Vertex splitting and connectivity augmentation in hypergraphs

We consider problems of splitting and connectivity augmentation in hypergraphs. In a hypergraph G = (V +s, E), to split two edges su, sv, is to replace them with a single edge uv. We are interested in doing this in such a way as to preserve a defined level of connectivity in V . The splitting technique is often used as a way of adding new edges into a graph or hypergraph, so as to augment the connectivity to some prescribed level. We begin by providing a short history of work done in this area. Then several preliminary results are given in a general form so that they may be used to tackle several problems. We then analyse the hypergraphs G = (V + s, E) for which there is no split preserving the local-edge-connectivity present in V. We provide two structural theorems, one of which implies a slight extension to Mader’s classical splitting theorem. We also provide a characterisation of the hypergraphs for which there is no such “good” split and a splitting result concerned with a specialisation of the local-connectivity function. We then use our splitting results to provide an upper bound on the smallest number of size-two edges we must add to any given hypergraph to ensure that in the resulting hypergraph we have λ(x, y) ≥ r(x, y) for all x, y in V, where r is an integer valued, symmetric requirement function on V*V. This is the so called “local-edge-connectivity augmentation problem” for hypergraphs. We also provide an extension to a Theorem of Szigeti, about augmenting to satisfy a requirement r, but using hyperedges. Next, in a result born of collaborative work with Zoltán Király from Budapest, we show that the local-connectivity augmentation problem is NP-complete for hypergraphs. Lastly we concern ourselves with an augmentation problem that includes a locational constraint. The premise is that we are given a hypergraph H = (V,E) with a bipartition P = {P1, P2} of V and asked to augment it with size-two edges, so that the result is k-edge-connected, and has no new edge contained in some P(i). We consider the splitting technique and describe the obstacles that prevent us forming “good” splits. From this we deduce results about which hypergraphs have a complete Pk-split. This leads to a minimax result on the optimal number of edges required and a polynomial algorithm to provide an optimal augmentation.

Neurofuzzy network model construction using Bézier-Bernstein polynomial functions

Neurofuzzy modelling systems combine fuzzy logic with quantitative artificial neural networks via a concept of fuzzification by using a fuzzy membership function usually based on B-splines and algebraic operators for inference, etc. The paper introduces a neurofuzzy model construction algorithm using Bezier-Bernstein polynomial functions as basis functions. The new network maintains most of the properties of the B-spline expansion based neurofuzzy system, such as the non-negativity of the basis functions, and unity of support but with the additional advantages of structural parsimony and Delaunay input space partitioning, avoiding the inherent computational problems of lattice networks. This new modelling network is based on the idea that an input vector can be mapped into barycentric co-ordinates with respect to a set of predetermined knots as vertices of a polygon (a set of tiled Delaunay triangles) over the input space. The network is expressed as the Bezier-Bernstein polynomial function of barycentric co-ordinates of the input vector. An inverse de Casteljau procedure using backpropagation is developed to obtain the input vector's barycentric co-ordinates that form the basis functions. Extension of the Bezier-Bernstein neurofuzzy algorithm to n-dimensional inputs is discussed followed by numerical examples to demonstrate the effectiveness of this new data based modelling approach.

A concept of approximated densities for efficient nonlinear estimation

This paper presents the theoretical development of a nonlinear adaptive filter based on a concept of filtering by approximated densities (FAD). The most common procedures for nonlinear estimation apply the extended Kalman filter. As opposed to conventional techniques, the proposed recursive algorithm does not require any linearisation. The prediction uses a maximum entropy principle subject to constraints. Thus, the densities created are of an exponential type and depend on a finite number of parameters. The filtering yields recursive equations involving these parameters. The update applies the Bayes theorem. Through simulation on a generic exponential model, the proposed nonlinear filter is implemented and the results prove to be superior to that of the extended Kalman filter and a class of nonlinear filters based on partitioning algorithms.

