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.

Tumors are complex tissues of cancerous cells surrounded by a heterogeneous cellular microenvironment with which they interact. Single-cell sequencing enables molecular characterization of single cells within the tumor. However, cell annotation—the assignment of cell type or cell state to each sequenced cell—is a challenge, especially identifying tumor cells within single-cell or spatial sequencing experiments. Here, we propose ikarus, a machine learning pipeline aimed at distinguishing tumor cells from normal cells at the single-cell level. We test ikarus on multiple single-cell datasets, showing that it achieves high sensitivity and specificity in multiple experimental contexts. **InferCNV** is a Bayesian method, which agglomerates the expression signal of genomically adjointed genes to ascertain whether there is a gain or loss of a certain larger genomic segment. We have used **inferCNV** to call copy number variations in all samples used in the manuscript.

In the realm of cancer research, grasping the intricacies of intratumor heterogeneity and its interplay with the immune system is paramount for deciphering treatment resistance and tumor progression. While single-cell RNA sequencing unveils diverse transcriptional programs, the challenge persists in automatically discerning malignant cells from non-malignant ones within complex datasets featuring varying coverage depths. Thus, there arises a compelling need for an automated solution to this classification conundrum. SCEVAN (De Falco et al., 2023), a variational algorithm, is designed to autonomously identify the clonal copy number substructure of tumors using single-cell data. It automatically separates malignant cells from non-malignant ones, and subsequently, groups of malignant cells are examined through an optimization-driven joint segmentation process.