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Qing Han

Publications and source records attributed to Qing Han.

At least 19 recordsLinked to original sources
arXiv2026

First law of thermodynamics for interacting charged black holes and applications

We derive a mass variation identity expressing the first law of black hole thermodynamics for asymptotically flat, stationary, axisymmetric Einstein-Maxwell solutions with multiple electrically charged horizons and finite conical axis singularities. Under the stated asymptotic and parameter regularity hypotheses, the identity holds for independent variations of all parameters within families of fixed horizon types. On the all-degenerate family, a correction to the ADM mass defines a scalar function whose derivatives with respect to angular momenta are the horizon angular velocities. At the Majumdar-Papapetrou family, its angular momentum Hessian is positive definite. Combining the first variation identity with a separate theorem on the sign of the conical parameters shows that this Hessian is nondecreasing in the positive-semidefinite order along admissible paths of increasing Weyl gaps at fixed positive charges.

gr-qc↗
arXiv2026

Resolving Primitive-Sharing Ambiguity in Long-Tailed TLS-Based Industrial MEP Point Cloud Segmentation via Spatial Context Constraints

In terrestrial laser scanning (TLS)-based mechanical, electrical, and plumbing (MEP) point cloud segmentation, safety-critical components such as reducers and valves are persistently misclassified, blocking reliable engineering knowledge extraction. This stems from a dual crisis--extreme class imbalance (215:1) compounded by geometric ambiguity, since most tail classes share cylindrical primitives with dominant head classes--that existing frequency-based re-weighting methods cannot resolve. We propose spatial context constraints that exploit neighborhood prediction consistency to disambiguate locally similar structures. Our approach extends Class-Balanced (CB) Loss with two architecture-agnostic mechanisms: Boundary-CB, an entropy-based constraint that emphasizes ambiguous boundaries and encodes an MEP assembly-topology prior, and Density-CB, a density-based constraint that compensates for scan-dependent variations and encodes TLS sensor-physics knowledge. Both operate at the loss level and require no backbone modifications; we evaluate them with ResPointNet++. On the Industrial3D dataset (612.7M labelled points from water treatment facilities), our method achieves 55.74% mIoU on the evaluation split, which also served as the validation split, exceeding the strongest of three backbone baselines (39.83-52.48% mIoU), with a 21.7% relative improvement on tail-class performance (29.59% vs. 24.32%) while preserving head-class accuracy (88.14%). Reducer improves from 0% to 21.12% IoU and valve by 24.3% relative. Evaluated per area, the gain comes from the area rich in these primitive-sharing components (tail mIoU 21.4% to 26.5%), while the other area's mIoU is 0.6 points lower. Spatial context constraints thus reduce primitive-sharing errors in the target MEP setting, supporting more reliable identification of safety-critical components for Digital Twin and Scan-to-BIM applications.

cs.CV↗
arXiv2026

A Parametrization of Solutions to the Yamabe Equation with Isolated Singularity

Inspired by a pioneering work by Caffarelli, Gidas, and Spruck, we study positive solutions to the Yamabe equation with nonremovable isolated singularities. It is known that there is a formal one-to-one correspondence between the collection of the solutions to the Yamabe equation with nonremovable isolated singularities and the collection of harmonic functions through formal infinite series determined by the harmonic functions. In this paper, we prove that these formal infinite series yield actual solutions to the Yamabe equation with a nonremovable isolated singularity. These solutions to the Yamabe equation have designated asymptotic behaviors determined by the harmonic functions. In a broader context, we provide a general method of constructing all solutions near their isolated singular points and all solutions near infinity.

math.AP↗
arXiv2026

The Mass-Angular Momentum Inequality for Multiple Black Holes

This is the second in a series of two papers to settle the conjectured mass-angular momentum inequality for multiple black holes. More precisely, we show that for a complete, simply connected, maximal initial data set for the Einstein equations with multiple ends that are either asymptotically flat or asymptotically cylindrical, the ADM mass of any asymptotically flat end admits a lower bound given by the square root of total angular momentum, under the assumption of nonnegative energy density and axisymmetry. Moreover, equality is achieved in this mass lower bound only for a constant time slice of an extreme Kerr spacetime. The proof is based on a novel flow of singular harmonic maps with hyperbolic plane target, under which the renormalized harmonic map energy is monotonically nonincreasing. Relevant properties of the flow are achieved through a refined asymptotic analysis of solutions to the harmonic map equations and their linearization.

math.DG↗
arXiv2026

A Parametrization of Solutions to the Liouville Equation in a Punctured Disc

In this paper, we study parametrization of solutions to the Liouville equation near their isolated singular points. We demonstrate that prescribing asymptotic behaviors forms a new type of problem leading to all such solutions. The harmonic functions determining the asymptotic behaviors play the role of ``free data" as the boundary values in the boundary value problems.

