2 citations · 5 across the 8 of their papers we have counts for
10 papers
Magnitude Homology Is the Associated Graded of the Length Filtration
Luciano Melodia
Magnitude homology is graded by length and knows nothing of persistence. Its persistent refinement knows nothing of where its bars begin and end. We show that the two are one const…
Groupoid Homology and Classifying-Space Homology Are Not Isomorphic: The Cantor Unit Groupoid
Luciano Melodia
For an ample groupoid , Matui-type groupoid homology is built from the nerve via the Moore complex of compact…
Learning Transfers: Kan Extensions for Neural Invariants
Luciano Melodia
A representation transfers if it stays usable once the task has changed. Standard evaluations report target accuracy or a distance between data distributions, but neither says whic…
Deep Learning Estimation of Absorbed Dose for Nuclear Medicine Diagnostics
Luciano Melodia
In radionuclide therapy with , the absorbed-dose distribution can be approximated by convolving the time-integrated activity distribution with a dose voxel kerne…
Universal Coefficients and Mayer-Vietoris Sequence for Groupoid Homology
Luciano Melodia
We study homology of ample groupoids via the compactly supported Moore complex of the nerve. Let be a topological abelian group. For set $C_n(\mathcal G;A) := C_c(\mat…
Homological Time Series Analysis of Sensor Signals from Power Plants
Luciano Melodia, Richard Lenz
In this paper, we use topological data analysis techniques to construct a suitable neural network classifier for the task of learning sensor signals of entire power plants accordin…