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Found 20 papers, 10 papers with code
Quiver Laplacians and Feature Selection
The challenge of selecting the most relevant features of a given dataset arises ubiquitously in data analysis and dimensionality reduction.
A roadmap for the computation of persistent homology
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
Geometric anomaly detection in data
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
Sampling real algebraic varieties for topological data analysis
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
Multiscale Topology Characterises Dynamic Tumour Vascular Networks
Advances in imaging techniques enable high resolution 3D visualisation of vascular networks over time and reveal abnormal structural features such as twists and loops, and their quantification is an active area of research.
Topological data analysis distinguishes parameter regimes in the Anderson-Chaplain model of angiogenesis
Here we simulate the Anderson-Chaplain model of angiogenesis at different parameter values and quantify the vessel architectures of the resulting synthetic data.
Multiscale methods for signal selection in single-cell data
Analysis of single-cell transcriptomics often relies on clustering cells and then performing differential gene expression (DGE) to identify genes that vary between these clusters.
Multiscale topology classifies and quantifies cell types in subcellular spatial transcriptomics
Spatial transcriptomics has the potential to transform our understanding of RNA expression in tissues.
Tensor clustering with algebraic constraints gives interpretable groups of crosstalk mechanisms in breast cancer
Our clustering method is general and can be tailored to a variety of applications in science and industry.
Stratifying multiparameter persistent homology
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)
Topological Data Analysis of Task-Based fMRI Data from Experiments on Schizophrenia
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 Approximate Bayesian Computation for Parameter Inference of an Angiogenesis Model
Here we focus on recent work using topological data analysis to study different regimes of parameter space for a well-studied model of angiogenesis.
Algebra, Geometry and Topology of ERK Kinetics
The MEK/ERK signalling pathway is involved in cell division, cell specialisation, survival and cell death.
Barcodes distinguish morphology of neuronal tauopathy
We introduce {topological morphology functions}, a class of functions similar to Sholl functions, that can be recovered from the associated topological morphology descriptor.
Brain Chains as Topological Signatures for Alzheimer's Disease
This sequence of edges defines a filtration of the graph.
Zigzag persistence for coral reef resilience using a stochastic spatial model
Finally, we apply this toolkit of multi-scale methods to empirical coral reef data, which distinguish spatio-temporal reef dynamics in different locations, and demonstrate the applicability to a range of datasets.
Stability of topological descriptors for neuronal morphology
These results guarantee that persistence images of topological morphology descriptors are stable against the same set of perturbations and reliable.
Algebraic network reconstruction of discrete dynamical systems
We present a computational algebra solution to reverse engineering the network structure of discrete dynamical systems from data.
Detecting Temporal shape changes with the Euler Characteristic Transform
Organoids are multi-cellular structures which are cultured in vitro from stem cells to resemble specific organs (e. g., brain, liver) in their three-dimensional composition.
Topological classification of tumour-immune interactions and dynamics
We find additionally that dimension 0 persistence applied to macrophage data, representing multi-scale clusters of the spatial arrangement of macrophages, performs best at this classification task at early time steps, prior to full tumour development, and performs even better when time-dependent data are included; in contrast, topological measures capturing the shape of the tumour, such as tortuosity and punctures in the cell arrangement, perform best at intermediate and later stages.