Impact of the earthworm Lumbricus terrestris (L.) on As, Cu, Pb and Zn mobility and speciation in contaminated soils

To assess the risks that contaminated soils pose to the environment properly a greater understanding of how soil biota influence the mobility of metal(loid)s in soils is required. Lumbricus terrestris L. were incubated in three soils contaminated with As, Cu, Pb and Zn. The concentration and speciation of metal(loid)s in pore waters and the mobility and partitioning in casts were compared with earthworm-free soil. Generally the concentrations of water extractable metal(loid)s in earthworm casts were greater than in earthworm-free soil. The impact of the earthworms on concentration and speciation in pore waters was soil and metal specific and could be explained either by earthworm induced changes in soil pH or soluble organic carbon. The mobilisation of metal(loid)s in the environment by earthworm activity may allow for leaching or uptake into biota.

Energy and protein interactions and their effect on nitrogen excretion in dairy cows

The principal driver of nitrogen (N) losses from the body including excretion and secretion in milk is N intake. However, other covariates may also play a role in modifying the partitioning of N. This study tests the hypothesis that N partitioning in dairy cows is affected by energy and protein interactions. A database containing 470 dairy cow observations was collated from calorimetry experiments. The data include N and energy parameters of the diet and N utilization by the animal. Univariate and multivariate meta-analyses that considered both within and between study effects were conducted to generate prediction equations based on N intake alone or with an energy component. The univariate models showed that there was a strong positive linear relationships between N intake and N excretion in faeces, urine and milk. The slopes were 0.28 faeces N, 0.38 urine N and 0.20 milk N. Multivariate model analysis did not improve the fit. Metabolizable energy intake had a significant positive effect on the amount of milk N in proportion to faeces and urine N, which is also supported by other studies. Another measure of energy considered as a covariate to N intake was diet quality or metabolizability (the concentration of metabolizable energy relative to gross energy of the diet). Diet quality also had a positive linear relationship with the proportion of milk N relative to N excreted in faeces and urine. Metabolizability had the largest effect on faeces N due to lower protein digestibility of low quality diets. Urine N was also affected by diet quality and the magnitude of the effect was higher than for milk N. This research shows that including a measure of diet quality as a covariate with N intake in a model of N execration can enhance our understanding of the effects of diet composition on N losses from dairy cows. The new prediction equations developed in this study could be used to monitor N losses from dairy systems.

A novel method for assessing risks to pollinators from plant protection products using honeybees as a model species

Pollination is one of the most important ecosystem services in agroecosystems and supports food production. Pollinators are potentially at risk being exposed to pesticides and the main route of exposure is direct contact, in some cases ingestion, of contaminated materials such as pollen, nectar, flowers and foliage. To date there are no suitable methods for predicting pesticide exposure for pollinators, therefore official procedures to assess pesticide risk are based on a Hazard Quotient. Here we develop a procedure to assess exposure and risk for pollinators based on the foraging behaviour of honeybees (Apis mellifera) and using this species as indicator representative of pollinating insects. The method was applied in 13 European field sites with different climatic, landscape and land use characteristics. The level of risk during the crop growing season was evaluated as a function of the active ingredients used and application regime. Risk levels were primarily determined by the agronomic practices employed (i.e. crop type, pest control method, pesticide use), and there was a clear temporal partitioning of risks through time. Generally the risk was higher in sites cultivated with permanent crops, such as vineyard and olive, than in annual crops, such as cereals and oil seed rape. The greatest level of risk is generally found at the beginning of the growing season for annual crops and later in June–July for permanent crops.

Kinetic multi-layer model of gas-particle interactions in aerosols and clouds (KM-GAP): linking condensation, evaporation and chemical reactions of organics, oxidants and water

We present a novel kinetic multi-layer model for gas-particle interactions in aerosols and clouds (KM-GAP) that treats explicitly all steps of mass transport and chemical reaction of semi-volatile species partitioning between gas phase, particle surface and particle bulk. KM-GAP is based on the PRA model framework (Pöschl-Rudich-Ammann, 2007), and it includes gas phase diffusion, reversible adsorption, surface reactions, bulk diffusion and reaction, as well as condensation, evaporation and heat transfer. The size change of atmospheric particles and the temporal evolution and spatial profile of the concentration of individual chemical species can be modelled along with gas uptake and accommodation coefficients. Depending on the complexity of the investigated system, unlimited numbers of semi-volatile species, chemical reactions, and physical processes can be treated, and the model shall help to bridge gaps in the understanding and quantification of multiphase chemistry and microphysics in atmo- spheric aerosols and clouds. In this study we demonstrate how KM-GAP can be used to analyze, interpret and design experimental investigations of changes in particle size and chemical composition in response to condensation, evaporation, and chemical reaction. For the condensational growth of water droplets, our kinetic model results provide a direct link between laboratory observations and molecular dynamic simulations, confirming that the accommodation coefficient of water at 270 K is close to unity. Literature data on the evaporation of dioctyl phthalate as a function of particle size and time can be reproduced, and the model results suggest that changes in the experimental conditions like aerosol particle concentration and chamber geometry may influence the evaporation kinetics and can be optimized for eðcient probing of specific physical effects and parameters. With regard to oxidative aging of organic aerosol particles, we illustrate how the formation and evaporation of volatile reaction products like nonanal can cause a decrease in the size of oleic acid particles exposed to ozone.

