arXiv subjects

Qing Xia

Publications and source records attributed to Qing Xia.

At least 19 recordsLinked to original sources

arXiv2026

CUFormer: Modality-Aware CT-Ultrasound Point Cloud Registration for Orthopedic Navigation

Registering intraoperative Ultrasound (US) bone-surface point clouds to preoperative Computed Tomography (CT) models can support radiation-free orthopedic navigation. Differences in imaging physics produce distinct surface sampling patterns, complicating cross-modal feature matching. Bone strongly reflects ultrasound and casts an acoustic shadow, so US captures only the probe-facing bone surface and leaves most CT points unmatched. This partial coverage makes correspondences ambiguous on near-symmetric bones. We propose CUFormer, a modality-aware registration framework. We introduce a Modality-Aware Transformer (MAT) that encodes input modality through identity embeddings and updates features through modality-specific adapters within a shared geometric matcher. We model imaging visibility and use predicted reference-side visibility to weight coarse and fine correspondences. CUFormer achieves the lowest mean registration errors among evaluated methods on two CT-US datasets, UltraBones100k and UltraBonesHip, and the CT-RGB-D dataset SpineDepth. On UltraBones100k, it reaches mean rotation error 4.53$^\circ$, translation error 3.19\,mm, and Root Mean Squared Error (RMSE) 2.54\,mm, reducing RMSE by 65.8\% relative to the best-performing baseline by this metric. These results demonstrate CUFormer's effectiveness in aligning partial bone surfaces with preoperative CT across anatomical sites.

cs.CV↗

arXiv2026

MoPort: A View-Aware 2D Interface for Motion Language Models

Motion language models (MoLMs) encode 3D human motion as discrete tokens for language-based understanding. Deploying them on monocular video raises two problems. Pose detection yields 2D joint sequences, leaving a dimensional gap from the 3D motion used in training. Moreover, the 2D observation changes with the camera viewpoint, while the depth lost in projection makes the 2D pose ambiguous across viewpoints. We propose MoPort, a view-aware 2D interface that enables MoLMs to take 2D observations as input. We introduce Paired View Alignment (PVA), which gives two views of the same motion a shared 3D teacher target and directly constrains the consistency of their latents, so that 2D observations from different viewpoints are mapped to a consistent semantic representation. Camera-Modulated Encoding (CME) estimates the camera extrinsics from the 2D sequence and uses them to modulate encoding, providing the 2D latents with geometric information about the viewpoint. MoPort achieves R@1 of 0.5674 on HumanML3D and 0.3286 on KIT-ML, outperforming all evaluated baselines. On HumanML3D, its R@1 decreases only from 0.5763 on in-distribution viewpoints to 0.5585 on out-of-distribution viewpoints. We validate portability on three downstream MoLMs. Furthermore, on the real-world RGB video dataset Fit3D, MoPort achieves 80.36\% accuracy. Code will be released upon acceptance.

cs.CV↗

arXiv2026

Curvature-Distortion Numbers of Graphs: Prescribed Lin--Lu--Yau Curvature Lower Bounds

We study an optimization problem for weighted Lin--Lu--Yau curvature. Given a graph $G=(V,E)$ and a prescribed lower curvature bound $k\ge0$, we ask for the smallest multiplicative distortion \[ \Dist(w):=\frac{\sup_{e\in E}w_e}{\inf_{e\in E}w_e} \] of the edge weights needed to make every edge have curvature at least $k$. This leads to the family \[ \DN_{\LLY}^{k}(G) := \inf\bigl\{ \Dist(w): κ_{\LLY}^{w}(e)\ge k \text{ for every }e\in E(G) \bigr\}, \] which extends the nonnegative-curvature invariant introduced in our preceding paper \cite{Xia2026InvariantI}. The edge weights change the transition probabilities, while the combinatorial graph distance remains fixed. Positive prescribed curvature leads to a fundamental distinction from the case $k=0$. If $G$ is a connected locally finite infinite graph and $k>0$, then \[ \DN_{\LLY}^{k}(G)=\infty. \] Thus no finite multiplicative distortion of the edge weights can impose a uniform positive curvature lower bound on such a graph. For a finite tree $T$ with $m$ edges, such weights exist exactly when $k\le2/m$. We prove that the minimum distortion is attained by a weight unique up to scaling, and that the normalized minimizer and its distortion depend continuously and nondecreasingly on $k$. We then extend the finite-tree theory to general connected graphs. As an application, we characterize the graphs of girth at least six for which finite $k$-distortion is possible.

