A jump-growth model for predator-prey dynamics: derivation and application to marine ecosystems

This paper investigates the dynamics of biomass in a marine ecosystem. A stochastic process is defined in which organisms undergo jumps in body size as they catch and eat smaller organisms. Using a systematic expansion of the master equation, we derive a deterministic equation for the macroscopic dynamics, which we call the deterministic jump-growth equation, and a linear Fokker-Planck equation for the stochastic fluctuations. The McKendrick--von Foerster equation, used in previous studies, is shown to be a first-order approximation, appropriate in equilibrium systems where predators are much larger than their prey. The model has a power-law steady state consistent with the approximate constancy of mass density in logarithmic intervals of body mass often observed in marine ecosystems. The behaviours of the stochastic process, the deterministic jump-growth equation and the McKendrick--von Foerster equation are compared using numerical methods. The numerical analysis shows two classes of attractors: steady states and travelling waves.Comment: 27 pages, 4 figures. Final version as published. Only minor change

Popular attitudes to memory, the body, and social identity : the rise of external commemoration in Britain, Ireland, and New England

A comparative analysis of samples of external memorials from burial grounds in Britain, Ireland and New England reveals a widespread pattern of change in monument style and content, and exponential growth in the number of permanent memorials from the 18th century onwards. Although manifested in regionally distinctive styles on which most academic attention has so far been directed, the expansion reflects global changes in social relationships and concepts of memory and the body. An archaeological perspective reveals the importance of external memorials in articulating these changing attitudes in a world of increasing material consumption

Structure dependent rearrangement of the cyclopropylmethyl cation - isolation of a bicyclo[3.2.0]heptene

Access to 7-allyl substituted norbornene derivatives for tandem olefin metathesis via cationic rearrangement of cyclopropylmethanol substituted norbornenes is shown to be structure dependent. In some cases products that arise from cationic rearrangement of a cyclopropylmethyl cation are furnished. Thionyl chloride is shown to be superior to silica for inducing the desired rearrangement. (c) 2007 Elsevier Ltd. All rights reserved

Ring-rearrangement metathesis of substituted 2-aminonorbornenes

In this report we describe the ring-rearrangement metathesis of 2-aminonorbornene derivatives. Ail efficient ruthenium-catalysed metathesis reaction Occurs with a wide range of pendent alkenes and alkynes to generate bicyclic amines and amides

Application of olefin metathesis for the synthesis of constrained beta-amino esters from norbornenes

Synthesis of a number of novel, conformationally rigid beta-amino esters has been achieved via a tandem olefin metathesis reaction. The starting materials are readily accessible from the Diels-Alder adduct between cyclopentadiene and maleic anhydride

Solid-phase synthesis of an A-B loop mimetic of the C epsilon 3 domain of human IgE: macrocyclization by Sonogashira coupling

The solid-phase synthesis of a cyclic peptide containing the 21-residue epitope found in the A-B loop of the Cepsilon3 domain of human immunoglobulin E has been carried out. The key macrocyclization step to form the 65-membered ring is achieved in similar to15% yield via an "on-resin" Sonogashira coupling reaction which concomitantly installs a diphenylacetylene amino acid conformational constraint within the loop

Correlations of measurements of subclinical claw horn lesions in dairy cattle

Measurements were made of the extent of sole and white line lesions on the claws of 1 15 Holstein-Friesian cows on at least three and at most 16 occasions, and some cows were followed up to their third lactation. All the measurements were made between 12 weeks before calving and 45 weeks after calving. In total, 1016 repeated observations were made. Correlations were calculated between pairs of claws, between types of lesion (sole and white line), and between pairs of the different measurements (number of lesions, proportion of the claw affected, maximum severity score and proportion of the claw affected weighted for severity). The outer hind claws had the greatest extent of lesions of both types. Spearman correlation coefficients and confidence intervals measured the strength of the association. All the associations between claws were positive, suggesting that the lesions did not occur in isolation. Sole and white line lesions were not associated at individual observation points. Lesions on the left and right claws were markedly similar, except for sole lesions on the two inner hind claws, and for white line lesions on the two outer hind claws

Ring-rearrangement metathesis of bicyclic amino acid derivatives

In this letter, we describe the ring-rearrangement metathesis (RRM) of bicyclic amino acid derivatives. The procedure is of use for the synthesis of constrained amino acid and peptide derivatives with potential as reverse-turn inducers. (c) 2005 Elsevier Ltd. All rights reserved

Self-Assembly of Peptide Nanotubes in an Organic Solvent

The self-assembly of a modified fragment of the amyloid β peptide, based on sequence Aβ(16-20), KLVFF, extended to give AAKLVFF is studied in methanol. Self-assembly into peptide nanotubes is observed, as confirmed by electron microscopy and small-angle X-ray scattering. The secondary structure of the peptide is probed by FTIR and circular dichroism, and UV/visible spectroscopy provides evidence for the important role of aromatic interactions between phenylalanine residues in driving β-sheet self-assembly. The β-sheets wrap helically to form the nanotubes, the nanotube wall comprising four wrapped β-sheets. At higher concentration, the peptide nanotubes form a nematic phase that exhibits spontaneous flow alignment as observed by small-angle neutron scattering