11,889 research outputs found
Relearning Professionalism: From High School Teacher to University Professor
In this narrative response to stories from the field, the author chronicles her transition from high school teacher to university professor. The transition was marked by a dissonance about what it means to be a professional in each setting. The author shares several lessons learned about the autonomy in higher education, which was at first daunting, and later a relief in her new environment
Encoding !-tensors as !-graphs with neighbourhood orders
Diagrammatic reasoning using string diagrams provides an intuitive language
for reasoning about morphisms in a symmetric monoidal category. To allow
working with infinite families of string diagrams, !-graphs were introduced as
a method to mark repeated structure inside a diagram. This led to !-graphs
being implemented in the diagrammatic proof assistant Quantomatic. Having a
partially automated program for rewriting diagrams has proven very useful, but
being based on !-graphs, only commutative theories are allowed. An enriched
abstract tensor notation, called !-tensors, has been used to formalise the
notion of !-boxes in non-commutative structures. This work-in-progress paper
presents a method to encode !-tensors as !-graphs with some additional
structure. This will allow us to leverage the existing code from Quantomatic
and quickly provide various tools for non-commutative diagrammatic reasoning.Comment: In Proceedings QPL 2015, arXiv:1511.0118
Permutation-based presentations for Brin's higher-dimensional Thompson groups
The higher-dimensional Thompson groups , for , were introduced
by Brin in 2005. We provide new presentations for each of these infinite simple
groups. The first is an infinite presentation, analogous to the Coxeter
presentation for the finite symmetric group, with generating set equal to the
set of transpositions in and reflecting the self-similar structure of
-dimensional Cantor space. We then exploit this infinite presentation to
produce further finite presentations that are considerably smaller than those
previously known.Comment: 24 pages, 2 figure
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