arXiv subjects

Xiaojing Dong

Publications and source records attributed to Xiaojing Dong.

10 recordsLinked to original sources

arXiv2026

A unifying framework for quantum algorithms for time-dependent non-unitary dynamics

Quantum algorithms for simulating linear differential equations have attracted growing interest, driven by applications ranging from Hamiltonian dynamics to general non-unitary dynamics. While time-independent cases are well studied, time-dependent non-unitary dynamics remains considerably less explored, and it is unclear how to systematically adapt existing solvers for time-independent systems to such problems. In this work, we address this gap by introducing an autonomization framework based on the clock-variable formulation, a technique originally developed for time-dependent Hamiltonian systems in~\cite{CJL23TimeSchr}. By lifting the original non-autonomous system to an autonomous transport-type equation on an extended space and applying the Fourier spectral discretization in the clock variable, we obtain an explicit time-independent linear system, together with a suitable initial state and a recovery map for the target solution. Crucially, this formulation decouples the treatment of time dependence from the choice of the quantum ODE solver, thereby enabling the direct application of existing solvers designed for time-independent systems to the resulting autonomous problem. We combine this framework with Schrödingerization and a Taylor-expansion-based quantum ODE solver. In the Schrödingerization-based combination, our complexity analysis shows that the precision dependence can scale as $\log^{5/4}(1/\varepsilon)$, improving upon the $\log^2(1/\varepsilon)$ scaling found in existing approaches. Numerical experiments validate the autonomization formulation and confirm the successful recovery of the target solution.

quant-ph↗

arXiv2026

$L^{2}$-Supercritical Nonlinear Klein-Gordon System with Quadratic Asymmetric Interaction

In this paper we investigate the global existence, blow-up and standing waves for the $L^{2}$-supercritical nonlinear Klein-Gordon equations with quadratic asymmetric interaction (LSNKG). First, by introducing a suitable auxiliary functional, using concavity analysis and virial estimates, we obtain a finite time blow-up result for solutions to the Cauchy problem of (LSNKG) when the initial energy is negative. Next, by defining appropriate functionals, manifolds and a constrained variational problem, we employ variational method and the Lagrange multiplier method to derive the existence of ground state solutions for the corresponding nonlinear elliptic (steady-state) system, thereby to establish the existence of standing wave with the ground state for (LSNKG). Then, using the variational characterization of the ground state solutions and constructing invariant sets under the flow generated by the Cauchy problem for (LSNKG), we combine the potential well argument with concavity analysis to establish a sharp threshold between blow-up in finite time and global existence. Finally, by exploiting the variational characterization of the ground state, introducing appropriate scalings, and choosing suitable initial data based on the ground state, we justify the instability of standing wave with the ground state for (LSNKG).

math.AP↗

arXiv2026

JD Oxygen AI Item Center (Oxygen AIIC) V1: An Industrial-Scale LLM/VLM-Centric Solution for Item Understanding, Management, and Applications

JD$.$com, one of the world's largest e-commerce platforms, serves over 700 million active users and millions of merchants, with a catalog of tens of billions of SKUs. At this scale, high-quality, structured item knowledge underpins a better consumer experience, lower management costs, and higher operational efficiency-yet producing and serving it poses three industrial-scale challenges: fast-emerging concepts, high-quality knowledge production for massive SKUs, and diverse downstream requirements. To address these challenges, we present the JD Oxygen AI Item Center (Oxygen AIIC), an industrial-scale platform built on LLMs/VLMs for item-knowledge production and service. Oxygen AIIC is built around four core pillars: (i) ontology engineering driven by efficient human-AI collaboration, which supports the dynamic evolution and agile expansion of an ontology with millions of entries; (ii) a "Semantic Search then Discrimination"(S2D) knowledge identification architecture that, combined with throughput improvement strategies, enables scalable, extensible, and high-throughput AI Item Library production for tens of billions of SKUs; (iii) self-evolving item-understanding LLMs/VLMs that improve in a stable and controllable manner, enabling knowledge production with 94.2% precision and 82.8% recall; and (iv) a unified item tunnel that serves as the data and service hub. Oxygen AIIC now covers tens of thousands of JD categories and processes hundreds of millions of item updates per day on Huawei Ascend NPUs. It has accumulated hundreds of billions of item-knowledge assets. Deployed across core business scenarios-including search, recommendation, operations, category planning-Oxygen AIIC has delivered measurable gains at scale. Search-traffic coverage reaches 80.4%, item-information quality issues drop by 37%, the automated fill rate of core attributes during item listing exceeds 80%.

cs.AI↗

arXiv2026

The grad-div conforming virtual element method for the quad-div problem in three dimensions

We propose a new stable variational formulation for the quad-div problem in three dimensions and prove its well-posedness. Using this weak form, we develop and analyze the $\boldsymbol{H}(\operatorname{grad-div})$-conforming virtual element method of arbitrary approximation orders on polyhedral meshes. Three families of $\boldsymbol{H}(\operatorname{grad-div})$-conforming virtual elements are constructed based on the structure of a de Rham sub-complex with enhanced smoothness, resulting in an exact discrete virtual element complex. In the lowest-order case, the simplest element has only one degree of freedom at each vertex and face, respectively. We rigorously prove the interpolation error estimates, the stability of discrete bilinear forms, the well-posedness of discrete formulation and the optimal error estimates. Some numerical examples are shown to verify the theoretical results.

math.NA↗

arXiv2025

A grad-curl conforming virtual element method for a grad-curl problem linking the 3D quad-curl problem and Stokes system

