39 citations · 94 across the 16 of their papers we have counts for
16 papers
Patnaik-Pearson intrinsic dimension for internal representations of neural networks
Tom Hadfield
We define a new measure of intrinsic dimension of a data manifold, which we call the Patnaik-Pearson dimension, and apply this to internal representations of neural networks, in pa…
Braided join comodule algebras of Galois objects
Ludwik Dabrowski, Tom Hadfield, Piotr M. Hajac +1
We construct the join of noncommutative Galois objects (quantum torsors) over a Hopf algebra H. To ensure that the join algebra enjoys the natural (diagonal) coaction of H, we brai…
Equivariant Join and Fusion of Noncommutative Algebras
Ludwik Dabrowski, Tom Hadfield, Piotr M. Hajac
We translate the concept of the join of topological spaces to the language of -algebras, replace the -algebra of functions on the interval with evaluation maps at…
Twisted Homology of Quantum SL(2) - Part II
Tom Hadfield, Ulrich Kraehmer
We complete the calculation of the twisted cyclic homology of the quantised coordinate ring of SL(2) that we began in math.QA/0405249. In particular, a nontrivial cyclic 3-cocycle…
Index pairings for pullbacks of C*-algebras
L. Dabrowski, T. Hadfield, P. M. Hajac +2
In this overview, we study how to reduce the index pairing for a fibre-product C*-algebra to the index pairing for the C*-algebra over which the fibre product is taken. As an examp…
Braided homology of quantum groups
Tom Hadfield, Ulrich Kraehmer
We study braided Hochschild and cyclic homology of ribbon algebras in braided monoidal categories, as introduced by Baez and by Akrami and Majid. We compute this invariant for seve…