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Bee declines have been partly attributed to the impacts of invasive or emerging parasite outbreaks. For western honeybees,Apis mellifera, major losses are associated with the virus-vectoring mite,Varroa destructor. In response, beekeepers have focused breeding efforts aimed at conferring resistance to this key parasite. One method of many is survival-based beekeeping where colonies that survive despite significantVarroainfestations produce subsequent colonies. We argue that this ‘hands-off’ approach will not always lead toVarroaresistance evolving but rather tolerance. Tolerance minimizes host fitness costs of parasitism without reducing parasite abundance, whereas resistance either prevents parasitism outright or keeps parasitism intensity low. With clear epidemiological distinctions, and as honeybee disease dynamics impact other wild bees owing to shared pathogens, we discuss why tolerance outcomes in honeybee breeding have important implications for wider pollinator health. Crucially, we argue that unintentional selection for tolerance will not only lead to more spillover from honeybees but may also select for pathogens that are more virulent in wild bees leading to ‘tragedies of tolerance’. These tragedies can be avoided through successful breeding regimes that specifically select for lowVarroa. We emphasize how insights from evolutionary ecology can be applied in ecologically responsible honeybee management. 

This paper introduces a type of circular causation called Congestive Mode-Switching (CMS) that may arise when an increase in congestion penalizes transit relative to driving. In turn, rising congestion persuades some transit riders to drive, which exacerbates congestion further, and so on. This circular causation can beget multiple equilibria with different levels of congestion and transit ridership. The paper explores this logic with a static model of a bus route. When the bus fleet size is fixed, CMS applies because congestion raises the bus cycle time and thus lowers bus frequency, resulting in higher wait times. When the fleet size depends on bus ridership, CMS is joined by economies of scale as a second source of circular causation. We derive the system’s equilibria using a static model in the vein of Walters (1961), which permits us to graphically characterize equilibria in useful ways. The comparative statics of a road improvement show how feedback alters first-order effects. A Downs-Thomson paradox is not possible, because a road improvement aids buses even more than cars. Continuous-time stability analysis shows that multiple equilibria may be stable. 

Studies of transit dwell times suggest that the delay caused by passengers boarding and alighting rises with the number of passengers on each vehicle. This paper incorporates such a “friction effect” into an isotropic model of a transit route with elastic demand. We derive a strongly unimodal “Network Alighting Function” giving the steady-state rate of passenger flows in terms of the accumulation of passengers on vehicles. Like the Network Exit Function developed for isotropic models of vehicle traffic, the system may exhibit hypercongestion. Since ridership depends on travel times, wait times and the level of crowding, the physical model is used to solve for (possibly multiple) equilibria as well as the social optimum. Using replicator dynamics to describe the evolution of demand, we also investigate the asymptotic local stability of different kinds of equilibria. 

Fractional evolution equations lack generally accessible and well-converged codes excepting anomalous diffusion. A particular equation of strong interest to the growing intersection of applied mathematics and quantum information science and technology is the fractional Schrödinger equation, which describes sub-and super-dispersive behavior of quantum wavefunctions induced by multiscale media. We derive a computationally efficient sixth-order split-step numerical method to converge the eigenfunctions of the FSE to arbitrary numerical precision for arbitrary fractional order derivative. We demonstrate applications of this code to machine precision for classic quantum problems such as the finite well and harmonic oscillator, which take surprising twists due to the non-local nature of the fractional derivative. For example, the evanescent wave tails in the finite well take a Mittag-Leffer-like form which decay much slower than the well-known exponential from integer-order derivative wave theories, enhancing penetration into the barrier and therefore quantum tunneling rates. We call this effect \emph{fractionally enhanced quantum tunneling}. This work includes an open source code for communities from quantum experimentalists to applied mathematicians to easily and efficiently explore the solutions of the fractional Schrödinger equation in a wide variety of practical potentials for potential realization in quantum tunneling enhancement and other quantum applications. 

This study highlights the application of self-regulated learning and cognitive strategy use research in the Connecting Students with Autism to Geographic Information Science & Technology (CSA-GIST) study, an NSF-funded project. This study investigated the program’s impact on autistic high school students’ self-regulated learning (SRL) and cognitive strategy use during STEM instruction. Though the findings were not significant regarding the impact of the program on students SRL and cognitive strategy use at the midpoint of the program, increased interest in math, science, and technology were reported for each cohort during year one. These findings provide implications for adaptations to this workforce development program to increase students’ SRL and cognitive strategy use for GIST and STEM careers among autistic students. Implications for research and practice are discussed. 

Indigenous research posits that practice-based evidence is fundamental to culturally grounded, multifaceted methods. The objective is to outline the key tenets and characteristics of Elder-centered research and relevant methodology using an interconnected progression of Alaska Native studies. Semi-structured interviews were conducted with 12 Alaska Native Elders, 21 Alaska Native caregivers, and 12 Alaska Native and non-Native caregivers in two studies exploring cultural understandings of memory and successful aging. The design and implementation of these studies employed Elders at every level, ensuring cultural relevance, outcomes, and dissemination. Results reflect the benefits of engaging Alaska Native Elders in research and reveal methods for best practices: (a) creating advisory councils, (b) identifying stakeholders, (c) weaving together Elder and western knowledge systems, and (d) the reciprocal nature of Elder engagement and well-being. This research centers Indigenous values and research for an Elder-centered methodology that encourages engagement of older adults in applicable, meaningful, restorative, and enculturated ways.