arXiv subjects

Bin Zhou

Publications and source records attributed to Bin Zhou.

At least 19 recordsLinked to original sources

arXiv2026

Uniform estimates for complex Monge-Ampère equations II: Hermitian manifolds

We establish uniform estimates for degenerate complex Monge--Ampère equations on compact Hermitian manifolds under weak Orlicz integrability assumptions on the densities. Our estimates apply uniformly to Hermitian metrics and to semipositive uniformly non-collapsing reference forms. For arbitrary big reference forms, we obtain uniform relative $L^\infty$-estimates with respect to the extremal function with minimal singularities, and establish continuity of the resulting solutions on the regular locus. As an application, we prove the existence of solutions with minimal singularities to degenerate complex Monge--Ampère equations associated with big forms. The proofs combine local Orlicz estimates with pluripotential-theoretic envelope techniques and uniform control of the Monge--Ampère masses, overcoming the lack of invariance of the total Monge--Ampère mass in the Hermitian setting.

math.CV↗

arXiv2026

LEBGen: An LLM-Enhanced Bayesian Network Framework for Few-Shot Travel Survey Data Generation

Travel survey data are essential for transportation planning and travel behavior analysis, yet collecting large-scale representative samples is costly and time-consuming. A practical alternative is to generate synthetic survey records from a few-shot sample. However, such samples provide incomplete coverage of heterogeneous traveler groups and insufficient evidence for recovering the complex dependencies between demographic characteristics and travel behavior. Existing approaches have complementary limitations. Probabilistic generative models such as Bayesian networks (BNs) offer explicit distributional control, but structures learned from few-shot samples may omit meaningful dependencies or retain spurious ones. Large language models (LLMs) can help address these difficulties in BN structure learning by providing behavioral knowledge that complements the limited statistical evidence. We therefore propose LEBGen, an LLM-enhanced BN framework that uses this knowledge to refine network structure for few-shot travel survey data generation. Specifically, the LLM first identifies traveler personas from demographic attribute and travel behavior statistics, then recovers dependencies missed by the persona-augmented BN structure and prune spurious ones. The refined BN is parameterized exclusively from the observed data to generate synthetic records. Under a 2% few-shot setting on the 2022 Hong Kong Travel Characteristics Survey, LEBGen reduces the mean marginal Jensen-Shannon divergence from 0.0671 to 0.0091 and the mean absolute Cramer's V error by 14.3% over the best-performing baseline, substantially improving both distributional and dependency fidelity.

cs.AI↗

arXiv2026

Demonstration-Based Robotic Feeding Using Dynamic Movement Primitives

This paper presents a demonstration-based robotic feeding framework that integrates human demonstration, Dynamic Movement Primitive-based motion planning, vision-based scene perception, and robot control. A human operator first demonstrates the scooping and feeding motions while the position and Euler-angle orientation of the spoon are recorded using a motion-capture system. The recorded trajectory is segmented into scooping and feeding motions, which are encoded using separate Dynamic Movement Primitives. Before task execution, an RGB-D camera estimates the participant's mouth position, while two AprilTags are used for robot-frame registration and tray localization. The detected tray pose is used to position the scooping motion, whereas the detected mouth position defines the positional goal of the feeding motion. The approach, scooping, and feeding trajectories are then executed sequentially by a Kinova Gen3 manipulator through a ROS~2-based framework. A real-world experiment demonstrates the feasibility of the integrated pipeline and shows that the learned spoon motions can be reproduced within the detected experimental scene.

cs.RO↗

arXiv2026

Global Hölder estimates for linearized Monge-Ampère equations in divergence form with applications to dual semigeostrophic equations and periodic homogenization

We establish interior and global Hölder estimates for linearized Monge-Ampère equations in divergence form in all dimensions $n\geq 3$, when the Hessian determinant of the convex Monge-Ampère potential is bounded above and below by positive constants and the vector field on the right-hand side is bounded. The estimates use the $L^p$ norm of the solution for any $p>1$. A key ingredient is an $L^1$ estimate, with appropriate decay rates, for the gradient of the Green's function of the linearized Monge-Ampère operator in small sections, uniform with respect to the pole. As applications, we obtain uniform Hölder estimates for the time derivatives of the primal and dual potentials in the three-dimensional periodic dual semigeostrophic system when the initial density is bounded away from zero and infinity, and establish a linear convergence rate for periodic homogenization of the Monge-Ampère equation.

math.AP↗

arXiv2026

DexGraspFlow: Topology-Aware SE(3) Flow Matching for Cross-Embodiment Dexterous Grasp Generation

