Related papers: Persistent Homology for MCI Classification: A Comp…
Computing Persistent Homology for large point clouds remains a bottleneck for the wider adoption of persistent homology by the scientific community. We present an algorithm which can compute the degree-1 Vietoris-Rips Persistent Homology of…
Mild cognitive impairment (MCI) is often at high risk of progression to Alzheimer's disease (AD). Existing works to identify the progressive MCI (pMCI) typically require MCI subtype labels, pMCI vs. stable MCI (sMCI), determined by whether…
We develop novel methods for using persistent homology to infer the homology of an unknown Riemannian manifold $(M, g)$ from a point cloud sampled from an arbitrary smooth probability density function. Standard distance-based filtered…
Finding the underlying relationships among multiple imaging modalities in a coherent fashion is one of challenging problems in the multimodal analysis. In this study, we propose a novel multimodal network approach based on multidi-…
Our study aims to utilize fMRI to identify the affected brain regions within the Default Mode Network (DMN) in subjects with Mild Cognitive Impairment (MCI), using a novel Node Significance Score (NSS). We construct subject-specific DMN…
We study a family of invariants of compact metric spaces that combines the Curvature Sets defined by Gromov in the 1980s with Vietoris-Rips Persistent Homology. For given integers $k\geq 0$ and $n\geq 1$ we consider the dimension $k$…
We investigate how hubs of functional brain networks are modified as a result of mild cognitive impairment (MCI), a condition causing a slight but noticeable decline in cognitive abilities, which sometimes precedes the onset of Alzheimer's…
Dynamic functional connectivity (dFC) using resting-state functional magnetic resonance imaging (rs-fMRI) is an advanced technique for capturing the dynamic changes of neural activities, and can be very useful in the studies of brain…
Persistent homology studies the evolution of k-dimensional holes along a nested sequence of simplicial complexes (called a filtration). The set of bars (i.e. intervals) representing birth and death times of k-dimensional holes along such…
Dimensionality reduction techniques are powerful tools for data preprocessing and visualization which typically come with few guarantees concerning the topological correctness of an embedding. The interleaving distance between the…
Intersection homology is a topological invariant which detects finer information in a space than ordinary homology. Using ideas from classical simple homotopy theory, we construct local combinatorial transformations on simplicial complexes…
Several brain disorders can be detected by observing alterations in the brain's structural and functional connectivities. Neurological findings suggest that early diagnosis of brain disorders, such as mild cognitive impairment (MCI), can…
Computation of the simplicial complexes of a large point cloud often relies on extracting a sample, to reduce the associated computational burden. The study considers sampling critical points of a Morse function associated to a point cloud,…
Scientific time series often encode predictive geometric structure, including connectivity, cycles, shell-like geometry, directional changes, and nonlinear neighborhoods, that standard dot-product attention does not explicitly represent. We…
Topological data analysis, as a tool for extracting topological features and characterizing geometric shapes, has experienced significant development across diverse fields. Its key mathematical techniques include persistent homology and the…
With respect to spatial overlap, CNN-based segmentation of short axis cardiovascular magnetic resonance (CMR) images has achieved a level of performance consistent with inter observer variation. However, conventional training procedures…
Topological data analysis can reveal higher-order structure beyond pairwise connections between vertices in complex networks. We present a new method based on discrete Morse theory to study topological properties of unweighted and…
We give an $O(n^2(k+\log n))$ algorithm for computing the $k$-dimensional persistent homology of a filtration of clique complexes of cyclic graphs on $n$ vertices. This is nearly quadratic in the number of vertices $n$, and therefore a…
Speech-based detection of cognitive impairment (CI) offers a promising non-invasive approach for early diagnosis, yet performance disparities across demographic and clinical subgroups remain underexplored, raising concerns around fairness…
Graph-based representations of point-cloud data are widely used in data science and machine learning, including epsilon-graphs that contain edges between pairs of data points that are nearer than epsilon and kNN-graphs that connect each…