithm. Case studies demonstrate the effectiveness and superiority of the proposed method.

Hydrogen-enriched compressed natural gas (HCNG) is a promising way to utilize surplus renewable energy through hydrogen electrolysis and blending it into natural gas. However, the optimal hydrogen volume fraction (HVF) of HCNG varies following the daily fluctuations of renewable energy. Besides, facing the rapid volatility of renewable energy, ensuring rapid and reliable real-time adjustments is challenging for electricity-HCNG (E-HCNG) coupling networks. To this end, this paper proposes a flexible operation framework for electricity-HCNG (E-HCNG) networks against the fluctuations and volatility of renewable energy. Based on operations with variable HVF, the framework developed an E-HCNG system-level affine policy, which allows real-time re-dispatch of operations according to the volatility. Meanwhile, to guarantee the operational reliability of the affine policy, a distributionally robust joint chance constraint (DRJCC) is introduced, which limits the violation probability of operational constraints under the uncertainties of renewable energy volatility. Furthermore, in the solving process, to mitigate the over-conservation in DRJCC decomposition, an improved risk allocation method is proposed, utilizing the correlations among violations under the affine policy. Moreover, to tackle the non-convexities arising from the variable HVF, customized approximations for HCNG flow formulations are developed. The problem is finally reformulated into a mix-integer second-order cone programming problem. The effectiveness of the proposed method is validated both in small-scale and large-scale experiments.

Extreme Multimodal Summarization with Multimodal Output (XMSMO) becomes an attractive summarization approach by integrating various types of information to create extremely concise yet informative summaries for individual modalities. Existing methods overlook the issue that multimodal data often contains more topic irrelevant information, which can mislead the model into producing inaccurate summaries especially for extremely short ones. In this paper, we propose SITransformer, a Shared Information-guided Transformer for extreme multimodal summarization. It has a shared information guided pipeline which involves a cross-modal shared information extractor and a cross-modal interaction module. The extractor formulates semantically shared salient information from different modalities by devising a novel filtering process consisting of a differentiable top-k selector and a shared-information guided gating unit. As a result, the common, salient, and relevant contents across modalities are identified. Next, a transformer with cross-modal attentions is developed for intra- and inter-modality learning with the shared information guidance to produce the extreme summary. Comprehensive experiments demonstrate that SITransformer significantly enhances the summarization quality for both video and text summaries for XMSMO. Our code will be publicly available at https://github.com/SichengLeoLiu/MMAsia24-XMSMO., Comment: 8 pages, 5 figures, submitted to ACM Multimedia Asia 2024

This paper investigates integrating large language models (LLMs) with advanced hardware, focusing on developing a general-purpose device designed for enhanced interaction with LLMs. Initially, we analyze the current landscape, where virtual assistants and LLMs are reshaping human-technology interactions, highlighting pivotal advancements and setting the stage for a new era of intelligent hardware. Despite substantial progress in LLM technology, a significant gap exists in hardware development, particularly concerning scalability, efficiency, affordability, and multimodal capabilities. This disparity presents both challenges and opportunities, underscoring the need for hardware that is not only powerful but also versatile and capable of managing the sophisticated demands of modern computation. Our proposed device addresses these needs by emphasizing scalability, multimodal data processing, enhanced user interaction, and privacy considerations, offering a comprehensive platform for LLM integration in various applications.

We investigate the general plasma-vacuum interface problems for the ideal incompressible MHD equations with or without surface tension and prove their nonlinear local well-posedness in standard Sobolev spaces under either non-zero surface tension or the stability condition that the magnetic fields are everywhere non-collinear on the interface. In particular, the results show that both capillary forces and tangential magnetic fields can stabilize the motion of the plasma-vacuum interfaces. Moreover, the vanishing surface tension limit results are established under the Rayleigh-Taylor sign condition or the non-collinearity condition. All these results hold with no graph assumption on the free interface., Comment: arXiv admin note: text overlap with arXiv:2309.03534

We prove the local well-posedness of the incompressible current-vortex sheet problems in standard Sobolev spaces under the surface tension or the Syrovatskij condition, which shows that both capillary forces and large tangential magnetic fields can stabilize the motion of current-vortex sheets. Furthermore, under the Syrovatskij condition, the vanishing surface tension limit is established for the motion of current-vortex sheets. These results hold without assuming the interface separating the two plasmas being a graph.