math.CO↗

arXiv2026

Background2Background: a self-supervised background removal framework for high dimensional microscopy

High-dimensional microscopy captures features across space, time, and spectrum, but complex backgrounds obscure signals. We present Background2Background (B2B), a self-supervised background removal framework leveraging the backgrounds larger correlation relative to the signal. Local pixel shuffling disrupts signal correlations while preserving background structure, transforming signals into effective noise for Noise2Noise-based background removal. Across fluorescence, stimulated Raman scattering and mid-infrared photothermal imaging, B2B achieves over 40-fold background suppression and reveals hidden signatures.

eess.IV↗

arXiv2026

Extremal Lin--Lu--Yau Curvature: Graph Density, Girth, and Short Cycles

We develop a variational framework for extremal Lin--Lu--Yau curvature under positive edge reweighting with the combinatorial metric fixed. For a connected locally finite graph $G$, define \[ \Kmax(G) := \sup_{w>0}\inf_{e\in E(G)}κ_{\LLY}^w(e). \] This invariant relates edgewise discrete curvature to global combinatorial and topological data. In the high-girth regime, we prove for every connected locally finite graph the exact identity \[ \Kmax(G)=\frac4{\mad(G)}-2, \] with the convention $1/\infty=0$. The formula is also equivalent to a normalized Euler-characteristic density: \[ \Kmax(G) = \inf_{\substack{H\subseteq G\text{ finite}\\E(H)\ne\varnothing}} \frac{2(c(H)-β(H))}{|E(H)|}. \] For arbitrary locally finite graphs, a nonnegative short-cycle surplus yields girth-dependent density bounds, with rigidity results in the finite case. We also classify the locally finite graphs of girth at least $6$ admitting a positive edge weight with nonnegative curvature on every edge: they are precisely the trees and the finite cycles.

math.CO↗

arXiv2026

Idleness Functions for Ollivier-Ricci Curvature on Hypergraphs

Let $\mathcal H=(V,E)$ be a locally finite simple hypergraph, equip $V$ with the hyperpath metric, and consider the equal-edges random walk \cite{CoupetteEtAl2023}. For adjacent vertices $x$ and $y$, we prove that the idleness function $α\mapstoκ_α^{\mathcal H}(x,y)$ is piecewise affine and with no more than three affine pieces. A separate mass-balance argument gives linearity on $[1/2,1]$ for every locally finite simple hypergraph and, consequently, a limit-free expression for the Lin--Lu--Yau curvature. In the $r$-uniform linear case, the hypergraph walk agrees exactly with the simple random walk on its 2-section. This reduction transfers the sharp endpoint intervals of Bourne, Cushing, Liu, Münch, and Peyerimhoff \cite{BourneEtAl2018}.

math.CO↗

arXiv2026

Ollivier--Ricci Idleness Functions and Edge-Connectivity of Hypergraphs

We give a local geometric criterion ensuring that the edge-connectivity of a hypergraph equals its minimum incidence degree: every locally finite connected $r$-uniform linear hypergraph with $r\ge3$ and nonnegative Lin--Lu--Yau curvature has this property. Among the various extensions of Ollivier--Ricci curvature to hypergraphs, we work with the equal-edges random walk on hypergraphs \cite{CoupetteEtAl2023}. Moreover, we show that both uniformity and linearity are essential: if either assumption is removed, there exist positively curved hypergraphs for which the gap between minimum incidence degree and edge-connectivity is arbitrarily large. For arbitrary locally finite simple hypergraphs, we also determine the dependence on idleness completely: every idleness function is piecewise affine with at most three affine pieces and is affine on the universal interval $[1/2,1]$. These results extend the corresponding theory for graphs \cite{BourneEtAl2018}. They also provide two useful tools below: the $2$-section reduction underlying the edge-connectivity argument and a limit-free formula used in the sharpness constructions.

math.CO↗

arXiv2026

REMEDY: How Far Is Video Generation from Medical Education World Models?

