A proof of van Aubel's theorem using orthogonal vectors

We show how two linearly independent vectors can be used to construct two orthogonal vectors of equal magnitude in a simple way. The proof that the constructed vectors are orthogonal and of equal magnitude is a good exercise for students studying properties of scalar and vector triple products. We then show how this result can be used to prove van Aubel's theorem that relates the two line segments joining the centres of squares on opposite sides of a plane quadrilateral.

Gender, race, and heterogeneous effects of epidemic malaria on human capital and income

This article investigates the impact of exposure to a serious, unusual, and unforeseen malaria epidemic in northeast Brazil in 1938–40 on subsequent human capital attainment and income. Arguing the event was exogenous, the article exploits cohort and regional heterogeneity in exposure to identify effects. Results are consistent with differential mortality rates according to gender and socioeconomic status, such that heterogeneous selection and scarring effects are observed. Analyzing by gender alone, positive (selection) effects are found for men, and mixed (positive and negative) effects for women. Allowing for heterogeneity by race, selection effects persist for men. In contrast, positive (selection) effects are observed for nonwhite women, and negative (scarring) effects for white women. Results contribute to evidence suggesting that exposure to negative environmental shocks affects human capital attainment, while also suggesting it heterogeneously affects cohort composition.

Quinine, mosquitoes and empire: reassembling malaria in British India, 1890-1910

The drug quinine figured as an object of enforced consumption in British India between the late 1890s and the 1910s, when the corresponding diagnostic category malaria itself was redefined as a mosquito-borne fever disease. This article details an overlapping milieu in which quinine, mosquitoes and malaria emerged as intrinsic components of shared and symbiotic histories. It combines insights from new imperial histories, constructivism in the histories of medicine and literature about non-humans in science studies to examine the ways in which histories of insects, drugs, disease and empire interacted and shaped one another. Firstly, it locates the production of historical intimacies between quinine, malaria and mosquitoes within the exigencies and apparatuses of imperial rule. In so doing, it explores the intersections between the worlds of colonial governance, medical knowledge, vernacular markets and pharmaceutical business. Secondly, it outlines ways to narrate characteristics and enabling properties of non-humans (such as quinines and mosquitoes) while retaining a constructivist critique of scientism and empire. Thirdly, it shows how empire itself was reshaped and reinforced while occasioning the proliferation of categories and entities like malaria, quinine and mosquitoes.

Cacao swollen shoot virus in Nigeria: analysis of a pathogen and its vectors

Cacao swollen shoot virus (CSSV) causes the Cacao swollen shoot virus disease (CSSVD) and significantly reduces production in West African cacao. This study characterised the current status of the disease in the major cacao growing States in Nigeria and attempted a clarification on the manner of CSSV transmission. Two separate field surveys and sample collections were conducted in Nigeria in summer 2012 and spring 2013. PCR-based screening of cacao leaf samples and subsequent DNA sequencing showed that the disease continues to persist in Ondo and Oyo States and in new cacao sites in Abia, Akwa Ibom, Cross River and Edo States. Mealybug samples collected were identified using a robust approach involving environmental scanning electron microscopy, histology and DNA barcoding, which highlighted the importance of integrative taxonomy in the study. The results show that the genus Planococcus (Planococcus citri (Risso) and/or Planococcus minor (Maskell)) was the most abundant vector (73.5%) at the sites examined followed by Formicococcus njalensis (Laing) (19.0 %). In a laboratory study, the feeding behaviour of Pl. citri, Pseudococcus longispinus (Targioni-Tozzetti) and Pseudococcus viburni (Signoret) on cacao were investigated using electrical penetration graph (EPG) analysis. EPG waveforms reflecting intercellular stylet penetration (C), extracellular salivation (E1e), salivation in sieve elements (E1), phloem ingestion (E2), derailed stylet mechanics (F), xylem ingestion (G) and non-probing phase (Np) were analysed. Individual mealybugs exhibited marked variation within species and significantly differed (p ≤ .05) between species for E1e and E1. PCR-based assessments of the retention time for CSSV in viruliferous Pl. citri, Ps. longispinus and Ps. viburni fed on a non-cacao diet showed that CSSV was still detectable after 144 hours. These unusually long durations for a pathogen currently classified as a semi-persistent virus have implications for the design of non-malvaceous barrier crops currently being considered for the protection of new cacao plantings.