math.AP↗
arXiv2026

Electrovacuum Black Hole Uniqueness

We prove the black hole uniqueness conjecture in the axially symmetric, stationary, electrovacuum setting, subject to the refined asymptotic analysis of the associated singular harmonic maps, which includes an analyticity hypothesis at the axes. More precisely, it is shown that any asymptotically flat solution of the Einstein--Maxwell equations in this class, with more than one black hole horizon component is either: Majumdar--Papapetrou, up to a duality rotation, in which case all logarithmic angle defects vanish, or every finite axis rod logarithmic angle defect is strictly negative and hence every interaction force is strictly attractive. The proof extends the singular harmonic map method used for vacuum Kerr uniqueness in [18].

gr-qc↗
arXiv2026

Kerr Black Hole Uniqueness

We prove the black hole uniqueness conjecture in the axially symmetric, stationary vacuum setting: there is no regular, asymptotically flat equilibrium configuration with more than one horizon component. More precisely, we establish that in every such multi-horizon configuration, the logarithmic angle defect along every bounded axis rod is negative, which implies that the net interaction force across each such segment is attractive. The proof is based on a refined asymptotic analysis of the associated singular harmonic maps, partially drawn from the companion work [16], together with a global maximum principle bound for the Weyl conformal factor arising from a novel scalar curvature related differential inequality.

gr-qc↗
arXiv2026

Asymptotic Analysis of Harmonic Maps With Prescribed Singularities

This is the first in a series of two papers to establish the mass-angular momentum inequality for multiple black holes. We study singular harmonic maps from domains of 3-dimensional Euclidean space to the hyperbolic plane having bounded hyperbolic distance to extreme Kerr harmonic maps. We prove that every such harmonic map admits a unique tangent harmonic map at the extreme black hole horizon. The possible tangent maps are classified and shown to be shifted `extreme Kerr' geodesics in the hyperbolic plane that depend on two parameters, one determined by angular momentum and another by conical singularities. In addition, rates of convergence to the tangent map are established. Similarly, expansions in the asymptotically flat end are presented. These results, together with those of Li-Tian [24,25] and Weinstein [35,36], provide a complete regularity theory for harmonic maps from $\mathbb R^3\setminus z\text{-axis}$ to $\mathbb H^2$ with these prescribed singularities. The analysis is additionally utilized to prove existence of the so called near horizon limit, and to compute the associated near horizon geometries of extreme black holes.

math.DG↗
arXiv2026

Industrial3D: A Water-Treatment TLS Point Cloud Dataset and Cross-Paradigm Benchmark for MEP Scene Understanding

Automated semantic understanding of dense terrestrial laser scanning (TLS) point clouds is a prerequisite for Scan-to-BIM, digital twin maintenance, and as-built verifcation. Yet for operational industrial mechanical, electrical, and plumbing (MEP) facilities, this challenge remains largely unsolved: water-treatment TLS scans exhibit extreme geometric ambiguity, severe occlusion, and extreme class imbalance that architectural benchmarks such as S3DIS and ScanNet cannot adequately represent. We present Industrial3D, a terrestrial LiDAR dataset with 612.7 million expert-labeled points at 6 mm resolution from 20 room scenes, 13 dataset areas, and 7 operational water treatment facilities. At 6.6x the scale of the closest comparable MEP dataset, Industrial3D provides the largest industrial MEP testbed for within-domain scene understanding. We further establish a cross-paradigm benchmark of nine methods across fully supervised, weakly supervised, unsupervised, and foundation-model settings. The best supervised method reaches 55.74% mIoU, whereas zero-shot Point-SAM reaches 15.79%, a 39.95 percentage-point gap that quantifes unresolved domain transfer for industrial TLS data. Analysis attributes this gap to a dual crisis: 215:1 statistical rarity and cylindrical geometric ambiguity between tail classes and head-class pipes. The dataset, benchmark code, and pre-trained models will be publicly released at https://github.com/pointcloudyc/Industrial3D.

cs.CV↗
arXiv2025

Sequential Treatment Effect Estimation with Unmeasured Confounders

This paper studies the cumulative causal effects of sequential treatments in the presence of unmeasured confounders. It is a critical issue in sequential decision-making scenarios where treatment decisions and outcomes dynamically evolve over time. Advanced causal methods apply transformer as a backbone to model such time sequences, which shows superiority in capturing long time dependence and periodic patterns via attention mechanism. However, even they control the observed confounding, these estimators still suffer from unmeasured confounders, which influence both treatment assignments and outcomes. How to adjust the latent confounding bias in sequential treatment effect estimation remains an open challenge. Therefore, we propose a novel Decomposing Sequential Instrumental Variable framework for CounterFactual Regression (DSIV-CFR), relying on a common negative control assumption. Specifically, an instrumental variable (IV) is a special negative control exposure, while the previous outcome serves as a negative control outcome. This allows us to recover the IVs latent in observation variables and estimate sequential treatment effects via a generalized moment condition. We conducted experiments on 4 datasets and achieved significant performance in one- and multi-step prediction, supported by which we can identify optimal treatments for dynamic systems.

