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.

Build single-cell trajectories with the software that introduced **pseudotime**. Find out about cell fate decisions and the genes regulated as they're made. Group and classify your cells based on gene expression. Identify new cell types and states and the genes that distinguish them. Find genes that vary between cell types and states, over trajectories, or in response to perturbations using statistically robust, flexible differential analysis. In development, disease, and throughout life, cells transition from one state to another. Monocle introduced the concept of **pseudotime**, which is a measure of how far a cell has moved through biological progress. Many researchers are using single-cell RNA-Seq to discover new cell types. Monocle 3 can help you purify them or characterize them further by identifying key marker genes that you can use in follow-up experiments such as immunofluorescence or flow sorting. **Single-cell trajectory analysis** shows how cells choose between one of several possible end states. The new reconstruction algorithms introduced in Monocle 3 can robustly reveal branching trajectories, along with the genes that cells use to navigate these decisions.

Single-cell RNA-seq datasets in diverse biological and clinical conditions provide great opportunities for the full transcriptional characterization of cell types. However, the integration of these datasets is challeging as they remain biological and techinical differences. **Harmony** is an algorithm allowing fast, sensitive and accurate single-cell data integration.