arXiv subjects
Publications and source records attributed to Yifei Li.
For a bounded and graded poset $P$, we show that if $P$ is EL-shellable, then so is its $t$-fold Segre power $P^{(t)}=P\circ \cdots \circ P$ ($t$ factors), as defined by Björner and Welker [J. Pure Appl. Algebra, 198(1-3), 43--55 (2005)]. Our EL-labeling leads to formulas for the rank-selected invariants of $P^{(t)}$, generalising those given by Stanley for the subspace lattice [J. Combinatorial Theory Ser. A, 20(3):336-356, 1976].
Segre products of posets were defined by Björner and Welker (2005). We investigate the homology representations of the $t$-fold Segre power $B_n^{(t)}$ of the Boolean lattice $B_n$. The direct product $\sym_n^{\times t}$ of the symmetric group $\sym_n$ acts on the homology of rank-selected subposets of $B_n^{(t)}$. We give an explicit formula for the decomposition into $\sym_n^{\times t}$-irreducibles of the homology of the full poset, as well as formulas for the diagonal action of the symmetric group $\sym_n$. For the rank-selected homology, we show that the stable principal specialisation of the product Frobenius characteristic of the $\sym_n^{\times t}$-module coincides with the corresponding rank-selected invariant of the $t$-fold Segre power of the subspace lattice.
The hexagonal structure is ubiquitous in nature. The propagation phenomena occurring in a media with a hexagonal structure remain to be explored. One way of exploring this question is to formulate lattice dynamical systems and analyze the propagation dynamics. In this paper, we propose a lattice differential equation model featuring a discrete diffusion operator with the hexagonal structure, and a monostable nonlinear term known as the Fisher-KPP mechanism in modeling population growth. A rigorous analysis is conducted on the traveling waves, thoroughly establishing the existence and uniqueness (up to translation) of the traveling waves. Moreover, the periodicity and monotonicity of the minimal wave speed concerning an angle are demonstrated, which is different from the existing results of the minimal wave speed in $\mathbb{R}^2$ and $\mathbb{Z}^2$. Numerical results validate theoretical analysis and further suggest that the minimal wave speed is also the spreading speed of solutions with compactly supported initial values.
Over the past decades, network systems have surged in significance, driven by merging technological advancements. These systems play pivotal roles in diverse applications ranging from autonomous driving to smart grids, yet they confront complexities arising from network imperfections and intricate interconnections, which challenge system identification, controller design, as well as stability and performance analysis. This survey provides an in-depth exploration of network systems from most recent data-driven perspective, across four key issues: communication delay, aperiodic sampling, network security, and distributed configurations. By doing so, this survey enhances our comprehension of the challenges and theoretical innovations within the realm of network systems.
A cascaded online learning flight control system has been developed and enhanced with respect to action smoothness. In this paper, we investigate the convergence performance of the control system, characterized by the increment of a Lyapunov function candidate. The derivation of this metric accounts for discretization errors and state prediction errors introduced by the incremental model. Comparative results are presented through flight control simulations.
Neural solvers have shown significant potential in solving the Traveling Salesman Problem (TSP), yet current approaches face significant challenges. Supervised learning (SL)-based solvers require large amounts of high-quality labeled data, while reinforcement learning (RL)-based solvers, though less dependent on such data, often suffer from inefficiencies. To address these limitations, we propose LocalEscaper, a novel weakly-supervised learning framework for large-scale TSP. LocalEscaper effectively combines the advantages of both SL and RL, enabling effective training on datasets with low-quality labels. To further enhance solution quality, we introduce a regional reconstruction strategy, which is the key technique of this paper and mitigates the local-optima problem common in existing local reconstruction methods. Experimental results on both synthetic and real-world datasets demonstrate that LocalEscaper outperforms existing neural solvers, achieving remarkable results.
The ultrashort time-integrated diagnosis of ions plays a vital role in high energy density physics research. However, it is extremely challenging to measure in experiment. Here, we demonstrate a reliable approach for investigating the dynamics of deuterium ions in dense plasma. By irradiating a heavy water stream with the hundred Hertz repetitive intense femtosecond laser pulses, the neutrons from D(D,n)3He reaction can be detected via a single Time-of-Flight detector to accumulate the spectrum with a fine energy-resolution. This spectrum has been utilized to calculate the temperature and angular distribution of deuterium ions transported in plasma. And the calculated results are well verified by particle-in-cell simulations of deuterium ions dynamics. Our method paves a new way for diagnosing ions picoseconds time-integrated dynamics in plasma and holds great potential for understanding the ions transport process in high-energy density matters and studying laser plasma ion acceleration.
