Papers and Preprints

1. Unsupervised Ensembling of Multiple Software Sensors with Phase Synchronization: A Robust Approach For Electrocardiogram-derived Respiration

Jacob McErlean*, John Malik*, Yu-Ting Lin, Ronen Talmon, Hau-Tieng Wu. *- co-first authors. Submitted for publication, April 2023.

Abstract: We aimed to fuse the outputs of different electrocardiogram-derived respiration (EDR) algorithms to create one EDR signal that is of higher quality. We viewed each EDR algorithm as a software sensor that recorded breathing activity from a different vantage point, identified high-quality software sensors based on the respiratory signal quality index, aligned the highest-quality EDRs with a phase synchronization technique based on the graph connection Laplacian, and finally fused those aligned, high-quality EDRs. We refer to the output as the sync-ensembled EDR signal. The proposed algorithm was evaluated on a large-scale database of 48 whole-night polysomnograms. We evaluated the performance of the proposed algorithm using three respiratory signals recorded from different hardware sensors, and compared it with other existing EDR algorithms. A sensitivity analysis was carried out, including two cases: without and with signal quality selection and without and with EDR signal alignment. The sync-ensembled EDR algorithm outperforms existing EDR algorithms when evaluated by the synchronized correlation (gamma-score) and optimal transport (OT) distance, all with statistical significance. The sensitivity analysis shows that the signal quality selection and EDR signal alignment are both critical for the performance, both with statistical significance.

2. Lower Bounds on Volumes of Hyperbolic 3-Manifolds via Decomposition

Colin Adams, Michele Capovilla-Searle, Darin Li, Qiao Li, Jacob McErlean, Alexander Simons, Natalie Stewart, and Xiwen Wang.  Uploaded to Arxiv, November 2021.

Abstract: In a variety of settings we provide a method for decomposing a 3-manifold M into pieces. When the pieces have the appropriate type of hyperbolicity, then the manifold M is hyperbolic and its volume is bounded below by the sum of the appropriately defined hyperbolic volumes of the pieces. A variety of examples of appropriately hyperbolic pieces and volumes are provided, with many examples from link complements in the 3-sphere. 

3.  Generalized Augmented Cellular Alternating Links in Thickened Surfaces are Hyperbolic

Colin Adams, Michele Capovilla-Searle, Darin Li, Qiao Li, Jacob McErlean, Alexander Simons, Natalie Stewart, and Xiwen Wang. Uploaded to Arxiv, July 2021.

Abstract: Menasco proved that nontrivial links in the 3-sphere with connected prime alternating non-2-braid projections are hyperbolic. This was further extended to augmented alternating links wherein non-isotopic trivial components bounding disks punctured twice by the alternating link were added. Lackenby proved that the first and second collections of links together form a closed subset of the set of all finite volume hyperbolic 3-manifolds in the geometric topology. Adams showed hyperbolicity for generalized augmented alternating links, which include additional trivial components that bound n-punctured disks for n≥2. Here we prove that generalized augmented cellular alternating links in I-bundles over closed surfaces are also hyperbolic and that in S×I, the cellular alternating links and the augmented cellular alternating together form a closed subset of finite volume hyperbolic 3-manifolds in the geometric topology. Explicit examples of additional links in S×I to which these results apply are included.