Prediction leaching of potassium using the convective-dispersive and the convective log-normal transfer function models

There is increasing concern about soil enrichment with K+ and subsequent potential losses following long-term application of poor quality water to agricultural land. Different models are increasingly being used for predicting or analyzing water flow and chemical transport in soils and groundwater. The convective-dispersive equation (CDE) and the convective log-normal transfer function (CLT) models were fitted to the potassium (K+) leaching data. The CDE and CLT models produced equivalent goodness of fit. Simulated breakthrough curves for a range of CaCl2 concentration based on parameters of 15 mmol l(-1) CaCl2 were characterised by an early peak position associated with higher K+ concentration as the CaCl2 concentration used in leaching experiments decreased. In another method, the parameters estimated from 15 mmol l(-1) CaCl2 solution were used for all other CaCl2 concentrations, and the best value of retardation factor (R) was optimised for each data set. A better prediction was found. With decreasing CaCl2 concentration the value of R is required to be more than that measured (except for 10 mmol l(-1) CaCl2), if the estimated parameters of 15 mmol l(-1) CaCl2 are used. The two models suffer from the fact that they need to be calibrated against a data set, and some of their parameters are not measurable and cannot be determined independently.

The diurnal course of soil moisture as measured by various dielectric sensors: Effects of soil temperature and the implications for evaporation estimates

Soil moisture content, theta, of a bare and vegetated UK gravelly sandy loam soil (in situ and repacked in small lysimeters) was measured using various dielectric instruments (single-sensor ThetaProbes, multi-sensor Profile Probes, and Aquaflex Sensors), at depths ranging between 0.03 and I m, during the summers of 2001 (in situ soil) and 2002 (mini-lysimeters). Half-hourly values of evaporation, E, were calculated from diurnal changes in total soil profile water content, using the soil water balance equation. For the bare soil field, Profile Probes and ML2x ThetaProbes indicated a diurnal course of theta that did not concur with typical soil physical observations: surface layer soil moisture content increased from early morning until about midday, after which theta declined, generally until the early evening. The unexpected course of theta was positively correlated to soil temperature, T-s, also at deeper depths. Aquaflex and ML1 ThetaProbe (older models) outputs, however, reflected common observations: 0 increased slightly during the night (capillary rise) and decreased from the morning until late afternoon (as a result of evaporation). For the vegetated plot, the spurious diurnal theta fluctuations were less obvious, because canopy shading resulted in lower amplitudes of T-s. The unrealistic theta profiles measured for the bare and vegetated field sites caused diurnal estimates of E to attain downward daytime and upward night-time values. In the mini-lysimeters, at medium to high moisture contents, theta values measured by (ML2x) ThetaProbes followed a relatively realistic course, and predictions of E from diurnal changes in vertically integrated theta generally compared well with lysimeter estimates of E. However, time courses of theta and E became comparable to those observed for the field plots when the soil in the lysimeters reached relatively low values of theta. Attempts to correct measured theta for fluctuations in T, revealed that no generally applicable formula could be derived. (c) 2005 Elsevier B.V. All rights reserved.

A well-posed integral equation formulation for three-dimensional rough surface scattering

We consider the problem of scattering of time-harmonic acoustic waves by an unbounded sound-soft rough surface. Recently, a Brakhage Werner type integral equation formulation of this problem has been proposed, based on an ansatz as a combined single- and double-layer potential, but replacing the usual fundamental solution of the Helmholtz equation with an appropriate half-space Green's function. Moreover, it has been shown in the three-dimensional case that this integral equation is uniquely solvable in the space L-2 (Gamma) when the scattering surface G does not differ too much from a plane. In this paper, we show that this integral equation is uniquely solvable with no restriction on the surface elevation or slope. Moreover, we construct explicit bounds on the inverse of the associated boundary integral operator, as a function of the wave number, the parameter coupling the single- and double-layer potentials, and the maximum surface slope. These bounds show that the norm of the inverse operator is bounded uniformly in the wave number, kappa, for kappa > 0, if the coupling parameter h is chosen proportional to the wave number. In the case when G is a plane, we show that the choice eta = kappa/2 is nearly optimal in terms of minimizing the condition number.

