Evans function and Fredholm determinants

We explore the relationship between the Evans function, transmission coefficient and Fredholm determinant for systems of first order linear differential operators on the real line. The applications we have in mind include linear stability problems associated with travelling wave solutions to nonlinear partial differential equations, for example reaction-diffusion or solitary wave equations. The Evans function and transmission coefficient, which are both finite determinants, are natural tools for both analytic and numerical determination of eigenvalues of such linear operators. However, inverting the eigenvalue problem by the free state operator generates a natural linear integral eigenvalue problem whose solvability is determined through the corresponding infinite Fredholm determinant. The relationship between all three determinants has received a lot of recent attention. We focus on the case when the underlying Fredholm operator is a trace class perturbation of the identity. Our new results include: (i) clarification of the sense in which the Evans function and transmission coefficient are equivalent; and (ii) proof of the equivalence of the transmission coefficient and Fredholm determinant, in particular in the case of distinct far fields.Comment: 26 page

Numerical heat transfer model for frost protection of citrus fruits by water from a spraying system

A simplified model is developed to simulate the conditions associated with the protection of fruits from frost damage using water from a spraying system. The model simulates the movement of the solidifying water front on a single fruit, and based on that determines the spray frequency needed for a water film to continuously surround the ice-coated fruit to prevent the fruit temperature from dropping below 0ºC. Simulations are presented for the frost protection of sweet oranges (citrus sinensis). The effect of environmental conditions such as air temperature, air velocity, surface radiation and water film evaporation on the development of the ice layer encasing is considered. Simulations show the effect the encasing ice sheet thickness has on the fruit temperature if water from a spraying system is turned off permanently. Experimental tests are also conducted to determine the change in the thermal properties of citrus sinensis for operating temperatures that range from above freezing to sub-freezing. The results of the experimental tests and the numerical simulations shall lead to a better understanding of fruit protection from frost damage by the application of water from a spraying system

Distinguishing Originality from Creativity in ADHD: An Assessment of Creative Personality, Self-Perception, and Cognitive Style among Attention-Deficit/Hyperactivity Disorder Adults

Debates over whether Attention-Deficit/Hyperactivity Disorder (ADHD) relates to high levels of creativity have been hampered by a lack of rigor when defining creativity. The purpose of the present study was to go beyond the rhetoric by empirically investigating creative personality, creative self-perception, and cognitive style among 49 ADHD adults. Comparative analysis to studies of non-ADHD samples revealed distinctive tendencies: A mean group score of 115.71 (SD=18.02) on the Kirton Adaption-Innovation Inventory (KAI) indicated preferences for originality, nonconformity, paradigm-breaking, and low efficiency that was over one standard deviation higher than average non-ADHD population scores. Combined inattentive/hyperactiveimpulsive subtypes (n=20) scored 124.30 (SD=12.96). Ideator tendencies on Puccio’s FourSight indicated preferences for generating novel ideas and overlooking details. Adjective Check List (ACL) scores were slightly elevated on the Domino Creative Personality and Gough Creativity scales, but more so on the Change scale, indicating a tendency to seek novelty and avoid routine. Creative self-perception was high, with 85.71% reporting themselves as more creative than average. Although their dispositions toward originality might benefit creativity, it might be undermined by their disinclination for effectiveness necessary for full-fledged creativity. Results may help clinicians distinguish maladaptive ADHD behaviors from concomitant behaviors that might play a valuable role in creativity

First report of Metarhizium anisopliae IP 46 pathogenicity in adult Anopheles gambiae s.s. and An. arabiensis (Diptera; Culicidae).

The entomopathogenic fungus Metarhizium anisopliae isolate IP 46, originating from a soil sample collected in 2001 in the Cerrado of Central Brazil, was tested for its ability to reduce the survival of adult male and female Anopheles gambiae s.s. and An. arabiensis mosquitoes. A 6-h exposure to the fungus coated on test paper at a concentration of 3.3 x 106 conidia cm-2 reduced the daily survival of both mosquito species (HR = 3.14, p < 0.001), with higher risk of dying in An. gambiae s.s relative to An. arabiensis (HR = 1.38, p < 0.001). Fungal sporulation was observed in >95% of mosquito cadavers in the treatment groups. The results indicate that M. anisopliae IP 46 has the potential to be a bio-control agent for African malaria vector species, and is a suitable candidate for further research and development

Selection on treatment in the target population of generalizabillity and transportability analyses

Investigators are increasingly using novel methods for extending (generalizing or transporting) causal inferences from a trial to a target population. In many generalizability and transportability analyses, the trial and the observational data from the target population are separately sampled, following a non-nested trial design. In practical implementations of this design, non-randomized individuals from the target population are often identified by conditioning on the use of a particular treatment, while individuals who used other candidate treatments for the same indication or individuals who did not use any treatment are excluded. In this paper, we argue that conditioning on treatment in the target population changes the estimand of generalizability and transportability analyses and potentially introduces serious bias in the estimation of causal estimands in the target population or the subset of the target population using a specific treatment. Furthermore, we argue that the naive application of marginalization-based or weighting-based standardization methods does not produce estimates of any reasonable causal estimand. We use causal graphs and counterfactual arguments to characterize the identification problems induced by conditioning on treatment in the target population and illustrate the problems using simulated data. We conclude by considering the implications of our findings for applied work