arXiv subjects

Fei Xue

Publications and source records attributed to Fei Xue.

At least 19 recordsLinked to original sources

arXiv2026

Non-Separable Homothetic Triangles, Part I: Constructions and Lower Bounds

A finite family of planar convex bodies is called a non-separable family if no line disjoint from its union has at least one member in each open half-plane. In this paper, we prove that there exist finite non-separable families of positive homothetic triangles with covering factors strictly exceeding the sharp three-member bound $\mu = \frac{2}{3} + \frac{2}{3\sqrt{3}}$. This resolves negatively a question posed by K. Bezdek and Z. L\'angi, who originally established this three-member bound after proving that the classic factor 1 covering theorem by A. W. Goodman and R. E. Goodman for disks fails for arbitrary positive homothets. Besides giving explicit algebraic examples with four, five, and six members having factors of approximately 1.0533161, 1.0551900, and 1.0572061 respectively, we provide a common cyclic recurrence that yields a 303-member family with the exact factor 250000000/235141779. Finally, we derive a continuous model suggested by increasingly fine recurrences, yielding a numerical candidate of 1.0633083; its attainability and optimality remain open.

math.MG↗

arXiv2026

Admissible Discrete Linear Propagators for High-Order Time Splittings of Rotational Nonlinear Schr\"odinger Equations with Arbitrary Three-Dimensional Rotation

We study robust high-order time splittings for nonlinear Schr\"odinger equations whose linear part is defined by the Laplacian and an arbitrary three-dimensional rotation operator. After Fourier pseudospectral discretization, a continuous exact factorization of the linear flow need not yield a method self-adjoint fixed-grid propagator. For the original stage-wise explicit exact integrator, we identify a quadratic even term in the local logarithm and show that its visibility is state-dependent, so the observed temporal order of accuracy can depend on the initial data. We then formulate fixed-grid admissibility for discrete linear propagators and construct two admissible propagators for arbitrary three-dimensional rotation: a symmetrized explicit exact integrator and a palindromic generalized shear propagator. Both are unitary, first-order consistent, method self-adjoint, and have odd local logarithms. Numerical experiments verify the predicted defect mechanism and demonstrate recovery of the designed second-, fourth-, and sixth-order behavior with the admissible propagators.

math.NA↗

arXiv2026

Length--Velocity Gauge Equivalence of Quantum Geometric Nonlinear Conductivity

Nonlinear transport has emerged as a sensitive probe of quantum geometry beyond the Berry-curvature physics of linear response. However, the intrinsic second-order dc response remains conceptually subtle: different quantum and semiclassical formulations can appear to give different static limits, with different assignments of Fermi sea and Fermi surface contributions. Here we resolve this ambiguity by developing a gauge-consistent density-matrix theory of intrinsic nonlinear conductivity in both the length gauge, where the electric field couples through the position operator, and the velocity gauge, where it enters through the vector potential. We show that the two gauges give the same adiabatic dc response when the same retarded continuation is used for all external frequencies and when the velocity gauge current includes all field-dependent vertices. The apparent Fermi sea terms cancel in the full expression, leaving a Fermi surface quantum geometric contribution determined by the band-normalized quantum metric. This result implies that a fully gapped insulator has no residual dc nonlinear Hall current in the adiabatic clean limit. The reactive part of the Fermi surface term agrees with the original semiclassical Berry-connection-polarizability response, while the dissipative Ohmic sector requires a more careful treatment of relaxation and impurity scattering. Our work establishes the length-velocity gauge equivalence for quantum geometric nonlinear response and provides a foundation for using nonlinear transport to probe magnetic quantum geometry, especially in PT-symmetric antiferromagnets.

cond-mat.mes-hall↗

arXiv2026

Statistical Proof as a Window into Human-AI Collaboration: Practical Insights and a Community Agenda