Recent video generation models produce realistic videos and show potential as a foundation for world models. These advances create opportunities for generating medical teaching demonstrations, which requires both convincing visual quality and precise procedural actions. However, whether current generators can meet these requirements has not been measured. To address this problem, we introduce Readiness Evaluation of Medical Education Demonstration sYnthesis (REMEDY), to our knowledge, the first benchmark for AI-generated medical teaching demonstrations. REMEDY provides 900 first frames from real demonstration videos, covering 12 tasks across four scenarios: operating room, imaging, clinic and bedside, and resuscitation. Five contemporary open-source video generation models produce 4,500 videos from these frames. We combine task-specific clinical checklists with video and motion quality metrics. Evaluation covers four dimensions: clinical action following, clinical profiles, video quality, and motion quality. Our results show that realistic appearance and temporal consistency do not ensure correct clinical actions. Even the most advanced MiniMax-H3 achieves only 28.25% on strict clinical success rate, and fine-grained clinical actions remain challenging. These findings establish a foundation and roadmap for developing future medical education world models.

cs.CV↗

arXiv2026

Can Motion-Language Models Ground Structure? STRIDE for Evaluating the Evaluators

Motion-language models are typically scored by motion-language evaluators, but how well these evaluators ground language structure remains unclear. Here, we introduce the Structure grounding via Temporal-order, Reflection, and Identity Diagnostic Evaluation (STRIDE) benchmark to systematically evaluate the ability of evaluators to track temporal order, mirror reflection, and action identity. STRIDE comprises $5{,}869$ triples, each consisting of a motion, its original caption, and a perturbed caption, spanning both short and long descriptions. We likelihood-balance caption pairs to reduce text-only bias and estimate each evaluator's caption preference under unrelated motions to measure the discrimination gain from matched motions relative to this baseline. Our experiments reveal weak structural grounding and severe deficits in mirror sensitivity among the audited evaluators, which commonly used evaluation protocols fail to expose. To understand why these limitations go undetected in standard tests, we examine the evaluators more closely. We find that text-only priors alone can solve naive perturbation tests on existing datasets, while common retrieval and distributional metrics barely respond to structural corruption introduced by mirroring ground-truth motions. These findings suggest a natural intervention: structural hard negatives. Our experiments show that a simple modification to contrastive learning substantially improves performance on temporal order and mirror reflection. The benchmark and code will be released.

cs.CV↗

arXiv2026

BridgeShield: Risk-Aware Graph Modeling for Cross-Chain Bridge Attack Detection

Cross-chain bridges enable asset and state transfers across heterogeneous blockchains, but their complex cross-domain interactions introduce new attack surfaces that are difficult to monitor using traditional single-chain analysis methods. Existing approaches often focus on isolated on-chain behaviors and fail to capture the multi-stage execution semantics of cross-chain transactions. This paper presents BridgeShield, a graph-based framework for detecting cross-chain bridge attacks through risk-aware modeling of cross-chain execution behaviors. BridgeShield reconstructs cross-chain behavior graphs from execution traces and event logs, capturing interactions across the source chain, off-chain relay components, and the destination chain. To highlight attack-relevant structures, the framework employs differential meta-path selection to identify execution patterns that exhibit structural deviations between normal and attack transactions, and hierarchical risk propagation to aggregate distributed risk signals across interaction stages. Experiments on real-world bridge incidents show that BridgeShield achieves an F1-score of 92.6% in cross-chain attack detection and consistently outperforms existing rule-based and graph-based baselines. In addition, the model remains effective in detecting previously unseen attack incidents, indicating that BridgeShield captures structural risk patterns rather than memorizing historical attack templates.

cs.CR↗

arXiv2026

Curvature-Distortion Numbers of Graphs: Nonnegative Lin--Lu--Yau Curvature

We introduce the curvature-distortion number, a scale-invariant parameter measuring the least multiplicative spread of positive edge weights required to make a weighted discrete curvature nonnegative everywhere. We develop the theory for Lin--Lu--Yau curvature when the transport distance is the fixed combinatorial graph distance. For trees, the invariant admits an explicit nonlinear fixed-point description, which produces a canonical optimal weight that is unique up to scaling. More importantly, the curvature-distortion number controls the branching topology of the tree: for every finite tree $T$, \[ |B(T)|\le \left\lceil \DN_{\LLY}(T)\right\rceil, \] where $B(T)$ is the set of branch vertices. Thus the amount of weight distortion required to achieve nonnegative curvature imposes a direct quantitative restriction on the topological complexity of the tree. For locally finite infinite trees, finite distortion is classified completely: it occurs precisely for the double ray and for one-ended trees obtained from a finite tree by attaching a single ray. This connection between curvature distortion and tree topology extends naturally to general connected graphs through the subgraph formed by edges lying in no cycle of length $3$, $4$, or $5$. Whenever the curvature-distortion number is finite, this tree-like part is a forest unless the whole graph is a cycle of length at least $6$, and each of its tree components inherits the corresponding distortion and topological bounds. In particular, the tree theory yields complete finite-distortion classifications for graphs of girth at least $6$.

