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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.

Cell2location is a principled Bayesian model that can resolve fine-grained cell types in spatial transcriptomic data and create comprehensive cellular maps of diverse tissues. Cell2location accounts for technical sources of variation and borrows statistical strength across locations, thereby enabling the integration of single cell and spatial transcriptomics with higher sensitivity and resolution than existing tools. This is achieved by estimating which combination of cell types in which cell abundance could have given the mRNA counts in the spatial data, while modelling technical effects (platform/technology effect, contaminating RNA, unexplained variance). This tutorial shows how to use cell2location method for spatially resolving fine-grained cell types by integrating 10X Visium data with scRNA-seq reference of cell types. Cell2location is a principled Bayesian model that estimates which combination of cell types in which cell abundance could have given the mRNA counts in the spatial data, while modelling technical effects (platform/technology effect, contaminating RNA, unexplained variance).

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.

Many spatially resolved transcriptomic technologies do not have single-cell resolution but measure the average gene expression for each spot from a mixture of cells of potentially heterogeneous cell types. Here, we introduce a deconvolution method, conditional autoregressive-based deconvolution (CARD), that combines cell-type-specific expression information from single-cell RNA sequencing (scRNA-seq) with correlation in cell-type composition across tissue locations. Modeling spatial correlation allows us to borrow the cell-type composition information across locations, improving accuracy of deconvolution even with a mismatched scRNA-seq reference. **CARD** can also impute cell-type compositions and gene expression levels at unmeasured tissue locations to enable the construction of a refined spatial tissue map with a resolution arbitrarily higher than that measured in the original study and can perform deconvolution without an scRNA-seq reference. Applications to four datasets, including a pancreatic cancer dataset, identified multiple cell types and molecular markers with distinct spatial localization that define the progression, heterogeneity and compartmentalization of pancreatic cancer.