Category: math.MG
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Maximum diversity, weighting and invariants of time series
Maximum diversity, weighting and invariants of time series arXiv:2509.11146v1 Announce Type: new Abstract: Magnitude, obtained as a special case of Euler characteristic of enriched category, represents a sense of the size of metric spaces and is related to classical notions such as cardinality, dimension, and volume. While the studies have explained the meaning of magnitude…
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Conic Formulations of Transport Metrics for Unbalanced Measure Networks and Hypernetworks
Conic Formulations of Transport Metrics for Unbalanced Measure Networks and Hypernetworks arXiv:2508.10888v1 Announce Type: new Abstract: The Gromov-Wasserstein (GW) variant of optimal transport, designed to compare probability densities defined over distinct metric spaces, has emerged as an important tool for the analysis of data with complex structure, such as ensembles of point clouds or networks.…
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A Survey of Dimension Estimation Methods
A Survey of Dimension Estimation Methods arXiv:2507.13887v1 Announce Type: new Abstract: It is a standard assumption that datasets in high dimension have an internal structure which means that they in fact lie on, or near, subsets of a lower dimension. In many instances it is important to understand the real dimension of the data, hence…