Large language models (LLMs) are increasingly woven into expert cognitive work in daily research, yet we know little about how human expertise should adapt when an AI system can execute substantial technical reasoning on its own. Here we use statistical proof development, a demanding and structured form of expert reasoning, as a window into this broader question. Drawing on day-to-day proof problems, we find that current general-purpose LLMs occupy a useful but limited role: they can execute technical components given a precisely formulated problem and targeted guidance, but become unreliable when the problem is open-ended or requires a long reasoning chain with multiple interdependent steps. This execution-strategy gap is rooted in what makes research-level statistical proof distinctive: unlike pure mathematics, where problems arrive pre-formulated and often demand novel techniques, statistical proof requires first modeling a scientific question into a statistical framework with appropriate assumptions, and then identifying and adapting the right strategy from a repertoire of reusable domain-specific tools. Each step requires deep expertise in both the statistical literature and the real-world context being modeled. In such work, current AI assistance does not reduce the need for human expertise; it relocates that expertise to where human decision-making matters most, such as problem formulation and verification of AI-generated results, and may raise the bar for both. These findings yield practical suggestions for how statisticians can structure AI-assisted proof workflows, and point to a broader community agenda for shared resources, better AI tools, and training the next generation of researchers. Using statistical proof as a window, our study has implications for how experts structure human-AI collaboration in technical cognitive domains more broadly.

stat.OT↗

arXiv2026

Minimal Covering Bodies and a Minkowski-Type Criterion for Lattice Coverings

The structural characterization of lattice coverings is a fundamental problem in the geometry of numbers. In particular, a covering analogue to Minkowski's criterion for lattice packings has remained open. In this paper, we introduce the concept of \textit{minimal covering bodies} and investigate their structural properties. First, we establish a lattice covering criterion in three dimensions based on the Kuhn triangulation. Furthermore, while three-dimensional parallelohedra admit only finitely many combinatorial types, we prove the existence of infinitely many combinatorial types of minimal covering bodies in both the three-dimensional asymmetric case and the four-dimensional centrally symmetric case. Finally, we propose a Minkowski-type geometric criterion and an algebraic intersection framework, which reduce the three-dimensional covering problem to a finite computational verification.

math.MG↗

arXiv2026

Post-Training Recipe, More Than Model Family, Shapes Multi-Agent LLM Conversational Behavior

Multi-LLM systems use multiple language models to deliberate, judge each other's outputs, or coordinate as agents. Their value depends on the models producing measurably different conversational behaviors when given the same input. Prior offline studies recommend drawing one model per family for behavioral diversity, because LLMs prefer outputs from their own family when rating one another in isolation. Whether the same family label predicts behavior in interactive multi-LLM systems, the setting that real deployed systems use, has not been tested. We study this with a 940,000-chain 11-checkpoint corpus and a 1.6M-chain same-base Llama factorial. On our validated headline metric, hedging, a reasoning-distilled Llama checkpoint shifts by 18% depending on which same-base partner it replies to, more than any cross-family hedging gap in the controlled subset. Qwen, closed-API, and runtime checks suggest the pattern is not isolated, while repair and challenge analyses remain exploratory because their surface-cue detectors are weaker. Overall, the results identify post-training recipe as a first-class axis for multi-LLM panel composition and show that model family alone is an incomplete proxy for conversational diversity.

cs.CL↗

arXiv2026

Online3R: Online Learning for Consistent Sequential Reconstruction Based on Geometry Foundation Model

We present Online3R, a new sequential reconstruction framework that is capable of adapting to new scenes through online learning, effectively resolving inconsistency issues. Specifically, we introduce a set of learnable lightweight visual prompts into a pretrained, frozen geometry foundation model to capture the knowledge of new environments while preserving the fundamental capability of the foundation model for geometry prediction. To solve the problems of missing groundtruth and the requirement of high efficiency when updating these visual prompts at test time, we introduce a local-global self-supervised learning strategy by enforcing the local and global consistency constraints on predictions. The local consistency constraints are conducted on intermediate and previously local fused results, enabling the model to be trained with high-quality pseudo groundtruth signals; the global consistency constraints are operated on sparse keyframes spanning long distances rather than per frame, allowing the model to learn from a consistent prediction over a long trajectory in an efficient way. Our experiments demonstrate that Online3R outperforms previous state-of-the-art methods on various benchmarks. Project page: https://shunkaizhou.github.io/online3r-1.0/

