arXiv subjects

Wang Jian

Publications and source records attributed to Wang Jian.

14 recordsLinked to original sources

arXiv2026

GA-VisAgent: A Multi-Agent application for code generation and visualization in interactive learning

Geometric Algebra (GA) presents challenges to learners due to its highly abstract mathematical structure and complex operational rules, as translating algebraic manipulations into concrete geometric interpretations is a non-intuitive process when developing related code. Currently, some existing GA software packages rely on manually written scripts for code generation and visualization, but their high learning curve hinders widespread adoption. Meanwhile, methods based on Large Language Models (LLMs) often produce logical errors when generating specific GA scripts, such as GAALOPScript, resulting in generally low accuracy. To address these issues, this study proposes GA-VisAgent -- a multi-agent interactive learning application for GA code generation and visualization -- building upon a Geometric algebra large language model (GAGPT). Integrating task planning mechanisms with ReAct reasoning strategies, GA-VisAgent can decompose complex operations into five standardized subtasks, including core operations like geometric products, rotations, and reflections. It supports natural language and mathematical formulas as input to automatically generate executable code, accompanied by interactive visualizations to aid user comprehension. Experimental results show that GA-VisAgent achieved a 90% code generation success rate across 40 typical Conformal GA tasks, representing a 70% improvement over GPT-4o. This application introduces an extensible new paradigm for teaching GA and developing visualization tools for related mathematical concepts. The online service for this project will be available at http://gagis.cn/gacrac.

cs.LG↗

arXiv2026

Structure-Aware Distributed Backdoor Attacks in Federated Learning

While federated learning protects data privacy, it also makes the model update process vulnerable to long-term stealthy perturbations. Existing studies on backdoor attacks in federated learning mainly focus on trigger design or poisoning strategies, typically assuming that identical perturbations behave similarly across different model architectures. This assumption overlooks the impact of model structure on perturbation effectiveness. From a structure-aware perspective, this paper analyzes the coupling relationship between model architectures and backdoor perturbations. We introduce two metrics, Structural Responsiveness Score (SRS) and Structural Compatibility Coefficient (SCC), to measure a model's sensitivity to perturbations and its preference for fractal perturbations. Based on these metrics, we develop a structure-aware fractal perturbation injection framework (TFI) to study the role of architectural properties in the backdoor injection process. Experimental results show that model architecture significantly influences the propagation and aggregation of perturbations. Networks with multi-path feature fusion can amplify and retain fractal perturbations even under low poisoning ratios, while models with low structural compatibility constrain their effectiveness. Further analysis reveals a strong correlation between SCC and attack success rate, suggesting that SCC can predict perturbation survivability. These findings highlight that backdoor behaviors in federated learning depend not only on perturbation design or poisoning intensity but also on the interaction between model architecture and aggregation mechanisms, offering new insights for structure-aware defense design.

cs.LG↗

arXiv2026

Asteroseismology study of a new faint ZZ Ceti J053009.62+594557.0 discovered in WFST

In this work, we present a detailed asteroseismological analysis of WFST J053009.62+594557.0, a newly discovered faint pulsating white dwarf by the Wide Field Survey Telescope (WFST) with a Gaia G magnitude of 19.13. Analysis of two nights of high-precision WFST g band photometry reveals three significant pulsation frequencies with high signal-to-noise ratios. Follow-up P200/DBSP spectroscopy classifies the object as a DA white dwarf with Teff=11,609 $\pm$ 605 K and M = 0.63$\pm$ 0.22 $M_{\odot}$. To probe its internal structure, we construct asteroseismological models with the White Dwarf Evolution Code (WDEC). After exploring sufficient matching models, best-fitting solutions yield Teff=11,850$\pm$ 10 K and M = 0.600 $\pm$ 0.005 $M_{\odot}$, consistent with independent constraints from Gaia color-magnitude diagram, Gaia XP spectrum, P200 spectral fitting, SED fitting, and Gaia parallax. It has shown that the asteroseismological distance agrees with the Gaia parallax to 1.45\%.