Development of a semantic graph-based scene description

Software representations of scenes, i.e. the modelling of objects in space, are used in many application domains. Current modelling and scene description standards focus on visualisation dimensions, and are intrinsically limited by their dependence upon their semantic interpretation and contextual application by humans. In this paper we propose the need for an open, extensible and semantically rich modelling language, which facilitates a machine-readable semantic structure. We critically review existing standards and techniques, and highlight a need for a semantically focussed scene description language. Based on this defined need we propose a preliminary solution, based on hypergraph theory, and reflect on application domains.

Manipulating resource allocation in plants

The distribution of nutrients and assimilates in different organs and tissues is in a constant state of flux throughout the growth and development of a plant. At key stages during the life cycle profound changes occur, and perhaps one of the most critical of these is during seed filling. By restricting the competition for reserves in Arabidopsis plants, the ability to manipulate seed size, seed weight, or seed content has been explored. Removal of secondary inflorescences and lateral branches resulted in a stimulation of elongation of the primary inflorescence and an increase in the distance between siliques. The pruning treatment also led to the development of longer and larger siliques that contained fewer, bigger seeds. This seems to be a consequence of a reduction in the number of ovules that develop and an increase in the fatty acid content of the seeds that mature. The data show that shoot architecture could have a substantial impact on the partitioning of reserves between vegetative and reproductive tissues and could be an important trait for selection in rapid phenotyping screens to optimize crop performance.

Determination of turbulent heat fluxes using a large aperture scintillometer over undulating mixed agricultural terrain

Scintillometry is an established technique for determining large areal average sensible heat fluxes. The scintillometer measurement is related to sensible heat flux via Monin–Obukhov similarity theory, which was developed for ideal homogeneous land surfaces. In this study it is shown that judicious application of scintillometry over heterogeneous mixed agriculture on undulating topography yields valid results when compared to eddy covariance (EC). A large aperture scintillometer (LAS) over a 2.4 km path was compared with four EC stations measuring sensible (H) and latent (LvE) heat fluxes over different vegetation (cereals and grass) which when aggregated were representative of the LAS source area. The partitioning of available energy into H and LvE varied strongly for different vegetation types, with H varying by a factor of three between senesced winter wheat and grass pasture. The LAS derived H agrees (one-to-one within the experimental uncertainty) with H aggregated from EC with a high coefficient of determination of 0.94. Chronological analysis shows individual fields may have a varying contribution to the areal average sensible heat flux on short (weekly) time scales due to phenological development and changing soil moisture conditions. Using spatially aggregated measurements of net radiation and soil heat flux with H from the LAS, the areal averaged latent heat flux (LvELAS) was calculated as the residual of the surface energy balance. The regression of LvELAS against aggregated LvE from the EC stations has a slope of 0.94, close to ideal, and demonstrates that this is an accurate method for the landscape-scale estimation of evaporation over heterogeneous complex topography.

