Computed Tomography (CT) is indispensable in clinical diagnostics, yet minimizing radiation dose without compromising image quality remains a critical challenge. Conventional low-dose protocols often rely on fixed, uniform angular sampling, independent of the underlying structural complexity of organs of individual patients. We propose ``Stochastic Adaptive Variance-Driven Exploration and Reconstruction'' (SAVER), an adaptive data acquisition framework that selects projection angles in real-time based on the statistical variance of acquired data. Utilizing a Softmax-based stochastic scheduling scheme with simulated annealing, SAVER prioritizes directions with high structural information while maintaining necessary exploration. Numerical experiments across 8 diverse phantoms demonstrate that SAVER achieves consistently higher reconstruction fidelity than conventional random sampling, particularly for objects with high structural anisotropy. Furthermore, the proposed method exhibits robust performance under significant measurement noise. By dynamically reallocating radiation dose to the most informative projections, SAVER provides a mathematically-grounded approach to maximize diagnostic quality per unit of radiation dose, marking a shift toward sample-dependent, data-driven CT acquisition.
Single-cell ATAC-seq (scATAC-seq) enables high-resolution mapping of chromatin accessibility, yet privacy regulations and data size constraints hinder multi-institutional sharing. Federated learning (FL) offers a privacy-preserving alternative, but faces three fundamental barriers in scATAC-seq analysis: ultra-high dimensionality, extreme sparsity, and severe cross-institutional heterogeneity. We propose FL-Sailer, the first FL framework designed for scATAC-seq data. FL-Sailer integrates two key innovations: (i) adaptive leverage score sampling, which selects biologically interpretable features while reducing dimensionality by 80%, and (ii) an invariant VAE architecture, which disentangles biological signals from technical confounders via mutual information minimization. We provide a convergence guarantee, showing that FL-Sailer converges to an approximate solution of the original high-dimensional problem with bounded error. Extensive experiments on synthetic and real epigenomic datasets demonstrate that FL-Sailer not only enables previously infeasible multi-institutional collaborations but also surpasses centralized methods by leveraging adaptive sampling as an implicit regularizer to suppress technical noise. Our work establishes that federated learning, when tailored to domain-specific challenges, can become a superior paradigm for collaborative epigenomic research.