cs.LG↗
arXiv2025

Solutions of the Special Lagrangian Equation near Infinity

Solutions to special Lagrangian equations near infinity, with supercritical phases or with semiconvexity on solutions, are known to be asymptotic to quadratic polynomials for dimension $n\ge 3$, with an extra logarithmic term for $n=2$. Via modified Kelvin transforms, we characterize remainders in the asymptotic expansions by a single function near the origin. Such a function is smooth in even dimension, but only $C^{n-1,α}$ in odd dimension $n$, for any $α\in (0,1)$.

math.AP↗
arXiv2024

The Isometric Immersion of Negatively Curved Surfaces with Finite Total Curvature

In this paper, we study the smooth isometric immersion of a complete, simply connected surface with a negative Gauss curvature into the three-dimensional Euclidean space. A fundamental and longstanding problem is to find a sufficient condition for a complete negatively curved surface to be isometrically embedded in R^3 [67]. It can be described as an initial and/or boundary value problem for a hyperbolic system of nonlinear partial differential equations derived from the Gauss-Codazzi equations. The mathematical theory associated with this system is largely incomplete. The global smooth isometric immersion has been proven in the literature when the Gauss curvature decays rapidly and monotonically. However, when the Gauss curvature oscillates or decays slowly, the problem becomes much more challenging and little is known. In our paper, we find a sufficient condition, consisting of a finite total Gauss curvature and appropriate oscillations of the Gauss curvature. Under this condition we prove the global existence of a smooth solution to the Gauss-Codazzi system, achieving a global smooth isometric immersion of the surface into R^3. Furthermore, we show that the finite total Gauss curvature is necessary for the existence of a solution in a special case of the Gauss-Codazzi system. New techniques are developed to overcome the difficulties posed by the slow decay and oscillations of the Gauss curvature. By observing that certain combinations of the Riemann invariants decay faster than others, we reformulate the Gauss-Codazzi equations as a symmetric hyperbolic system and uncover a crucial structure of partial dampings. These partial dampings, along with the finite total curvature and appropriate oscillations of the Gauss curvature, enable us to obtain a global smooth solution through delicate analysis, and consequently establish a global smooth isometric immersion of such surfaces.

math.DG↗
arXiv2024

Full State Estimation of Continuum Robots from Tip Velocities: A Cosserat-Theoretic Boundary Observer

State estimation of robotic systems is essential to implementing feedback controllers, which usually provide better robustness to modeling uncertainties than open-loop controllers. However, state estimation of soft robots is very challenging because soft robots have theoretically infinite degrees of freedom while existing sensors only provide a limited number of discrete measurements. This work focuses on soft robotic manipulators, also known as continuum robots. We design an observer algorithm based on the well-known Cosserat rod theory, which models continuum robots by nonlinear partial differential equations (PDEs) evolving in geometric Lie groups. The observer can estimate all infinite-dimensional continuum robot states, including poses, strains, and velocities, by only sensing the tip velocity of the continuum robot, and hence it is called a ``boundary'' observer. More importantly, the estimation error dynamics is formally proven to be locally input-to-state stable. The key idea is to inject sequential tip velocity measurements into the observer in a way that dissipates the energy of the estimation errors through the boundary. The distinct advantage of this PDE-based design is that it can be implemented using any existing numerical implementation for Cosserat rod models. All theoretical convergence guarantees will be preserved, regardless of the discretization method. We call this property ``one design for any discretization''. Extensive numerical studies are included and suggest that the domain of attraction is large and the observer is robust to uncertainties of tip velocity measurements and model parameters.

cs.RO↗
arXiv2024

Explainable AutoML (xAutoML) with adaptive modeling for yield enhancement in semiconductor smart manufacturing

Enhancing yield is recognized as a paramount driver to reducing production costs in semiconductor smart manufacturing. However, optimizing and ensuring high yield rates is a highly complex and technical challenge, especially while maintaining reliable yield diagnosis and prognosis, and this shall require understanding all the confounding factors in a complex condition. This study proposes a domain-specific explainable automated machine learning technique (termed xAutoML), which autonomously self-learns the optimal models for yield prediction, with an extent of explainability, and also provides insights on key diagnosis factors. The xAutoML incorporates tailored problem-solving functionalities in an auto-optimization pipeline to address the intricacies of semiconductor yield enhancement. Firstly, to capture the key diagnosis factors, knowledge-informed feature extraction coupled with model-agnostic key feature selection is designed. Secondly, combined algorithm selection and hyperparameter tuning with adaptive loss are developed to generate optimized classifiers for better defect prediction, and adaptively evolve in response to shifting data patterns. Moreover, a suite of explainability tools is provided throughout the AutoML pipeline, enhancing user understanding and fostering trust in the automated processes. The proposed xAutoML exhibits superior performance, with domain-specific refined countermeasures, adaptive optimization capabilities, and embedded explainability. Findings exhibit that the proposed xAutoML is a compelling solution for semiconductor yield improvement, defect diagnosis, and related applications.

cs.CE↗