Traditional knowledge graph (KG) embedding methods aim to represent entities and relations in a low-dimensional space, primarily focusing on static graphs. However, real-world KGs are dynamically evolving with the constant addition of entities, relations and facts. To address such dynamic nature of KGs, several continual knowledge graph embedding (CKGE) methods have been developed to efficiently update KG embeddings to accommodate new facts while maintaining learned knowledge. As KGs grow at different rates and scales in real-world scenarios, existing CKGE methods often fail to consider the varying scales of updates and lack systematic evaluation throughout the entire update process. In this paper, we propose SAGE, a scale-aware gradual evolution framework for CKGE. Specifically, SAGE firstly determine the embedding dimensions based on the update scales and expand the embedding space accordingly. The Dynamic Distillation mechanism is further employed to balance the preservation of learned knowledge and the incorporation of new facts. We conduct extensive experiments on seven benchmarks, and the results show that SAGE consistently outperforms existing baselines, with a notable improvement of 1.38% in MRR, 1.25% in H@1 and 1.6% in H@10. Furthermore, experiments comparing SAGE with methods using fixed embedding dimensions show that SAGE achieves optimal performance on every snapshot, demonstrating the importance of adaptive embedding dimensions in CKGE. The codes of SAGE are publicly available at: https://github.com/lyfxjtu/Dynamic-Embedding.
This paper presents a convergence analysis of the evolving surface finite element method (ESFEM) applied to the original Eyles-King-Styles model of tumour growth. The model consists of a Poisson equation in the bulk, a forced mean curvature flow on the surface, and a coupled velocity law between bulk and surface. Due to the non-trivial bulk-surface coupling, all previous analyses required an additional regularization term. By introducing a $H^{1/2}(Γ)$ energy estimates theory, we develop an essentially new theoretical framework that addresses the intrinsic bulk-surface coupling. Based on this framework, we provide the first rigorous convergence proof for the original model without regularization.
Agentic search such as Deep Research systems-where agents autonomously browse the web, synthesize information, and return comprehensive citation-backed answers-represents a major shift in how users interact with web-scale information. While promising greater efficiency and cognitive offloading, the growing complexity and open-endedness of agentic search have outpaced existing evaluation benchmarks and methodologies, which largely assume short search horizons and static answers. In this paper, we introduce Mind2Web 2, a benchmark of 130 realistic, high-quality, and long-horizon tasks that require real-time web browsing and extensive information synthesis, constructed with over 1000 hours of human labor. To address the challenge of evaluating time-varying and complex answers, we propose a novel Agent-as-a-Judge framework. Our method constructs task-specific judge agents based on a tree-structured rubric design to automatically assess both answer correctness and source attribution. We conduct a comprehensive evaluation of ten frontier agentic search systems and human performance, along with a detailed error analysis to draw insights for future development. The best-performing system, OpenAI Deep Research, can already achieve 50-70% of human performance while spending half the time, highlighting its great potential. Altogether, Mind2Web 2 provides a rigorous foundation for developing and benchmarking the next generation of agentic search systems.
In recent years, the demand for customized, on-demand production has grown in the manufacturing sector. Additive Manufacturing (AM) has emerged as a promising technology to enhance customization capabilities, enabling greater flexibility, reduced lead times, and more efficient material usage. However, traditional AM systems remain constrained by static setups and human worker dependencies, resulting in long lead times and limited scalability. Mobile robots can improve the flexibility of production systems by transporting products to designated locations in a dynamic environment. By integrating AM systems with mobile robots, manufacturers can optimize travel time for preparatory tasks and distributed printing operations. Mobile AM robots have been deployed for on-site production of large-scale structures, but often neglect critical print quality metrics like surface roughness. Additionally, these systems do not have the precision necessary for producing small, intricate components. We propose a model predictive control framework for a mobile AM platform that ensures safe navigation on the plant floor while maintaining high print quality in a dynamic environment. Three case studies are used to test the feasibility and reliability of the proposed systems.