Consistent approximate models of the global atmosphere: shallow, deep, hydrostatic, quasi-hydrostatic and non-hydrostatic

We study global atmosphere models that are at least as accurate as the hydrostatic primitive equations (HPEs), reviewing known results and reporting some new ones. The HPEs make spherical geopotential and shallow atmosphere approximations in addition to the hydrostatic approximation. As is well known, a consistent application of the shallow atmosphere approximation requires omission of those Coriolis terms that vary as the cosine of latitude and of certain other terms in the components of the momentum equation. An approximate model is here regarded as consistent if it formally preserves conservation principles for axial angular momentum, energy and potential vorticity, and (following R. Müller) if its momentum component equations have Lagrange's form. Within these criteria, four consistent approximate global models, including the HPEs themselves, are identified in a height-coordinate framework. The four models, each of which includes the spherical geopotential approximation, correspond to whether the shallow atmosphere and hydrostatic (or quasi-hydrostatic) approximations are individually made or not made. Restrictions on representing the spatial variation of apparent gravity occur. Solution methods and the situation in a pressure-coordinate framework are discussed. © Crown copyright 2005.

Research note: amendments to the model for predicting age at sexual maturity for growing pullets of layer strains following changes in photoperiod

A model was published by Lewis et al. (2002) to predict the mean age at first egg (AFE) for pullets of laying strains reared under non-limiting environmental conditions and exposed to a single change in photoperiod during the rearing stage. Subsequently, Lewis et al. (2003) reported the effects of two opposing changes in photoperiod, which showed that the first change appears to alter the pullet's physiological age so that it responds to the second change as though it had been given at an earlier age (if photoperiod was decreased), or later age (if photoperiod was increased) than the true chronological age. During the construction of a computer model based on these two publications, it became apparent that some of the components of the models needed adjustment. The amendments relate to (1) the standard deviation (S.D.) used for calculating the proportion of a young flock that has attained photosensitivity, (2) the equation for calculating the slope of the line relating AFE to age at transfer from one photoperiod to another, (3) the equation used for estimating the distribution of AFE as a function of the mean value, (4) the point of no return when pullets which have started spontaneous maturation in response to the current photoperiod can no longer respond to a late change in photoperiod and (5) the equations used for calculating the distribution of AFE when the trait is bimodal.

The ModFOLD server for the quality assessment of protein structural models

The reliable assessment of the quality of protein structural models is fundamental to the progress of structural bioinformatics. The ModFOLD server provides access to two accurate techniques for the global and local prediction of the quality of 3D models of proteins. Firstly ModFOLD, which is a fast Model Quality Assessment Program (MQAP) used for the global assessment of either single or multiple models. Secondly ModFOLDclust, which is a more intensive method that carries out clustering of multiple models and provides per-residue local quality assessment.

Overview of mathematical approaches used to model bacterial chemotaxis I: the single cell

Mathematical modeling of bacterial chemotaxis systems has been influential and insightful in helping to understand experimental observations. We provide here a comprehensive overview of the range of mathematical approaches used for modeling, within a single bacterium, chemotactic processes caused by changes to external gradients in its environment. Specific areas of the bacterial system which have been studied and modeled are discussed in detail, including the modeling of adaptation in response to attractant gradients, the intracellular phosphorylation cascade, membrane receptor clustering, and spatial modeling of intracellular protein signal transduction. The importance of producing robust models that address adaptation, gain, and sensitivity are also discussed. This review highlights that while mathematical modeling has aided in understanding bacterial chemotaxis on the individual cell scale and guiding experimental design, no single model succeeds in robustly describing all of the basic elements of the cell. We conclude by discussing the importance of this and the future of modeling in this area.

