This paper establishes connections between three of the most prominent metrics used in the analysis of persistence diagrams in topological data analysis: the bottleneck distance, Patel's erosion distance, and Bubenik's landscape distance. Our main result shows that the erosion and landscape distances are equal, thereby bridging the former's natural category-theoretic interpretation with the latter's computationally convenient structure. The proof utilizes the category with a flow framework of de Silva et al., and leads to additional insights into the structure of persistence landscapes. Our equivalence result is applied to prove several results on the geometry of the erosion distance. We show that the erosion distance is not a length metric, and that its intrinsic metric is the bottleneck distance. We also show that the erosion distance does not coarsely embed into any Hilbert space, even when restricted to persistence diagrams arising from degree-0 persistent homology. Moreover, we show that erosion distance agrees with bottleneck distance on this subspace, so that our non-embeddability theorem generalizes several results in the recent literature.
Wildfire spread is strongly influenced by the transport and ignition of embers. While long-range spotting driven by plume lofting has received significant attention, embers transported near the surface by turbulent winds can also influence fire propagation. We develop a stochastic model for near-surface ember transport, referred to as ember wash. The model represents ember motion as a sequence of short displacements analogous to saltation-like transport and incorporates a probabilistic ignition process that depends on ember survival during transport. This formulation leads to an exponential distribution of ember flight times. The model is implemented within a simplified fire spread model to examine burn patterns and growth dynamics. Simulations demonstrate that ember wash produces spread behavior that differs fundamentally from classical plume-driven spotting. These results suggest that ember wash provides a plausible mechanism for wildfire spread regimes that differ from those predicted by geometric or plume-driven spread models.
We introduce a new method for constructing local-in-time solutions of the incompressible Euler equations in Sobolev spaces on an arbitrary Sobolev bounded domain. The method is based on a construction of an analytic solution in an analytically approximated domain, after which we apply analytic persistence to extend the analytic solution using given a priori bounds in Sobolev spaces. The method does not introduce any modification or regularization of the equations themselves and appears applicable to many other PDEs.
Artificial intelligence (AI) has become a disruptive force reshaping the entire economy through automation, productivity gains, and changing labor dynamics. Under supportive labor policies, AI may drive substantial productivity gains across many sectors and generate a “leisure dividend” through increased leisure time and disposable income, driving greater demand for experience-based services central to the hospitality and tourism (HT) industry. This study develops a conditional optimistic scenario in which the HT industry may emerge as a primary beneficiary of this AI-driven shift, with AI serving not as a threat but as a conditional catalyst for the industry’s growth and the elevation of human roles. Drawing on socio-technical systems theory and the experience economy framework, a conceptual framework is proposed wherein, under certain conditions, AI may generate a positive cyclical relationship among AI-integration, HT industry expansion, employee wellbeing, and guest satisfaction. The implications of AI-driven transformation in the HT industry are discussed.
The influence of perceptions of offender redeemability on support for punitive versus rehabilitative practices has been widely documented. An understudied area, however, concerns law enforcement perceptions of redeemability and whether these perceptions impact buy-in and implementation of interventions. The current research addresses this gap through a mixed methods case study of a researcher-practitioner partnership (RPP), assessing the influence of law enforcement partner perceptions of offenders on the implementation of a focused deterrence strategy. Qualitative findings suggest that project partners' views of younger, lower-risk offenders being more redeemable than older, higher-risk offenders impacted implementation of the focused deterrence intervention. Quantitative client contact data support these findings, demonstrating that, over time, partners increased engagement with youth and low-risk offenders, focusing more on prevention while largely abandoning the original intervention efforts. This research informs our understanding of how law enforcement perceptions of offender redeemability can shape the implementation process. We discuss potential future directions of research in this area and highlight policy recommendations for RPPs and law enforcement interventions more broadly.
