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Understanding the dynamics of fire propagation is essential in improving predictive models and developing effective fire management strategies. This study applies computer vision techniques to complement traditional fire behaviour modelling. We employ the Segment Anything Model to achieve the accurate segmentation of experimental fire videos, enabling the frame-by-frame segmentation of fire perimeters, quantification of the rate of spread in multiple directions, and explicit analysis of slope effects. Our laboratory experiments reveal that the ROS increases exponentially with slope, but with coefficients differing from those prescribed in the Canadian Fire Behaviour Prediction System, reflecting differences in field conditions. Complementary field data from prescribed burns in coniferous fuels (C-7) further demonstrate that slope effects vary under operational conditions, suggesting field-dependent dynamics not fully captured by existing deterministic models. Our experiments show that, even under controlled laboratory conditions, substantial variability in spread rate is observed, underscoring the inherent stochasticity of fire spread. Together, these findings highlight the value of vision-based perimeter extraction in generating precise spread data and reinforce the need for probabilistic modelling approaches that explicitly account for uncertainty and emergent dynamics in fire behaviour. 

Abstract This work investigates how students interpret various eigenequations in different contexts for$$2 \times 2$$ $2\times 2$matrices:$$A\vec {x}=\lambda \vec {x}$$ $A\overrightarrow{x}=\lambda \overrightarrow{x}$in mathematics and either$$\hat{S}_x| + \rangle _x=\frac{\hbar }{2}| + \rangle _x$$ ${\hat{S}}_x{|+⟩}_x=\frac{ħ}{2}{|+⟩}_x$or$$\hat{S}_z| + \rangle =\frac{\hbar }{2}| + \rangle$$ ${\hat{S}}_z|+⟩=\frac{ħ}{2}|+⟩$in quantum mechanics. Data were collected from two sources in a senior-level quantum mechanics course; one is video, transcript and written work of individual, semi-structured interviews; the second is written work from the same course three years later. We found two principal ways in which students reasoned about the equal sign within the mathematics eigenequation and at times within the quantum mechanical eigenequations: with a functional interpretation and/or a relational interpretation. Second, we found three distinct ways in which students explained how they made sense of the physical meaning conveyed by the quantum mechanical eigenequations: via a measurement interpretation, potential measurement interpretation, or correspondence interpretation of the equation. Finally, we present two themes that emerged in the ways that students compared the different eigenequations: attention to form and attention to conceptual (in)compatibility. These findings are discussed in relation to relevant literature, and their instructional implications are also explored.