Weak constraints in four-dimensional variational data assimilation

The formulation of four-dimensional variational data assimilation allows the incorporation of constraints into the cost function which need only be weakly satisfied. In this paper we investigate the value of imposing conservation properties as weak constraints. Using the example of the two-body problem of celestial mechanics we compare weak constraints based on conservation laws with a constraint on the background state.We show how the imposition of conservation-based weak constraints changes the nature of the gradient equation. Assimilation experiments demonstrate how this can add extra information to the assimilation process, even when the underlying numerical model is conserving.

How to save a bad element with weak boundary conditions

The P-1-P-1 finite element pair is known to allow the existence of spurious pressure (surface elevation) modes for the shallow water equations and to be unstable for mixed formulations. We show that this behavior is strongly influenced by the strong or the weak enforcement of the impermeability boundary conditions. A numerical analysis of the Stommel model is performed for both P-1-P-1 and P-1(NC)-P-1 mixed formulations. Steady and transient test cases are considered. We observe that the P-1-P-1 element exhibits stable discrete solutions with weak boundary conditions or with fully unstructured meshes. (c) 2005 Elsevier Ltd. All rights reserved.

British Nutrition Foundation annual lecture: chips with everything? Nutritional genomics and the application of diet in disease prevention

The development of high throughput techniques ('chip' technology) for measurement of gene expression and gene polymorphisms (genomics), and techniques for measuring global protein expression (proteomics) and metabolite profile (metabolomics) are revolutionising life science research, including research in human nutrition. In particular, the ability to undertake large-scale genotyping and to identify gene polymorphisms that determine risk of chronic disease (candidate genes) could enable definition of an individual's risk at an early age. However, the search for candidate genes has proven to be more complex, and their identification more elusive, than previously thought. This is largely due to the fact that much of the variability in risk results from interactions between the genome and environmental exposures. Whilst the former is now very well defined via the Human Genome Project, the latter (e.g. diet, toxins, physical activity) are poorly characterised, resulting in inability to account for their confounding effects in most large-scale candidate gene studies. The polygenic nature of most chronic diseases offers further complexity, requiring very large studies to disentangle relatively weak impacts of large numbers of potential 'risk' genes. The efficacy of diet as a preventative strategy could also be considerably increased by better information concerning gene polymorphisms that determine variability in responsiveness to specific diet and nutrient changes. Much of the limited available data are based on retrospective genotyping using stored samples from previously conducted intervention trials. Prospective studies are now needed to provide data that can be used as the basis for provision of individualised dietary advice and development of food products that optimise disease prevention. Application of the new technologies in nutrition research offers considerable potential for development of new knowledge and could greatly advance the role of diet as a preventative disease strategy in the 21st century. Given the potential economic and social benefits offered, funding for research in this area needs greater recognition, and a stronger strategic focus, than is presently the case. Application of genomics in human health offers considerable ethical and societal as well as scientific challenges. Economic determinants of health care provision are more likely to resolve such issues than scientific developments or altruistic concerns for human health.

Shrubs, granivores and annual plant community stability in an arid ecosystem

Compensatory population dynamics among species stabilise aggregate community variables. Inter-specific competition is thought to be stabilising as it promotes asynchrony among populations. However, we know little about other inter-specific interactions, such as facilitation and granivory. Such interactions are also likely to influence population synchrony and community stability, especially in harsh environments where they are thought to have relatively strong effects in plant communities. We use a manipulative experiment to test the effects of granivores (harvester ants) and nurse plants (dwarf shrubs) on annual plant community dynamics in the Negev desert, Israel. We present evidence for weak and inconsistent effects of harvester ants on plant abundance and on population and community stability. By contrast, we show that annual communities under shrubs were more species rich, had higher plant density and were temporally less variable than communities in the inter-shrub matrix. Species richness and plant abundance were also more resistant to drought in the shrub under-storey compared with the inter-shrub matrix, although population dynamics in both patch types were synchronised. Hence, we show that inter-specific interactions other than competition affect community stability, and that hypothesised mechanisms linking compensatory dynamics and community stability may not operate to the same extent in arid plant communities.

The symbiotic roles of empirical experimentation and thought experimentation in the learning of physics

This study was an attempt to identify the epistemological roots of knowledge when students carry out hands-on experiments in physics. We found that, within the context of designing a solution to a stated problem, subjects constructed and ran thought experiments intertwined within the processes of conducting physical experiments. We show that the process of alternating between these two modes- empirically experimenting and experimenting in thought- leads towards a convergence on scientifically acceptable concepts. We call this process mutual projection. In the process of mutual projection, external representations were generated. Objects in the physical environment were represented in an imaginary world and these representations were associated with processes in the physical world. It is through this coupling that constituents of both the imaginary world and the physical world gain meaning. We further show that the external representations are rooted in sensory interaction and constitute a semi-symbolic pictorial communication system, a sort of primitive 'language', which is developed as the practical work continues. The constituents of this pictorial communication system are used in the thought experiments taking place in association with the empirical experimentation. The results of this study provide a model of physics learning during hands-on experimentation.

Food for thought: the role of dietary flavonoids in enhancing human memory, learning and neuro-cognitive performance

Emerging evidence suggests that dietary-derived flavonoids have the potential to improve human memory and neuro-cognitive performance via their ability to protect vulnerable neurons, enhance existing neuronal function and stimulate neuronal regeneration. Long-term potentiation (LTP) is widely considered to be one of the major mechanisms underlying memory acquisition, consolidation and storage in the brain and is known to be controlled at the molecular level by the activation of a number of neuronal signalling pathways. These pathways include the phosphatidylinositol-3 kinase/protein kinase B/Akt (Akt), protein kinase C, protein kinase A, Ca-calmodulin kinase and mitogen-activated protein kinase pathways. Growing evidence suggests that flavonoids exert effects on LTP, and consequently memory and cognitive performance, through their interactions with these signalling pathways. Of particular interest is the ability of flavonoids to activate the extracellular signal-regulated kinase and the Akt signalling pathways leading to the activation of the cAMP-response element-binding protein, a transcription factor responsible for increasing the expression of a number of neurotrophins important in LTP and long-term memory. One such neurotrophin is brain-derived neurotrophic factor, which is known to be crucial in controlling synapse growth, in promoting an increase in dendritic spine density and in enhancing synaptic receptor density. The present review explores the potential of flavonoids and their metabolite forms to promote memory and learning through their interactions with neuronal signalling pathways pivotal in controlling LTP and memory in human subjects.