Based on the Stokes complex with vanishing boundary conditions and its dual complex, we reinterpret a grad-curl problem arising from the quad-curl problem as a new vector potential formulation of the three-dimensional Stokes system. By extending the analysis to the corresponding non-homogeneous problems and the accompanying trace complex, we construct a novel $\boldsymbol{H}(\operatorname{grad-curl})$-conforming virtual element space with arbitrary approximation order that satisfies the exactness of the associated discrete Stokes complex. In the lowest-order case, three degrees of freedom are assigned to each vertex and one to each edge. For the grad-curl problem, we rigorously establish the interpolation error estimates, the stability of discrete bilinear forms, and the convergence of the proposed element on polyhedral meshes. As a discrete vector potential formulation of the Stokes problem, the resulting system is pressure-decoupled and symmetric positive definite. Some numerical examples are presented to verify the theoretical results.

math.NA↗

arXiv2025

MEF: A Systematic Evaluation Framework for Text-to-Image Models

Rapid advances in text-to-image (T2I) generation have raised higher requirements for evaluation methodologies. Existing benchmarks center on objective capabilities and dimensions, but lack an application-scenario perspective, limiting external validity. Moreover, current evaluations typically rely on either ELO for overall ranking or MOS for dimension-specific scoring, yet both methods have inherent shortcomings and limited interpretability. Therefore, we introduce the Magic Evaluation Framework (MEF), a systematic and practical approach for evaluating T2I models. First, we propose a structured taxonomy encompassing user scenarios, elements, element compositions, and text expression forms to construct the Magic-Bench-377, which supports label-level assessment and ensures a balanced coverage of both user scenarios and capabilities. On this basis, we combine ELO and dimension-specific MOS to generate model rankings and fine-grained assessments respectively. This joint evaluation method further enables us to quantitatively analyze the contribution of each dimension to user satisfaction using multivariate logistic regression. By applying MEF to current T2I models, we obtain a leaderboard and key characteristics of the leading models. We release our evaluation framework and make Magic-Bench-377 fully open-source to advance research in the evaluation of visual generative models.

cs.AI↗

arXiv2024

Conservative nonconforming virtual element method for stationary incompressible magnetohydrodynamics

In this paper, we propose a conservative nonconforming virtual element method for the full stationary incompressible magnetohydrodynamics model. We leverage the virtual element satisfactory divergence-free property to ensure mass conservation for the velocity field. The condition of the well-posedness of the proposed method, as well as the stability are derived. We establish optimal error estimates in the discrete energy norm for both the velocity and magnetic field. Furthermore, by employing a new technique, we obtain the optimal error estimates in $L^2$-norm without any additional conditions. Finally, numerical experiments are presented to validate the theoretical analysis. In the implementation process, we adopt the effective Oseen iteration to handle the nonlinear system.

math.NA↗

arXiv2024

A virtual element method with IMEX-SAV scheme for the incompressible magnetohydrodynamics equations

This paper proposes a virtual element method (VEM) combined with a second-order implicit-explicit scheme based on the scalar auxiliary variable (SAV) method for the incompressible magnetohydrodynamics (MHD) equations. We employ the BDF2 scheme for time discretization and a conservative VEM for spatial discretization, in which the mass conservation in the velocity field is kept by taking advantage of the virtual element method's adaptability and its divergence-free characteristics. In our scheme, the nonlinear terms are handled explicitly using the SAV method, and the magnetic field is decoupled from the velocity and pressure. This decoupling only requires solving a sequence of linear systems with constant coefficient at each time step. The stability estimate of the fully discrete scheme is developed, demonstrating the scheme is unconditionally stable. Moreover, rigorous error estimates for the velocity and magnetic field are provided. Finally, numerical experiments are presented to verify the valid of theoretical analysis.

math.NA↗

arXiv2024

Investigation on a quantum algorithm for linear differential equations

Ref.[BCOW17] introduced a pioneering quantum approach (coined BCOW algorithm) for solving linear differential equations with optimal error tolerance. Originally designed for a specific class of diagonalizable linear differential equations, the algorithm was extended by Krovi in [Kro23] to encompass broader classes, including non-diagonalizable and even singular matrices. Despite the common misconception, the original algorithm is indeed applicable to non-diagonalizable matrices, with diagonalisation primarily serving for theoretical analyses to establish bounds on condition number and solution error. By leveraging basic estimates from [Kro23], we derive bounds comparable to those outlined in the Krovi algorithm, thereby reinstating the advantages of the BCOW approach. Furthermore, we extend the BCOW algorithm to address time-dependent linear differential equations by transforming non-autonomous systems into higher-dimensional autonomous ones, a technique also applicable for the Krovi algorithm.

quant-ph↗

arXiv2018

Dynamic Hierarchical Empirical Bayes: A Predictive Model Applied to Online Advertising

Predicting keywords performance, such as number of impressions, click-through rate (CTR), conversion rate (CVR), revenue per click (RPC), and cost per click (CPC), is critical for sponsored search in the online advertising industry. An interesting phenomenon is that, despite the size of the overall data, the data are very sparse at the individual unit level. To overcome the sparsity and leverage hierarchical information across the data structure, we propose a Dynamic Hierarchical Empirical Bayesian (DHEB) model that dynamically determines the hierarchy through a data-driven process and provides shrinkage-based estimations. Our method is also equipped with an efficient empirical approach to derive inferences through the hierarchy. We evaluate the proposed method in both simulated and real-world datasets and compare to several competitive models. The results favor the proposed method among all comparisons in terms of both accuracy and efficiency. In the end, we design a two-phase system to serve prediction in real time.

stat.ML↗