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Wang Jian

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Machine Learning astro-ph.SR Computer Vision eess.IV math.AP math.FA math.PR

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preprint2026arXiv

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\%.

preprint2026arXiv

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.

preprint2023arXiv

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.

preprint2020arXiv

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.

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