2 citations · 5 across the 10 of their papers we have counts for
10 papers
Persistent Magnitude Homology for Quantitative Equational Theories
Luciano Melodia
A quantitative equational theory reasons about terms that agree up to a numerical error. It presents a free algebra over a metric space of generators, the terms of t…
Learning Transfers: Kan Extensions of Topological Invariants of Learned Representations
Luciano Melodia
When a learned representation is reused for a new task, which of its structure should survive? A task is a small category, a change of task is a functor , and the invariants of…
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…
Discrete Coefficients and Open Invariant Covers in the Homology of Ample Groupoids
Luciano Melodia
The homology of an ample groupoid is computed from the complex of compactly supported continuous functions on the nerve. Two hypotheses routinely imposed on this complex behave in…
Groupoid Homology and Classifying-Space Homology Are Not Isomorphic
Luciano Melodia
For an ample groupoid , Matui-type groupoid homology is built from the nerve via the Moore complex of compact…
Algebraic and Topological Persistence
Luciano Melodia
This thesis addresses the theory of topological spaces and the foundations of persistence theory. We will discuss chain complexes and the associated simplicial homology groups, as…
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…
Estimate of the Neural Network Dimension using Algebraic Topology and Lie Theory
Luciano Melodia, Richard Lenz
In this paper we present an approach to determine the smallest possible number of neurons in a layer of a neural network in such a way that the topology of the input space can be l…
Persistent Homology as Stopping-Criterion for Voronoi Interpolation
Luciano Melodia, Richard Lenz
In this study the Voronoi interpolation is used to interpolate a set of points drawn from a topological space with higher homology groups on its filtration. The technique is based…
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…