cs.CV↗

arXiv2026

Identifiable Deep Latent Variable Models for MNAR Data

Missing data is a ubiquitous challenge in data analysis, often leading to biased and inaccurate results. Traditional imputation methods usually assume that the missingness mechanism is missing-at-random (MAR), where the missingness is independent of the missing values themselves. This assumption is frequently violated in real-world scenarios, prompted by recent advances in imputation methods using deep learning to address this challenge. However, these methods neglect the crucial issue of nonparametric identifiability in missing-not-at-random (MNAR) data, which can lead to biased and unreliable results. This paper seeks to bridge this gap by proposing a novel framework based on deep latent variable models for MNAR data. Building on the assumption of conditional no self-censoring given latent variables, we establish the identifiability of the data distribution. This crucial theoretical result guarantees the feasibility of our approach. To effectively estimate unknown parameters, we develop an efficient algorithm utilizing importance-weighted autoencoders. We demonstrate, both theoretically and empirically, that our estimation process accurately recovers the ground-truth joint distribution under specific regularity conditions. Extensive simulation studies and real-world data experiments showcase the advantages of our proposed method compared to various classical and state-of-the-art approaches to missing data imputation.

stat.ME↗

arXiv2026

Field-Tunable Meissner-Levitated Ferromagnetic Microsphere Sensor for Cryogenic Casimir and Short-Range Gravity Tests

Near-field force measurements at submicron separations can probe Casimir effects and hypothetical short-range interactions, but require cryogenic operation and stable, \textit{in situ} control of separation-dependent backgrounds. We propose a self-calibrating quantum force-gradient sensor in which a ferromagnetic microsphere is Meissner-levitated above a type-I superconducting plane, while a bias magnetic field reproducibly tunes the equilibrium gap for in situ separation scans without mechanical approach. The force gradient is encoded as a resonance-frequency shift tracked by a phase-locked loop, and the motion is read out with a SQUID-coupled, flux-tunable microwave resonator that provides adjustable measurement strength without optical heating. Using the input--output formalism, we derive the conditions for reaching the standard quantum limit (SQL) and identify a counterintuitive scaling law: because displacement-to-flux transduction increases with microsphere size, larger microspheres require fewer photons to reach the SQL, enabling a pathway to macroscopic quantum metrology. We quantify the trade-off between suppression of electrostatic patch potentials (via Au coating) and eddy-current dissipation, project force sensitivities of $\sim 10^{-19}\,\rm{N\,Hz^{-1/2}}$ at millikelvin temperatures, and outline protocols to extract Casimir pressure and constrain Yukawa-type deviations from Newtonian gravity over $0.1$--$10\,\mu\mathrm{m}$.

quant-ph↗

arXiv2026

Empirical Bayes data integreation for multi-response regression

Motivated by applications in tissue-wide association studies (TWAS), we develop a flexible and theoretically grounded empirical Bayes approach for integrating %vector-valued outcomes data obtained from different sources. We propose a linear shrinkage estimator that effectively shrinks singular values of a data matrix. This problem is closely connected to estimating covariance matrices under a specific loss, for which we develop asymptotically optimal estimators. The basic linear shrinkage estimator is then extended to a local linear shrinkage estimator, offering greater flexibility. Crucially, the proposed method works under sparse/dense or low-rank/non low-rank parameter settings unlike well-known sparse or reduced rank estimators in the literature. Furthermore, the empirical Bayes approach offers greater scalability in computation compared to intensive full Bayes procedures. The method is evaluated through an extensive set of numerical experiments, and applied to a real TWAS data obtained from the Genotype-Tissue Expression (GTEx) project.

stat.ME↗

arXiv2026

2D ferroelectric narrow-bandgap semiconductor Wurtzite' type alpha-In2Se3 and its silicon-compatible growth