Fitting models for the joint action of two drugs using SAS(R)

Combinations of drugs are increasingly being used for a wide variety of diseases and conditions. A pre-clinical study may allow the investigation of the response at a large number of dose combinations. In determining the response to a drug combination, interest may lie in seeking evidence of synergism, in which the joint action is greater than the actions of the individual drugs, or of antagonism, in which it is less. Two well-known response surface models representing no interaction are Loewe additivity and Bliss independence, and Loewe or Bliss synergism or antagonism is defined relative to these. We illustrate an approach to fitting these models for the case in which the marginal single drug dose-response relationships are represented by four-parameter logistic curves with common upper and lower limits, and where the response variable is normally distributed with a common variance about the dose-response curve. When the dose-response curves are not parallel, the relative potency of the two drugs varies according to the magnitude of the desired effect and the models for Loewe additivity and synergism/antagonism cannot be explicitly expressed. We present an iterative approach to fitting these models without the assumption of parallel dose-response curves. A goodness-of-fit test based on residuals is also described. Implementation using the SAS NLIN procedure is illustrated using data from a pre-clinical study. Copyright © 2007 John Wiley & Sons, Ltd.

Population genetic models can be used to study the evolution of the interacting behaviours of parents and their progeny

An example of the evolution of the interacting behaviours of parents and progeny is studied using iterative equations linking the frequencies of the gametes produced by the progeny to the frequencies of the gametes in the parental generation. This population genetics approach shows that a model in which both behaviours are determined by a single locus can lead to a stable equilibrium in which the two behaviours continue to segregate. A model in which the behaviours are determined by genes at two separate loci leads eventually to fixation of the alleles at both loci but this can take many generations of selection. Models of the type described in this paper will be needed to understand the evolution of complex behaviour when genomic or experimental information is available about the genetic determinants of behaviour and the selective values of different genomes. (c) 2007 Elsevier Inc. All rights reserved.

Neural and wavelet network models for financial distress classification

This work analyzes the use of linear discriminant models, multi-layer perceptron neural networks and wavelet networks for corporate financial distress prediction. Although simple and easy to interpret, linear models require statistical assumptions that may be unrealistic. Neural networks are able to discriminate patterns that are not linearly separable, but the large number of parameters involved in a neural model often causes generalization problems. Wavelet networks are classification models that implement nonlinear discriminant surfaces as the superposition of dilated and translated versions of a single "mother wavelet" function. In this paper, an algorithm is proposed to select dilation and translation parameters that yield a wavelet network classifier with good parsimony characteristics. The models are compared in a case study involving failed and continuing British firms in the period 1997-2000. Problems associated with over-parameterized neural networks are illustrated and the Optimal Brain Damage pruning technique is employed to obtain a parsimonious neural model. The results, supported by a re-sampling study, show that both neural and wavelet networks may be a valid alternative to classical linear discriminant models.

Wigner Transport models of the electron-phonon kinetics in quantum wires

Two quantum-kinetic models of ultrafast electron transport in quantum wires are derived from the generalized electron-phonon Wigner equation. The various assumptions and approximations allowing one to find closed equations for the reduced electron Wigner function are discussed with an emphasis on their physical relevance. The models correspond to the Levinson and Barker-Ferry equations, now generalized to account for a space-dependent evolution. They are applied to study the quantum effects in the dynamics of an initial packet of highly nonequilibrium carriers, locally generated in the wire. The properties of the two model equations are compared and analyzed.

