Most probable transition paths in piecewise-smooth stochastic differential equations

We develop a path integral framework for determining most probable paths in a class of systems of stochastic differential equations with piecewise-smooth drift and additive noise. This approach extends the Freidlin-Wentzell theory of large deviations to cases where the system is piecewise-smooth and may be non-autonomous. In particular, we consider an $n-$dimensional system with a switching manifold in the drift that forms an $(n-1)-$dimensional hyperplane and investigate noise-induced transitions between metastable states on either side of the switching manifold. To do this, we mollify the drift and use $\Gamma-$convergence to derive an appropriate rate functional for the system in the piecewise-smooth limit. The resulting functional consists of the standard Freidlin-Wentzell rate functional, with an additional contribution due to times when the most probable path slides in a crossing region of the switching manifold. We explore implications of the derived functional through two case studies, which exhibit notable phenomena such as non-unique most probable paths and noise-induced sliding in a crossing region.Comment: 38 pages, 9 figure

Gendered Risk Perceptions Associated with Human-Wildlife Conflict: Implications for Participatory Conservation

This research aims to foster discourse about the extent to which gender is important to consider within the context of participatory approaches for biological conservation. Our objectives are to: (1) gender-disaggregate data about stakeholders' risk perceptions associated with human-wildlife conflict (HWC) in a participatory conservation context, and (2) highlight insights from characterizing gendered similarities and differences in the way people think about HWC-related risks. Two communal conservancies in Caprivi, Namibia served as case study sites. We analyzed data from focus groups (n = 2) to create gendered concept maps about risks to wildlife and livelihoods and any associations of those risks with HWC, and semi-structured interviews (n = 76; men = 38, women = 38) to measure explicit risk attitudes associated with HWC. Concept maps indicated some divergent perceptions in how groups characterized risks to wildlife and livelihoods; however, not only were identified risks to wildlife (e.g., pollution, hunting) dissimilar in some instances, descriptions of risks varied as well. Study groups reported similar risk perceptions associated with HWC with the exception of worry associated with HWC effects on local livelihoods. Gendered differences in risk perceptions may signal different priorities or incentives to participate in efforts to resolve HWC-related risks. Thus, although shared goals and interests may seem to be an obvious reason for cooperative wildlife management, it is not always obvious that management goals are shared. Opportunity exists to move beyond thinking about gender as an explanatory variable for understanding how different groups think about participating in conservation activities