arXiv subjects

John Jones

Publications and source records attributed to John Jones.

8 recordsLinked to original sources

arXiv2026

The directional localization game on graphs

In the localization game on a graph $G$, a team of cops searches for an invisible, mobile robber on $G$ by "probing" vertices; each probe tells the cops the distance from the probed vertex to the robber. The cops win if they can uniquely determine the robber's location. In this paper, we introduce a related game: the directional localization game. In this game, instead of probes returning distances, they return directions: when the cops probe a vertex $v$, the robber must respond with one or more neighbors of $v$ that lie on a shortest path from $v$ to the robber's location. The minimum number of cops needed to win this game on $G$ is the directional localization number of $G$. We study the directional localization game on several classes of graphs, including chordal graphs, Cartesian products, and incidence graphs of projective planes. We also bound the directional localization number of a graph $G$ in terms of the degeneracy and the treewidth of $G$.

math.CO↗

arXiv2026

One at a Time? The Personal Productivity Bias in Emergency Department Patient Assignment

Emergency departments (EDs) often use a shared-queue setup in which physicians self-assign cases from a pool of triaged patients. We conduct a multi-method study to examine this self-assignment behavior and its effects on system performance. Using data from five EDs spanning 1.4 million patient visits, we show that batching, i.e., self-assigning multiple patients at once, is common and associated with longer stays for batched patients, even after controlling for clinical acuity, physician fixed effects, and ED congestion. We then develop a continuous-time queueing model that characterizes the optimal self-assignment policy under individual and group throughput incentives. We use the model predictions to test experimentally with 203 healthcare workers and 73 ED physicians whether batching is a rational response to incentives or a deeper behavioral tendency that persists independent of incentives. Indeed, batching is pervasive across both samples, with 94% of healthcare workers and 73% of physicians choosing to batch even when it reduces their own payoffs -- a behavior that we term the personal productivity bias. Together, these results suggest that compensation redesign alone is unlikely to eliminate batching, and suggest changes to the assignment interface in the electronic health record system as a more promising remedy.

econ.GN↗

arXiv2025

Limited-visibility Cops and Robbers on Hamming graphs

In the classic game of Cops and Robbers, a team of cops pursues a robber through a graph. The traditional model of Cops and Robbers operates under the assumption that the cops know the robber's location at all times. Recently, however, there has been growing interest in models wherein the cops have only partial information about the robber's location. In this paper, we study the limited-visibility variant of Cops and Robbers, in which the cops only know the robber's position if some cop is within a fixed distance of the robber. For this variant of the game, we give bounds on the number of cops needed to capture a robber on Hamming graphs, and we use these results to settle several open problems posed by Clarke et al.

math.CO↗

arXiv2023

On the 32-dimensional Rosenfeld projective plane

Following on from arXiv:2310.14365 [math.AT], we make a detailed study of the $32$-dimensional Rosenfeld projective plane which is the symmetric space EIII in Cartan's list of compact symmetric spaces.

math.AT↗

arXiv2023

The classical topological invariants of homogeneous spaces

We study the homogeneous spaces of a simply connected, compact, simple Lie group $G$ through the lens of K-theory. Our methods apply equally well to the case where $G$ is in one of the four infinite families of classical groups, or one of the five exceptional groups. The main examples we study in detail are the four symmetric spaces FII, EIII, EVI, EVIII in Cartan's list of symmetric spaces. These are, respectively, homogeneous spaces for $F_4$, $E_6$, $E_7$, $E_8$ with dimensions $16$, $32$, $64$, $128$. They are the four Rosenfeld projective planes.

math.AT↗

arXiv2023

Generative AI: Implications and Applications for Education

The launch of ChatGPT in November 2022 precipitated a panic among some educators while prompting qualified enthusiasm from others. Under the umbrella term Generative AI, ChatGPT is an example of a range of technologies for the delivery of computer-generated text, image, and other digitized media. This paper examines the implications for education of one generative AI technology, chatbots responding from large language models, or C-LLM. It reports on an application of a C-LLM to AI review and assessment of complex student work. In a concluding discussion, the paper explores the intrinsic limits of generative AI, bound as it is to language corpora and their textual representation through binary notation. Within these limits, we suggest the range of emerging and potential applications of Generative AI in education.

cs.CY↗

arXiv2021

Compact Lie Groups and Complex Reductive Groups

We show that the categories of compact Lie groups and complex reductive groups (not necessarily connected) are homotopy equivalent topological categories. In other words, the corresponding categories enriched in the homotopy category of topological spaces are equivalent. This can also be interpreted as an equivalence of infinity categories.

math.RT↗

arXiv2020

General Comodule-Contramodule Correspondence

This paper is a fundamental study of comodules and contramodules over a comonoid in a symmetric closed monoidal category. We study both algebraic and homotopical aspects of them. Algebraically, we enrich the comodule and contramodule categories over the original category, construct enriched functors between them and enriched adjunctions between the functors. Homotopically, for simplicial sets and topological spaces, we investigate the categories of comodules and contramodules and the relations between them.

math.CT↗