Kinetic multi-layer model of gas-particle interactions in aerosols and clouds (KM-GAP): linking condensation, evaporation and chemical reactions of organics, oxidants and water

We present a novel kinetic multi-layer model for gas-particle interactions in aerosols and clouds (KMGAP) that treats explicitly all steps of mass transport and chemical reaction of semi-volatile species partitioning between gas phase, particle surface and particle bulk. KMGAP is based on the PRA model framework (P¨oschl-Rudich- Ammann, 2007), and it includes gas phase diffusion, reversible adsorption, surface reactions, bulk diffusion and reaction, as well as condensation, evaporation and heat transfer. The size change of atmospheric particles and the temporal evolution and spatial profile of the concentration of individual chemical species can be modeled along with gas uptake and accommodation coefficients. Depending on the complexity of the investigated system and the computational constraints, unlimited numbers of semi-volatile species, chemical reactions, and physical processes can be treated, and the model shall help to bridge gaps in the understanding and quantification of multiphase chemistry and microphysics in atmospheric aerosols and clouds. In this study we demonstrate how KM-GAP can be used to analyze, interpret and design experimental investigations of changes in particle size and chemical composition in response to condensation, evaporation, and chemical reaction. For the condensational growth of water droplets, our kinetic model results provide a direct link between laboratory observations and molecular dynamic simulations, confirming that the accommodation coefficient of water at 270K is close to unity (Winkler et al., 2006). Literature data on the evaporation of dioctyl phthalate as a function of particle size and time can be reproduced, and the model results suggest that changes in the experimental conditions like aerosol particle concentration and chamber geometry may influence the evaporation kinetics and can be optimized for efficient probing of specific physical effects and parameters. With regard to oxidative aging of organic aerosol particles, we illustrate how the formation and evaporation of volatile reaction products like nonanal can cause a decrease in the size of oleic acid particles exposed to ozone.

Effluent quality and ammonia emissions from out-wintering pads in England, Wales and Ireland

Out-wintering pads offer a reduced cost system for wintering cattle, minimising damage to pasture, providing animal welfare and production benefits, and generate, potentially, a more manageable effluent and lower ammonia emissions. The objectives of the present study were (i) to contribute to improved understanding of the factors impacting on effluent quality, ammonia emissions and animal welfare via observations on four farm-based out-wintering pads (ComOWPs) in England, Wales and Ireland and more detailed studies undertaken on four experimental OWPs (ExpOWPs) constructed at Rothamsted Research North Wyke, Devon, England and (ii) to corroborate the effluent quality data from both the ComOWPs and the ExpOWPs, with findings in the literature. Woodchip size, feeding management and area allowance were the treatment factors applied on the ExpOWPs. These three factors were randomised across the four ExpOWPs, over four 6–7 week periods. Effluent quality from the ExpOWPs was sampled frequently in a flow proportional way and analysed for total N (TN); total P (TP); total solids (TS); ammonium-N (NH4+-N); nitrate-N (NO3−-N). Beef cattle were periodically weighed for determination of live weight gain (LWG). An approximate nitrogen balance was calculated as a means of understanding its partitioning and fate during and after the ExpOWPs use. Effluent quality from the ComOWPs was sampled frequently, also in a flow-proportional way, and analysed for TN, TP, TS, NH4+-N, NO3−-N, total K and COD. Effluent quality data from the ExpOWPs showed no significant differences (P > 0.05) between treatments, with average concentrations of 1095 mg l−1, and 806 mg l−1, for TN and NH4+-N, respectively. Average effluent concentrations from the ComOWPs were 356 mg l−1 TN and 124 mg l−1 NH4+-N. Ammonia emissions from the ExpOWPs showed no significant differences (P > 0.05) between the treatments, with average mean emission rates of 2.5 g m−2 d−1 NH3-N, respectively. A positive correlation was established between NH3-N emission rate and wind speed. Emission rates from the ComOWPs ranged from 0.7 to 1.6 g m−2 d−1 NH3-N. Average daily LWG on the ExpOWPs was 1.33 kg steer−1 d−1. The effluent from both the ComOWPs and ExpOWPs were more similar with dirty water and of consistently lower strength than beef cattle slurry, as supported by findings in the literature, and therefore, it is suggested to be subject to the regulatory requirements of dirty water rather than slurry.

