Related papers: Multiscale Topology Characterises Dynamic Tumour V…
Vascular graphs can embed a number of high-level features, from morphological parameters, to functional biomarkers, and represent an invaluable tool for longitudinal and cross-sectional clinical inference. This, however, is only feasible…
We propose an unsupervised learning methodology with descriptors based on Topological Data Analysis (TDA) concepts to describe the local structural properties of materials at the atomic scale. Based only on atomic positions and without a…
We present a way to use Topological Data Analysis (TDA) for machine learning tasks on grayscale images. We apply persistent homology to generate a wide range of topological features using a point cloud obtained from an image, its natural…
Scientific data has been growing in both size and complexity across the modern physical, engineering, life and social sciences. Spatial structure, for example, is a hallmark of many of the most important real-world complex systems, but its…
The network architecture of the human brain has become a feature of increasing interest to the neuroscientific community, largely because of its potential to illuminate human cognition, its variation over development and aging, and its…
Classical topological concepts are applied to understand high performance computing simulations of molecules writhing in three dimensional space. These simulations produce peta-bytes of floating point data, to describe 3 dimensional changes…
We present a new method for exploring cancer gene expression data based on tools from algebraic topology. Our method selects a small relevant subset from tens of thousands of genes while simultaneously identifying nontrivial higher order…
Junctions in the retinal vasculature are key points to be able to extract its topology, but they vary in appearance, depending on vessel density, width and branching/crossing angles. The complexity of junction patterns is usually…
With superiorities on low cost, portability, and free of radiation, echocardiogram is a widely used imaging modality for left ventricle (LV) function quantification. However, automatic LV segmentation and motion tracking is still a…
Computed tomography imaging is a standard modality for detecting and assessing lung cancer. In order to evaluate the malignancy of lung nodules, clinical practice often involves expert qualitative ratings on several criteria describing a…
We introduce a method of time series analysis for two-dimensional transient flow patterns based on Topological Flow Data Analysis (TFDA), a new approach to topological data analysis. TFDA identifies local topological flow structures from an…
One of the most crucial tasks in the future will be to understand what is going on in neural networks, as they will become even more powerful and widely deployed. This work aims to use TDA methods to analyze neural representations. We…
The manifold hypothesis, which assumes that data lies on or close to an unknown manifold of low intrinsic dimension, is a staple of modern machine learning research. However, recent work has shown that real-world data exhibits distinct…
The identification of vascular networks is an important topic in the medical image analysis community. While most methods focus on single vessel tracking, the few solutions that exist for tracking complete vascular networks are usually…
Topological data analysis is an emerging field that applies the study of topological invariants to data. Perhaps the simplest of these invariants is the number of connected components or clusters. In this work, we explore a topological…
Topology, which originated as a mathematical discipline, nowadays advances the understanding of many branches of science and technology from elementary particle physics and cosmology to condensed matter physics. In optics, the topology of…
We construct algorithms and topological invariants that allow us to distinguish the topological type of a surface, as well as functions and vector fields for their topological equivalence. In the first part (arXiv:2501.15657), we discused…
Many complex networks, ranging from social to biological systems, exhibit structural patterns consistent with an underlying hyperbolic geometry. Revealing the dimensionality of this latent space can disentangle the structural complexity of…
Accurate characterisation of visual attributes such as spiculation, lobulation, and calcification of lung nodules is critical in cancer management. The characterisation of these attributes is often subjective, which may lead to high inter-…
In this article, we introduce a Topological Data Analysis (TDA) pipeline for neural spike train data. Understanding how the brain transforms sensory information into perception and behavior requires analyzing coordinated neural population…