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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. 

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. 

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. 

Abstract Honey bees (Apis mellifera L. Hymeoptera: Apidae) use hydrogen peroxide (synthesized by excreted glucose oxidase) as an important component of social immunity. However, both tolerance of hydrogen peroxide and the production of glucose oxidase in honey is costly. Hydrogen peroxide may also be encountered by honey bees at high concentrations in nectar while foraging, however despite its presence both in their foraged and stored foods, it is unclear if and how bees monitor concentrations of, and their behavioral responses to, hydrogen peroxide. The costs of glucose oxidase production and the presence of hydrogen peroxide in both nectar and honey suggest hypotheses that honey bees preferentially forage on hydrogen peroxide supplemented feed syrups at certain concentrations, and avoid feed syrups supplemented with hydrogen peroxide at concentrations above some tolerance threshold. We test these hypotheses and find that, counter to expectation, honey bees avoid glucose solutions supplemented with field-relevant hydrogen peroxide concentrations and either avoid or don’t differentiate supplemented sucrose solutions when given choice assays. This is despite honey bees showing high tolerance for hydrogen peroxide in feed solutions, with no elevated mortality until concentrations of hydrogen peroxide exceed 1% (v/v) in solution, with survival apparent even at concentrations up to 10%. The behavioral interaction of honey bees with hydrogen peroxide during both within-colony synthesis in honey and when foraging on nectar therefore likely relies on interactions with other indicator molecules, and maybe constrained evolutionarily in its plasticity, representing a constitutive immune mechanism. 

Numerous studies have documented the negative effects of neonicotinoids on bees; it remains crucial to examine how neonicotinoids affect other non‐target nectar‐feeding insects, such as the monarch butterfly,Danaus plexippus.

Wildflowers growing near agricultural areas can be contaminated with neonicotinoids that affect survival or cause sublethal changes to behaviours of nectar‐feeding insects. Nectar residues of imidacloprid and clothianidin found in milkweeds and wildflowers adjacent to agricultural field range from 0 to 72.8 ng/mL.

At field‐relevant doses, two neonicotinoids (imidacloprid and clothianidin) were studied for their effects on adult monarch survival, reproduction, flight and behaviour. First, we fed adult monarchs artificial nectar solutions ranging from 15 to 386 ng/mL of imidacloprid and 19 to 531 ng/mL of clothianidin. Neonicotinoid ingestion slightly reduced monarch reproduction but had no significant effects on survival, weight change, or activity levels.

Second, we fed monarchs higher clothianidin doses (909 and 4030 ng/mL), that exceed field‐relevant levels by 22 and 99 times. These higher doses reduced monarch nectar consumption, survival, flight performance and reaction time in response to a drop test.

Results show that adult monarchs tolerate field‐relevant doses as high as 54 ng/mL for imidacloprid and 75 ng/mL for clothianidin, with minimal lethal or sub‐lethal effects until much higher doses are supplied. We conclude that adult monarchs are more tolerant of ingested clothianidin and imidacloprid than indicated by previous research.