Stochastic and deterministic models for age-structured populations with genetically variable traits

Understanding how stochastic and non-linear deterministic processes interact is a major challenge in population dynamics theory. After a short review, we introduce a stochastic individual-centered particle model to describe the evolution in continuous time of a population with (continuous) age and trait structures. The individuals reproduce asexually, age, interact and die. The 'trait' is an individual heritable property (d-dimensional vector) that may influence birth and death rates and interactions between individuals, and vary by mutation. In a large population limit, the random process converges to the solution of a Gurtin-McCamy type PDE. We show that the random model has a long time behavior that differs from its deterministic limit. However, the results on the limiting PDE and large deviation techniques \textit{\`a la} Freidlin-Wentzell provide estimates of the extinction time and a better understanding of the long time behavior of the stochastic process. This has applications to the theory of adaptive dynamics used in evolutionary biology. We present simulations for two biological problems involving life-history trait evolution when body size is plastic and individual growth is taken into account.Comment: This work is a proceeding of the CANUM 2008 conferenc

A numerical approach for modelling thin cracked plates with XFEM

The modelization of bending plates with through the thickness cracks is investigated. We consider the Kirchhoff-Love plate model which is valid for very thin plates. We apply the eXtended Finite Element Method (XFEM) strategy: enrichment of the finite element space with the asymptotic bending and with the discontinuity across the crack. We present two variants and their numerical validations and also a numerical computation of the stress intensity factors

Pragmatic randomised controlled trial of an allergy intervention for children aged 6 to 16 with asthma and rhinitis in general practice

Background: It is widely believed that for allergic rhinitis and asthma, avoidance of specific triggers can improve symptom control. Whilst many children with asthma or rhinitis are sensitised to airborne allergens, primary care diagnostic and management decisions are often made without a detailed history of the allergic triggers or allergy testing. Thus, treatment decisions are empirical and allergen avoidance advice is either not given or, if given, not tailored to the child’s sensitivities. Objective: To ascertain whether allergy assessment and tailored advice in General Practice enhances outcomes of children with asthma and rhinitis. Method: Pragmatic RCT of allergy intervention (structured allergy history, skin prick testing and appropriate allergy avoidance advice) versus usual care in children with asthma and/or rhino-conjunctivitis. A blinded observer assessed outcomes at 12 months. Main outcome measures were symptom scores and disease-specific health-related QoL. Secondary outcomes were health care utilisation, days unable to pursue usual activities, and self-rated improvement. Results: 335 participants were randomised to formal allergy assessment or normal care. There were no differences in participants’ demographic or clinical characteristics at baseline (all p>.05). At 12 months, participants receiving the allergy intervention had fewer rhinitis symptoms (MD -3.14, 95% CI -6.01, -0.81) and an improvement in QoL (MD -0.50, 95% CI 0.32, 0.68). There were no significant changes in asthma symptoms, health care utilisation or number of days unable to pursue usual activities. Conclusion: Amongst children with known asthma and/or rhinitis in primary care, taking a structured allergy history with skin prick testing and tailored advice on allergy avoidance resulted in reduced symptoms of rhinitis and improved QoL

Structural Analysis of Cell Wall Polysaccharides Using PACE

The plant cell wall is composed of many complex polysaccharides. The composition and structure of the polysaccharides affect various cell properties including cell shape, cell function and cell adhesion. PACE (Polysaccharide Analysis using Carbohydrate gel Electrophoresis) uses a simple, rapid technique to analyze polysaccharide quantity and structure (Goubet et al., Anal Biochem 300:53-68, 2002)

The sources and dynamics of fine-grained sediment degrading the Freshwater Pearl Mussel (Margaritifera margaritifera) beds of the River Torridge, Devon, UK

The Freshwater Pearl Mussel (Margaritifera margaritifera) is an endangered organism across its entire range. It has a complex life cycle and stringent habitat requirements and is therefore an indicator species for the general ecosystem health of host rivers. Whereas historical intensive pearl fishing contributed to population declines, excess nutrient and sediment loss associated with current land use pressures in host river catchments, including modern intensive farming practices, are now highlighted as primary contributory factors. Accordingly, this study investigated the sources and dynamics of fine-grained sediment sampled in the mussel beds of the River Torridge, SW England. Sediment source fingerprinting using a combination of colorimetric and radiometric tracers to construct different composite signatures revealed the importance of roads both as a sediment source and delivery pathway for fine-grained sediment mobilised from fields predominantly supporting lowland livestock farming. Grassland fields with evidence of soil poaching were highlighted as important sediment sources, but equally, riparian woodland was also identified as important, especially during the latter stages of consecutive runoff events when its rainfall buffering capacity was exceeded. Bed sediment storage levels (median up to 393 g m−2) were found to be low (41st percentile) compared to typical values reported by a recent strategic scale survey across England and Wales, whereas elevated turbidity peaks were shown to be long duration (days) in conjunction with consecutive days of rainfall and corresponding runoff events. Hysteresis patterns varied but were generally clockwise during the largest runoff events associated with consecutive rain days; again, suggesting mobilisation of sediment from proximal woodland sources following exceedance of rainfall buffering capacity. In combination, the data assembled by this study provides a basis for planning sediment control measures for protecting the Freshwater Pearl Mussel (FPM) beds from excessive fine-grained sediment inputs associated with the intensive use of primarily grazing land

Travelling waves for the Gross-Pitaevskii equation II

The purpose of this paper is to provide a rigorous mathematical proof of the existence of travelling wave solutions to the Gross-Pitaevskii equation in dimensions two and three. Our arguments, based on minimization under constraints, yield a full branch of solutions, and extend earlier results, where only a part of the branch was built. In dimension three, we also show that there are no travelling wave solutions of small energy.Comment: Final version accepted for publication in Communications in Mathematical Physics with a few minor corrections and added remark