Differences in hand geometry, joint parameterization, and kinematic topology pose challenges for cross-embodiment dexterous grasp generation. However, spatial relations among links alone are insufficient to fully capture the hand's kinematic topology. We propose DexGraspFlow, a conditional link-level $\mathrm{SE}(3)$ flow-matching framework integrating geometric relations and kinematic topology. The framework encodes local object geometry, link geometry, and current poses. A dual-stream DiT models link--link coordination and link--object interaction, while attention biases derived from kinematic-tree distances provide explicit structural information for modeling evolving geometric interactions. The model jointly learns translational and rotational velocity fields, integrates them to generate link poses, and recovers joint configurations through inverse kinematics. Additionally, inference-time palm-orientation guidance enables controllable grasp generation without retraining. Across three robotic hands and 30 object--hand pairs, DexGraspFlow achieves a 95.33\% average simulation success rate, with an average generation latency, including inverse kinematics, approximately 49\% lower than that of a state-of-the-art baseline. Further experiments demonstrate zero-shot adaptability to seven finger-removal variants and palm-orientation control. A model trained on demonstrations for the deployed hand achieves a 91\% success rate over 100 real-robot grasping trials, supporting the framework's applicability to physical grasp execution.

cs.RO↗

arXiv2026

CoRe-WAM: Correspondence-Aligned Temporal Residuals for World Action Models

Comparing current and past observations helps robots understand scene changes and select subsequent actions during manipulation. However, comparing visual features at the same image location can mix different scene content when objects or the camera move. We introduce CoRe-WAM, a world-action model that incorporates correspondence-aligned visual changes through a parameter-efficient temporal interface. Its TraceDelta module uses correspondences from a frozen tracking model to transport historical visual features to current locations before computing signed differences in a shared pretrained feature space. Correspondence thus determines which historical content is compared with the present, rather than entering the policy as a separate trajectory representation. A lightweight adapter converts these differences into validity-gated residuals that supplement current visual conditioning, allowing the policy to use recent changes alongside current-scene information. Built on Motus, CoRe-WAM keeps the pretrained backbone weights frozen and optimizes 1.59 million parameters. With a 5,000-update adaptation budget, CoRe-WAM achieves 92.22% clean success across 50 RoboTwin 2.0 tasks, 3.56 percentage points above Motus; on randomized evaluation, it achieves 89.60% success, a 2.58-point gain. Integrating TraceDelta into a StarVLA-based policy improves clean success from 58.10% to 67.62%, supporting transfer of the temporal interface beyond Motus.

cs.RO↗

arXiv2026

A Vision-Language Foundation Model for Precise and Comprehensive Brain Tumor Diagnosis from Preoperative Multimodal Data

We developed BrainVLM to classify all 12 World Health Organization (WHO) 2021 brain tumor types. BrainVLM integrates an uncertainty quantification strategy to indicate prediction reliability and a module for generating radiology reports to elucidate the clinical rationale. BrainVLM was trained on multi-modal data (MRI scans, demographics, and radiology reports) from 40,043 individuals. It was validated on 5,211 patients with pathologically confirmed brain tumors, including 3,877 held-out patients from the primary hospital and 1,334 patients from 11 independent hospitals. We further conducted two proof-of-concept studies to validate its clinical utility in AI-clinician workflows: 1) a blinded multireader study where 12 neuroradiologists across varying experience levels interpreted 248 retrospective cases with or without AI assistance, and 2) a real-world prospective study in which 1,009 patients were independently and blindly assessed by BrainVLM and radiologists before surgery. Additionally, we demonstrated BrainVLM's utility in preoperative molecular subgroup prediction for adult-type diffuse gliomas, using a multi-center cohort of 632 patients. In primary evaluation, BrainVLM achieved an area under the curve (macro-AUC) of 0.85 (95% CI: 0.84-0.86), and an F1 score of 0.82 (95% CI: 0.81-0.83), surpassing neuroradiologists (F1 = 0.80 (95% CI: 0.79-0.81)). In external validation across 11 centers, BrainVLM achieved an AUC = 0.80 (95% CI: 0.79-0.82) and F1 = 0.75 (95% CI: 0.73-0.78), compared with F1 = 0.71 (95% CI: 0.69-0.73) for neuroradiologists. In prospective real-world evaluation, BrainVLM maintained performance comparable to neuroradiologists. The BrainVLM project page is available at https://hku-healthai.github.io/brainvlm_project.github.io/.

