arXiv subjects

Hua Tian

Publications and source records attributed to Hua Tian.

8 recordsLinked to original sources

arXiv2026

Mathematical Basis for Analyzing Superconducting Phase Transitions Using Catastrophe Theory

We establish a rigorous mathematical bridge from quantum many-body path integrals to the cusp catastrophe model by Lyapunov-Schmidt reduction, which provides a theoretical foundation for analyzing superconducting phase transition using the catastrophe theory. First, it is proved that, near the critical point the infinite-dimensional effective action is diffeomorphic to a finite-dimensional catastrophe. Secondly, starting from Ginzburg-Landau free energy functional, the Euler-Lagrange partial differential equation can be reduced to the cusp catastrophe model. Thirdly, the fermionic imaginary-time path integral to the cusp catastrophe is derived through the Hubbard-Stratonovich transformation, Matsubara frequency expansion, and Grassmann algebra. Furthermore, we connect this framework with the adsorption potential theory we proposed, elucidating the catastrophic topological nature of the electron pairing mechanism in high-temperature superconductivity. The precise microscopic derivation of the adsorption potential from first-principles electronic structure calculations would strengthen the predictive power of the theory.

cond-mat.supr-con↗

arXiv2026

Interfacial charge-induced adsorption mode for electron pairing in high-temperature superconductors

The electron pairing mechanism by the interfacial charge-induced adsorption mode of high-temperature superconductors is revealed. For the YBCO superconductors, the coupling of electrons and valence-flexible state of oxygen ions forms a charge-regulated interfacial layer induced by the adsorption potential, and electrons are paired by sharing the optimized interfacial structure and exchanging the adsorption mode, generating strong attraction to form Cooper pairs. Then the effective interaction potential between electrons is exactly derived in details, as well as the electron-adsorption-mode coupling strength, in which the adsorption coupling constant is up to 43.4. Furthermore, we verify that d-wave come from the anisotropy of interfacial adsorption forces, and explain the pseudo-energy gap behavior. By using the one-dimensional Ginzburg-Landau equation in the absence of a magnetic field, we obtain the coherence length expression, and the coherence length calculated is very close to the literature results. By establishing the energy gap equation, we obtain the superconducting gap , which is very close to the measured result of 17meV by Scanning Tunneling Microscopy/Spectroscopy. These quantitative predictions close to the known results could verify our theoretical framework.

cond-mat.supr-con↗

arXiv2026

Bilattice-Catastrophe Isomorphism for Four-Valued Logic in Digital Systems

Belnap's four-valued logic, distinguished by its inherent bilattice structure, provides a natural algebraic bridge between discrete Four-valued logic (4VL) in circuit and continuous catastrophe theory (CT). Building on the rigorous verification of the bilattice-catastrophe isomorphism theorem, we establish a categorical correspondence spanning the catastrophe category, interlaced bilattice category, and 4VL category, with the cusp catastrophe emerging as the canonical CT counterpart to 4VL.This unification provides a foundational framework for explaining 4VL's robustness. Crucially, we demonstrate that the four-valued algebra FOUR is the minimal complete algebraic structure capable of describing continuous-discrete interfaces with involution symmetry. Unlike the empirical adoption of X and Z in engineering practice, our work reveals their mathematical necessity: X and Z are topological invariants of discretized continuous dynamical systems, encoding fundamental properties of catastrophe-induced discontinuities. The work enables cross-disciplinary extensions to uncertainty propagation, complex system modeling, and fault-tolerant design.

cond-mat.dis-nn↗

arXiv2025

Deep Learning-Based Automatic Diagnosis System for Developmental Dysplasia of the Hip

Objective: The clinical diagnosis of developmental dysplasia of the hip (DDH) typically involves manually measuring key radiological angles -- Center-Edge (CE), Tonnis, and Sharp angles -- from pelvic radiographs, a process that is time-consuming and susceptible to variability. This study aims to develop an automated system that integrates these measurements to enhance the accuracy and consistency of DDH diagnosis. Methods and procedures: We developed an end-to-end deep learning model for keypoint detection that accurately identifies eight anatomical keypoints from pelvic radiographs, enabling the automated calculation of CE, Tonnis, and Sharp angles. To support the diagnostic decision, we introduced a novel data-driven scoring system that combines the information from all three angles into a comprehensive and explainable diagnostic output. Results: The system demonstrated superior consistency in angle measurements compared to a cohort of eight moderately experienced orthopedists. The intraclass correlation coefficients for the CE, Tonnis, and Sharp angles were 0.957 (95% CI: 0.952--0.962), 0.942 (95% CI: 0.937--0.947), and 0.966 (95% CI: 0.964--0.968), respectively. The system achieved a diagnostic F1 score of 0.863 (95% CI: 0.851--0.876), significantly outperforming the orthopedist group (0.777, 95% CI: 0.737--0.817, p = 0.005), as well as using clinical diagnostic criteria for each angle individually (p<0.001). Conclusion: The proposed system provides reliable and consistent automated measurements of radiological angles and an explainable diagnostic output for DDH, outperforming moderately experienced clinicians. Clinical impact: This AI-powered solution reduces the variability and potential errors of manual measurements, offering clinicians a more consistent and interpretable tool for DDH diagnosis.

