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Dat Cao

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Published work

3 published item(s)

preprint2026arXiv

JI-ADF: Joint-Individual Learning with Adaptive Decision Fusion for Multimodal Skin Lesion Classification

Skin lesion classification is essential for early dermatological diagnosis, yet many existing computer-aided systems rely primarily on dermoscopic images and underutilize the multimodal evidence routinely available in clinical practice. To address this gap, we propose \textbf{JI-ADF}, a trimodal deep learning framework that integrates dermoscopic images, clinical photographs, and structured patient metadata for clinically grounded skin lesion classification. The proposed architecture combines joint multimodal representation learning with modality-specific auxiliary supervision and an adaptive decision fusion mechanism that dynamically calibrates modality contributions on a per-sample basis. To enhance cross-modal reasoning while preserving modality-specific evidence, we further introduce a multimodal fusion attention (MMFA) module. We evaluate JI-ADF on the large-scale MILK10k benchmark, which reflects real-world clinical acquisition conditions and severe class imbalance. The proposed method demonstrates strong and well-balanced performance across lesion categories, improving sensitivity and Dice score while maintaining high specificity and good calibration. Extensive analyses, including modality ablation, calibration evaluation, and Grad-CAM visualization, further confirm the robustness and clinically meaningful behavior of the model. These results indicate that JI-ADF provides a reliable and practical foundation for multimodal skin lesion classification in real-world clinical settings.

preprint2020arXiv

Asymptotic expansions with exponential, power, and logarithmic functions for non-autonomous nonlinear differential equations

This paper develops further and systematically the asymptotic expansion theory that was initiated by Foias and Saut in [11]. We study the long-time dynamics of a large class of dissipative systems of nonlinear ordinary differential equations with time-decaying forcing functions. The nonlinear term can be, but not restricted to, any smooth vector field which, together with its first derivative, vanishes at the origin. The forcing function can be approximated, as time tends to infinity, by a series of functions which are coherent combinations of exponential, power and iterated logarithmic functions. We prove that any decaying solution admits an asymptotic expansion, as time tends to infinity, corresponding to the asymptotic structure of the forcing function. Moreover, these expansions can be generated by more than two base functions and go beyond the polynomial formulation imposed in previous work.

preprint2016arXiv

Weighted-$W^{1,p}$ estimates for weak solutions of degenerate and singular elliptic equations

Global weighted $L^{p}$-estimates are obtained for the gradient of solutions to a class of linear singular, degenerate elliptic Dirichlet boundary value problems over a bounded non-smooth domain. The coefficient matrix is symmetric, nonnegative definite, and both its smallest and largest eigenvalues are proportion to a weight in a Muckenhoupt class. Under a smallness condition on the mean oscillation of the coefficients with the weight and a Reifenberg flatness condition on the boundary of the domain, we establish a weighted gradient estimate for weak solutions of the equation. A class of degenerate coefficients satisfying the smallness condition is characterized. A counter example to demonstrate the necessity of the smallness condition on the coefficients is given. Our $W^{1,p}$-regularity estimates can be viewed as the Sobolev's counterpart of the Hölder's regularity estimates established by B. Fabes, C. E. Kenig, and R. P. Serapioni in 1982.