math.CO↗

arXiv2026

A penalty-free bulk--surface CutFEM stabilized by lattice Green's function extensions

We introduce a penalty-free cut finite element method for surface elliptic problems coupled to a harmonic bulk field on a Cartesian grid. Instead of adding a stabilization term, the method restricts the active finite element space by a discrete bulk harmonic extension represented with the lattice Green's function, together with a local extrapolation near the interface. The resulting method is a symmetric Galerkin scheme posed on a reduced space embedded in the standard active-mesh finite element space. Under stated geometric, regularity, and approximation assumptions, we establish optimal $\mathcal{O}(h)$ and $\mathcal{O}(h^2)$ surface convergence rates, as well as robust, cut-independent algebraic conditioning. Furthermore, a density formulation based on lattice layer potentials is shown to act as an operator preconditioner; the single-layer parametrization yields an $\mathcal{O}(1)$ algebraically well-conditioned system without introducing any tunable parameters. Two-dimensional experiments on circular, deformed, and smooth nonconvex interfaces confirm the predicted convergence and robustness under changes in the cut position. Finally, a three-dimensional torus experiment demonstrates the identical construction using a seven-point bulk stencil and trilinear surface traces, exhibiting the expected optimal error rates.

math.NA↗

arXiv2026

VoxStruct3D: Structure-Leading Flow Matching for Voxel-Space 3D MRI Synthesis

High-fidelity 3D MRI synthesis requires both globally coherent anatomy and fine-grained voxel-level detail. Although latent diffusion makes volumetric generation tractable, its image autoencoder introduces a reconstruction bottleneck that can limit the fine detail recoverable in the final volume. We present VoxStruct3D, a voxel-space flow-matching framework that directly models full-resolution MRI volumes using a clean-data prediction objective. Its Volumetric Voxel Generator (VVG) combines factorized 3D patch embedding with overlapping upsampling, time-modulated residual refinement, and skip fusion, enabling neighboring tokens to jointly reconstruct shared voxel regions and suppress patch-boundary artifacts. To complement direct voxel-space modeling with an explicit anatomical prior, we further introduce a Structure-First, Image-Follows (SFIF) strategy. A frozen pretrained 3D medical encoder and a StructVAE extract compact structure tokens that preserve dominant anatomy, while a structure-leading schedule keeps their trajectory ahead of the image trajectory. Patch-Aligned RoPE spatially aligns the unequal token grids, and asymmetric attention enforces one-way guidance from structure to image. Experiments on pathological and healthy T1-weighted brain MRI datasets show that VoxStruct3D achieves the strongest overall performance across feature-distribution alignment, sample diversity, and perceptual quality, producing anatomically coherent and visually realistic volumes.

cs.CV↗

arXiv2026

An unfitted boundary algebraic equation method with Calderón preconditioning for 2D Stokes flow in irregular geometry

We present an unfitted boundary algebraic equation method for the two-dimensional exterior/interior Stokes equations on a staggered MAC grid. By constructing an explicit free-space pair of velocity and pressure lattice Green's functions (LGFs) from free-space Laplace LGFs, we represent homogeneous fields using sources supported exclusively on thin staggered boundary layers. This formulation imposes physical Dirichlet data at cut points via local interpolation, while sampled-normal rank updates remove hydrostatic null modes associated with single or multiple obstacles. The workflow parallels that of classical boundary integral formulations and requires no artificial boundary conditions for exterior flows, but follows a discretize-then-represent route and does not require singular/near-singular quadrature. The resulting dense boundary system is solved via GMRES, utilizing a componentwise discrete Calderón preconditioner built from the scalar Laplace kernel and padded FFTs for fast volume convolutions. Extensive numerical validation, including multiply connected domains, narrow gaps, and Moffatt eddies, confirms discrete incompressibility to solver accuracy and recovers the expected Moffatt eddy scaling. We achieve second-order velocity and pressure convergence and bound maximum discrete divergence within numerical accuracy. The discrete Calderón preconditioner reduces the condition number by orders of magnitude and yields nearly mesh-independent conditioning in exterior configurations, while remaining effective---though more demanding---for narrow-gap and fine-grid interior problems.

math.NA↗

arXiv2026

An unfitted boundary algebraic equation method with static-dynamic reduction for evolving implicit geometries

