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Tracing the evolutionary history of the morpho‐anatomy of baculum in primates
The Anatomical Record, EarlyView.Abstract Animal morphology reflects both evolutionary history and present‐day adaptation. Male mammal copulatory structures such as the baculum (penile bone) are ideal for studying these processes because of their complexity and high interspecific variability. In primates, however, research has focused mostly on baculum length.
Federica Spani +3 more
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Persistent Intersection Homology
Foundations of Computational Mathematics, 2010 Persistent homology uses a filtration on a topological space to define birth and death of a homology class. The \(r\)-dimensional classes that are born at stage \(i\) and die at stage \(j\) form the pair group \(P^{i,j}_r\), a vector space over the field with 2 elements, of the filtered space.
Paul Bendich, John Harer
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A directed persistent homology theory for dissimilarity functions
Journal of Applied and Computational Topology, 2023 We develop a theory of persistent homology for directed simplicial complexes which detects persistent directed cycles in odd dimensions. We relate directed persistent homology to classical persistent homology, prove some stability results, and discuss ...
David Méndez, Ruben J Sanchez-Garcia
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Persistent homology in ℓ∞ metric
Computational Geometry, 2022Abstract Proximity complexes and filtrations are central constructions in topological data analysis. Built using distance functions, or more generally metrics, they are often used to infer connectivity information from point clouds. Here we investigate proximity complexes and filtrations built over the Chebyshev metric, also known as the maximum ...
Gabriele Beltramo, Primoz Skraba
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The Persistence Space in Multidimensional Persistent Homology
2013Multidimensional persistent modules do not admit a concise representation analogous to that provided by persistence diagrams for real-valued functions. However, there is no obstruction for multidimensional persistent Betti numbers to admit one. Therefore, it is reasonable to look for a generalization of persistence diagrams concerning those properties ...
Andrea Cerri, Claudia Landi 0001
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Persistence Cycles for Visual Exploration of Persistent Homology
IEEE Transactions on Visualization and Computer Graphics, 2022Persistent homology is a fundamental tool in topological data analysis used for the most diverse applications. Information captured by persistent homology is commonly visualized using scatter plots representations. Despite being widely adopted, such a visualization technique limits user understanding and is prone to misinterpretation.
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Computational Tools in Weighted Persistent Homology
Chinese Annals of Mathematics Series B, 2021Chengyuan Wu, Jie Wu
exaly
Persistent Homology of Geospatial Data: A Case Study with Voting
SIAM Review, 2021Michelle Feng, Mason A Porter
exaly
The better turbulence index? Forecasting adverse financial markets regimes with persistent homology
Financial Markets and Portfolio Management, 2021Eduard Baitinger
exaly