🍩 Database of Original & Non-Theoretical Uses of Topology
(found 3 matches in 0.001569s)
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Quantitative and Interpretable Order Parameters for Phase Transitions From Persistent Homology (2020)
Alex Cole, Gregory J. Loges, Gary ShiuAbstract
We apply modern methods in computational topology to the task of discovering and characterizing phase transitions. As illustrations, we apply our method to four two-dimensional lattice spin models: the Ising, square ice, XY, and fully-frustrated XY models. In particular, we use persistent homology, which computes the births and deaths of individual topological features as a coarse-graining scale or sublevel threshold is increased, to summarize multiscale and high-point correlations in a spin configuration. We employ vector representations of this information called persistence images to formulate and perform the statistical task of distinguishing phases. For the models we consider, a simple logistic regression on these images is sufficient to identify the phase transition. Interpretable order parameters are then read from the weights of the regression. This method suffices to identify magnetization, frustration, and vortex-antivortex structure as relevant features for phase transitions in our models. We also define "persistence" critical exponents and study how they are related to those critical exponents usually considered. -
A Proof-of-Concept Investigation Into Predicting Follicular Carcinoma on Ultrasound Using Topological Data Analysis and Radiomics (2025)
Andrew M. Thomas, Ann C. Lin, Grace Deng, Yuchen Xu, Gustavo Fernandez Ranvier, Aida Taye, David S. Matteson, Denise LeeAbstract
Background Sonographic risk patterns identified in established risk stratification systems (RSS) may not accurately stratify follicular carcinoma from adenoma, which share many similar US characteristics. The purpose of this study is to investigate the performance of a multimodal machine learning model utilizing radiomics and topological data analysis (TDA) to predict malignancy in follicular thyroid neoplasms on ultrasound. Patients & Methods This is a retrospective study of patients who underwent thyroidectomy with pathology confirmed follicular adenoma or carcinoma at a single academic medical center between 2010 and 2022. Features derived from radiomics and TDA were calculated from processed ultrasound images and high-dimensional features in each modality were projected onto their first two principal components. Logistic regression with L2 penalty was used to predict malignancy and performance was evaluated using leave-one-out cross-validation and area under the curve (AUC). Results Patients with follicular adenomas (n = 7) and follicular carcinomas (n = 11) with available imaging were included. The best multimodal model achieved an AUC of 0.88 (95% CI: [0.85, 1]), whereas the best radiomics model achieved an AUC of 0.68 (95% CI: [0.61, 0.84]). Conclusions We demonstrate that inclusion of topological features yields strong improvement over radiomics-based features alone in the prediction of follicular carcinoma on ultrasound. Despite low volume data, the TDA features explicitly capture shape information that likely augments performance of the multimodal machine learning model. This approach suggests that a quantitative based US RSS may contribute to the preoperative prediction of follicular carcinoma.