astro-ph.SR↗

arXiv2024

ESC-Eval: Evaluating Emotion Support Conversations in Large Language Models

Emotion Support Conversation (ESC) is a crucial application, which aims to reduce human stress, offer emotional guidance, and ultimately enhance human mental and physical well-being. With the advancement of Large Language Models (LLMs), many researchers have employed LLMs as the ESC models. However, the evaluation of these LLM-based ESCs remains uncertain. Inspired by the awesome development of role-playing agents, we propose an ESC Evaluation framework (ESC-Eval), which uses a role-playing agent to interact with ESC models, followed by a manual evaluation of the interactive dialogues. In detail, we first re-organize 2,801 role-playing cards from seven existing datasets to define the roles of the role-playing agent. Second, we train a specific role-playing model called ESC-Role which behaves more like a confused person than GPT-4. Third, through ESC-Role and organized role cards, we systematically conduct experiments using 14 LLMs as the ESC models, including general AI-assistant LLMs (ChatGPT) and ESC-oriented LLMs (ExTES-Llama). We conduct comprehensive human annotations on interactive multi-turn dialogues of different ESC models. The results show that ESC-oriented LLMs exhibit superior ESC abilities compared to general AI-assistant LLMs, but there is still a gap behind human performance. Moreover, to automate the scoring process for future ESC models, we developed ESC-RANK, which trained on the annotated data, achieving a scoring performance surpassing 35 points of GPT-4. Our data and code are available at https://github.com/AIFlames/Esc-Eval.

cs.CL↗

arXiv2024

Long time behavior of one-dimensional McKean-Vlasov SDEs with common noise

In this paper, by introducing a new type asymptotic coupling by reflection, we explore the long time behavior of random probability measure flows associated with a large class of one-dimensional McKean-Vlasov SDEs with common noise. Concerning the McKean-Vlasov SDEs with common noise under consideration in the present work, in contrast to the existing literature, the drift terms are much more general rather than of the convolution form, and, in particular, can be of polynomial growth with respect to the spatial variables, and moreover idiosyncratic noises are allowed to be of multiplicative type. Most importantly, our main result indicates that both the common noise and the idiosyncratic noise facilitate the exponential contractivity of the associated measure-valued processes.

math.PR↗

arXiv2024

$L^2$-exponential ergodicity of stochastic Hamiltonian systems with $α$-stable Lévy noises

Based on the hypocoercivity approach due to Villani \cite{Villani}, Dolbeault, Mouhot and Schmeiser \cite{DMS} established a new and simple framework to investigate directly the $L^2$-exponential convergence to the equilibrium for the solution to the kinetic Fokker-Planck equation. Nowadays, the general framework advanced in \cite{DMS} is named as the DMS framework for hypocoercivity. Subsequently, Grothaus and Stilgenbauer \cite{Grothaus} builded a dual version of the DMS framework in the kinetic Fokker-Planck setting. No matter what the abstract DMS framework in \cite{DMS} and the dual counterpart in \cite{Grothaus}, the densely defined linear operator involved is assumed to be decomposed into two parts, where one part is symmetric and the other part is anti-symmetric. Thus, the existing DMS framework is not applicable to investigate the $L^2$-exponential ergodicity for stochastic Hamiltonian systems with $α$-stable Lévy noises, where one part of the associated infinitesimal generators is anti-symmetric whereas the other part is not symmetric. In this paper, we shall develop a dual version of the DMS framework in the fractional kinetic Fokker-Planck setup, where one part of the densely defined linear operator under consideration need not to be symmetric. As a direct application, we explore the $L^2$-exponential ergodicity of stochastic Hamiltonian systems with $α$-stable Lévy noises. The proof is also based on Poincaré inequalities for non-local stable-like Dirichlet forms and the potential theory for fractional Riesz potentials.