This paper introduces a Sobolev-like space of order $3/2$, denoted as $\widehat{H}^{3/2}$, for Lagrangian finite elements, especially for $C^0$ elements. It is motivated by the limitations of current stability analysis of the evolving surface finite element method (ESFEM), which relies exclusively on an energy estimate framework. To establish a PDE-based analysis framework for ESFEM, we encounter a fundamental regularity mismatch: the ESFEM adopts the $C^0$ elements, while the PDE regularity theory requires $H^{3/2}$ regularity for solutions. To overcome this difficulty, we first examine the properties of the continuous $H^{3/2}$ space, then introduce a Dirichlet lift and Scott-Zhang type interpolation operators to bridge to the discrete $\widehat{H}^{3/2}$ space. Our new $\widehat{H}^{3/2}$ space is shown to be compatible with the elliptic PDE regularity theory, the trace inequality, and the inverse inequality. Notably, we extend the critical domain deformation estimate in ESFEM to the $\widehat{H}^{3/2}$ setting. The $\widehat{H}^{3/2}$ theory provides a foundation for establishing a PDE-based convergence analysis framework of ESFEM.
This paper introduces PROTEUS, a fully automated system that produces data-driven hypotheses from raw data files. We apply PROTEUS to clinical proteogenomics, a field where effective downstream data analysis and hypothesis proposal is crucial for producing novel discoveries. PROTEUS uses separate modules to simulate different stages of the scientific process, from open-ended data exploration to specific statistical analysis and hypothesis proposal. It formulates research directions, tools, and results in terms of relationships between biological entities, using unified graph structures to manage complex research processes. We applied PROTEUS to 10 clinical multiomics datasets from published research, arriving at 360 total hypotheses. Results were evaluated through external data validation and automatic open-ended scoring. Through exploratory and iterative research, the system can navigate high-throughput and heterogeneous multiomics data to arrive at hypotheses that balance reliability and novelty. In addition to accelerating multiomic analysis, PROTEUS represents a path towards tailoring general autonomous systems to specialized scientific domains to achieve open-ended hypothesis generation from data.
We introduce MedXpertQA, a highly challenging and comprehensive benchmark to evaluate expert-level medical knowledge and advanced reasoning. MedXpertQA includes 4,460 questions spanning 17 specialties and 11 body systems. It includes two subsets, Text for text evaluation and MM for multimodal evaluation. Notably, MM introduces expert-level exam questions with diverse images and rich clinical information, including patient records and examination results, setting it apart from traditional medical multimodal benchmarks with simple QA pairs generated from image captions. MedXpertQA applies rigorous filtering and augmentation to address the insufficient difficulty of existing benchmarks like MedQA, and incorporates specialty board questions to improve clinical relevance and comprehensiveness. We perform data synthesis to mitigate data leakage risk and conduct multiple rounds of expert reviews to ensure accuracy and reliability. We evaluate 18 leading models on \benchmark. Moreover, medicine is deeply connected to real-world decision-making, providing a rich and representative setting for assessing reasoning abilities beyond mathematics and code. To this end, we develop a reasoning-oriented subset to facilitate the assessment of o1-like models. Code and data are available at: https://github.com/TsinghuaC3I/MedXpertQA
Recent advances in diffusion models can generate high-quality and stunning images from text. However, multi-turn image generation, which is of high demand in real-world scenarios, still faces challenges in maintaining semantic consistency between images and texts, as well as contextual consistency of the same subject across multiple interactive turns. To address this issue, we introduce TheaterGen, a training-free framework that integrates large language models (LLMs) and text-to-image (T2I) models to provide the capability of multi-turn image generation. Within this framework, LLMs, acting as a "Screenwriter", engage in multi-turn interaction, generating and managing a standardized prompt book that encompasses prompts and layout designs for each character in the target image. Based on these, Theatergen generate a list of character images and extract guidance information, akin to the "Rehearsal". Subsequently, through incorporating the prompt book and guidance information into the reverse denoising process of T2I diffusion models, Theatergen generate the final image, as conducting the "Final Performance". With the effective management of prompt books and character images, TheaterGen significantly improves semantic and contextual consistency in synthesized images. Furthermore, we introduce a dedicated benchmark, CMIGBench (Consistent Multi-turn Image Generation Benchmark) with 8000 multi-turn instructions. Different from previous multi-turn benchmarks, CMIGBench does not define characters in advance. Both the tasks of story generation and multi-turn editing are included on CMIGBench for comprehensive evaluation. Extensive experimental results show that TheaterGen outperforms state-of-the-art methods significantly. It raises the performance bar of the cutting-edge Mini DALLE 3 model by 21% in average character-character similarity and 19% in average text-image similarity.
