1,856 research outputs found
Crystal growth kinetics of two-step growth process in liquid fluidized-bed crystallizers
No full text[Tribute to Michi Weglyn by Dr. Clifford I. Uyeda, February 21, 1998]
No full textA speech by Dr. Clifford Uyeda for the Day of Remembrance celebration and tribute to Michi Weglyn on February 21, 1998.These materials are from box 73 and 74 of the Frank Chin Papers. The Frank Chin Papers contain personal and professional correspondence between Frank Chin and Michi Weglyn relating to particular projects on which either author was working as well as files related to the Day of Remembrance Tribute to Michi Weglyn
Machine Learning Clifford invariants of ADE Coxeter elements
Full text linkThere 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 , and 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 element, we expect huge degeneracy in the mapping.
This provides the perfect setup for machine learning, and indeed we see that
the datasets can be machine learned to very high accuracy. This paper is a
pump-priming study in experimental mathematics using Clifford algebras, showing
that such Clifford algebraic datasets are amenable to machine learning, and
shedding light on relationships between these novel and other well-known
geometric invariants and also giving rise to analytic results.Comment: v1: 34 pages, 16 Figures, 12 Tables. v2: Typos corrected and some
comments added. Matches the author-accepted version for publication in
Advances in Applied Clifford Algebra
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