math.PR↗

arXiv2023

Exponential ergodicity of Lévy driven Langevin dynamics with singular potentials

In this paper, we address exponential ergodicity for Lévy driven Langevin dynamics with singular potentials, which can be used to model the time evolution of a molecular system consisting of $N$ particles moving in $\R^d$ and subject to discontinuous stochastic forces. In particular, our results are applicable to the singular setups concerned with not only the Lennard-Jones-like interaction potentials but also the Coulomb potentials. In addition to Harris' theorem, the approach is based on novel constructions of proper Lyapunov functions (which are completely different from the setting for Langevin dynamics driven by Brownian motions), on invoking the Hörmander theorem for non-local operators and on solving the issue on an approximate controllability of the associated deterministic system as well as on exploiting the time-change idea.

math.PR↗

arXiv2023

Two-sided heat kernel estimates for Schrödinger operators with unbounded potentials

Consider the Schrödinger operator $ \mathcal L^V=-Δ+V $ on $\R^d$, where $V:\R^d\to [0,\infty)$ is a nonnegative and locally bounded potential on $\R^d$ so that for all $x\in \R^d$ with $|x|\ge 1$, $c_1g(|x|)\le V(x)\le c_2g(|x|)$ with some constants $c_1,c_2>0$ and a nondecreasing and strictly positive function $g:[0,\infty)\to [1,+\infty)$ that satisfies $g(2r)\le c_0 g(r)$ for all $r>0$ and $\lim_{r\to \infty} g(r)=\infty.$ We establish global in time and qualitatively sharp bounds for the heat kernel of the associated Schrödinger semigroup by the probabilistic method. In particular, we can present global in space and time two-sided bounds of heat kernel even when the Schrödinger semigroup is not intrinsically ultracontractive. Furthermore, two-sided estimates for the corresponding Green's functions are also obtained.

math.PR↗

arXiv2022

Quantum Symbolic Execution

With advances in quantum computing, researchers can now write and run many quantum programs. However, there is still a lack of effective methods for debugging quantum programs. In this paper, quantum symbolic execution (QSE) is proposed to generate test cases, which helps to finding bugs in quantum programs. The main idea of quantum symbolic execution is to find the suitable test cases from all possible ones (i.e. test case space). It is different from the way of classical symbol execution, which gets test cases by calculating instead of searching. QSE utilizes quantum superposition and parallelism to store the test case space with only a few qubits. According to the conditional statements in the debugged program, the test case space is continuously divided into subsets, subsubsets and so on. Elements in the same subset are suitable test cases that can test the corresponding branch in the code to be tested. QSE not only provides a possible way to debug quantum programs, but also avoids the difficult problem of solving constraints in classical symbolic execution.

quant-ph↗

arXiv2022

Three-point Step Size Gradient Method with Relaxed Generalized Armijo Step Size Rule

Based on differences of points and differences of gradients over the most recent three iterations, together with the Taylor's theorem, two forms of the quasi-Newton equations at the recent iteration are constructed. By using the two forms of the quasi-Newton equation and the method of least squares, three-point step size gradient methods for solving unconstrained optimization problem are proposed. It is proved by using the relaxed generalized Armijo step size rule that the new method is of global convergence properties if the gradient function is uniformly continuous. Moreover, it is shown that, when the objective function is pseudo-convex (quasi-convex) function, the new method has strong convergence results. In addition, it is also shown under some suitable assumptions that the new method is of super-linear and linear convergence. Although multi-piont information is used, TBB has the feature of simplicity, low memory requirement and only first order information being used, the new method is very suitable for solving large-scale optimization problems. Numerical experiments are provided and the efficiency, robustness and analysis of TBB are confirmed.

