Multiscale Cell-Cell Interactive Spatial Transcriptomics Analysis.

Spatial transcriptomics data analysis integrates gene expression profiles with their corresponding spatial locations to identify spatial domains, infer cell-type dynamics, and detect gene expression patterns within tissues. However, the current spatial transcriptomics analysis neglects the multiscale cell-cell interactions that are crucial in biology. To fill this gap, we propose multiscale cell-cell interactive spatial transcriptomics (MCIST) analysis.

K-nearest-neighbors induced topological PCA for single cell RNA-sequence data analysis.

Single-cell RNA sequencing (scRNA-seq) is widely used to reveal heterogeneity in cells, which has given us insights into cell-cell communication, cell differentiation, and differential gene expression. However, analyzing scRNA-seq data is a challenge due to sparsity and the large number of genes involved. Therefore, dimensionality reduction and feature selection are important for removing spurious signals and enhancing downstream analysis.

Multiscale differential geometry learning of networks with applications to single-cell RNA sequencing data.

Single-cell RNA sequencing (scRNA-seq) has emerged as a transformative technology, offering unparalleled insights into the intricate landscape of cellular diversity and gene expression dynamics. scRNA-seq analysis represents a challenging and cutting-edge frontier within the field of biological research. Differential geometry serves as a powerful mathematical tool in various applications of scientific research.

K-Nearest-Neighbors Induced Topological PCA for Single Cell RNA-Sequence Data Analysis.

Single-cell RNA sequencing (scRNA-seq) is widely used to reveal heterogeneity in cells, which has given us insights into cell-cell communication, cell differentiation, and differential gene expression. However, analyzing scRNA-seq data is a challenge due to sparsity and the large number of genes involved. Therefore, dimensionality reduction and feature selection are important for removing spurious signals and enhancing downstream analysis.

PLPCA: Persistent Laplacian-Enhanced PCA for Microarray Data Analysis.

Over the years, Principal Component Analysis (PCA) has served as the baseline approach for dimensionality reduction in gene expression data analysis. Its primary objective is to identify a subset of disease-causing genes from a vast pool of thousands of genes. However, PCA possesses inherent limitations that hinder its interpretability, introduce class ambiguity, and fail to capture complex geometric structures in the data.