Topological and Geometric Data Analysis

The Topology of Evasion: Persistent Homology of Gene Repertoires of Immunity

The paper applies persistent homology to analyze gene repertoires in adaptive immunity across different species, finding higher-dimensional topological features in some gene families.

Topological Analysis of Vascular Networks: A Proof-of-Concept Study in Cerebral Angiography

This study applies topological methods to cerebral angiography to analyze vascular network structure, identifying potential biomarkers for cerebrovascular diseases.

Local Topological Structures and Global Connectivity Patterns in a Trachelospermum jasminoides: a Pilot Study

This study analyzes the topological structure of a star jasmine bush using computational methods to show how it balances local constraints with global connectivity for efficient resource distribution.

Topological Analysis of Macaca mulatta's Cortical Structures Through the Lens of Poincare Duality

The paper applies Poincare duality to analyze cortical structures in Macaca mulatta, revealing topological relationships between dense neuronal clusters and sparse integration regions.

Leveraging Persistent Homology of Eye Movements for Neural Disorder Screening

This study uses persistent homology to extract topological features from eye movement data for screening dyslexia and ADHD, showing promising results with a simple classifier.

Topological Structures in the Space of Treatment-Naive Patients With Chronic Lymphocytic Leukemia

The paper applies topological data analysis to clinical data from CLL patients to identify complex structures like loops and voids, revealing prognostically important factors.

Quantifying Contributions from TopologicalCycles in the Brain Network towards Cognition

This study introduces H-VIP to quantify vertex contributions to topological cycles in brain networks and finds a positive correlation with cognitive measures in both structural and functional connectomes.

Persistent homology centrality improves link prediction performance in PubMed co-occurrence networks

This paper introduces a method using persistent homology to predict links in PubMed co-occurrence networks by analyzing the dynamic structure of scientific literature.

Quantifying the distribution of feature values over data represented in arbitrary dimensional spaces

The paper introduces the Structure Index (SI), a graph-based metric to quantify feature distribution in arbitrary dimensional spaces, demonstrating its application to neuroscience and data science.

Comparing structure and dynamics of transition graphs by the symmetric difference metric over an edge-filtration

The paper introduces a method to compare transition graphs from different datasets using a metric called WFCC, demonstrating its application to antimicrobial resistance data.

Deconstructing the Mapper algorithm to extract richer topological and temporal features from functional neuroimaging data

The paper examines Mapper parameter choices in functional neuroimaging data to improve the extraction of topological and temporal features using synthetic and real fMRI data.

A topological perspective on the dual nature of the neural state space and the correlation structure

The paper compares neural correlations and state space approaches using topology to infer neural representations, showing their complementary value in characterizing covariate spaces.

Neurospectrum: A Geometric and Topological Deep Learning Framework for Uncovering Spatiotemporal Signatures in Neural Activity

Neurospectrum extracts interpretable spatiotemporal features from neural activity using a geometric and topological deep learning framework, outperforming traditional methods in simulations and fMRI data.

Topological Data Analysis of Human Brain Networks Through Order Statistics

This paper develops a statistical framework using persistent homology and order statistics to analyze brain networks, finding significant topological differences between male and female brain networks.

Persistent spectral theory-guided protein engineering

This paper introduces TopFit, a framework that combines persistent spectral theory and sequence embeddings to predict protein fitness from mutations, validated on 34 benchmark datasets.

Persistent homology analysis distinguishes pathological bone microstructure in non-linear microscopy images

This paper uses persistent homology to analyze bone microstructure in non-linear microscopy images, showing significant differences between pathological and healthy samples.

Topological Structure of Population Activity in Mouse Visual Cortex Encodes Visual Scene Rotations

The paper analyzes neural activity in mouse visual cortex to show that population activity encodes visual scene rotations through a circular manifold structure.

Topological Learning for Brain Networks

This paper introduces a topological learning framework using persistent homology to integrate networks of different sizes and topology, validated on brain imaging data to assess genetic heritability.

Estimation of animal location from grid cell populationactivity using persistent cohomology

This paper estimates animal position from grid cell activity using persistent cohomology, showing it outperforms traditional methods in high nonlinearity scenarios.

A topological characterization of DNA sequences based on chaos geometry and persistent homology

This paper introduces a topological method for DNA sequence analysis using persistent homology and chaos geometry, applied to Hantavirus, Influenza A, and Human Papillomavirus genomes.

Geometry of spiking patterns in early visual cortex: a Topological Data Analytic approach

The paper applies topological data analysis to spiking patterns in macaque visual cortex, revealing a low-dimensional geometric structure similar to Euclidean or hyperbolic spaces.

Determining clinically relevant features in cytometry data using persistent homology

This paper applies persistent homology to cytometry data to identify structural differences between healthy donors and COVID-19 patients, revealing downregulation of T-bet and Eomes in patient non-naive CD8+ T cells.

Geodesic-based distance reveals non-linear topological features in neural activity from mouse visual cortex

The paper introduces a geodesic-based distance method to better capture non-linear topological features in neural activity data from mouse visual cortex.

Spatial representability of neuronal activity

The paper argues that firing fields in neuronal activity can be identified theoretically through topological analysis rather than empirical trial and error.

Topological insights into the neural basis of flexible behavior

This paper uses topological data analysis to link neural activity, cognitive processes, and behavior by showing how topological changes in neural populations relate to task performance and model discrimination.

Computing the Riemannian curvature of image patch and single-cell RNA sequencing data manifolds using extrinsic differential geometry

The paper estimates Riemannian curvature of image and scRNA-seq data manifolds using extrinsic differential geometry, revealing curvature in scRNA-seq datasets.

Promises and pitfalls of Topological Data Analysis for brain connectivity analysis

This study evaluates the use of persistent homology in topological data analysis for distinguishing brain states in epilepsy and schizophrenia using functional connectivity data.

Evaluating state space discovery by persistent cohomology in the spatial representation system

This study evaluates persistent cohomology's ability to detect topological structures in simulated neural data and identifies conditions for successful application.

A topological approach to DNA similarity analysis from 5-dimensional representation

The paper introduces a topological method for DNA similarity analysis using 5D vector representations and Wasserstein distance on zeroth persistence diagrams, tested on HRV and Influenza A virus datasets.

Identifying persistent structures in multiscale 'omics data

This paper introduces a method to identify persistent structures in multiscale omics data, expanding cell type catalogs and revealing SARS-COV-2 protein interactions.