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Aidan Duncan

Publications and source records attributed to Aidan Duncan.

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A Conceptual Framework for Enhancing Workforce Readiness for Smart Manufacturing in the AI Era

The convergence of artificial intelligence (AI), Industrial Internet of Things, cyber-physical systems, and advanced robotics is reshaping manufacturing faster than engineering curricula can adapt, widening the gap between the competencies required on the shop floor and those delivered by traditional engineering and technology education. This paper proposes a Workforce Readiness Level (WRL) framework, which adapts the Technology Readiness Level scale into nine progressive competency stages and a four-pillar rubric, digital and AI literacy, cyber-physical systems fluency, human-machine collaboration, and data-driven decision making, aggregated through a composite stage score and a cohort-level workforce-readiness index under a ``no-thin-pillar'' rule. The framework is instantiated at a university smart-manufacturing teaching laboratory and draws on 89 sponsored capstone projects delivered over four semesters, four of which are analyzed in depth. Four pillars jointly span the relevant ABET student outcomes. Across the highlighted cohorts the workforce-readiness index ranged from 5.2 to 6.4, and the no-thin-pillar rule was diagnostically informative in three of the four cases and the binding certification constraint in one, repeatedly surfacing cyber-physical and data-driven-decision gaps concealed behind strong analytics profiles; advancement to the highest stages was gated by industry-embedded experience rather than additional coursework. WRL offers educators, accreditation bodies, and regional workforce systems a common, evidence-based instrument for diagnosing and advancing workforce readiness; future work will calibrate pillar weights and test reliability and predictive validity.

eess.SY

Sequences of the Stable Matching Problem

In this paper, we begin by discussing different types of preference profiles related to the stable marriage problem. We then introduce the concept of soulmates, which are a man and a woman who rank each other first. Inversely, we examine hell-pairs, where a man and a woman rank each other last. We generate sequences enumerating preference profiles of different types. We also calculate sequences related to the egalitarian cost, or "quality", of a matching. In total, we introduce and discuss 30 new sequences related to the stable marriage problem and discuss 6 sequences that are already in the OEIS.

math.HO

The Stable Matching Problem and Sudoku

Are you having trouble getting married? These days, there are lots of products on the market for dating, from apps to websites and matchmakers, but we know a simpler way! That's right -- your path to coupled life isn't through Tinder: it's through Sudoku! Read our fabulous paper where we explore the Stable Marriage Problem to help you find happiness and stability in marriage through math. As a bonus, you get two Sudoku puzzles with a new flavor.

math.HO

The No-Flippancy Game

We analyze a coin-based game with two players where, before starting the game, each player selects a string of length $n$ comprised of coin tosses. They alternate turns, choosing the outcome of a coin toss according to specific rules. As a result, the game is deterministic. The player whose string appears first wins. If neither player's string occurs, then the game must be infinite. We study several aspects of this game. We show that if, after $4n-4$ turns, the game fails to cease, it must be infinite. Furthermore, we examine how a player may select their string to force a desired outcome. Finally, we describe the result of the game for particular cases.

math.CO

It's Common Knowledge

We discuss some old common knowledge puzzles and introduce a lot of new common knowledge puzzles.

math.HO