[Book review] Barry Mazur, Imagining Numbers: (Particularly the Square Root of Minus Fifteen)

Tony Mann provides a review of the book: Barry Mazur, Imagining Numbers: (Particularly the Square Root of Minus Fifteen), London: Allen Lane, 2003, ISBN: 0713996307

The effect of spatial scale on interactions between two weevils and their parasitoid

1. The effect of spatial scale on the interactions between three hymenopteran parasitoids and their weevil hosts was investigated. The parasitoid Mesopolobus incultus (Walker) parasitised Gymnetron pascuorum Gyll.; the parasitoids Entodon sparetus (Walker) and Bracon sp. parasitised Mecinus pyraster Herbst. Both of these weevils develop inside the seedhead of Plantago lanceolata L. but occupy different niches. Seedheads were sampled annually from 162 plants at each of two experimental sites consisting of a series of habitat patches of two distinct sizes. Data were analysed from three site-years. 2. Parasitoid densities at each site-year were closely related to the abundance of their respective weevil hosts. The overall proportion of hosts parasitised was more variable for M. incultus than for E. sparetus and Bracon sp. 3. Changes in spatial scale affected the variability of parasitoid densities. For M. incultus, there was generally a greater degree of additional heterogeneity for all increases of scale; for E. sparetus, this was true only at the largest scales; for Bracon sp., all components of variance were negative. 4. The rate of parasitism was related to host density in different ways at different spatial scales. Mesopolobus incultus exhibited inverse density dependence at the finest (seedhead) scale, direct density dependence at the intermediate (plant) scale, and density independence at the large (habitat area 729 m2) scale. Entodon sparetus showed no response to variation in host density at any spatial scale. Bracon sp. showed direct density dependence only at the intermediate and largest scales. 5. Parasitoids E. sparetus and Bracon sp. seemed able to detect more than one M. pyraster individual in seedheads with multiple host occupancy; a greater incidence of conspecific parasitoids than expected emerged from such seedheads.

Association of fever and severe clinical course in bronchiolitis

Little attention has been given to the relation between fever and the severity of bronchiolitis. Therefore, the relation between fever and the clinical course of 90 infants (59 boys, 31 girls) hospitalised during one season with bronchiolitis was studied prospectively. Fever (defined as a single recording > 38.0°C or two successive recording > 37.8°C) was present in 28 infants. These infants were older (mean age, 5.3 v 4.0 months), had a longer mean hospital stay (4.2 v2.7 days), and a more severe clinical course (71.0%v 29.0%) than those infants without fever. Radiological abnormalities (collapse/consolidation) were found in 60.7% of the febrile group compared with 14.8% of the afebrile infants. These results suggest that monitoring of body temperature is important in bronchiolitis and that fever is likely to be associated with a more severe clinical course and radiological abnormalities.

Mechanism of motion of an optical fiber aligned by a solder droplet

Solder is often used as an adhesive to attach optical fibers to a circuit board. In this proceeding we will discuss efforts to model the motion of an optical fiber during the wetting and solidification of the adhesive solder droplet. The extent of motion is determined by several competing forces, during three “stages” of solder joint formation. First, capillary forces of the liquid phase control the fiber position. Second, during solidification, the presence of the liquid-solid-vapor triple line as well as a reduced liquid solder volume leads to a change in the net capillary force on the optical fiber. Finally, the solidification front itself impinges on the fiber. Publicly-available finite element models are used to calculate the time-dependent position of the solidification front and shape of the free surface.

Fitting host-parasitoid models with CV² > 1 using hierarchical generalized linear models

The powerful general Pacala-Hassell host-parasitoid model for a patchy environment, which allows host density–dependent heterogeneity (HDD) to be distinguished from between-patch, host density–independent heterogeneity (HDI), is reformulated within the class of the generalized linear model (GLM) family. This improves accessibility through the provision of general software within well–known statistical systems, and allows a rich variety of models to be formulated. Covariates such as age class, host density and abiotic factors may be included easily. For the case where there is no HDI, the formulation is a simple GLM. When there is HDI in addition to HDD, the formulation is a hierarchical generalized linear model. Two forms of HDI model are considered, both with between-patch variability: one has binomial variation within patches and one has extra-binomial, overdispersed variation within patches. Examples are given demonstrating parameter estimation with standard errors, and hypothesis testing. For one example given, the extra-binomial component of the HDI heterogeneity in parasitism is itself shown to be strongly density dependent.

Casual link and consensual arrangements in estoppel

Analyses the Court of Appeal decision in Powell v Benney on whether in a claim of proprietary estoppel the expectation of a couple that they would receive two properties owned, and promised to them, by a deceased friend was out of proportion to the detriment suffered by them in looking after the friend and improving his properties for their own use. Considers: (1) the approach to be taken to the requirement of a causal link between the assurance given and the conduct constituting the detriment relied on; and (2) consensual arrangements and estoppel equity.

The use of fluorescence microscopy to define polymer localisation to the late endocytic compartments in cells that are targets for drug delivery

Macromolecular therapeutics and nano-sized drug delivery systems often require localisation to specific intracellular compartments. In particular, efficient endosomal escape, retrograde trafficking, or late endocytic/lysosomal activation are often prerequisites for pharmacological activity. The aim of this study was to define a fluorescence microscopy technique able to confirm the localisation of water-soluble polymeric carriers to late endocytic intracellular compartments. Three polymeric carriers of different molecular weight and character were studied: dextrin (Mw~50,000 g/mol), a N-(2-hydroxypropyl)methacrylamide (HPMA) copolymer (Mw approximately 35,000 g/mol) and polyethylene glycol (PEG) (Mw 5000 g/mol). They were labelled with Oregon Green (OG) (0.3-3 wt.%; <3% free OG in respect of total). A panel of relevant target cells were used: THP-1, ARPE-19, and MCF-7 cells, and primary bovine chondrocytes (currently being used to evaluate novel polymer therapeutics) as well as NRK and Vero cells as reference controls. Specific intracellular compartments were marked using either endocytosed physiological standards, Marine Blue (MB) or Texas-red (TxR)-Wheat germ agglutinin (WGA), TxR-Bovine Serum Albumin (BSA), TxR-dextran, ricin holotoxin, C6-7-nitro-2,1,3-benzoxadiazol-4-yl (NBD)-labelled ceramide and TxR-shiga toxin B chain, or post-fixation immuno-staining for early endosomal antigen 1 (EEA1), lysosomal-associated membrane proteins (LAMP-1, Lgp-120 or CD63) or the Golgi marker GM130. Co-localisation with polymer-OG conjugates confirmed transfer to discreet, late endocytic (including lysosomal) compartments in all cells types. The technique described here is a particularly powerful tool as it circumvents fixation artefacts ensuring the retention of water-soluble polymers within the vesicles they occupy.