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Tao Zhou

Publications and source records attributed to Tao Zhou.

At least 55 records · Page 3Linked to original sources
arXiv2026

A modified projected walk on spheres method for elliptic equations on high-dimensional embedded manifolds: algorithm and error estimates

In this paper, we propose a modified projected Walk on Spheres method (MPWoS) for screened Poisson equations on embedded manifolds. The method employs local extensions together with the Green representation in local Euclidean balls, coupled with a closest-point projection that maps the boundary samples back to the manifold. This formulation yields a meshfree and highly parallelizable stochastic recursion in the ambient Euclidean space, rather than a direct discretization of the Laplace-Beltrami operator on the manifold. The proposed approach can be viewed as a high-dimensional extension and modification of the projected Walk on Spheres method introduced for surface PDEs in [Sugimoto et al., SIGGRAPH Asia 2024 Conference Papers, pp. 1-10], with three main distinctions: a compensation term that corrects the discrepancy between the ambient Laplacian applied to the closest-point extension and the intrinsic Laplace-Beltrami operator on the manifold, an adaptive radius strategy determined by local geometric and boundary information, and a rigorous error analysis for the proposed algorithm. Under assumptions on the geometric projection and the prescribed compensation accuracy, we establish mean-square error estimates for the proposed Monte Carlo method in both the boundary and closed-manifold settings. Extensive numerical examples on parametrized, implicit, high-dimensional (up to 1000 dimensions), and point-cloud manifolds are presented to illustrate the convergence and efficiency of the proposed method across different geometries.

math.NA↗
arXiv2026

From Stacking Disorder to Cubic Order: Ice Crystallization from Deeply Supercooled Water

Crystallization far from equilibrium can generate morphologies that defy classical crystal habits, yet the microscopic mechanisms linking atomic-scale disorder to emergent macroscopic order remain elusive. Here we use in situ cryogenic transmission electron microscopy with a membrane-encapsulated microdroplet platform to directly visualize the freezing of deeply supercooled water at molecular resolution. We show that homogeneous nucleation produces stacking-disordered ice composed of mixed hexagonal and cubic sequences, in which cubic ice initially exists only as isolated monolayers. The gradual thickening of these cubic layers constitutes the key kinetic mechanism that governs the entire crystallization pathway. As thickening proceeds, nanoscale, defect-free cubic ice germs nucleate on the basal planes of the disordered lattice. These faceted cubic germs act as facet-registered kinetic seeds that enforce cubic twinning and sequentially multiply growth branches. This kinetic pathway reproducibly generates robust eight-branched dendrites with global cubic (octahedral) symmetry, even though each branch remains highly stacking-disordered. At later stages, latent heat release drives a crossover to the thermodynamically favored hexagonal phase; remarkably, the pre-established global cubic symmetry is retained. These results reveal how strong kinetic driving forces convert microscopic disorder into emergent macroscopic symmetry, providing a general framework for understanding and controlling rapid crystallization far from equilibrium.

cond-mat.mtrl-sci↗
arXiv2026

Spreading speeds for Fisher-KPP equations with slowly decaying initial data in an almost periodic setting

This paper investigates the long-times behavior of the Fisher-KPP equation with slowly decaying initial data in an almost periodic medium. We mainly focus on two classes of initial data: exponentially decaying initial data and inital data that decay more slowly than any exponential function. Employing the Hamilton-Jacobi approach, we provide a unified framwork for analyzing the Cauchy problem with initial data in both cases. We demonstrate that the level sets of the solution can be estimated by the generalized principal eigenvalue of the linearized operator and the decay rate of the initial data.

