This is a first step towards a larger framework of spatial parameter inference for biological systems, for which there may be a variety of filtrations, vectorisations, and summary statistics to be considered.
Here we simulate the Anderson-Chaplain model of angiogenesis at different parameter values and quantify the vessel architectures of the resulting synthetic data.
Advances in imaging techniques enable high resolution 3D visualisation of vascular networks over time and reveal abnormal structural features such as twists and loops.
Quantitative Methods Algebraic Topology Tissues and Organs
This paper describes the systematic application of local topological methods for detecting interfaces and related anomalies in complicated high-dimensional data.
Algebraic Topology Algebraic Geometry 57N80
With these tools, which allow one to characterize topological invariants such as loops in high-dimensional data, we are able to gain understanding into low-dimensional structures in networks in a way that complements traditional approaches that are based on pairwise interactions.
Topological data analysis (TDA) provides a growing body of tools for computing geometric and topological information about spaces from a finite sample of points.
Algebraic Topology Algebraic Geometry Numerical Analysis
A fundamental tool in topological data analysis is persistent homology, which allows extraction of information from complex datasets in a robust way.
Algebraic Topology Commutative Algebra 55B55, 68U05, 68Q17, 13P25 (primary)
Our clustering method is general and can be tailored to a variety of applications in science and industry.
We give a friendly introduction to PH, navigate the pipeline for the computation of PH with an eye towards applications, and use a range of synthetic and real-world data sets to evaluate currently available open-source implementations for the computation of PH.
Algebraic Topology Computational Geometry Data Analysis, Statistics and Probability Quantitative Methods