Diagonalization and Jordan Normal Form – motivation through Maple

Following an introduction to the diagonalization of matrices, one of the more difficult topics for students to grasp in linear algebra is the concept of Jordan normal form. In this note, we show how the important notions of diagonalization and Jordan normal form can be introduced and developed through the use of the computer algebra package Maple®.

Food-chain transfer of zinc from contaminated Urtica dioica and Acer pseudoplatanus L. to Microlophium carnosum and Drepanosiphum platanoidis Schrank

This study examines the food-chain transfer of Zn from two plant species, Urtica dioica (stinging nettle) and Acer pseudoplatanus (sycamore maple), into their corresponding aphid species, Microlophium carnosum and Drepanosiphum platanoidis. The plants were grown in a hydroponic system using solutions with increasing concentrations of Zn from 0.02 to 41.9 mg Zn/l. Above-ground tissue concentrations in U. dioica and M. carnosum increased with increasing Zn exposure (p < 0.001). Zn concentrations in A. pseudoplatanus also increased with solution concentration from the control to the 9.8 mg Zn/l solution, above which concentrations remained constant. Zn concentrations in both D. platanoidis and the phloem tissue of A. pseudoplatanus were not affected by the Zn concentration in the watering solution. It appears that A. pseudoplatanus was able to limit Zn transport in the phloem, resulting in constant Zn exposure to the aphids. Zn concentrations in D. platanoidis were around three times those in M. carnosum. Concentrations of Zn in two aphid species are dependant on species and exposure.

Persistence of varicella-zoster virus viraemia in patients with herpes zoster.

BACKGROUND: Herpes zoster is caused by the reactivation of varicella-zoster virus from sensory neurons. The commonest complication following zoster is chronic pain termed post herpetic neuralgia. OBJECTIVES: To investigate the dynamics of VZV viraemia and viral load following the resolution of zoster and its relationship to PHN development. STUDY DESIGN: Blood samples were collected at baseline, 1 month, 3 months and 6 month from a prospective study of 63 patients with active zoster. Quantification of VZV DNA in whole blood was performed using a real-time PCR assay. RESULTS: During acute zoster, all patients had detectable VZV DNA in their blood. VZV DNA remained detectable in the blood of 91% of patients at 6 months although levels declined significantly (p<0.0001). A history of prodromal symptoms (p=0.005) and severity of pain at baseline (p=0.038) as well as taking antivirals (p=0.046) and being immunocompromised (p=0.043) were associated, with longer time to recovery from PHN. Viral DNA loads were consistently higher in patients with risk factors for PHN and higher viral DNA loads over time were associated with longer time to recovery (p=0.058 overall and 0.038 in immunocompetent). CONCLUSIONS: Based on these observations we hypothesise that VZV replication persists following acute shingles and that higher viral DNA loads contribute to the risk factors for PHN.

Evaluation of the time resolved fluorescence immunoassay (TRFIA) for the detection of varicella zoster virus (VZV) antibodies following vaccination of healthcare workers

Determination of varicella zoster virus (VZV) immunity in healthcare workers without a history of chickenpox is important for identifying those in need of vOka vaccination. Post immunisation, healthcare workers in the UK who work with high risk patients are tested for seroconversion. To assess the performance of the time-resolved fluorescence immunoassay (TRFIA) for the detection of antibody in vaccinated as well as unvaccinated individuals, a cut-off was first calculated. VZV-IgG specific avidity and titres six weeks after the first dose of vaccine were used to identify subjects with pre-existing immunity among a cohort of 110 healthcare workers. Those with high avidity (≥60%) were considered to have previous immunity to VZV and those with low or equivocal avidity (<60%) were considered naive. The former had antibody levels ≥400mIU/mL and latter had levels <400mIU/mL. Comparison of the baseline values of the naive and immune groups allowed the estimation of a TRFIA cut-off value of >130mIU/mL which best discriminated between the two groups and this was confirmed by ROC analysis. Using this value, the sensitivity and specificity of TRFIA cut-off were 90% (95% CI 79-96), and 78% (95% CI 61-90) respectively in this population. A subset of samples tested by the gold standard Fluorescence Antibody to Membrane Antigen (FAMA) test showed 84% (54/64) agreement with TRFIA.