arXiv subjects

Yunjie Wang

Publications and source records attributed to Yunjie Wang.

4 recordsLinked to original sources

arXiv2026

Thermo-responsive self-oscillating gel: mathematical model and theoretical analysis

Internally heated LCST thermo-responsive gels can show self-sustained swelling and collapse oscillations through feedback between temperature-induced collapse and collapse-suppressed heating. In this work, a minimal two-variable model is developed by coupling gel swelling dynamics with a lumped thermal balance. The analysis shows that stable large-amplitude oscillations are mainly controlled by global bifurcations of limit cycles, rather than by the local Hopf bifurcation. The Hopf bifurcation is subcritical in the studied parameter range, leading to a broad coexistence region where a stable fixed point and a stable limit cycle are both possible. The oscillatory behavior remains robust for different heating-gate functions, indicating that local linear instability is neither necessary nor sufficient for self-oscillation. Fast-slow analysis further shows that the oscillation period is mainly governed by the cooling rate, while the amplitude is determined by the geometry of the swelling equilibrium manifold. These results clarify the bifurcation mechanism of thermo-responsive gel oscillations and provide guidance for controlling their period, amplitude, and waveform.

cond-mat.soft↗

arXiv2025

On the Generalized Harmonic Measure

The axiomatization of harmonic measure theory is established, including the generalized maximum principle, Harnack inequality and Harnack principle. As the applications of the established theory, Dahlberg's theory is generalized. The theory provides an interpretation from the measure theory view point of the elliptic equation theory.

math.FA↗

arXiv2024

Interpretable QSPR Modeling using Recursive Feature Machines and Multi-scale Fingerprints

This study pioneers the application of Recursive Feature Machines (RFM) in QSPR modeling, introducing a tailored feature importance analysis approach to enhance interpretability. By leveraging deep feature learning through AGOP, RFM achieves state-of-the-art (SOTA) results in predicting molecular properties, as demonstrated through solubility prediction across nine benchmark datasets. To capture a wide array of structural information, we employ diverse molecular representations, including MACCS keys, Morgan fingerprints, and a custom multi-scale hybrid fingerprint (HF) derived from global descriptors and SMILES local fragmentation techniques. Notably, the HF offers significant advantages over MACCS and Morgan fingerprints in revealing structural determinants of molecular properties. The feature importance analysis in RFM provides robust local and global explanations, effectively identifying structural features that drive molecular behavior and offering valuable insights for drug development. Additionally, RFM demonstrates strong redundancy-filtering abilities, as model performance remains stable even after removing redundant features within custom fingerprints. Importantly, RFM introduces the deep feature learning capabilities of the average gradient outer product (AGOP) matrix into ultra-fast kernel machine learning, to imbue kernel machines with interpretable deep feature learning capabilities. We extend this approach beyond the Laplace Kernel to the Matern, Rational Quadratic, and Gaussian kernels, to find that the Matern and Laplace kernels deliver the best performance, thus reinforcing the flexibility and effectiveness of AGOP in RFM. Experimental results show that RFM-HF surpasses both traditional machine learning models and advanced graph neural networks.

q-bio.BM↗

arXiv2017

Refined Bounds on the Number of Distinct Eigenvalues of a Matrix After Perturbation

The eigenproblem of low-rank updated matrices are of crucial importance in many applications. Recently, an upper bound on the number of distinct eigenvalues of a perturbed matrix was established. The result can be applied to estimate the number of Krylov iterations required for solving a perturbed linear system. In this paper, we revisit this problem and establish some refined bounds. Some {\it a prior} upper bounds that only rely on the information of the matrix in question and the low-rank update are provided. Examples show the superiority of our theoretical results over the existing ones. The number of distinct singular values of a matrix after perturbation is also investigated.

math.NA↗