Citation

BibTex format

@article{Chen:2024:10.1007/s00006-024-01325-y,
author = {Chen, S and Dechant, P-P and He, Y-H and Heyes, E and Hirst, E and Riabchenko, D},
doi = {10.1007/s00006-024-01325-y},
journal = {Advances in Applied Clifford Algebras},
title = {Machine Learning Clifford Invariants of ADE Coxeter Elements},
url = {http://dx.doi.org/10.1007/s00006-024-01325-y},
volume = {34},
year = {2024}
}
Download

RIS format (EndNote, RefMan)

TY  - JOUR
AB  - <jats:title>Abstract</jats:title><jats:p>There has been recent interest in novel Clifford geometric invariants of linear transformations. This motivates the investigation of such invariants for a certain type of geometric transformation of interest in the context of root systems, reflection groups, Lie groups and Lie algebras: the Coxeter transformations. We perform exhaustive calculations of all Coxeter transformations for<jats:inline-formula><jats:alternatives><jats:tex-math>$$A_8$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>A</mml:mi><mml:mn>8</mml:mn></mml:msub></mml:math></jats:alternatives></jats:inline-formula>,<jats:inline-formula><jats:alternatives><jats:tex-math>$$D_8$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>D</mml:mi><mml:mn>8</mml:mn></mml:msub></mml:math></jats:alternatives></jats:inline-formula>and<jats:inline-formula><jats:alternatives><jats:tex-math>$$E_8$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>E</mml:mi><mml:mn>8</mml:mn></mml:msub></mml:math></jats:alternatives></jats:inline-formula>for a choice of basis of simple roots and compute their invariants, using high-performance computing. This computational algebra paradigm generates a dataset that can then be mined using techniques from data science such as supervised and unsupervised machine learning. In this paper we focus on neural network classification and principal component analysis. Since the output—the invariants—is fully determined by the choice of simple roots and the permutation order of the corresponding reflections in the Coxeter elemen
AU  - Chen,S
AU  - Dechant,P-P
AU  - He,Y-H
AU  - Heyes,E
AU  - Hirst,E
AU  - Riabchenko,D
DO  - 10.1007/s00006-024-01325-y
PY  - 2024///
SN  - 0188-7009
TI  - Machine Learning Clifford Invariants of ADE Coxeter Elements
T2  - Advances in Applied Clifford Algebras
UR  - http://dx.doi.org/10.1007/s00006-024-01325-y
UR  - https://doi.org/10.1007/s00006-024-01325-y
VL  - 34
ER  -
Download

Note to staff:  Adding new publications to a research group

  1. Log in to Symplectic.
  2. Click on Menu > Create Links
  3. Choose what you want to create links between – in this case ‘Publications’ and ‘Organisational structures’.
  4. Choose the organisational structure (research group) into which you want to link the publications and check the box next to it.
  5. Now check the box of any publication you want to add to that group. You can use the filters to find what you want and select multiple publications if necessary. 
  6. Scroll to the bottom and click the blue ‘Create new link’ button to link them.
  7. The publications will be added to the group, and will be displayed on the group publications feed within 24 hours (it is not immediate).

Any problems, talk to Tim Evans or the Faculty Web Team.