cs.CV↗

arXiv2026

Determination of the output injection of invertible linear systems for guaranteeing a regular relative degree

For an invertible linear time-invariant system, the Morse normal form reveals that there exist an output injection and an output transformation such that the resulting system possesses a regular relative degree. Based on this fact, this paper develops a method to determine all admissible output injections and output transformations that achieve this property. In contrast to the recursive and implicit computation methods in the existing literature, the proposed determination method for the output injections is explicit and easy to use, since the solutions are obtained by solving linear matrix equations. A rigorous proof of the proposed method is provided, and an illustrative example is presented to demonstrate the applicability of the approach.

math.DS↗

arXiv2026

Polarized Semi-Inclusive Deep-Inelastic Scattering at $\mathcal O(α_s^3)$ in QCD

Unraveling the partonic origin of the proton spin requires precise determinations of polarized parton distribution functions (PDFs), which depend on comparably precise theoretical predictions for polarized scattering, particularly in view of the high-precision measurements anticipated at the future Electron-Ion Collider. We present the first next-to-next-to-next-to-leading order (N$^3$LO) QCD predictions for longitudinally polarized semi-inclusive deep-inelastic scattering (SIDIS) in a fully differential form, together with next-to-next-to-leading order predictions for the hadron transverse-momentum spectrum. These results are obtained by extending the two-dimensional transverse-momentum subtraction framework to the spin-dependent cross section. Together with the corresponding unpolarized calculation, these results enable consistent N$^3$LO predictions for longitudinal double-spin asymmetries and provide a precision baseline for future analyses of helicity PDFs and transverse-momentum-dependent helicity distributions.

hep-ph↗

arXiv2026

Inverse design of exceptional points in a single-resonance two-port network

Exceptional points (EPs) in non-Hermitian photonic systems enable unconventional control of wave amplitude and phase. However, identifying the EPs in a multidimensional parameter space of a system can be nontrivial and, in some cases, even infeasible. Here we propose an inverse-design method to efficiently locate the scattering EPs for a two-port resonant system supporting a single mode. The proposed method provides a direct way for tuning of geometric parameters to realize scattering EPs, as confirmed by both full-wave simulation and equivalent circuit model. In principle, our method is compatible with multi-mode system and applicable to a broad class of resonant systems.

physics.optics↗

arXiv2026

Semi-global exact prescribed-time stabilization of linear systems by bounded linear time-varying feedback

This paper addresses the problem of semi-global exact prescribed-time stabilization of linear systems by bounded controls. To solve such a problem, one needs to construct a parameterized quadratic control Lyapunov function whose corresponding level set can be made arbitrarily large (for achieving semi-global stabilization) and such that the real parts of the poles of the closed-loop system approach minus infinity as the parameter approaches infinity (for achieving prescribed-time stabilization). This objective is achieved by proposing a nested parametric Lyapunov equation (PLE)-based approach, through which only two linear matrix equations need to be solved in the controller design stage without using real-time state information. Under the proposed structural condition, the nested PLE-based approach guarantees semi-global exact prescribed-time stabilization for any prescribed bounded set of initial conditions, provided that the prescribed settling time is sufficiently large. A numerical example is provided to demonstrate the effectiveness of the designed controller.

math.DS↗

arXiv2026

Uniqueness and Stability of Monge--Ampère Potentials in Big Cohomology Classes

In this paper, we establish a stability estimate and a uniform estimate for the modulus of continuity of solutions to the degenerate complex Monge-Ampère equation in big cohomology classes. Consequently, we prove the uniqueness of solutions to complex Monge-Ampère mean field equations for a sufficiently small parameter.

math.DG↗

arXiv2026

Interior $C^{1,α}$ estimates for the linearized Monge--Ampère equation in two dimensions

We prove an interior $C^{1,α}$ estimate for solutions of the homogeneous linearized Monge--Ampère equation in dimension two under the assumption \[ 0<λ\leq \det D^2φ\leqΛ<+\infty. \] No continuity assumption on the Monge--Ampère density is required. Our result is an affine-invariant analogue of the classical Morrey--Nirenberg $C^{1,α}$ estimate in two dimensions. The core of the proof is the partial Legendre transform. After the transform, the first derivatives of the solution are quotients of adjoint solutions for a uniformly elliptic non-divergence form equation. Bauman's Harnack inequality gives the Hölder control of the quotient, while the Jacobian identity of the partial Legendre transform and a Caccioppoli estimate give its local boundedness. As an application, we prove a Liouville theorem for entire solutions with at most linear growth.