math.AP↗
arXiv2026

Towards Robust EEG Decoding Based on Riemannian Self-Attention

Brain-Computer Interface (BCI) based on electroencephalography (EEG) enables direct interaction between the brain and external environments and has significant applications in assistive technologies, medical rehabilitation, and entertainment. Recently, EEG decoding methods based on Symmetric Positive Definite (SPD) learning have demonstrated superior performance. However, these methods typically employ basic network architectures and do not explicitly capture local relationships between EEG signals. This limitation is problematic for EEG signals due to their inherently low Signal-to-Noise Ratio (SNR). Moreover, most existing Riemannian manifold-based methods are restricted to specific metrics. The most widely used is the Affine-Invariant Metric (AIM). However, it has a quadratic dependency on the SPD matrices and cannot handle ill-conditioned SPD matrices, which hinders the effectiveness of networks. In contrast, the Bures-Wasserstein Metric (BWM) exhibits linear dependence on SPD matrices and demonstrates superior performance for ill conditioning. To overcome these challenges, we propose a Riemannian self-attention network based on the BWM. Additionally, the recently introduced power-deformed generalized Bures-Wasserstein metric reveals a nonlinear relationship between SPD matrices and matrix power deformation. This metric provides a more nuanced representation of the geometric structure of the SPD manifold. Consequently, we extend our model to a learnable version. For simplicity, we refer to it as GBWAtt. Experimental results on three EEG benchmarking datasets validate the robustness and effectiveness of our proposed method. The code is available at https://github.com/jissc/GBWAtt.

cs.LG↗
arXiv2026

PI-DOSnet: A Physics-Informed Deep Operator-Splitting Network for Evolution Partial Differential Equations

Evolution partial differential equations (PDEs) describe time-dependent physical systems governed by differential laws and arise widely across science and engineering. In recent years, operator learning has emerged as a powerful and efficient paradigm for solving evolution PDEs by learning mappings between infinite-dimensional function spaces, enabling solution prediction without explicit time-step integration. In this work, we propose PI-DOSnet, a physics-informed operator learning framework built upon DOSnet and operator splitting. Unlike purely data-driven operator learning methods, PI-DOSnet incorporates physical constraints during training, allowing it to operate even in the absence of paired input-output data. Once trained, PI-DOSnet performs long-time inference of PDE solutions through an iterative strategy. We analyze the linear stability and approximation error of PI-DOSnet and demonstrate its accuracy, efficiency, and robustness through multiple numerical experiments. Moreover, for the Allen--Cahn equation, PI-DOSnet achieves energy stable solutions even with a large time-step size.

math.NA↗
arXiv2026

Rethinking Sampling Strategy in Link Prediction

Many real-world networks are incomplete, making link prediction a fundamental challenge in network science. To train parameters and evaluate algorithms, observed links are usually divided into three subsets, namely training, validation, and probe sets. This division implicitly involves two sampling processes: first-stage sampling yields the probe set and second-stage sampling obtains the variation set. To date, our understanding of how these two sampling processes affect algorithm performance remains quite limited. To address this issue, we propose a sampling scheme called $β$-sampling, where the sampling probability of a link is proportional to the product of the degrees of its two endpoints raised to the power of $β$. Experiments on 45 real-world networks reveal that the structural characteristics of missing links, as simulated via varying probe sets, substantially impact prediction accuracy. When missing links tend to connect high-degree nodes, such links can be predicted accurately with ease. Furthermore, even with a fixed probe set, second-stage sampling still exerts a significant influence on prediction accuracy. Notably, the optimal second-stage sampling strategy differs from \textit{random sampling} (which randomly selects links to form the validation set) and \textit{consistent sampling} (which guarantees that links in the validation and probe sets share identical structural characteristics).

cs.SI↗
arXiv2026

Beyond Visual Cues: CoT-Enhanced Reasoning for Semi-supervised Medical Image Segmentation

Semi-supervised medical image segmentation has emerged as a dominant research problem in medical image analysis, mitigating annotation scarcity by leveraging consistency regularization on unlabeled data. However, existing approaches operate predominantly via visual pattern matching, relying heavily on pixel-level similarities. This visual-centric dependency often falters in clinical scenarios characterized by the visual-semantic mismatch, where visually similar lesions warrant distinct diagnostic conclusions, thus failing to capture the underlying diagnostic logic used by experts. To address this, we move beyond visual cues and propose CERS (CoT-Enhanced Reasoning Segmentation), a framework that integrates Chain-of-Thought (CoT) reasoning to distinguish pathologically distinct cases. Specifically, we construct a knowledge pool enriched with linguistic reasoning descriptions generated by large language models (LLMs). A semantic-aware reference selection strategy is introduced to identify historical evidence, filtering candidates first by morphology, and then refining them via CoT consistency to eliminate hard negatives. Furthermore, a multi-scale coordinate attention module (MCAM) is designed to effectively fuse this reasoning-derived context into the decoding process. Extensive experiments demonstrate the superiority of CERS against state-of-the-art approaches, particularly in resolving boundary ambiguities and semantic inconsistencies. The code is available at https://github.com/cymasuna/CERS.