math.OC↗

arXiv2020

Auto-weighting for Breast Cancer Classification in Multimodal Ultrasound

Breast cancer is the most common invasive cancer in women. Besides the primary B-mode ultrasound screening, sonographers have explored the inclusion of Doppler, strain and shear-wave elasticity imaging to advance the diagnosis. However, recognizing useful patterns in all types of images and weighing up the significance of each modality can elude less-experienced clinicians. In this paper, we explore, for the first time, an automatic way to combine the four types of ultrasonography to discriminate between benign and malignant breast nodules. A novel multimodal network is proposed, along with promising learnability and simplicity to improve classification accuracy. The key is using a weight-sharing strategy to encourage interactions between modalities and adopting an additional cross-modalities objective to integrate global information. In contrast to hardcoding the weights of each modality in the model, we embed it in a Reinforcement Learning framework to learn this weighting in an end-to-end manner. Thus the model is trained to seek the optimal multimodal combination without handcrafted heuristics. The proposed framework is evaluated on a dataset contains 1616 set of multimodal images. Results showed that the model scored a high classification accuracy of 95.4%, which indicates the efficiency of the proposed method.

eess.IV↗

arXiv2018

The focusing effect of electron flow and negative refraction in three dimensional topological insulators

We studied the focusing effect of electron flow induced by a single p-n junction (PNJ) in three-dimensional topological insulator. It is found that the electrons flowing from the n region can be focused at the symmetric position in the p region, acting as a perfect Veselago lens, regardless whether the incident energy is within or beyond the bulk energy gap. In the former case, the focusing effect occurs only in the surfaces. While in the latter case, the focusing effect occurs beyond the surfaces. These results show that the focusing effect of electron flow is a general phenomenon. It means the negative refraction may arise in all materials that are described by the massive or massless Dirac equation of 2D or beyond 2D system. Furthermore, we also find the focusing effect is robust in resisting the moderate random disorders. Finally, in the presence of a weak perpendicular magnetic field, the focusing effect remains well except that the position of the focal point is deflected by the transverse Lorentz force. Due to the finite size effect, the position of focal point oscillates periodically with a period of Delta B.

cond-mat.mes-hall↗

arXiv2018

Influence of magnetic disorders on Quantum Anomalous Hall Effect in Magnetic Topological Insulator Films beyond the two-dimensional limit

Quantum anomalous Hall effect (QAHE) has been experimentally realized in magnetic topological insulator (MTI) thin films fabricated on magnetically doped (Bi,Sb)2Te3. In a MTI thin film with the magnetic easy axis along the normal direction (z-direction), orientations of magnetic dopants are randomly distributed around the magnetic easy axis, acting as magnetic disorders. With the aid of the non-equilibrium Green's function and Landauer-Buttiker formalism, we numerically study the influence of magnetic disorders on QAHE in a MTI thin film modeled by a three-dimensional tight-binding Hamiltonian. It is found that, due to the existence of gapless side surface states, QAHE is protected even in the presence of magnetic disorders as long as the z-component of magnetic moment of all magnetic dopants are positive. More importantly, such magnetic disorders also suppress the dissipation of the chiral edge states and enhance the quality of QAHE in MTI films. In addition, the effect of magnetic disorders depends very much on the film thickness, and the optimal influence is achieved at certain thickness. These findings are new features for QAHE in three-dimensional systems, not present in two-dimensional systems.

cond-mat.mes-hall↗

arXiv2006

Grid-independent Issue in Numerical Heat Transfer

Grid independent is associated with the accuracy or even rationality of numerical results. This paper takes two-dimensional steady heat transfer for example to reveal the effect of grid resolution on numerical results. The law of grid dependence is obtained and a simple mathematical formula is presented. The production acquired here can be used as the guidance in choosing grid density in numerical simulation and get exact grid independent value without using infinite fine grid. Through analyzing grid independent, we can find the minimum number of grid cells that is needed to get grid-independent results. Such strategy can save computational resource while ensure a rational computational result.

math-ph↗