Charts are high-density visualization carriers for complex data, serving as a crucial medium for information extraction and analysis. Automated chart understanding poses significant challenges to existing multimodal large language models (MLLMs) due to the need for precise and complex visual reasoning. Current step-by-step reasoning models primarily focus on text-based logical reasoning for chart understanding. However, they struggle to refine or correct their reasoning when errors stem from flawed visual understanding, as they lack the ability to leverage multimodal interaction for deeper comprehension. Inspired by human cognitive behavior, we propose ChartSketcher, a multimodal feedback-driven step-by-step reasoning method designed to address these limitations. ChartSketcher is a chart understanding model that employs Sketch-CoT, enabling MLLMs to annotate intermediate reasoning steps directly onto charts using a programmatic sketching library, iteratively feeding these visual annotations back into the reasoning process. This mechanism enables the model to visually ground its reasoning and refine its understanding over multiple steps. We employ a two-stage training strategy: a cold start phase to learn sketch-based reasoning patterns, followed by off-policy reinforcement learning to enhance reflection and generalization. Experiments demonstrate that ChartSketcher achieves promising performance on chart understanding benchmarks and general vision tasks, providing an interactive and interpretable approach to chart comprehension.
Recently, large language models (LLMs) have demonstrated impressive performance in Knowledge Graph Question Answering (KGQA) tasks, which aim to find answers based on knowledge graphs (KGs) for natural language questions. Existing LLMs-based KGQA methods typically follow the Graph Retrieval-Augmented Generation (GraphRAG) paradigm, which first retrieves reasoning paths from the large KGs, and then generates the answers based on them. However, these methods emphasize the exploration of new optimal reasoning paths in KGs while ignoring the exploitation of historical reasoning paths, which may lead to sub-optimal reasoning paths. Additionally, the complex semantics contained in questions may lead to the retrieval of inaccurate reasoning paths. To address these issues, this paper proposes a novel and training-free framework for KGQA tasks called Reward-guided Tree Search on Graph (RTSoG). RTSoG decomposes an original question into a series of simpler and well-defined sub-questions to handle the complex semantics. Then, a Self-Critic Monte Carlo Tree Search (SC-MCTS) guided by a reward model is introduced to iteratively retrieve weighted reasoning paths as contextual knowledge. Finally, it stacks the weighted reasoning paths according to their weights to generate the final answers. Extensive experiments on four datasets demonstrate the effectiveness of RTSoG. Notably, it achieves 8.7\% and 7.0\% performance improvement over the state-of-the-art method on the GrailQA and the WebQSP respectively.
Output regulation is a fundamental problem in control theory, extensively studied since the 1970s. Traditionally, research has primarily addressed scenarios where the system model is explicitly known, leaving the problem in the absence of a system model less explored. Leveraging the recent advancements in Willems et al.'s fundamental lemma, data-driven control has emerged as a powerful tool for stabilizing unknown systems. This paper tackles the output regulation problem for unknown single and multi-agent systems (MASs) using noisy data. Previous approaches have attempted to solve data-based output regulation equations (OREs), which are inadequate for achieving zero tracking error with noisy data. To circumvent the need for solving data-based OREs, we propose an internal model-based data-driven controller that reformulates the output regulation problem into a stabilization problem. This method is first applied to linear time-invariant (LTI) systems, demonstrating exact solution capabilities, i.e., zero tracking error, through solving a straightforward data-based linear matrix inequality (LMI). Furthermore, we extend our approach to solve the $k$th-order output regulation problem for nonlinear systems. Extensions to both linear and nonlinear MASs are discussed. Finally, numerical tests validate the effectiveness and correctness of the proposed controllers.