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.

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.

CellRank2 (Weiler et al, 2023) is a powerful framework for studying cellular fate using single-cell RNA sequencing data. It can handle millions of cells and different data types efficiently. This tool can identify cell fate and probabilities across various data sets. It also allows for analyzing transitions over time and uncovering key genes in developmental processes. Additionally, CellRank2 estimates cell-specific transcription and degradation rates, aiding in understanding differentiation trajectories and regulatory mechanisms. In this notebook, we will use a primary tumor sample of patient T71 from the dataset GSE137804 (Dong R. et al, 2020) as an example. We have performed RNA-velocity analysis and pseudotime calculation on this dataset in scVelo (Bergen et al, 2020) notebook. The output will be then loaded into this CellRank2 notebook for further analysis. This notebook is based on the tutorial provided on CellRank2 documentation. We have modified the notebook and changed the input data to show how the tool works on BioTuring's platform.