Cong Ma

. However, current methods capture only one layer of omics information at a time, precluding the possibility of examining the mechanistic relationship across the central dogma of molecular biology. Here, we present two technologies for spatially resolved, genome-wide, joint profiling of the epigenome and transcriptome by cosequencing chromatin accessibility and gene expression, or histone modifications (H3K27me3, H3K27ac or H3K4me3) and gene expression on the same tissue section at near-single-cell resolution. These were applied to embryonic and juvenile mouse brain, as well as adult human brain, to map how epigenetic mechanisms control transcriptional phenotype and cell dynamics in tissue. Although highly concordant tissue features were identified by either spatial epigenome or spatial transcriptome we also observed distinct patterns, suggesting their differential roles in defining cell states. Linking epigenome to transcriptome pixel by pixel allows the uncovering of new insights in spatial epigenetic priming, differentiation and gene regulation within the tissue architecture. These technologies are of great interest in life science and biomedical research.

Recent years have seen a flurry of activities in designing provably efficient nonconvex procedures for solving statistical estimation problems. Due to the highly nonconvex nature of the empirical loss, state-of-the-art procedures often require proper regularization (e.g., trimming, regularized cost, projection) in order to guarantee fast convergence. For vanilla procedures such as gradient descent, however, prior theory either recommends highly conservative learning rates to avoid overshooting, or completely lacks performance guarantees. This paper uncovers a striking phenomenon in nonconvex optimization: even in the absence of explicit regularization, gradient descent enforces proper regularization implicitly under various statistical models. In fact, gradient descent follows a trajectory staying within a basin that enjoys nice geometry, consisting of points incoherent with the sampling mechanism. This "implicit regularization" feature allows gradient descent to proceed in a far more aggressive fashion without overshooting, which in turn results in substantial computational savings. Focusing on three fundamental statistical estimation problems, i.e., phase retrieval, low-rank matrix completion, and blind deconvolution, we establish that gradient descent achieves near-optimal statistical and computational guarantees without explicit regularization. In particular, by marrying statistical modeling with generic optimization theory, we develop a general recipe for analyzing the trajectories of iterative algorithms via a leave-one-out perturbation argument. As a by-product, for noisy matrix completion, we demonstrate that gradient descent achieves near-optimal error control-measured entrywise and by the spectral norm-which might be of independent interest.

. Although the genetic contributions to oncogenic transitions have been investigated, epigenetic drivers remain less understood. Here we constructed a pan-cancer epigenetic and transcriptomic atlas using single-nucleus chromatin accessibility data (using single-nucleus assay for transposase-accessible chromatin) from 225 samples and matched single-cell or single-nucleus RNA-sequencing expression data from 206 samples. With over 1 million cells from each platform analysed through the enrichment of accessible chromatin regions, transcription factor motifs and regulons, we identified epigenetic drivers associated with cancer transitions. Some epigenetic drivers appeared in multiple cancers (for example, regulatory regions of ABCC1 and VEGFA; GATA6 and FOX-family motifs), whereas others were cancer specific (for example, regulatory regions of FGF19, ASAP2 and EN1, and the PBX3 motif). Among epigenetically altered pathways, TP53, hypoxia and TNF signalling were linked to cancer initiation, whereas oestrogen response, epithelial-mesenchymal transition and apical junction were tied to metastatic transition. Furthermore, we revealed a marked correlation between enhancer accessibility and gene expression and uncovered cooperation between epigenetic and genetic drivers. This atlas provides a foundation for further investigation of epigenetic dynamics in cancer transitions.