arXiv subjects

Ke Wu

Publications and source records attributed to Ke Wu.

At least 73 records · Page 4Linked to original sources

arXiv2025

A Liouville theorem for supercritical Fujita equation and its applications

We prove a Liouville theorem for ancient solutions to the supercritical Fujita equation \[\partial_tu-Δu=|u|^{p-1}u, \quad -\infty \frac{n+2}{n-2},\] which says if $u$ is close to the ODE solution $u_0(t):=(p-1)^{-\frac{1}{p-1}}(-t)^{-\frac{1}{p-1}}$ at large scales, then it is an ODE solution (i.e. it depends only on $t$). This implies a stability property for ODE blow ups in this problem. As an application of these results, we show that for a suitable weak solution, its singular set at the end time can be decomposed into two parts: one part is relatively open and $(n-1)$-rectifiable, and it is characterized by the property that tangent functions at these points are the two constants $\pm(p-1)^{-\frac{1}{p-1}}$; the other part is relatively closed and its Hausdorff dimension is not larger than $n-\left[2\frac{p+1}{p-1}\right]-1$.

math.AP↗

arXiv2025

Lightweight Kinematic and Static Modeling of Cable-Driven Continuum Robots via Actuation-Space Energy Formulation

Continuum robots, inspired by octopus arms and elephant trunks, combine dexterity with intrinsic compliance, making them well suited for unstructured and confined environments. Yet their continuously deformable morphology poses challenges for motion planning and control, calling for accurate but lightweight models. We propose the Lightweight Actuation Space Energy Modeling (LASEM) framework for cable driven continuum robots, which formulates actuation potential energy directly in actuation space. LASEM yields an analytical forward model derived from geometrically nonlinear beam and rod theories via Hamilton's principle, while avoiding explicit modeling of cable backbone contact. It accepts both force and displacement inputs, thereby unifying kinematic and static formulations. Assuming the friction is neglected, the framework generalizes to nonuniform geometries, arbitrary cable routings, distributed loading and axial extensibility, while remaining computationally efficient for real-time use. Numerical simulations validate its accuracy, and a semi-analytical iterative scheme is developed for inverse kinematics. To address discretization in practical robots, LASEM further reformulates the functional minimization as a numerical optimization, which also naturally incorporates cable potential energy without explicit contact modeling.

cs.RO↗

arXiv2025

Correlators in two rainbow tensor and complex multi-matrix models

We construct two rainbow tensor models with multi-tensors of rank-$3$ and present their $W$-representations. We give the formula of counting number of independent gauge-invariant operators in terms of Hurwitz numbers and establish a one-to-one correspondence between connected operators and colored Dessins. By means of the colored Dessins and $W$-representations, respectively, we derive two compact expressions of correlators for each of rainbow tensor models. Furthermore, two complex multi-matrix models from the degradations of the constructed rainbow tensor models are also discussed.

hep-th↗

arXiv2025

Drive in Corridors: Enhancing the Safety of End-to-end Autonomous Driving via Corridor Learning and Planning

Safety remains one of the most critical challenges in autonomous driving systems. In recent years, the end-to-end driving has shown great promise in advancing vehicle autonomy in a scalable manner. However, existing approaches often face safety risks due to the lack of explicit behavior constraints. To address this issue, we uncover a new paradigm by introducing the corridor as the intermediate representation. Widely adopted in robotics planning, the corridors represents spatio-temporal obstacle-free zones for the vehicle to traverse. To ensure accurate corridor prediction in diverse traffic scenarios, we develop a comprehensive learning pipeline including data annotation, architecture refinement and loss formulation. The predicted corridor is further integrated as the constraint in a trajectory optimization process. By extending the differentiability of the optimization, we enable the optimized trajectory to be seamlessly trained within the end-to-end learning framework, improving both safety and interpretability. Experimental results on the nuScenes dataset demonstrate state-of-the-art performance of our approach, showing a 66.7% reduction in collisions with agents and a 46.5% reduction with curbs, significantly enhancing the safety of end-to-end driving. Additionally, incorporating the corridor contributes to higher success rates in closed-loop evaluations. Project page: https://zhiwei-pg.github.io/Drive-in-Corridors.

cs.RO↗

arXiv2025

Simulation-Based Equations for Propagation Constant in Uniform or Periodic Transmission

