Recent technological advancements have enabled spatially resolved transcriptomic profiling but at multi-cellular pixel resolution, thereby hindering the identification of cell-type-specific spatial patterns and gene expression variation. To address this challenge, we develop STdeconvolve as a reference-free approach to deconvolve underlying cell types comprising such multi-cellular pixel resolution spatial transcriptomics (ST) datasets. Using simulated as well as real ST datasets from diverse spatial transcriptomics technologies comprising a variety of spatial resolutions such as Spatial Transcriptomics, 10X Visium, DBiT-seq, and Slide-seq, we show that STdeconvolve can effectively recover cell-type transcriptional profiles and their proportional representation within pixels without reliance on external single-cell transcriptomics references. **STdeconvolve** provides comparable performance to existing reference-based methods when suitable single-cell references are available, as well as potentially superior performance when suitable single-cell references are not available. STdeconvolve is available as an open-source R software package with the source code available at https://github.com/JEFworks-Lab/STdeconvolve .

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.

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.