2 citations · 3 across the 8 of their papers we have counts for
9 papers
Canonical quantization of neurons
Alexander He, Nana Liu, Mark M. Wilde
Canonical quantization provides a systematic procedure for constructing quantum models from classical Hamiltonians. Here, we apply this principle to a fundamental computational pri…
Fermi-Dirac machines as quantizations of neurons
Alexander He, Nana Liu, Mark M. Wilde
Fermi-Dirac machines were proposed recently as an approach to solving semidefinite optimization problems on quantum computers. Here, we reinterpret them as canonical quantizations…
A Practical Algorithm for Knot Factorisation
Alexander He, Eric Sedgwick, Jonathan Spreer
We present an algorithm for computing the prime factorisation of a knot, which is practical in the following sense: using Regina, we give an implementation that works well for inpu…
Crushing Surfaces of Positive Genus
Benjamin A. Burton, Thiago de Paiva, Alexander He +1
The operation of crushing a normal surface has proven to be a powerful tool in computational -manifold topology, with applications both to triangulation complexity and to algori…
An algorithm to construct one-vertex triangulations of Heegaard splittings
Alexander He, James Morgan, Em K. Thompson
Following work of Jaco and Rubinstein (2006), which (non-constructively) proved that any 3-manifold admits a one-vertex layered triangulation, we present an algorithm, with impleme…
Finding large counterexamples by selectively exploring the Pachner graph
Benjamin A. Burton, Alexander He
We often rely on censuses of triangulations to guide our intuition in -manifold topology. However, this can lead to misplaced faith in conjectures if the smallest counterexample…
Arc diagrams on 3-manifold spines
Jack Brand, Benjamin A. Burton, Zsuzsanna Dancso +3
We develop a theory of link projections to trivalent spines of 3-manifolds. We prove a Reidemeister Theorem providing a set of combinatorial moves sufficient to relate the projecti…
Connecting 3-manifold triangulations with unimodal sequences of elementary moves
Benjamin A. Burton, Alexander He
A key result in computational 3-manifold topology is that any two triangulations of the same 3-manifold are connected by a finite sequence of bistellar flips, also known as Pachner…
On the hardness of finding normal surfaces
Benjamin A. Burton, Alexander He
For many fundamental problems in computational topology, such as unknot recognition and -sphere recognition, the existence of a polynomial-time solution remains unknown. A major…