Repeated elliptic solves on domains with evolving boundaries arise in moving-interface simulation, design, and reactive navigation. Even when a fixed Cartesian grid avoids remeshing, rebuilding all boundary interactions for every configuration can limit the efficiency of repeated solves. We develop a static--dynamic boundary reduction for an unfitted lattice Green's function method on prescribed moving planar domains. Like boundary integral and boundary element methods, the formulation reduces the problem to boundary-supported unknowns through a Green representation. Its construction, however, reverses the usual order: the Cartesian operator is discretized before the Green representation is formed, rather than representing the continuous problem first and then discretizing the boundary. This discretize-then-represent viewpoint avoids boundary meshes and singular quadrature. The method also separates interactions associated with stationary geometry from those affected by motion, reuses the invariant part throughout a simulation, and updates only couplings involving the changing boundary. Boundary conditions are imposed at true interface intersections, lattice-kernel data are reused, and the interior field is reconstructed by a fast sine-transform solver. The principal contribution is an implemented and validated update strategy for translating, deforming, appearing, and topology-changing obstacles.

math.NA↗

arXiv2026

Infinite-lattice discrete Calderón projection via the lattice Green's function for active noise shielding and confinement

We construct an infinite-lattice discrete Calderón projection for the Helmholtz equation by convolution with the lattice Green's function (LGF), and apply it to active noise shielding and confinement on Cartesian grids with arbitrary geometry. The LGF fixes the outgoing radiation condition and removes the geometry-dependent auxiliary Helmholtz problem and artificial outer boundary from the projection and control synthesis; its finite numerical tabulation depends only on $(h,k)$ and is reusable across geometries. We prove idempotence, characterize the range as the trace space of interior lattice-Helmholtz solutions, and establish range equivalence with a well-posed Tsynkov-type projection. The two projectors coincide as operators when the auxiliary problem reproduces the exact lattice radiation condition. A capacity-matrix realization yields closed-form shielding and confinement densities supported on the exterior and interior sublayers of a single lattice boundary strip, respectively. For pure-noise shielding, exterior-sublayer measurements suffice under explicit invertibility assumptions; preservation of an unknown wanted interior field requires the full strip trace. Experiments on circular, L-shaped, and star-shaped regions verify machine-precision cancellation for LGF-consistent sources and near-second-order convergence for analytic plane waves and point sources. Conditioning and measurement noise tests quantify the configuration dependence of the reconstruction.

math.NA↗

arXiv2026

Bifurcation of the quasi-stationary velocity of strongly discrete transition waves driven by gravity

Transition waves are common in multistable mechanical metamaterials, and the dynamics of weakly discrete transition waves under driving forces have been extensively discussed. However, as lattice effects become more pronounced, strongly discrete transition waves may exhibit dynamics that cannot be predicted by the continuum limit. Here, by tilting a bistable chain, we introduce a gravitational perturbation term into the dynamical equations, under which the transition waves are continuously accelerated. In the strongly discrete regime, we find that transition waves under gravitational driving possess quasi-stationary velocity plateaus (QSVPs), and the number of these plateaus first increases and then decreases as the tilt angle increases. We theoretically elucidate that the emergence of the velocity plateaus originates from the balance between gravitational driving and phonon radiation. In further analysis, the theoretical model reveals that the balance point undergoes a bifurcation at the radiation resonance, which leads to a change in the number of velocity plateaus. Our study extends the investigation of transition waves into the strongly discrete regime, and the emergence of multiple velocity plateaus opens up new possibilities for programmable solitary waves.

nlin.PS↗

arXiv2026

Chem-SIM: Super-resolution Chemical Imaging via Photothermal Modulation of Structured-Illumination Fluorescence

Structured illumination microscopy (SIM) has attained high spatiotemporal delineation of subcellular architecture, yet offers limited insight into chemical composition. We develop Chem-SIM, a structured-illumination fluorescence detected mid-infrared photothermal microscopy, for super-resolved chemical imaging of microorganisms and mammalian cells. Poisson maximum-likelihood demodulation and spectral normalization across wavenumber recover the weak IR-induced fluorescence intensity change under low photon budgets and convert the fluorescence intensity modulation to chemical fingerprints. Photothermal gating further rejects water backgrounds in aqueous samples, while the IR pump maintains cellular activity at near-physiological temperature. Chem-SIM preserves full vibrational fingerprints, achieves SIM-grade lateral resolution in a high-throughput camera-based format. Here, we show that this platform distinguishes stationary- from log-phase bacteria through chemical content mapping, reports deuterated fatty-acid incorporation in ovarian cancer cells, and resolves lipid-droplet dynamics in live cells, establishing a high-throughput route to super-resolved imaging of organelle chemistry, metabolism, and dynamics.

physics.optics↗