cs.CV↗
arXiv2026

Propagating Structural Guidance: Synthesizing Fluorescein Angiography from Fundus Images and Sparse OCT Scans

Fundus fluorescein angiography (FFA) is critical for assessing retinal vascular abnormalities, but its acquisition is invasive and not always feasible. In contrast, color fundus photography (CFP) is non-invasive and widely accessible, which has motivated studies on CFP-to-FFA synthesis. However, prior works rely solely on CFP surface texture, fundamentally limiting the ability to reconstruct functional vascular information and subtle pathological changes. To address this, we propose a novel framework that synthesizes FFA from CFP with structural guidance provided by optical coherence tomography (OCT). We construct a multi-modal retinal imaging dataset with paired CFP, FFA, and OCT from 3,676 patient eyes--the first tri-modally aligned dataset in retinal imaging. To bridge the spatial gap between OCT and fundus modalities, we propose a Spatially Aligned Cross-Modal Fusion (SACMF) module that projects depth-resolved OCT features onto the fundus plane and injects them into the CFP encoder via adaptive layer normalization. Beyond feature fusion, we further introduce Token-wise Cross-Modality Alignment (TCMA), a token-level contrastive learning strategy that explicitly aligns CFP and FFA representations at corresponding spatial positions. Our method achieves superior synthesis performance compared to state-of-the-art methods. Moreover, extensive experiments demonstrate that the FFA images synthesized by our approach bring greater improvements in downstream disease diagnosis performance than existing methods, highlighting the clinical potential of our approach as a non-invasive decision-support tool in routine workflows. The code is available at https://github.com/while-plus/OCT-guide-FFA-Syn.

cs.CV↗
arXiv2026

Dynamical Steering and Unambiguous Signature of Majorana Corner Modes in Altermagnetic Josephson Junctions

Dynamical manipulation of Majorana zero modes and their unambiguous distinction from topologically trivial states remain paramount challenges in topological quantum computation. Here, we propose a phase-biased altermagnetic Josephson junction as a versatile platform for generating and controlling Majorana corner configurations. Moving beyond conventional global parameter tuning that merely toggles the topological phase in situ, our platform utilizes the macroscopic superconducting phase difference and the Néel-vector orientation as independent control knobs to dynamically reshape the boundary mass. This synergistically enables the deterministic spatial relocation of Majorana corner modes (MCMs) among selected corners of a fixed device geometry. Crucially, this spatial reconfiguration yields a definitive experimental fingerprint: a control-correlated conductance switching. As the MCMs are relocated, the quantized zero-bias peak perfectly emerges at the target corner while simultaneously vanishing at the initial one. This macroscopically phase-locked spatial correlation effectively eliminates false positives from trivial Andreev bound states, establishing a control-correlated diagnostic and a promising route toward future Majorana braiding architectures.

cond-mat.supr-con↗
arXiv2026

Sublattice polarization and filamentary superconductivity in strained graphene

Periodic strain engineering in monolayer graphene provides a versatile platform to generate colossal pseudo-magnetic fields and flat pseudo-Landau levels directly in a single atomic sheet. While the electronic topology and transport properties of the normal state in these systems have been extensively studied, the superconducting ground state in such strain-modulated landscapes remains an unexplored frontier. In this work, we investigate the superconducting phase of periodically corrugated graphene using a self-consistent Bogoliubov-de Gennes framework. We find that, contrary to the conventional expectation that a high density of states universally enhances pairing, the macroscopic superconducting coherence is significantly hindered in the flat-band regions. This limitation originates from strain-induced sublattice polarization, where the zero-energy electronic states are spatially segregated between the $A$ and $B$ sublattices. Such spatial disjointedness hampers the inter-sublattice coherence required for a robust pairing instability, effectively decoupling the high-density flat-band states from the superconducting condensate. Consequently, as the pairing interaction increases, the system undergoes a striking spatial crossover: superconductivity sharply relocates from the flat-band regions to emerge as robust, quasi-one-dimensional filaments at the geometric nodes where local sublattice symmetry is restored. Our findings reveal that the spatial distribution of wavefunctions, governed by sublattice degrees of freedom, is a decisive factor in determining the superconducting properties of strain-engineered Dirac materials.