2D van der Waals ferroelectrics, particularly alpha-In2Se3, have emerged as an attractive building block for next-generation information storage technologies due to their moderate band gap and robust ferroelectricity stabilized by dipole locking. alpha-In2Se3 can adopt either the distorted zincblende or wurtzite structures; however, the wurtzite phase has yet to be experimental-ly validated, and its large-scale synthesis poses significant challenges. Here, we report an in-situ transport growth of centimeter-scale wurtzite type alpha-In2Se3 films directly on SiO2 substrates using a process combining pulsed laser deposition and chemical vapor deposition. We demonstrate that it is a narrow bandgap ferroelectric semiconductor, featuring a Curie tem-perature exceeding 620 K, a tunable bandgap (0.8-1.6 eV) modulated by charged domain walls, and a large optical absorption coefficient of 1.3 times 10 powers 6 per centemeter. Moreover, light absorption promotes the dynamic conductance range, linearity, and symmetry of the synapse devices, leading to a high recognition accuracy of 92.3 percent in a supervised pattern classification task for neuromorphic computing. Our findings demonstrate a ferroelectric polymorphism of In2Se3, highlighting its potential in ferroelectric synapses for neuromorphic computing.

cond-mat.mtrl-sci↗

arXiv2026

Packing minima of convex bodies

In 2021, Henk, Schymura and Xue introduced packing minima, associated with a convex body and a lattice, as packing counterparts to the covering minima of Kannan and Lov\'asz. Motivated by conjectures on the volume inequalities for the successive minima, we generalized the definition of the packing minima to the class of all convex bodies that contain the origin in their interior. For these packing minima, we presented several novel volume inequalities and calculated the specific values of the packing minima for several special convex bodies.

math.MG↗

arXiv2026

Generalized Heterogeneous Functional Model with Applications to Large-scale Mobile Health Data

Physical activity is crucial for human health. With the increasing availability of large-scale mobile health data, strong associations have been found between physical activity and various diseases. However, accurately capturing this complex relationship is challenging, possibly because it varies across different subgroups of subjects, especially in large-scale datasets. To fill this gap, we propose a generalized heterogeneous functional method which simultaneously estimates functional effects and identifies subgroups within the generalized functional regression framework. The proposed method captures subgroup-specific functional relationships between physical activity and diseases, providing a more nuanced understanding of these associations. Additionally, we develop a pre-clustering method that enhances computational efficiency for large-scale data through a finer partition of subjects compared to true subgroups. We further introduce a testing procedure to assess whether the different subgroups exhibit distinct functional effects. In the real data application, we examine the impact of physical activity on the risk of dementia using the UK Biobank dataset, which includes over 96,433 participants. Our proposed method outperforms existing methods in future-day prediction accuracy, identifying three distinct subgroups, with detailed scientific interpretations for each subgroup. We also demonstrate the theoretical consistency of our methods. Codes implementing the proposed method are available at: https://github.com/xiaojing777/GHFM.

stat.ME↗

arXiv2026

Search for Ultralight Axion Dark Matter with a Levitated Ferromagnetic Torsional Oscillator

We present a search for ultralight axion dark matter coupled to electron spins using a levitated ferromagnetic torsional oscillator (FMTO). This platform directly measures axion-induced torques on a macroscopic spin-polarized body, combining large spin density with strong mechanical isolation to probe magnetic fluctuations below 10 Hz while suppressing gradient-field noise. In a first implementation, the experiment yielded 18000 s of analyzable data at room temperature under high vacuum with optical readout and triple-layer magnetic shielding. A likelihood-based statistical framework, incorporating stochastic fluctuations in the axion-field amplitude, was used to evaluate the data. No excess consistent with an axion-induced pseudo-magnetic field was observed near 2e-14 eV. To account for possible shielding-induced signal attenuation, we quantify its effect and report both the uncorrected (g_aee < 1e-7) and attenuation-corrected (g_aee < 6e-5) 90% CL limits on the axion-electron coupling. Looking ahead, improvements guided by both noise-budget analysis and shielding-attenuation considerations, including optimized levitation geometry, cryogenic operation, and superconducting shielding, are expected to boost sensitivity by multiple orders of magnitude.

hep-ph↗

arXiv2025

Deterministic Switching of Perpendicular Ferromagnets by Higher harmonics of Spin-orbit Torque in Noncentrosymmetric Weyl Semimetals

