78 research outputs found
Tangled Circuits
The theme of the paper is the use of commutative Frobenius algebras in
braided strict monoidal categories in the study of varieties of circuits and
communicating systems which occur in Computer Science, including circuits in
which the wires are tangled. We indicate also some possible novel geometric
interest in such algebras
Calculating Colimits Compositionally
We show how finite limits and colimits can be calculated
compositionally using the algebras of spans and cospans, and give as an application a proof of the Kleene Theorem on regular languages
Calculating Colimits Compositionally
We show how finite limits and colimits can be calculated compositionally
using the algebras of spans and cospans, and give as an application a proof of
the Kleene Theorem on regular languages
Interacting Frobenius Algebras are Hopf
Theories featuring the interaction between a Frobenius algebra and a Hopf
algebra have recently appeared in several areas in computer science: concurrent
programming, control theory, and quantum computing, among others. Bonchi,
Sobocinski, and Zanasi (2014) have shown that, given a suitable distributive
law, a pair of Hopf algebras forms two Frobenius algebras. Here we take the
opposite approach, and show that interacting Frobenius algebras form Hopf
algebras. We generalise (BSZ 2014) by including non-trivial dynamics of the
underlying object---the so-called phase group---and investigate the effects of
finite dimensionality of the underlying model. We recover the system of Bonchi
et al as a subtheory in the prime power dimensional case, but the more general
theory does not arise from a distributive law.Comment: 32 pages; submitte
Rewriting modulo symmetric monoidal structure
String diagrams are a powerful and intuitive graphical syntax for terms of symmetric monoidal categories (SMCs). They find many applications in computer science and are becoming increasingly relevant in other fields such as physics and control theory.An important role in many such approaches is played by equational theories of diagrams, typically oriented and applied as rewrite rules. This paper lays a comprehensive foundation for this form of rewriting. We interpret diagrams combinatorially as typed hypergraphs and establish the precise correspondence between diagram rewriting modulo the laws of SMCs on the one hand and double pushout (DPO) rewriting of hypergraphs, subject to a soundness condition called convexity, on the other. This result rests on a more general characterisation theorem in which we show that typed hypergraph DPO rewriting amounts to diagram rewriting modulo the laws of SMCs with a chosen special Frobenius structure.We illustrate our approach with a proof of termination for the theory of non-commutative bimonoids
Probing Stereoselectivity in Ring-Opening Metathesis Polymerization Mediated by Cyclometalated Ruthenium-Based Catalysts: A Combined Experimental and Computational Study
The microstructures of polymers produced by ring-opening metathesis polymerization (ROMP) with cyclometalated Ru-carbene metathesis catalysts were investigated. A strong bias for a cis,syndiotactic microstructure with minimal head-to-tail bias was observed. In instances where trans errors were introduced, it was determined that these regions were also syndiotactic. Furthermore, hypothetical reaction intermediates and transition structures were analyzed computationally. Combined experimental and computational data support a reaction mechanism in which cis,syndio-selectivity is a result of stereogenic metal control, while microstructural errors are predominantly due to alkylidene isomerization via rotation about the Ru═C double bond
- …