Ocean acoustic models for low frequency propagation in 2D and 3D environments

In this paper we are mainly concerned with the development of efficient computer models capable of accurately predicting the propagation of low-to-middle frequency sound in the sea, in axially symmetric (2D) and in fully 3D environments. The major physical features of the problem, i.e. a variable bottom topography, elastic properties of the subbottom structure, volume attenuation and other range inhomogeneities are efficiently treated. The computer models presented are based on normal mode solutions of the Helmholtz equation on the one hand, and on various types of numerical schemes for parabolic approximations of the Helmholtz equation on the other. A new coupled mode code is introduced to model sound propagation in range-dependent ocean environments with variable bottom topography, where the effects of an elastic bottom, of volume attenuation, surface and bottom roughness are taken into account. New computer models based on finite difference and finite element techniques for the numerical solution of parabolic approximations are also presented. They include an efficient modeling of the bottom influence via impedance boundary conditions, they cover wide angle propagation, elastic bottom effects, variable bottom topography and reverberation effects. All the models are validated on several benchmark problems and versus experimental data. Results thus obtained were compared with analogous results from standard codes in the literature.

Algorithmic statistical analysis of electrophysiological data for the investigation of structure-activity relationship in single neurons

We are developing computational tools supporting the detailed analysis of the dependence of neural electrophysiological response on dendritic morphology. We approach this problem by combining simulations of faithful models of neurons (experimental real life morphological data with known models of channel kinetics) with algorithmic extraction of morphological and physiological parameters and statistical analysis. In this paper, we present the novel method for an automatic recognition of spike trains in voltage traces, which eliminates the need for human intervention. This enables classification of waveforms with consistent criteria across all the analyzed traces and so it amounts to reduction of the noise in the data. This method allows for an automatic extraction of relevant physiological parameters necessary for further statistical analysis. In order to illustrate the usefulness of this procedure to analyze voltage traces, we characterized the influence of the somatic current injection level on several electrophysiological parameters in a set of modeled neurons. This application suggests that such an algorithmic processing of physiological data extracts parameters in a suitable form for further investigation of structure-activity relationship in single neurons.

Four-dimensional variational data assimilation for high resolution nested models

Four-dimensional variational data assimilation (4D-Var) is used in environmental prediction to estimate the state of a system from measurements. When 4D-Var is applied in the context of high resolution nested models, problems may arise in the representation of spatial scales longer than the domain of the model. In this paper we study how well 4D-Var is able to estimate the whole range of spatial scales present in one-way nested models. Using a model of the one-dimensional advection–diffusion equation we show that small spatial scales that are observed can be captured by a 4D-Var assimilation, but that information in the larger scales may be degraded. We propose a modification to 4D-Var which allows a better representation of these larger scales.

Impacts of pollution and climate change on ombrotrophic Sphagnum species in the UK: analysis of uncertainties in two empirical niche models

A significant challenge in the prediction of climate change impacts on ecosystems and biodiversity is quantifying the sources of uncertainty that emerge within and between different models. Statistical species niche models have grown in popularity, yet no single best technique has been identified reflecting differing performance in different situations. Our aim was to quantify uncertainties associated with the application of 2 complimentary modelling techniques. Generalised linear mixed models (GLMM) and generalised additive mixed models (GAMM) were used to model the realised niche of ombrotrophic Sphagnum species in British peatlands. These models were then used to predict changes in Sphagnum cover between 2020 and 2050 based on projections of climate change and atmospheric deposition of nitrogen and sulphur. Over 90% of the variation in the GLMM predictions was due to niche model parameter uncertainty, dropping to 14% for the GAMM. After having covaried out other factors, average variation in predicted values of Sphagnum cover across UK peatlands was the next largest source of variation (8% for the GLMM and 86% for the GAMM). The better performance of the GAMM needs to be weighed against its tendency to overfit the training data. While our niche models are only a first approximation, we used them to undertake a preliminary evaluation of the relative importance of climate change and nitrogen and sulphur deposition and the geographic locations of the largest expected changes in Sphagnum cover. Predicted changes in cover were all small (generally <1% in an average 4 m2 unit area) but also highly uncertain. Peatlands expected to be most affected by climate change in combination with atmospheric pollution were Dartmoor, Brecon Beacons and the western Lake District.