arXiv subjects

Malcolm Jones

Publications and source records attributed to Malcolm Jones.

5 recordsLinked to original sources

arXiv2026

Steinberg Algebras of Ample Semicategories and their Boolean-Cartan Restriction Semigroups

We extend the construction of Steinberg algebras of ample groupoids to \'etale semicategories. We also relate ample semicategories to Boolean restriction semigroups via a representation result extending previously known results for categories. Furthermore, we prove a reconstruction result which characterises an abstract algebra $A$ with a certain Cartan-like restriction subsemigroup $B$ (subject to conditions resembling those defining quasi-Cartan pairs) as the Steinberg algebra of the ultrafilter groupoid of $B$. In this way we obtain a twist-free extension of previous Steinberg algebra reconstruction results.

math.RA↗

arXiv2025

Groupoids of finitely aligned higher-rank graphs via filters and graph morphisms

Path and boundary-path groupoids of finitely aligned higher-rank graphs are often constructed using either filters or graph morphisms. We generalise the graph morphism approach to finitely aligned P-graphs where (Q, P) is a weakly quasi-lattice ordered group, and we show the filter approach and the graph morphism approach yield isomorphic path and boundary-path groupoids. To do this, we define conjugacy of partial semigroup actions such that conjugate actions have isomorphic semidirect product groupoids. Combining our results with others in the literature, we survey many isomorphic presentations of path and boundary-path groupoids at different levels of generality.

math.RA↗

arXiv2025

A local treatment of finite alignment and path groupoids of nonfinitely aligned higher-rank graphs

We give a local treatment of finite alignment by identifying the finitely aligned part of any (not necessarily finitely aligned) higher-rank graph. We show the finitely aligned part is itself a constellation and forms a finitely aligned relative category of paths together with the original higher-rank graph. We show that the elements of the finitely aligned part are precisely those whose cylinder sets are compact, which allows us to give novel definitions of locally compact path and boundary-path spaces for nonfinitely aligned higher-rank graphs. We extend a semigroup action and the associated semidirect product groupoid developed by Renault and Williams to define ample Hausdorff path and boundary-path groupoids. The groupoids are amenable for nonfinitely aligned k-graphs by a result of Renault and Williams. In the finitely aligned case, the path groupoids coincide with Spielberg's groupoids, and the boundary-path groupoid has an inverse semigroup model via a result of Ortega and Pardo.

math.RA↗

arXiv2024

Dynamic nowcast of the New Zealand greenhouse gas inventory

As efforts to mitigate the effects of climate change grow, reliable and thorough reporting of greenhouse gas emissions are essential for measuring progress towards international and domestic emissions reductions targets. New Zealand's national emissions inventories are currently reported between 15 to 27 months out-of-date. We present a machine learning approach to nowcast (dynamically estimate) national greenhouse gas emissions in New Zealand in advance of the national emissions inventory's release, with just a two month latency due to current data availability. Key findings include an estimated 0.2% decrease in national gross emissions since 2020 (as at July 2022). Our study highlights the predictive power of a dynamic view of emissions intensive activities. This methodology is a proof of concept that a machine learning approach can make sub-annual estimates of national greenhouse gas emissions by sector with a relatively low error that could be of value for policy makers.

cs.LG↗

arXiv2020

Filtering germs: Groupoids associated to inverse semigroups

We investigate various groupoids associated to an arbitrary inverse semigroup with zero. We show that the groupoid of filters with respect to the natural partial order is isomorphic to the groupoid of germs arising from the standard action of the inverse semigroup on the space of idempotent filters. We also investigate the restriction of this isomorphism to the groupoid of tight filters and to the groupoid of ultrafilters.

math.RA↗