In this work, simulation-based equations to calculate propagation constant in uniform or periodic structures (SES) are deduced and verified through simulations in various types of structures. The modeling of those structures are essentially based on field distributions from a driven-mode solver, and the field distributions are used as the input parameters of the FPPS. It allows the separation of forward and backward waves from a total wave inside such a uniform or periodic structure, and thus it can be used to calculate the propagation constants inside both uniform and periodic structures even with a strong reflection. In order to test the performance and function of the FPPS, it has been applied to a variety of typical structures, including uniform waveguides, lossfree closed structures, lossy closed structures, and open radiation structures, and compared with the results of eigenmode solvers, equivalent network methods, and spectral domain integral equation methods. The comparison shows the easy-to-use and adaptable nature of the FPPS. the FPPS. This FPPS could be also applied to open radiating structures, and even multi-dimensional periodic/uniform structures.

cs.CE↗

arXiv2025

O2V-Mapping: Online Open-Vocabulary Mapping with Neural Implicit Representation

Online construction of open-ended language scenes is crucial for robotic applications, where open-vocabulary interactive scene understanding is required. Recently, neural implicit representation has provided a promising direction for online interactive mapping. However, implementing open-vocabulary scene understanding capability into online neural implicit mapping still faces three challenges: lack of local scene updating ability, blurry spatial hierarchical semantic segmentation and difficulty in maintaining multi-view consistency. To this end, we proposed O2V-mapping, which utilizes voxel-based language and geometric features to create an open-vocabulary field, thus allowing for local updates during online training process. Additionally, we leverage a foundational model for image segmentation to extract language features on object-level entities, achieving clear segmentation boundaries and hierarchical semantic features. For the purpose of preserving consistency in 3D object properties across different viewpoints, we propose a spatial adaptive voxel adjustment mechanism and a multi-view weight selection method. Extensive experiments on open-vocabulary object localization and semantic segmentation demonstrate that O2V-mapping achieves online construction of language scenes while enhancing accuracy, outperforming the previous SOTA method.

cs.CV↗

arXiv2025

UniAP: Unifying Inter- and Intra-Layer Automatic Parallelism by Mixed Integer Quadratic Programming

Distributed learning is commonly used for training deep learning models, especially large models. In distributed learning, manual parallelism (MP) methods demand considerable human effort and have limited flexibility. Hence, automatic parallelism (AP) methods have recently been proposed for automating the parallel strategy optimization process. Existing AP methods suffer from sub-optimal solutions because they do not jointly optimize the two categories of parallel strategies (i.e., inter-layer parallelism and intra-layer parallelism). In this paper, we propose a novel AP method called UniAP, which unifies inter- and intra-layer automatic parallelism by mixed integer quadratic programming. To the best of our knowledge, UniAP is the first parallel method that can jointly optimize the two categories of parallel strategies to find an optimal solution. Experimental results show that UniAP outperforms state-of-the-art methods by up to 3.80$\times$ in throughput and reduces strategy optimization time by up to 107$\times$ across five Transformer-based models.

cs.LG↗

arXiv2025

Quantitative stratification for the fractional Allen-Cahn equation and stationary nonlocal minimal surface

We study properties of solutions to the fractional Allen-Cahn equation when $s\in (0, 1/2)$ and dimension $n\geq 2$. By applying the quantitative stratification principle developed by Naber and Valtorta, we obtain an optimal quantitative estimate on the transition set. As an application of this estimate, we improve the potential energy estimates of Cabre, Cinti, and Serra (2021), providing sharp versions for the fractional Allen-Cahn equation. Similarly, we obtain optimal perimeter estimates for stationary nonlocal minimal surfaces, extending previous results of Cinti, Serra, and Valdinoci (2019) from the stable case.

math.AP↗

arXiv2025

VINGS-Mono: Visual-Inertial Gaussian Splatting Monocular SLAM in Large Scenes

VINGS-Mono is a monocular (inertial) Gaussian Splatting (GS) SLAM framework designed for large scenes. The framework comprises four main components: VIO Front End, 2D Gaussian Map, NVS Loop Closure, and Dynamic Eraser. In the VIO Front End, RGB frames are processed through dense bundle adjustment and uncertainty estimation to extract scene geometry and poses. Based on this output, the mapping module incrementally constructs and maintains a 2D Gaussian map. Key components of the 2D Gaussian Map include a Sample-based Rasterizer, Score Manager, and Pose Refinement, which collectively improve mapping speed and localization accuracy. This enables the SLAM system to handle large-scale urban environments with up to 50 million Gaussian ellipsoids. To ensure global consistency in large-scale scenes, we design a Loop Closure module, which innovatively leverages the Novel View Synthesis (NVS) capabilities of Gaussian Splatting for loop closure detection and correction of the Gaussian map. Additionally, we propose a Dynamic Eraser to address the inevitable presence of dynamic objects in real-world outdoor scenes. Extensive evaluations in indoor and outdoor environments demonstrate that our approach achieves localization performance on par with Visual-Inertial Odometry while surpassing recent GS/NeRF SLAM methods. It also significantly outperforms all existing methods in terms of mapping and rendering quality. Furthermore, we developed a mobile app and verified that our framework can generate high-quality Gaussian maps in real time using only a smartphone camera and a low-frequency IMU sensor. To the best of our knowledge, VINGS-Mono is the first monocular Gaussian SLAM method capable of operating in outdoor environments and supporting kilometer-scale large scenes.

