arXiv subjects
Publications and source records attributed to Jiachen Shi.
We construct pairs of noncongruent bounded Euclidean plane domains with identical Steklov spectra, including multiplicities. This gives a negative answer to the planar Steklov analogue of Kac's question ``Can one hear the shape of a drum?'' The domains are simply connected and strictly convex, have real-analytic boundaries, and may be chosen arbitrarily close to a disk in the $C^\infty$ topology.
The explosive growth of multimodal data - spanning text, image, video, spatial, and relational modalities, coupled with the need for real-time semantic search and retrieval over these data - has outpaced the capabilities of existing multimodal and real-time database systems, which either lack efficient ingestion and continuous query capability, or fall short in supporting expressive hybrid analytics. We introduce ARCADE, a real-time data system that efficiently supports high-throughput ingestion and expressive hybrid and continuous query processing across diverse data types. ARCADE introduces unified disk-based secondary index on LSM-based storage for vector, spatial, and text data modalities, a comprehensive cost-based query optimizer for hybrid queries, and an incremental materialized view framework for efficient continuous queries. Built on open-source RocksDB storage and MySQL query engine, ARCADE outperforms leading multimodal data systems by up to 7.4x on read-heavy and 1.4x on write-heavy workloads.
Index recommendation is one of the most important problems in database management system (DBMS) optimization. Given queries and certain index-related constraints, traditional methods rely on heuristic optimization or learning-based models to select effective indexes and improve query performance. However, heuristic optimization suffers from high computation time, and learning-based models lose generalisability due to training for different workloads and database schemas. With the recent rapid development of large language models (LLMs), methods using prompt tuning have been proposed to enhance the efficiency of index selection. However, such methods still can not achieve the state-of-the-art (SOTA) results, and preparing the index selection demonstrations is also resource-intensive. To address these issues, we propose AMAZe, a zero-shot LLM-based index advisor with a multi-agent framework. We decompose the index recommendation problem into sub-steps, including planning, selection, combination, revision, and reflection. A set of LLM-embedded agents is designed to handle each one of the different sub-steps. Our method utilizes high-level agents to control the index selection process and low-level agents to select and revise indexes. Through extensive experiments, we show that our proposed AMAZe not only achieves the SOTA performance compared to the heuristic methods, but also outperforms learning-based and prompt-based methods with higher efficiency and better zero-shot inference ability.