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Dynamic Snake Convolution based on Topological Geometric Constraints for Tubular Structure Segmentation

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Statistical topological data analysis using persistence landscapesPreprint

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Sliding Windows and Persistence: An Application of Topological Methods to Signal Analysis

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Persistent homology analysis of brain artery trees

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Probability measures on the space of persistence diagrams

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Topological pattern recognition for point cloud data

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A Survey of Topological Machine Learning Methods

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Fréchet Means for Distributions of Persistence Diagrams

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The Theory of the Interleaving Distance on Multidimensional Persistence Modules

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An Introduction to Topological Data Analysis: Fundamental and Practical Aspects for Data Scientists

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A persistence landscapes toolbox for topological statistics

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Topology-Preserving Deep Image SegmentationPreprint

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Geometry Helps to Compare Persistence Diagrams

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Persistent Homology: Theory and Practice

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Improved Statistical Methods Enable Greater Sensitivity in Rhythm Detection for Genome-Wide Data

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Betti numbers in multidimensional persistent homology are stable functions

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Chatter detection in turning using persistent homology

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Deep Learning with Topological SignaturesPreprint

Hofer, C. D., Kwitt, R., Niethammer, M., & Uhl, A. (2017) · arXiv (Cornell University) · doi:10.48550/arxiv.1707.04041 · Cited by 123 · see citing works

Persistence weighted Gaussian kernel for topological data analysisPreprint

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SW1PerS: Sliding windows and 1-persistence scoring; discovering periodicity in gene expression time series data

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Topological Data Analysis with Applications

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On the stability of persistent entropy and new summary functions for topological data analysis

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Circadian rhythms and post-transcriptional regulation in higher plants

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Topological data analysis of single-trial electroencephalographic signals

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Robust Statistics, Hypothesis Testing, and Confidence Intervals for Persistent Homology on Metric Measure Spaces

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Scalar Field Comparison with Topological Descriptors: Properties and Applications for Scientific Visualization

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Topological methods for data modelling

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Metrics for comparing neuronal tree shapes based on persistent homology

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Topological Data Analysis of Critical Transitions in Financial Networks

Gidea, M. (2017) · Springer proceedings in complexity · doi:10.1007/978-3-319-55471-6_5 · Cited by 70 · see citing works

Exploring uses of persistent homology for statistical analysis of landmark-based shape data

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Neural Persistence: A Complexity Measure for Deep Neural Networks Using Algebraic TopologyPreprint

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Persistence Curves: A canonical framework for summarizing persistence diagrams

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Clique Community Persistence: A Topological Visual Analysis Approach for Complex Networks

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Learning metrics for persistence-based summaries and applications for graph classificationPreprint

Zhao, Q., & Wang, Y. (2019) · arXiv (Cornell University) · doi:10.48550/arxiv.1904.12189 · Cited by 56 · see citing works

Persistent Homology for the Evaluation of Dimensionality Reduction Schemes

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A Persistent Homology Approach to Heart Rate Variability Analysis With an Application to Sleep-Wake Classification

Chung, Y.-M., Hu, C.-S., Lo, Y., & Wu, H. (2021) · Frontiers in Physiology · doi:10.3389/fphys.2021.637684 · Cited by 54 · see citing works

Time series classification via topological data analysis

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Investigating Conservation of the Cell-Cycle-Regulated Transcriptional Program in the Fungal Pathogen, Cryptococcus neoformans

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Topological Analysis of Variance and the Maxillary Complex

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Understanding the topology and the geometry of the space of persistence diagrams via optimal partial transport

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How Many Directions Determine a Shape and other Sufficiency Results for Two Topological Transforms

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Topology‐Aware Surface Reconstruction for Point Clouds

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Proteome-scale movements and compartment connectivity during the eukaryotic cell cycle

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Topological Machine Learning with Persistence Indicator Functions

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TopoGAN: A Topology-Aware Generative Adversarial Network

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A Riemannian Framework for Statistical Analysis of Topological Persistence Diagrams

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Embeddings of persistence diagrams into Hilbert spaces

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A Framework for Differential Calculus on Persistence Barcodes

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Persistent homology analysis of ion aggregations and hydrogen-bonding networks

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Methods detecting rhythmic gene expression are biologically relevant only for strong signal

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Topological persistence machine of phase transitions

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Wasserstein Stability for Persistence DiagramsPreprint