cs.RO↗

arXiv2025

Foundations of Platform-Assisted Auctions

Today, many auctions are carried out with the help of intermediary platforms like Google and eBay. We refer to such auctions as platform-assisted auctions.Traditionally, the auction theory literature mainly focuses on designing auctions that incentivize the buyers to bid truthfully,assuming that the platform always faithfully implements the auction. In practice, however, the platforms have been found to manipulate the auctions to earn more profit, resulting in high-profile anti-trust lawsuits. We propose a new model for studying platform-assisted auctions in the permissionless setting. We explore whether it is possible to design a dream auction in thisnew model, such that honest behavior is the utility-maximizing strategy for each individual buyer, the platform, the seller, as well as platform-seller or platform-buyer coalitions.Through a collection of feasibility and infeasibility results,we carefully characterize the mathematical landscape of platform-assisted auctions. We show how cryptography can lend to the design of an efficient platform-assisted auction with dream properties. Although a line of works have also used MPC or the blockchain to remove the reliance on a trusted auctioneer, our work is distinct in nature in several dimensions.First, we initiate a systematic exploration of the game theoretic implications when the service providers are strategic and can collude with sellers or buyers. Second, we observe that the full simulation paradigm is too stringent and leads to high asymptotical costs. Specifically, because every player has a different private outcomein an auction protocol, running any generic MPC protocol among the players would incur at least $n^2$ total cost. We propose a new notion of simulation calledutility-dominated emulation.Under this new notion, we showhow to design efficient auction protocols with quasilinear efficiency.

cs.GT↗

arXiv2024

HGS-Planner: Hierarchical Planning Framework for Active Scene Reconstruction Using 3D Gaussian Splatting

In complex missions such as search and rescue,robots must make intelligent decisions in unknown environments, relying on their ability to perceive and understand their surroundings. High-quality and real-time reconstruction enhances situational awareness and is crucial for intelligent robotics. Traditional methods often struggle with poor scene representation or are too slow for real-time use. Inspired by the efficacy of 3D Gaussian Splatting (3DGS), we propose a hierarchical planning framework for fast and high-fidelity active reconstruction. Our method evaluates completion and quality gain to adaptively guide reconstruction, integrating global and local planning for efficiency. Experiments in simulated and real-world environments show our approach outperforms existing real-time methods.

cs.RO↗

arXiv2024

Semantic-Type-Guided Bug Finding

In recent years, there has been an increased interest in tools that establish \emph{incorrectness} rather than correctness of program properties. In this work we build on this approach by developing a novel methodology to prove incorrectness of \emph{semantic typing} properties of functional programs, extending the incorrectness approach to the model theory of functional program typing. We define a semantic type refuter which refutes semantic typings for a simple functional language. We prove our refuter is co-recursively enumerable, and that it is sound and complete with respect to a semantic typing notion. An initial implementation is described which uses symbolic evaluation to efficiently find type errors over a functional language with a rich type system.

cs.PL↗

arXiv2024

A Novel Aerial-Aquatic Locomotion Robot with Variable Stiffness Propulsion Module

In recent years, the development of robots capable of operating in both aerial and aquatic environments has gained significant attention. This study presents the design and fabrication of a novel aerial-aquatic locomotion robot (AALR). Inspired by the diving beetle, the AALR incorporates a biomimetic propulsion mechanism with power and recovery strokes. The variable stiffness propulsion module (VSPM) uses low melting point alloy (LMPA) and variable stiffness joints (VSJ) to achieve efficient aquatic locomotion while reduce harm to marine life. The AALR's innovative design integrates the VSPM into the arms of a traditional quadrotor, allowing for effective aerial-aquatic locomotion. The VSPM adjusts joint stiffness through temperature control, meeting locomotion requirements in both aerial and aquatic modes. A dynamic model for the VSPM was developed, with optimized dimensional parameters to increase propulsion force. Experiments focused on aquatic mode analysis and demonstrated the AALR's swimming capability, achieving a maximum swimming speed of 77 mm/s underwater. The results confirm the AALR's effective performance in water environment, highlighting its potential for versatile, eco-friendly operations.

