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1. When Can We Treat Trajectories As Points?

   Duggirala, Parasara Sridhar; Sheehy, Donald (July 2017, Canadian Conference on Computational Geometry)

   In the formal verification of dynamical systems, one often looks at a trajectory through a state space as a sample behavior of the system. Thus, metrics on trajectories give important information about the different behavior of the system given different starting states. In the important special case of linear dynamical systems, the set of trajectories forms a finite-dimensional vector space. In this paper, we exploit this vector space structure to define (semi)norms on the trajectories, give an isometric embedding from the trajectory metric into low-dimensional Euclidean space, and bound the Lipschitz constant on the map from start states to trajectories as measured in one of several different metrics. These results show that for an interesting class of trajectories, one can treat the trajectories as points while losing little or no information. 

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2. When Can We Treat Trajectories as Points?

   Duggirala, Parasara Sridhar; Sheehy, Donald (July 2017, Candian Conference on Computational Geometry)
3. When automation hits jobs: Entrepreneurship as an alternative career path

   https://doi.org/10.1371/journal.pone.0331244  

   Kim, Daehyun; Kim, Taekyun; Kim, Wonjoon; Youn, Hyejin (September 2025, PLOS One)

   de_Almeida, Rafael Galvão (Ed.)

   This study investigates the relationship between occupational automation risks and workers’ transitions to entrepreneurship using data from the Current Population Survey. We find that employees facing automation-related job displacement are inclined to shift toward unincorporated entrepreneurship, emphasizing entrepreneurship as a viable alternative career path. Noteworthy variations emerge when examining specific automation technologies, revealing a positive association between industrial robots and entrepreneurial transitions, whereas artificial intelligence displays a negative relationship. Gender disparities are observed, with female workers exhibiting a lower likelihood than males of transitioning into entrepreneurship. This study also shows a heightened prominence of entrepreneurial transitions during the early stages of the COVID-19 pandemic. By illuminating entrepreneurship as a response to job displacement, our results offer crucial policy insights into the labor market implications of automation. 

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4. Necessary Considerations When Framing Urban Heat Resilience as an Infrastructure Issue

   https://doi.org/10.1080/01944363.2023.2259358  

   Lim, Theodore C (July 2024, Journal of the American Planning Association)
5. Genericity of pseudo-Anosov mapping classes, when seen as mapping classes

   https://doi.org/10.4171/LEM/66-3/4-6  

   Erlandsson, Viveka; Souto, Juan; Tao, Jing (January 2020, L’Enseignement Mathématique)

   null (Ed.)