eess.IV↗

arXiv2023

Machine learning of percolation models using graph convolutional neural networks

Percolation is an important topic in climate, physics, materials science, epidemiology, finance, and so on. Prediction of percolation thresholds with machine learning methods remains challenging. In this paper, we build a powerful graph convolutional neural network to study the percolation in both supervised and unsupervised ways. From a supervised learning perspective, the graph convolutional neural network simultaneously and correctly trains data of different lattice types, such as the square and triangular lattices. For the unsupervised perspective, combining the graph convolutional neural network and the confusion method, the percolation threshold can be obtained by the "W" shaped performance. The finding of this work opens up the possibility of building a more general framework that can probe the percolation-related phenomenon.

cond-mat.stat-mech↗

arXiv2022

Facilitating Self-monitored Physical Rehabilitation with Virtual Reality and Haptic feedback

Physical rehabilitation is essential to recovery from joint replacement operations. As a representation, total knee arthroplasty (TKA) requires patients to conduct intensive physical exercises to regain the knee's range of motion and muscle strength. However, current joint replacement physical rehabilitation methods rely highly on therapists for supervision, and existing computer-assisted systems lack consideration for enabling self-monitoring, making at-home physical rehabilitation difficult. In this paper, we investigated design recommendations that would enable self-monitored rehabilitation through clinical observations and focus group interviews with doctors and therapists. With this knowledge, we further explored Virtual Reality(VR)-based visual presentation and supplemental haptic motion guidance features in our implementation VReHab, a self-monitored and multimodal physical rehabilitation system with VR and vibrotactile and pneumatic feedback in a TKA rehabilitation context. We found that the third point of view real-time reconstructed motion on a virtual avatar overlaid with the target pose effectively provides motion awareness and guidance while haptic feedback helps enhance users' motion accuracy and stability. Finally, we implemented \systemname to facilitate self-monitored post-operative exercises and validated its effectiveness through a clinical study with 10 patients.

cs.HC↗

arXiv2020

Deep Learning-based End-to-end Diagnosis System for Avascular Necrosis of Femoral Head

As the first diagnostic imaging modality of avascular necrosis of the femoral head (AVNFH), accurately staging AVNFH from a plain radiograph is critical yet challenging for orthopedists. Thus, we propose a deep learning-based AVNFH diagnosis system (AVN-net). The proposed AVN-net reads plain radiographs of the pelvis, conducts diagnosis, and visualizes results automatically. Deep convolutional neural networks are trained to provide an end-to-end diagnosis solution, covering tasks of femoral head detection, exam-view identification, side classification, AVNFH diagnosis, and key clinical notes generation. AVN-net is able to obtain state-of-the-art testing AUC of 0.97 (95% CI: 0.97-0.98) in AVNFH detection and significantly greater F1 scores than less-to-moderately experienced orthopedists in all diagnostic tests (p<0.01). Furthermore, two real-world pilot studies were conducted for diagnosis support and education assistance, respectively, to assess the utility of AVN-net. The experimental results are promising. With the AVN-net diagnosis as a reference, the diagnostic accuracy and consistency of all orthopedists considerably improved while requiring only 1/4 of the time. Students self-studying the AVNFH diagnosis using AVN-net can learn better and faster than the control group. To the best of our knowledge, this study is the first research on the prospective use of a deep learning-based diagnosis system for AVNFH by conducting two pilot studies representing real-world application scenarios. We have demonstrated that the proposed AVN-net achieves expert-level AVNFH diagnosis performance, provides efficient support in clinical decision-making, and effectively passes clinical experience to students.

eess.IV↗

arXiv2012

Segmentation of ultrasound images of thyroid nodule for assisting fine needle aspiration cytology

The incidence of thyroid nodule is very high and generally increases with the age. Thyroid nodule may presage the emergence of thyroid cancer. The thyroid nodule can be completely cured if detected early. Fine needle aspiration cytology is a recognized early diagnosis method of thyroid nodule. There are still some limitations in the fine needle aspiration cytology, and the ultrasound diagnosis of thyroid nodule has become the first choice for auxiliary examination of thyroid nodular disease. If we could combine medical imaging technology and fine needle aspiration cytology, the diagnostic rate of thyroid nodule would be improved significantly. The properties of ultrasound will degrade the image quality, which makes it difficult to recognize the edges for physicians. Image segmentation technique based on graph theory has become a research hotspot at present. Normalized cut (Ncut) is a representative one, which is suitable for segmentation of feature parts of medical image. However, how to solve the normalized cut has become a problem, which needs large memory capacity and heavy calculation of weight matrix. It always generates over segmentation or less segmentation which leads to inaccurate in the segmentation. The speckle noise in B ultrasound image of thyroid tumor makes the quality of the image deteriorate. In the light of this characteristic, we combine the anisotropic diffusion model with the normalized cut in this paper. After the enhancement of anisotropic diffusion model, it removes the noise in the B ultrasound image while preserves the important edges and local details. This reduces the amount of computation in constructing the weight matrix of the improved normalized cut and improves the accuracy of the final segmentation results. The feasibility of the method is proved by the experimental results.

cs.CV↗