The REFLEX project: Comparing different algorithms and implementations for the inversion of a terrestrial ecosystem model against eddy covariance data

We describe a model-data fusion (MDF) inter-comparison project (REFLEX), which compared various algorithms for estimating carbon (C) model parameters consistent with both measured carbon fluxes and states and a simple C model. Participants were provided with the model and with both synthetic net ecosystem exchange (NEE) of CO2 and leaf area index (LAI) data, generated from the model with added noise, and observed NEE and LAI data from two eddy covariance sites. Participants endeavoured to estimate model parameters and states consistent with the model for all cases over the two years for which data were provided, and generate predictions for one additional year without observations. Nine participants contributed results using Metropolis algorithms, Kalman filters and a genetic algorithm. For the synthetic data case, parameter estimates compared well with the true values. The results of the analyses indicated that parameters linked directly to gross primary production (GPP) and ecosystem respiration, such as those related to foliage allocation and turnover, or temperature sensitivity of heterotrophic respiration, were best constrained and characterised. Poorly estimated parameters were those related to the allocation to and turnover of fine root/wood pools. Estimates of confidence intervals varied among algorithms, but several algorithms successfully located the true values of annual fluxes from synthetic experiments within relatively narrow 90% confidence intervals, achieving >80% success rate and mean NEE confidence intervals <110 gC m−2 year−1 for the synthetic case. Annual C flux estimates generated by participants generally agreed with gap-filling approaches using half-hourly data. The estimation of ecosystem respiration and GPP through MDF agreed well with outputs from partitioning studies using half-hourly data. Confidence limits on annual NEE increased by an average of 88% in the prediction year compared to the previous year, when data were available. Confidence intervals on annual NEE increased by 30% when observed data were used instead of synthetic data, reflecting and quantifying the addition of model error. Finally, our analyses indicated that incorporating additional constraints, using data on C pools (wood, soil and fine roots) would help to reduce uncertainties for model parameters poorly served by eddy covariance data.

Markov models of aging: theory and practice

We review and structure some of the mathematical and statistical models that have been developed over the past half century to grapple with theoretical and experimental questions about the stochastic development of aging over the life course. We suggest that the mathematical models are in large part addressing the problem of partitioning the randomness in aging: How does aging vary between individuals, and within an individual over the lifecourse? How much of the variation is inherently related to some qualities of the individual, and how much is entirely random? How much of the randomness is cumulative, and how much is merely short-term flutter? We propose that recent lines of statistical inquiry in survival analysis could usefully grapple with these questions, all the more so if they were more explicitly linked to the relevant mathematical and biological models of aging. To this end, we describe points of contact among the various lines of mathematical and statistical research. We suggest some directions for future work, including the exploration of information-theoretic measures for evaluating components of stochastic models as the basis for analyzing experiments and anchoring theoretical discussions of aging.

Synergistic effects of mixing cocksfoot and sainfoin on in vitro rumen fermentation: role of condensed tannins

Some bioactive secondary metabolites in forage legumes can cause digestive interactions, so that the rumen fermentation pattern of a mixture of forages can differ from the average values of its components. The objective of this study was to investigate the potential role of condensed tannins (CT) on the synergistic effects between one grass species, cocksfoot, and one CT-containing legume species, sainfoin, on in vitro rumen fermentation characteristics. Cocksfoot and sainfoin in different proportions (in g/kg, 1000:0, 750:250, 500:500, 250:750 and 0:1000) were incubated under anaerobic conditions in culture bottles containing buffered rumen fluid from sheep. Incubations were carried out using artificial saliva with and without polyethylene glycol (PEG), which binds and thus inactivates CT. Rumen fermentation parameters describing the degradation and the fate of the energetic and nitrogenous substrates were measured at 3.5 and 24 h. At the early fermentation stage, when the sainfoin level increased from 0 to 1000 g/kg, the ammonia concentration in the medium quadratically decreased from 3.20 to 0.53 mmol/l in absence of PEG (P<0.01) but not in its presence. This result demonstrates that sainfoin CT decreased the rumen degradation of the proteins in the whole mixture, including the proteins in cocksfoot, rather than just the proteins in sainfoin. Interestingly, the total gas and methane productions were lower in mixtures incubated in absence of PEG than in presence of PEG (P<0.001) while no significant PEG effect was observed on digestibility. At the late fermentation stage, a positive quadratic effect on dry matter digestibility was detected without PEG (P<0.05), indicating a synergistic action of cocksfoot plus sainfoin on plant substrate degradation due to CT. The presence of PEG increased gas production (P<0.001) and NH3-N concentration in the medium (P<0.001). Our results suggest that CT could allow a better utilization of plant substrates in mixtures by the rumen ecosystem by improving the partitioning of degraded substrates toward lower gas losses, and decreasing the protein degradation.