9 citations · 16 across the 7 of their papers we have counts for
7 papers
Axiomatic field theory and Hida-Colombeau algebras
Alexei Filinkov, Ian G. Fuss
An axiomatic quantum field theory applied to the self-interacting boson field is realised in terms of generalised operators that allows us to form products and take derivatives of…
On the composition of integral operators acting in tempered Colombeau algebras
Alexei Filinkov, Ian Fuss
We show that the generalised composition of generalised integral operators is well defined on the space Colombeau algebras of tempered generalised functions.
Critical initialisation in continuous approximations of binary neural networks
George Stamatescu, Federica Gerace, Carlo Lucibello +2
The training of stochastic neural network models with binary () weights and activations via continuous surrogate networks is investigated. We derive new surrogates using a no…
An introduction to generalised functions in periodic quantum theory
Ian G Fuss, Alexei Filinkov
A proof that minimum uncertainty states of the simplest periodic quantum system exist in a state space that is represented by a Colombeau algebra of generalised functions but not i…
An analytic solution for one-dimensional quantum walks
Ian Fuss, Lang White, Peter Sherman +1
The first general analytic solutions for the one-dimensional walk in position and momentum space are derived. These solutions reveal, among other things, new symmetry features of q…
Momentum Dynamics of One Dimensional Quantum Walks
Ian Fuss, Langord B. White, Peter J. Sherman +1
We derive the momentum space dynamic equations and state functions for one dimensional quantum walks by using linear systems and Lie group theory. The momentum space provides an an…