Droop models of nutrient–plankton interaction with intratrophic predation

Droop models of nutrient–phytoplankton–zooplankton interaction with intratrophic predation of zooplankton are introduced and investigated. The models proposed in this study are open ecosystems which include both a constant and a periodic input nutrient models. A simple stochastic model mimics a randomly varying nutrient input is also presented. For the deterministic models it is shown analytically that intratrophic predation has no effect on the global asymptotic dynamics of the systems if either one of the populations has a negative growth rate. Numerical simulations are also used to investigate the effects of intratrophic predation. Unlike the deterministic models for which both populations can coexist with each other if populations’ net growth rates are positive, plankton populations can become extinct if the input nutrient concentration is varied randomly

Nutrient-plankton models with nutrient recycling

Abstract. Nutrient-phytoplankton-zooplankton interaction with general uptake functions in which nutrient recycling is either instantaneous or delayed is considered. To account for higher predation, zooplankton's death rate is modeled by a quadratic term instead of the usual linear function. Persistence conditions for each of the delayed and non-delayed models are derived. Numerical simulations with data from the existing literature are explored to compare the two models. It is demonstrated numerically that increasing zooplankton death rate can eliminate periodic solutions of the system in both the instantaneous and the delayed nutrient recycling models. However, the delayed nutrient recycling can actually stabilize the nutrientplankton interaction

Physical activity and nutrition program for seniors (PANS): protocol of a randomized controlled trial

Background Along with reduced levels of physical activity, older Australian's mean energy consumption has increased. Now over 60% of older Australians are considered overweight or obese. This study aims to confirm if a low-cost, accessible physical activity and nutrition program can improve levels of physical activity and diet of insufficiently active 60-70 year-olds. Methods/Design This 12-month home-based randomised controlled trial (RCT) will consist of a nutrition and physical activity intervention for insufficiently active people aged 60 to 70 years from low to medium socio-economic areas. Six-hundred participants will be recruited from the Australian Federal Electoral Role and randomly assigned to the intervention (n = 300) and control (n = 300) groups. The study is based on the Social Cognitive Theory and Precede-Proceed Model, incorporating voluntary cooperation and self-efficacy. The intervention includes a specially designed booklet that provides participants with information and encourages dietary and physical activity goal setting. The booklet will be supported by an exercise chart, calendar, bi-monthly newsletters, resistance bands and pedometers, along with phone and email contact. Data will be collected over three time points: pre-intervention, immediately post-intervention and 6-months post-study. Discussion This trial will provide valuable information for community-based strategies to improve older adults' physical activity and dietary intake. The project will provide guidelines for appropriate sample recruitment, and the development, implementation and evaluation of a minimal intervention program, as well as information on minimising barriers to participation in similar programs

The ReLPM Exponential Integrator for FE Discretizations of Advection-Diffusion Equations

We implement an exponential integrator for large and sparse systems of ODEs, generated by FE (Finite Element) discretization with mass-lumping of advection-diffusion equations. The relevant exponential-like matrix function is approximated by polynomial interpolation, at a sequence of real Leja points related to the spectrum of the FE matrix (ReLPM, Real Leja Points Method). Application to 2D and 3D advection-dispersion models shows speed-ups of one order of magnitude with respect to a classical variable step-size Crank-Nicolson solver

Preconditioning Newton-Krylov Methods in Non-Convex Large Scale Optimization

We consider an iterative preconditioning technique for non-convex large scale optimization. First, we refer to the solution of large scale indefinite linear systems by using a Krylov subspace method, and describe the iterative construction of a preconditioner which does not involve matrices products or matrices storage. The set of directions generated by the Krylov subspace method is used, as by product, to provide an approximate inverse preconditioner. Then, we experience our preconditioner within Truncated Newton schemes for large scale unconstrained optimization, where we generalize the truncation rule by Nash–Sofer (Oper. Res. Lett. 9:219–221, 1990) to the indefinite case, too. We use a Krylov subspace method to both approximately solve the Newton equation and to construct the preconditioner to be used at the current outer iteration. An extensive numerical experience shows that the proposed preconditioning strategy, compared with the unpreconditioned strategy and PREQN (Morales and Nocedal in SIAM J. Optim. 10:1079–1096, 2000), may lead to a reduction of the overall inner iterations. Finally, we show that our proposal has some similarities with the Limited Memory Preconditioners (Gratton et al. in SIAM J. Optim. 21:912–935, 2011)

Persistence in variable-yield nutrient-plankton models

Nutrient-phytoplankton-zooplankton models with general uptake functions in which only the internal nutrient concentration is capable of catalyzing cell growth and division for phytoplankton are proposed and analyzed. For the constant nutrient input model, it is shown that extinction or persistence of the population depends on its maximal growth rate relative to the total removal rate. The same biological conclusions hold for the periodic nutrient input model. However, while extinction and persistence are expressed in terms of convergence to steady states for the constant nutrient input model, these biological phenomena are exhibited in terms of asymptotic attraction to periodic solutions for the periodic nutrient input model. © 2003 Elsevier Ltd. All rights reserved