Accelerated Sinkhorn Algorithms for Partial Optimal Transport

Partial Optimal Transport (POT) addresses the problem of transporting only a fraction of the total mass between two distributions, making it suitable when marginals have unequal size or contain outliers. While Sinkhorn-based methods are widely used, their complexity bounds for POT remain suboptimal and can limit scalability. We introduce Accelerated Sinkhorn for POT (ASPOT), which integrates alternating minimization with Nesterov-style acceleration in the POT setting, yielding a complexity of $\mathcal{O}(n^{7/3}\varepsilon^{-5/3})$. We also show that an informed choice of the entropic parameter $γ$ improves rates for the classical Sinkhorn method. Experiments on real-world applications validate our theories and demonstrate the favorable performance of our proposed methods.

D-SarcNet: A Dual-stream Deep Learning Framework for Automatic Analysis of Sarcomere Structures in Fluorescently Labeled hiPSC-CMs

Human-induced pluripotent stem cell-derived cardiomyocytes (hiPSC-CMs) are a powerful tool in advancing cardiovascular research and clinical applications. The maturation of sarcomere organization in hiPSC-CMs is crucial, as it supports the contractile function and structural integrity of these cells. Traditional methods for assessing this maturation like manual annotation and feature extraction are labor-intensive, time-consuming, and unsuitable for high-throughput analysis. To address this, we propose D-SarcNet, a dual-stream deep learning framework that takes fluorescent hiPSC-CM single-cell images as input and outputs the stage of the sarcomere structural organization on a scale from 1.0 to 5.0. The framework also integrates Fast Fourier Transform (FFT), deep learning-generated local patterns, and gradient magnitude to capture detailed structural information at both global and local levels. Experiments on a publicly available dataset from the Allen Institute for Cell Science show that the proposed approach not only achieves a Spearman correlation of 0.868 marking a 3.7% improvement over the previous state-of-the-art but also significantly enhances other key performance metrics, including MSE, MAE, and R2 score. Beyond establishing a new state-of-the-art in sarcomere structure assessment from hiPSC-CM images, our ablation studies highlight the significance of integrating global and local information to enhance deep learning networks ability to discern and learn vital visual features of sarcomere structure.

SarcNet: A Novel AI-based Framework to Automatically Analyze and Score Sarcomere Organizations in Fluorescently Tagged hiPSC-CMs

Quantifying sarcomere structure organization in human-induced pluripotent stem cell-derived cardiomyocytes (hiPSC-CMs) is crucial for understanding cardiac disease pathology, improving drug screening, and advancing regenerative medicine. Traditional methods, such as manual annotation and Fourier transform analysis, are labor-intensive, error-prone, and lack high-throughput capabilities. In this study, we present a novel deep learning-based framework that leverages cell images and integrates cell features to automatically evaluate the sarcomere structure of hiPSC-CMs from the onset of differentiation. This framework overcomes the limitations of traditional methods through automated, high-throughput analysis, providing consistent, reliable results while accurately detecting complex sarcomere patterns across diverse samples. The proposed framework contains the SarcNet, a linear layers-added ResNet-18 module, to output a continuous score ranging from one to five that captures the level of sarcomere structure organization. It is trained and validated on an open-source dataset of hiPSC-CMs images with the endogenously GFP-tagged alpha-actinin-2 structure developed by the Allen Institute for Cell Science (AICS). SarcNet achieves a Spearman correlation of 0.831 with expert evaluations, demonstrating superior performance and an improvement of 0.075 over the current state-of-the-art approach, which uses Linear Regression. Our results also show a consistent pattern of increasing organization from day 18 to day 32 of differentiation, aligning with expert evaluations. By integrating the quantitative features calculated directly from the images with the visual features learned during the deep learning model, our framework offers a more comprehensive and accurate assessment, thereby enhancing the further utility of hiPSC-CMs in medical research and therapy development.