cond-mat.supr-con↗
arXiv2026

Text-Driven Fusion for Infrared and Visible Images: Achieving Image Scene Adaptation on Hyperbolic Space

Infrared and visible image fusion aims to integrate complementary modalities, while existing Euclidean methods impose rigid distance metrics that distort multi-modal interactions and parent-to-child semantic hierarchies. To overcome these limitations, we introduce a text-driven fusion framework empowered by hyperbolic manifold learning. During training, BLIP-extracted text prompts serve as topological anchors within the hyperbolic space, guiding vision-attribute alignment through hyperbolic embeddings that naturally accommodate varying semantic granularities. By exploiting the exponential volume growth dictated by the Poincaré ball's negative curvature, this approach seamlessly embeds hierarchical trees to encode coarse-to-fine semantics without metric saturation, while the vast peripheral space prevents texture distortion during cross-modal fusion. At inference, the fusion process autonomously adapts to input content using the learned text-attribute priors, completely eliminating the need for textual input. Experimental results show our method outperforms state-of-the-art approaches on benchmark datasets, with code available at https://github.com/Shaoyun2023/TEDFusion.

cs.CV↗
arXiv2026

Spreading speeds for nonlocal Fisher--KPP equations with time-dependent asymmetric kernels

This paper investigates spreading speeds for nonautonomous Fisher--KPP equations with nonlocal diffusion. The dispersal kernel depends on time and may be asymmetric in space. We assume exponential boundedness of the kernel and the existence of uniform mean values. Under these assumptions, the rightward and leftward spreading speeds are proved to be given by the linearly determined formula. The proof is based on comparison arguments, a refined maximum principle and proper sub- and super-solutions. The result includes, in particular, periodic, almost periodic, and uniquely ergodic time dependence. And it allows kernels whose support does not contain the neighborhood of the origin.

math.AP↗
arXiv2026

Quantifying and Mitigating Self-Preference Bias of LLM Judges

LLM-as-a-Judge has become a dominant approach in automated evaluation systems, playing critical roles in model alignment, leaderboard construction, quality control, and so on. However, the scalability and trustworthiness of this approach can be substantially distorted by Self-Preference Bias (SPB), which is a directional evaluative deviation in which LLMs systematically favor or disfavor their own generated outputs during evaluation. Existing measurements rely on costly human annotations and conflate generative capability with evaluative stance, and thus are impractical for large-scale deployment in real-world systems. To address this issue, we introduce a fully automated framework to quantifying and mitigating SPB, which constructs equal-quality pairs of responses with negligible quality differences, enabling statistical disentanglement of discriminability from bias propensity without human gold standards. Empirical analysis across 20 mainstream LLMs reveals that advanced capabilities are often uncorrelated, or even negatively correlated, with low SPB. To mitigate this bias, we propose a structured multi-dimensional evaluation strategy grounded in cognitive load decomposition, which reduces SPB by 31.5\% on average.

cs.LG↗
arXiv2026

Unified Flux Control Architecture for Fluxonium Qubits

Control architectures that reduce hardware overhead while maintaining high-fidelity operations are essential for the continued scaling of superconducting quantum processors. Here we experimentally realize a unified control architecture for fluxonium qubits, in which both transverse ($XY$) and longitudinal ($Z$) operations are implemented through a single flux-control channel driven by a single arbitrary waveform generator channel. This architecture imposes competing requirements on the shared control channel, which must simultaneously support low-frequency flux transmission for reset operations while strongly attenuating broadband noise near the qubit transition frequency. We address this challenge through frequency-selective cryogenic filtering together with compensated waveform synthesis that corrects the pulse distortion introduced by the filtered control line. Experimentally, this approach preserves coherence times above 100 $μ$s while enabling active reset with approximately 98% fidelity and 20-ns single-qubit gates with fidelities exceeding 99.99%. We further demonstrate FPGA-native instruction-level waveform synthesis based on reusable pulse primitives for unified flux control. These results establish unified flux control as a scalable architecture for fluxonium qubits that reduces control hardware overhead while preserving high-fidelity operation.

