Combinatorics

[no abstract available

Collection of abstracts of the 24th European Workshop on Computational Geometry

International audienceThe 24th European Workshop on Computational Geomety (EuroCG'08) was held at INRIA Nancy - Grand Est & LORIA on March 18-20, 2008. The present collection of abstracts contains the 63 scientific contributions as well as three invited talks presented at the workshop

LIPIcs, Volume 248, ISAAC 2022, Complete Volume

LIPIcs, Volume 248, ISAAC 2022, Complete Volum

Topological data analysis of organoids

Organoids are multi-cellular structures which are cultured in vitro from stem cells to resemble specific organs (e.g., colon, liver) in their three- dimensional composition. The gene expression and the tissue composition of organoids constantly affect each other. Dynamic changes in the shape, cellular composition and transcriptomic profile of these model systems can be used to understand the effect of mutations and treatments in health and disease. In this thesis, I propose new techniques in the field of topological data analysis (TDA) to analyse the gene expression and the morphology of organoids. I use TDA methods, which are inspired by topology, to analyse and quantify the continuous structure of single-cell RNA sequencing data, which is embedded in high dimensional space, and the shape of an organoid. For single-cell RNA sequencing data, I developed the multiscale Laplacian score (MLS) and the UMAP diffusion cover, which both extend and im- prove existing topological analysis methods. I demonstrate the utility of these techniques by applying them to a published benchmark single-cell data set and a data set of mouse colon organoids. The methods validate previously identified genes and detect additional genes with known involvement cancers. To study the morphology of organoids I propose DETECT, a rotationally invariant signature of dynamically changing shapes. I demonstrate the efficacy of this method on a data set of segmented videos of mouse small intestine organoid experiments and show that it outperforms classical shape descriptors. I verify the method on a synthetic organoid data set and illustrate how it generalises to 3D to conclude that DETECT offers rigorous quantification of organoids and opens up computationally scalable methods for distinguishing different growth regimes and assessing treatment effects. Finally, I make a theoretical contribution to the statistical inference of the method underlying DETECT