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Persistent topology of decision boundaries
2015 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 2015Topological signal processing, especially persistent homology, is a growing field of study for analyzing sets of data points that has been heretofore applied to unlabeled data. In this work, we consider the case of labeled data and examine the topology of the decision boundary separating different labeled classes.
Karthikeyan Natesan Ramamurthy +1 more
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Nature Materials, 2021 Entropy and topology for manifolds with boundary
Nuclear Physics B - Proceedings Supplements, 1997A relation between the thermodynamical properties and the topology of manifolds with boundary is obtained. The expression for the Euler characteristic, through the Gauss-Bonnet integral, and that for the entropy of gravitational instantons are proposed in a form which makes the relation between them self-evident.
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On the Bishop boundary in topological algebras
Rendiconti del Circolo Matematico di Palermo, 1997We characterize the existence of the Bishop boundary in the context of an Urysohn (topological) algebra, by means ofG δ points. Considering a subset of its spectrum and the restriction of its Gel'fand transform algebra on the previous subset, we realize its Bishop boundary, as the trace of the Bishop boundary of the initial algebra on the spectrum of ...
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A Poisson boundary for topological semigroups
Archiv der Mathematik, 2014We give a non-probabilistic proof for the boundary integral representation of μ-harmonic functions on topological semigroups.
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h-Adaptive Immersed-Boundary Topology Optimization of Nonlinear Thermoelastic Structures
, 2020semanticscholar +1 more source
Carrier grain boundary scattering in thermoelectric materials
Energy and Environmental Science, 2022Chaoliang Hu, Chenguang Fu, Xinbing Zhao
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