Spatial transcriptomic studies are becoming increasingly common and large, posing important statistical and computational challenges for many analytic tasks. Here, we present SPARK-X, a non-parametric method for rapid and effective detection of spatially expressed genes in large spatial transcriptomic studies. SPARK-X not only produces effective type I error control and high power but also brings orders of magnitude computational savings. We apply SPARK-X to analyze three large datasets, one of which is only analyzable by SPARK-X. In these data, SPARK-X identifies many spatially expressed genes including those that are spatially expressed within the same cell type, revealing new biological insights.

Understanding global communications among cells requires accurate representation of cell-cell signaling links and effective systems-level analyses of those links. We construct a database of interactions among ligands, receptors and their cofactors that accurately represent known heteromeric molecular complexes. We then develop **CellChat**, a tool that is able to quantitatively infer and analyze intercellular communication networks from single-cell RNA-sequencing (scRNA-seq) data. CellChat predicts major signaling inputs and outputs for cells and how those cells and signals coordinate for functions using network analysis and pattern recognition approaches. Through manifold learning and quantitative contrasts, CellChat classifies signaling pathways and delineates conserved and context-specific pathways across different datasets. Applying **CellChat** to mouse and human skin datasets shows its ability to extract complex signaling patterns.

Mapping out the coarse-grained connectivity structures of complex manifolds Biological systems often change over time, as old cells die and new cells are created through differentiation from progenitor cells. This means that at any given time, not all cells will be at the same stage of development. In this sense, a single-cell sample could contain cells at different stages of differentiation. By analyzing the data, we can identify which cells are at which stages and build a model for their biological transitions. By quantifying the connectivity of partitions (groups, clusters) of the single-cell graph, partition-based graph abstraction (PAGA) generates a much simpler abstracted graph (PAGA graph) of partitions, in which edge weights represent confidence in the presence of connections. In this notebook, we will introduce the concept of single-cell Trajectory Analysis using PAGA (Partition-based graph abstraction) in the context of hematopoietic differentiation.