math.AP↗

arXiv2026

A negative exponent range for Audenaert's complementary McCarthy trace inequality

Audenaert introduced a class of complementary McCarthy type trace inequalities in his work on completely monotone functions and Bernstein functions; the same problem was later included in the problem list of Audenaert and Kittaneh. The known results cover the corresponding directions for $q\le -2$, $0<q\le 1$, $1\le q\le 2$, and $2\le q\le 3$, while the negative range $-2<q<0$ was left as a conjectural case. We prove the negative exponent inequality, in fact for every $q<0$. After the inversion $X=A^{-1}$, $Y=B^{-1}$, the problem reduces to a trace inequality for the parallel sum $X:Y$. The proof uses the Kubo--Ando mean chain, an Ando--Hiai type log-majorization for matrix geometric means, and a finite-dimensional Schatten Hölder inequality, including the quasi-norm range. We also record that the positive exponent side $q\ge 3$ follows directly from Audenaert's norm-compression inequality for positive semidefinite $2\times2$ block matrices, and in fact holds for all $q\ge 2$. Finally, we determine the equality case on the negative side: equality holds if and only if $A=B$.

math.RA↗

arXiv2026

Uniform estimates for complex Monge-Ampère equations: big cohomology classes

We prove uniform a priori estimates for solutions to degenerate complex Monge--Ampère equations in big cohomology classes, using both auxiliary-function technique developed by Guo, Phong and Tong [On $L^\infty$-estimates for complex Monge-Ampère equations, Ann. of Math. (2) 198 (2023), no.1, 393-418], and quasi-psh envelope approach developed by Guedj and Lu [Quasi-plurisubharmonic envelopes 1: Uniform estimates on Kähler manifolds, J. Eur. Math. Soc. (JEMS) 27 (2025), no. 3, 1185-1208.]. As an application, we apply our method to prove the Moser-Trudinger and Brezis-Merle-type inequalities for complex Monge-Ampère equations.

math.DG↗

arXiv2026

High second Chern number induced by long-range hopping in a four-dimensional Dirac model

Four-dimensional (4D) topological systems provide a promising platform for exploring topological phenomena beyond three dimensions. So far, extensive recent studies on 4D topological insulators have focused on the 4D Dirac model, while its second Chern number is restricted to a limited set of values. In this work, we demonstrate that introducing long-range hopping into the 4D Dirac model induces topological phases with high second Chern numbers. Furthermore, we show that the long-range hopping can transform a trivial insulator into a topological insulator with a nonzero second Chern number. Our work establishes long-range hopping as a powerful route for engineering 4D topological states and reveals new possibilities for realizing unconventional topological phases beyond minimal models.

cond-mat.mes-hall↗

arXiv2026

Topological surface altermagnets in SSH-stacked magnetic layers

Surface altermagnetism opens new avenues in spintronics by unlocking altermagnetic spin-splitting at the boundaries of conventional antiferromagnets, bypassing the strict symmetry requirements of bulk altermagnets. In this work, we propose creating topological surface altermagnet by stacking magnetic layers in a Su-Schrieffer-Heeger pattern. We show that while the bulk of the system is a standard antiferromagnet with degenerate bands protected by $PT$ symmetry, breaking the local symmetry at the boundary gives rise to a topologically protected surface altermagnetic state residing within the topological gap. Furthermore, we propose that this effect can be experimentally detected by applying a perpendicular electric field. Besides, this approach can be readily generalized to surface altermagnetism of different types. Our work establishes topological boundaries as a natural platform for surface altermagnetism, offering a distinct route for realizing and manipulating topological surface altermagnets.

cond-mat.mes-hall↗

arXiv2026

Numerical calculation of the $k$-space second Chern number in four dimensions

We propose an efficient numerical method to compute the $k$-space second Chern number in four-dimensional (4D) topological systems. Our approach employs an adaptive mesh refinement scheme to evaluate the Brillouin-zone integral, which automatically increases the grid density in regions where the Berry curvature is sharply peaked. We compare our method with the 4D lattice-gauge extension of the Fukui-Hatsugai-Suzuki method and a direct uniform grid integration scheme. Compared with these approaches, our method (i) achieves the same accuracy with substantially fewer diagonalizations, and thus runs faster; (ii) requires minimal memory to execute, enabling calculations for larger systems; and (iii) remains accurate even near topological phase transitions where conventional methods often face challenges. These results demonstrate that the adaptive subdivision strategy is a practical and powerful tool for calculating the $k$-space second Chern number.

cond-mat.mes-hall↗