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In this article, we study weighted estimates for a general class of lacunary maximal functions on homogeneous groups. As an application we derive improved weighted estimates for the lacunary maximal function associated to the Kor\'anyi spherical means as well as for the lacunary maximal function associated to codimension two spheres in the Heisenberg group.

This paper presents a numerical method to solve a time-fractional Burgers equation, achieving order of convergence $(2-\alpha)$ in time, here $\alpha$ represents the order of the time derivative. The fractional derivative is modeled by Caputo-Prabhakar (CP) formulation, which incorporates a kernel defined by the three-parameter Mittag-Leffler function. Finite difference methods are employed for the discretization of the derivatives. To handle the non-linear term, the Newton iteration method is used. The proposed numerical scheme is proven to be stable and convergent in the $L_{\infty}$ norm. The validity of the theory is supported by two numerical examples.

Motion time series collected from mobile and wearable devices such as smartphones and smartwatches offer significant insights into human behavioral patterns, with wide applications in healthcare, automation, IoT, and AR/XR due to their low-power, always-on nature. However, given security and privacy concerns, building large-scale motion time series datasets remains difficult, preventing the development of pre-trained models for human activity analysis. Typically, existing models are trained and tested on the same dataset, leading to poor generalizability across variations in device location, device mounting orientation and human activity type. In this paper, we introduce UniMTS, the first unified pre-training procedure for motion time series that generalizes across diverse device latent factors and activities. Specifically, we employ a contrastive learning framework that aligns motion time series with text descriptions enriched by large language models. This helps the model learn the semantics of time series to generalize across activities. Given the absence of large-scale motion time series data, we derive and synthesize time series from existing motion skeleton data with all-joint coverage. Spatio-temporal graph networks are utilized to capture the relationships across joints for generalization across different device locations. We further design rotation-invariant augmentation to make the model agnostic to changes in device mounting orientations. Our model shows exceptional generalizability across 18 motion time series classification benchmark datasets, outperforming the best baselines by 340% in the zero-shot setting, 16.3% in the few-shot setting, and 9.2% in the full-shot setting., Comment: NeurIPS 2024. Code: https://github.com/xiyuanzh/UniMTS. Model: https://huggingface.co/xiyuanz/UniMTS

Large Language Model (LLM) Agents are an emerging computing paradigm that blends generative machine learning with tools such as code interpreters, web browsing, email, and more generally, external resources. These agent-based systems represent an emerging shift in personal computing. We contribute to the security foundations of agent-based systems and surface a new class of automatically computed obfuscated adversarial prompt attacks that violate the confidentiality and integrity of user resources connected to an LLM agent. We show how prompt optimization techniques can find such prompts automatically given the weights of a model. We demonstrate that such attacks transfer to production-level agents. For example, we show an information exfiltration attack on Mistral's LeChat agent that analyzes a user's conversation, picks out personally identifiable information, and formats it into a valid markdown command that results in leaking that data to the attacker's server. This attack shows a nearly 80% success rate in an end-to-end evaluation. We conduct a range of experiments to characterize the efficacy of these attacks and find that they reliably work on emerging agent-based systems like Mistral's LeChat, ChatGLM, and Meta's Llama. These attacks are multimodal, and we show variants in the text-only and image domains., Comment: website: https://imprompter.ai code: https://github.com/Reapor-Yurnero/imprompter v2 changelog: add new results to Table 3, correct several typos

In this paper, we introduce a novel framework for building learning and control, focusing on ventilation and thermal management to enhance energy efficiency. We validate the performance of the proposed framework in system model learning via two case studies: a synthetic study focusing on the joint learning of temperature and CO2 fields, and an application to a real-world dataset for CO2 field learning. For building control, we demonstrate that the proposed framework can optimize the control actions and significantly reduce the energy cost while maintaining a comfort and healthy indoor environment. When compared to existing traditional methods, an optimization-based method with ODE models and reinforcement learning, our approach can significantly reduce the energy consumption while guarantees all the safety-critical air quality and control constraints. Promising future research directions involve validating and improving the proposed PDE models through accurate estimation of airflow fields within indoor environments. Additionally, incorporating uncertainty modeling into the PDE framework for HVAC control presents an opportunity to enhance the efficiency and reliability of building HVAC system management.

Masked Autoencoder (MAE) is a notable method for self-supervised pretraining in visual representation learning. It operates by randomly masking image patches and reconstructing these masked patches using the unmasked ones. A key limitation of MAE lies in its disregard for the varying informativeness of different patches, as it uniformly selects patches to mask. To overcome this, some approaches propose masking based on patch informativeness. However, these methods often do not consider the specific requirements of downstream tasks, potentially leading to suboptimal representations for these tasks. In response, we introduce the Multi-level Optimized Mask Autoencoder (MLO-MAE), a novel framework that leverages end-to-end feedback from downstream tasks to learn an optimal masking strategy during pretraining. Our experimental findings highlight MLO-MAE's significant advancements in visual representation learning. Compared to existing methods, it demonstrates remarkable improvements across diverse datasets and tasks, showcasing its adaptability and efficiency. Our code is available at: https://github.com/Alexiland/MLOMAE

Large Language Models (LLMs) have seen significant use in domains such as natural language processing and computer vision. Going beyond text, image and graphics, LLMs present a significant potential for analysis of time series data, benefiting domains such as climate, IoT, healthcare, traffic, audio and finance. This survey paper provides an in-depth exploration and a detailed taxonomy of the various methodologies employed to harness the power of LLMs for time series analysis. We address the inherent challenge of bridging the gap between LLMs' original text data training and the numerical nature of time series data, and explore strategies for transferring and distilling knowledge from LLMs to numerical time series analysis. We detail various methodologies, including (1) direct prompting of LLMs, (2) time series quantization, (3) aligning techniques, (4) utilization of the vision modality as a bridging mechanism, and (5) the combination of LLMs with tools. Additionally, this survey offers a comprehensive overview of the existing multimodal time series and text datasets and delves into the challenges and future opportunities of this emerging field. We maintain an up-to-date Github repository which includes all the papers and datasets discussed in the survey., Comment: GitHub repository: https://github.com/xiyuanzh/awesome-llm-time-series