Field-free deterministic switching of perpendicular ferromagnets is a central challenge for spintronics applications, typically requiring explicit symmetry breaking. Here we show that deterministic switching can instead be achieved through higher angular harmonics of spin-orbit torques, even in systems that preserve in-plane mirror symmetries. Using a vector spherical harmonics expansion, we demonstrate that these higher-harmonic torque components naturally give rise to additional out-of-equator fixed points, enabling reliable magnetization reversal when their magnitude is comparable to conventional lowest-order torques. We illustrate this mechanism with first-principles calculations on the noncentrosymmetric Weyl ferromagnet PrAlGe, where the combination of Weyl-node band topology and strong spin-orbit coupling produces sizable higher-harmonic torque components. Because the Fermi surface is small, the conventional lowest-order torques are relatively weak, allowing the higher-order harmonics to compete on equal footing and strongly reshape the magnetization dynamics. The resulting spin dynamics confirm deterministic switching without additional symmetry breaking. Our results establish higher-harmonic spin-orbit torque as a key ingredient for understanding and controlling magnetization dynamics in topological and spintronic materials.

cond-mat.mes-hall↗

arXiv2025

On Higher-Power Moments of $ \Delta_a(x) $ for $-1/2<a<0$

Let $-1/2<a<0$ be a fixed real number and \begin{equation*} \Delta_{a}(x)=\sideset{}{'}\sum_{n\leq x} \sigma_a(n)-\zeta(1-a)x-\frac{\zeta(1+a)}{1+a}x^{1+a}+\frac{1}{2}\zeta(-a). \end{equation*} In this paper, we investigate the higher--power moments of $\Delta_a(x)$ and give the corresponding asymptotic formula for the integral $\int_{1}^{T}\Delta_a^k(x)\mathrm{d}x$, which constitutes an improvement upon the previous result of Zhai [9] for $k=3,4,5$ and an enlargement of the upper bound of $k$ to $7$.

math.NT↗

arXiv2025

A ferroelectric junction transistor memory made from switchable van der Waals p-n heterojunctions

Van der Waals (vdW) p-n heterojunctions are important building blocks for advanced electronics and optoelectronics, in which high-quality heterojunctions essentially determine device performances or functionalities. Creating tunable depletion regions with substantially suppressed leakage currents presents huge challenges, but is crucial for heterojunction applications. Here, by using band-aligned p-type SnSe and n-type ferroelectric {\alpha}-In2Se3 as a model, we report near-ideal multifunctional vdW p-n heterojunctions with small reverse leakage currents (0.1 pA) and a desired diode ideality factor (1.95). We realize ferroelectric-tuned band alignment with a giant barrier modulation of 900 meV. Based on such tunable heterojunctions, we propose and demonstrate a fundamental different memory device termed ferroelectric junction field-effect transistor memory, which shows large memory windows (1.8 V), ultrafast speed (100 ns), high operation temperature (393 K), and low cycle-to-cycle variation (2%). Additionally, the reliable synaptic characteristics of these memory devices promise low-power neuromorphic computing. Our work provides a new device platform with switchable memory heterojunctions, applicable to high performance brain-inspired electronics and optoelectronics.

cond-mat.mtrl-sci↗

arXiv2025

Spin-orbit torque switching of N\'eel order in band-inverted antiferromagnetic bilayer MnBi$_2$Te$_4$

Magnetic topological insulators host exotic phenomena such as the quantum anomalous Hall effect and quantized magnetoelectric responses, but dynamic electrical control of their topological phases remains elusive. Here we demonstrate from first principles that spin-orbit torque enables direct electrical switching of the N\'eel configuration in intrinsic antiferromagnetic bilayer MnBi$_2$Te$_4$, thereby reconfiguring its boundary spectrum. A symmetry-allowed interband (time-reversal even) torque persists inside the bulk gap, and deterministically reverses the N\'eel order and layer-resolved Chern marker without free carriers. Upon doping, both interband and intraband torques are amplified, lowering the critical electric field for switching by two orders of magnitude. Together, these results establish two complementary regimes of control: dissipationless in-gap torques without Joule heating and enhanced current-induced torques, providing a robust route to manipulate a layer-resolved Chern marker and helical-like gapped edge modes in antiferromagnetic MnBi$_2$Te$_4$.

cond-mat.mes-hall↗