cs.RO↗

arXiv2024

F-stability, entropy and energy gap for supercritical Fujita equation

We study some problems on self similar solutions to the Fujita equation when $p>(n+2)/(n-2)$, especially, the characterization of constant solutions by the energy. Motivated by recent advances in mean curvature flows, we introduce the notion of $F-$functional, $F$-stability and entropy for solutions of supercritical Fujita equation. Using these tools, we prove that among bounded positive self similar solutions, the constant solution has the lowest entropy. Furthermore, there is also a gap between the entropy of constant and non-constant solutions. As an application of these results, we prove that if $p>(n+2)/(n-2)$, then the blow up set of type I blow up solutions is the union of a $(n-1)-$ rectifiable set and a set of Hausdorff dimension at most $n-3$.

math.AP↗

arXiv2024

NumLLM: Numeric-Sensitive Large Language Model for Chinese Finance

Recently, many works have proposed various financial large language models (FinLLMs) by pre-training from scratch or fine-tuning open-sourced LLMs on financial corpora. However, existing FinLLMs exhibit unsatisfactory performance in understanding financial text when numeric variables are involved in questions. In this paper, we propose a novel LLM, called numeric-sensitive large language model (NumLLM), for Chinese finance. We first construct a financial corpus from financial textbooks which is essential for improving numeric capability of LLMs during fine-tuning. After that, we train two individual low-rank adaptation (LoRA) modules by fine-tuning on our constructed financial corpus. One module is for adapting general-purpose LLMs to financial domain, and the other module is for enhancing the ability of NumLLM to understand financial text with numeric variables. Lastly, we merge the two LoRA modules into the foundation model to obtain NumLLM for inference. Experiments on financial question-answering benchmark show that NumLLM can boost the performance of the foundation model and can achieve the best overall performance compared to all baselines, on both numeric and non-numeric questions.

cs.CE↗

arXiv2024

Maximizing Miner Revenue in Transaction Fee Mechanism Design

Transaction fee mechanism design is a new decentralized mechanism design problem where users bid for space on the blockchain. Several recent works showed that the transaction fee mechanism design fundamentally departs from classical mechanism design. They then systematically explored the mathematical landscape of this new decentralized mechanism design problem in two settings: in the plain setting where no cryptography is employed, and in a cryptography-assisted setting where the rules of the mechanism are enforced by a multi-party computation protocol. Unfortunately, in both settings, prior works showed that if we want the mechanism to incentivize honest behavior for both users as well as miners (possibly colluding with users), then the miner revenue has to be zero. Although adopting a relaxed, approximate notion of incentive compatibility gets around this zero miner-revenue limitation, the scaling of the miner revenue is nonetheless poor. In this paper, we show that if we make a mildly stronger reasonable-world assumption than prior works, we can circumvent the known limitations on miner revenue, and design auctions that generate optimal miner revenue. We also systematically explore the mathematical landscape of transaction fee mechanism design under the new reasonable-world and demonstrate how such assumptions can alter the feasibility and infeasibility landscape.

cs.GT↗

arXiv2024

HGS-Mapping: Online Dense Mapping Using Hybrid Gaussian Representation in Urban Scenes

Online dense mapping of urban scenes forms a fundamental cornerstone for scene understanding and navigation of autonomous vehicles. Recent advancements in mapping methods are mainly based on NeRF, whose rendering speed is too slow to meet online requirements. 3D Gaussian Splatting (3DGS), with its rendering speed hundreds of times faster than NeRF, holds greater potential in online dense mapping. However, integrating 3DGS into a street-view dense mapping framework still faces two challenges, including incomplete reconstruction due to the absence of geometric information beyond the LiDAR coverage area and extensive computation for reconstruction in large urban scenes. To this end, we propose HGS-Mapping, an online dense mapping framework in unbounded large-scale scenes. To attain complete construction, our framework introduces Hybrid Gaussian Representation, which models different parts of the entire scene using Gaussians with distinct properties. Furthermore, we employ a hybrid Gaussian initialization mechanism and an adaptive update method to achieve high-fidelity and rapid reconstruction. To the best of our knowledge, we are the first to integrate Gaussian representation into online dense mapping of urban scenes. Our approach achieves SOTA reconstruction accuracy while only employing 66% number of Gaussians, leading to 20% faster reconstruction speed.

cs.CV↗

arXiv2024

A two-tensor model with order-three

We construct a two-tensor model with order-3 and present its $W$-representation. Moreover we derive the compact expressions of correlators from the $W$-representation and analyze the free energy in large $N$ limit. In addition, we establish the correspondence between two colored Dyck walks in the Fredkin spin chain and tree operators in the ring. Based on the classification Dyck walks, we give the number of tree operators with the given level. Furthermore, we show the entanglement scaling of Fredkin spin chain beyond logarithmic scaling in the ordinary critical systems from the viewpoint of tensor model.

hep-th↗