Exploring a Quantum Theory with Graph Rewriting and Computer Algebra by Kissinger, A

Heterotic compactification, an algorithmic approach by Anderson, L, He, Y, Lukas, A

“…We approach string phenomenology from the perspective of computational algebraic geometry, by providing new and efficient techniques for proving stability and calculating particle spectra in heterotic compactifications. …”

The groups with order p7 for odd prime p by O'Brien, E, Vaughan-Lee, MR

“…We provide access to the resulting presentations for the groups via a database distributed with computer algebra systems. © 2005 Elsevier Inc. All rights reserved.…”

Algorithmic algebraic geometry and flux vacua by Gray, J, He, Y, Lukas, A

“…The issue of finding vacua of such systems, both supersymmetric and non-supersymmetric, is mapped into a problem in computational algebraic geometry. Using recent developments in computer algebra, the problem can then be rapidly dealt with in a completely algorithmic fashion. …”

Groups and nilpotent Lie rings whose order is the sixth power of a prime by Newman, M, O'Brien, E, Vaughan-Lee, M

“…Public access to the group presentations is provided via a database distributed with computer algebra systems. © 2003 Elsevier Inc. All rights reserved.…”

On the equations defining some Hilbert schemes by Hauenstein, JD, Manivel, L, Szendroi, B

“…While the explicit equations we find are controlled in a precise way by the representation theory of SL_3, our arguments also rely on computer algebra.…”

STRINGVACUA. A Mathematica package for studying vacuum configurations in string phenomenology by Gray, J, He, Y, Ilderton, A, Lukas, A

“…The package uses powerful algebro-geometric methods, as implemented in the free computer algebra system Singular, but requires no knowledge of the mathematics upon which it is based. …”

On some configurations of oppositely charged trapped vortices in the plane by Dufresne, E, Harrington, HA, Hauenstein, JD, Kevrekidis, PG, Tripoli, P

“…In this effort, we deploy the use of a computational algebra approach in order to identify stationary multi-vortex states with up to 6 vortices. …”

Algebra, geometry and topology of ERK kinetics by Marsh, L, Dufresne, E, Byrne, HM, Harrington, HA

“…We demonstrate how methods from computational algebraic geometry, differential algebra, Bayesian statistics and computational algebraic topology can inform the model reduction, identification and parameter inference of MEK variants, respectively. …”

Algebraic systems biology: a case study for the Wnt pathway by Gross, E, Harrington, H, Rosen, Z, Sturmfels, B

“…We employ current methods from computational algebraic geometry, polyhedral geometry, and combinatorics.…”

Multivariate central limit theorems for random clique complexes by Temčinas, T, Nanda, V, Reinert, G

“…<p>Motivated by open problems in applied and computational algebraic topology, we establish multivariate normal approximation theorems for three random vectors which arise organically in the study of random clique complexes. …”

Joining and decomposing reaction networks by Gross, E, Harrington, H, Meshkat, N, Shiu, A

“…Our proofs use techniques from computational algebraic geometry, including elimination theory and differential algebra.…”

Joining and decomposing reaction networks by Gross, E, Harrington, H, Meshkat, N, Shiu, A

“…Our proofs use techniques from computational algebraic geometry, including elimination theory and differential algebra.…”

Topological data analysis of task-based fMRI data from experiments on schizophrenia by Stolz, BJ, Emerson, T, Nahkuri, S, Porter, MA, Harrington, H

“…We use methods from computational algebraic topology to study functional brain networks in which nodes represent brain regions and weighted edges encode the similarity of functional magnetic resonance imaging (fMRI) time series from each region. …”