The four subspace problem is a known matrix problem, which is equivalent to determining all the indecomposable representations of a poset consisting of four incomparable points. In this paper, we use solutions of this problem and invariants associate...
The Müller-Wichards model (MW) is an algebraic method that quantitatively estimates the performance of sequential and/or parallel computer applications. Because of category theory’s expressive power and mathematical precision, a category t...
We present an application of the program of groupoidification leading up to a sketch of a categorification of the Hecke algebroid—the category of permutation representations of a finite group. As an immediate consequence, we obtain a categorification...
This paper explores two-way relations between visualizations in mathematics and mathematical art, as well as art in general. A collection of vignettes illustrates connection points, including visualizing higher dimensions, tessellations, knots and li...
Let
It is demonstrated how to construct a Galois connection between two related systems with entropy. The construction, called the Landauer’s connection, describes coupling between two systems with entropy. It is straightforward and transfers chang...
We survey the recent developments on quantum invariants of 3-manifolds and links:
In this paper, we explore the algebraic and geometric structures that arise from a procedure we dub “gauging the gauge”, which involves the promotion of a certain global, coordinate independent symmetry to a local one. By gauging the glob...