quant-ph↗
arXiv2026

Deep Adaptive Dimension Reduction for Bayesian Inference in Inverse Problems

Solving high-dimensional PDE-governed inverse problems is often challenging due to complex non-Gaussian posterior distributions, expensive forward model evaluations, and misspecified prior information. To address these issues, we propose a deep adaptive dimension-reduction Bayesian inference framework based on the Variational Flow (VF) model. Since standard normalizing flows are restricted by bijective mappings and cannot directly reduce dimensions, VF overcomes this limitation by integrating VAE-based nonlinear dimension reduction with dual normalizing flows for the latent prior and encoder. This design provides a strictly higher evidence lower bound than VAE and allows more flexible approximation of complex posterior distributions. We further introduce an iterative prior updating strategy that gradually moves the prior mean toward high-probability posterior regions, avoiding manual prior tuning. These components form a closed adaptive loop together with an adaptively fine-tuned Fourier Neural Operator (FNO) surrogate: VF generates posterior-concentrated samples to refine the surrogate, while the updated surrogate further improves posterior inference. Numerical experiments on a 100-dimensional Rosenbrock problem and three standard PDE-governed inverse problems show that our method delivers competitive or superior accuracy compared with MCMC, UKI, and SVGD baselines across all tested configurations, with the most pronounced advantages emerging in challenging scenarios such as high-noise observations and high-dimensional parameter spaces.

cs.LG↗
arXiv2026

Defect-engineered scaling of lead-free ferroelectrics with ultralow-voltage switching

Scaling ferroelectrics to nanometer thicknesses remains a central challenge for low-power, nonvolatile electronics, as leakage currents increasingly dominate with reduced dimensions. Alkali-based, lead-free ferroelectrics offer an environmentally sustainable alternative to lead-based systems, yet their scaling is severely limited by leakage arising from volatile alkali constituents. Here, we show that this intrinsic limitation can be transformed into an advantageous degree of freedom through defect engineering. By precisely modulating alkali deficiency during thin-film synthesis, we engineer clustered defect complexes that function as deep trap states, strongly suppressing leakage and enabling robust ferroelectric operation in ultrathin films down to the sub-10 nm regime at voltages below 100 mV. Our results establish defect-enabled scaling as a viable pathway for advancing environmentally benign ferroelectrics toward ultra-low-power, non-volatile electronic technologies.

cond-mat.mtrl-sci↗
arXiv2026

Direction-selective triplet pairing and spin-edge locking in altermagnetic metals

We investigate self-consistent unconventional superconductivity in a two-dimensional $d$-wave altermagnetic metal. We find that momentum-dependent altermagnetic spin splitting suppresses opposite-spin singlet pairing and stabilizes highly anisotropic equal-spin triplet order. In the spin-conserving limit, this directional triplet pairing gives rise to nearly dispersionless Majorana boundary states associated with effective one-dimensional topological channels. Rashba spin-orbit coupling mixes spin sectors, activates additional pairing components, and drives the system into a mixed-parity superconducting state with dispersive Majorana boundary states. The spin-resolved boundary spectra further reveal a characteristic locking between boundary orientation and spin polarization, reflecting the underlying altermagnetic symmetry. These results identify altermagnetic spin splitting as an intrinsic mechanism for selecting unconventional pairing and generating spin-resolved Majorana boundary states without external magnetic fields.

cond-mat.supr-con↗
arXiv2026

$L_μ-L_τ$ gauge bosons in beam dumps and supernovae

We study the phenomenology of a sub-GeV $L_μ-L_τ$ gauge boson. We find discrepancies with existing literature in sensitivity projections for the upcoming SHiP experiment and in the treatment of supernovae cooling constraints. We present a quantitative analysis of different production modes in beam dumps and compare our results to previous work. In the context of supernovae, we re-evaluate the standard supernova cooling bounds from SN1987A and analyze additional supernova-based probes: diffusive cooling, constraints from the existence of low-energy supernovae, and the absence of a high-energy neutrino signal from SN1987A.

hep-ph↗