Škraba, P., & Turner, K. (2020) · arXiv (Cornell University) · doi:10.48550/arxiv.2006.16824 · Cited by 35 · see citing works

On the choice of weight functions for linear representations of persistence diagrams

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A concise and persistent feature to study brain resting‐state network dynamics: Findings from the Alzheimer's Disease Neuroimaging Initiative

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Statistical Inference Over Persistent Homology Predicts Fluid Flow in Porous Media

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A fast algorithm for constructing topological structure in large data

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Persistent homology and applied homotopy theory

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A kernel for multi-parameter persistent homology

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Cell cycle controls long-range calcium signaling in the regenerating epidermis

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Critical transitions in a model of a genetic regulatory system

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Atom-specific persistent homology and its application to protein flexibility analysis

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Topological and statistical behavior classifiers for tracking applications

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Topological learning for brain networks

Songdechakraiwut, T., & Chung, M. K. (2023) · The Annals of Applied Statistics · doi:10.1214/22-aoas1633 · Cited by 26 · see citing works

Randomly Weighted $d$-Complexes: Minimal Spanning Acycles and Persistence Diagrams

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Persistent Homology in Data Science

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Statistical topology using persistence landscapesPreprint

Bubenik, P. (2012) · arXiv (Cornell University) · Cited by 24 · see citing works

Exploring and Comparing Clusterings of Multivariate Data Sets Using Persistent Homology

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Topological data analysis for true step detection in periodic piecewise constant signals

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Diffusion runs low on persistence fast

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Geometry-Aware Merge Tree Comparisons for Time-Varying Data With Interleaving Distances

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Ranking Viscous Finger Simulations to an Acquired Ground Truth with Topology-Aware Matchings

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Applications of Persistent Homology to Time Varying Systems

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Perturbation Robust Representations of Topological Persistence Diagrams

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Advanced image-free analysis of the nano-organization of chromatin and other biomolecules by Single Molecule Localization Microscopy (SMLM)

Weidner, J., Neitzel, C., Gote, M. J., Deck, J., Küntzelmann, K., Pilarczyk, G., Falk, M., & Hausmann, M. (2023) · Computational and Structural Biotechnology Journal · doi:10.1016/j.csbj.2023.03.009 · Cited by 21 · see citing works

Topology Data Analysis of Critical Transitions in Financial NetworksPreprint

Gidea, M. (2017) · SSRN Electronic Journal · doi:10.2139/ssrn.2903278 · Cited by 21 · see citing works

Persistent homology as a new method of the assessment of heart rate variability

Graff, G., Graff, B., Pilarczyk, P., Jabłoński, G., Gąsecki, D., & Narkiewicz, K. (2021) · PLoS ONE · doi:10.1371/journal.pone.0253851 · Cited by 20 · see citing works

Topological Learning and Its Application to Multimodal Brain Network Integration

Songdechakraiwut, T., Shen, L., & Chung, M. K. (2021) · Lecture notes in computer science · doi:10.1007/978-3-030-87196-3_16 · Cited by 20 · see citing works

Fractal dimension and the persistent homology of random geometric complexes

Schweinhart, B. (2020) · Advances in Mathematics · doi:10.1016/j.aim.2020.107291 · Cited by 20 · see citing works

Representations of energy landscapes by sublevelset persistent homology: An example with n -alkanes

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Cycle Registration in Persistent Homology With Applications in Topological Bootstrap

Reani, Y., & Bobrowski, O. (2022) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.2022.3217443 · Cited by 20 · see citing works

Optimizing persistent homology based functionsPreprint

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Evolutionary homology on coupled dynamical systems with applications to protein flexibility analysis

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A novel approach for wafer defect pattern classification based on topological data analysis

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Finding self-similar behavior in quantum many-body dynamics via persistent homology

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Persistent Homology and the Upper Box Dimension

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Computing Wasserstein Distance for Persistence Diagrams on a Quantum ComputerPreprint

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Topological Detection of Trojaned Neural NetworksPreprint

Zheng, S., Zhang, Y., Wagner, H., Goswami, M., & Chen, C. (2021) · arXiv (Cornell University) · doi:10.48550/arxiv.2106.06469 · Cited by 18 · see citing works

Topological machine learning for multivariate time series

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Noise robustness of persistent homology on greyscale images, across filtrations and signatures

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Topology-Guided Multi-Class Cell Context Generation for Digital Pathology

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