Fast three dimensional r-adaptive mesh redistribution

This paper describes a fast and reliable method for redistributing a computational mesh in three dimensions which can generate a complex three dimensional mesh without any problems due to mesh tangling. The method relies on a three dimensional implementation of the parabolic Monge–Ampère (PMA) technique, for finding an optimally transported mesh. The method for implementing PMA is described in detail and applied to both static and dynamic mesh redistribution problems, studying both the convergence and the computational cost of the algorithm. The algorithm is applied to a series of problems of increasing complexity. In particular very regular meshes are generated to resolve real meteorological features (derived from a weather forecasting model covering the UK area) in grids with over 2×107 degrees of freedom. The PMA method computes these grids in times commensurate with those required for operational weather forecasting.

Estimating Lorenz's reference state in an ocean with a nonlinear equation of state for seawater

The study of the mechanical energy budget of the oceans using Lorenz available potential energy (APE) theory is based on knowledge of the adiabatically re-arranged Lorenz reference state of minimum potential energy. The compressible and nonlinear character of the equation of state for seawater has been thought to cause the reference state to be ill-defined, casting doubt on the usefulness of APE theory for investigating ocean energetics under realistic conditions. Using a method based on the volume frequency distribution of parcels as a function of temperature and salinity in the context of the seawater Boussinesq approximation, which we illustrate using climatological data, we show that compressibility effects are in fact minor. The reference state can be regarded as a well defined one-dimensional function of depth, which forms a surface in temperature, salinity and density space between the surface and the bottom of the ocean. For a very small proportion of water masses, this surface can be multivalued and water parcels can have up to two statically stable levels in the reference density profile, of which the shallowest is energetically more accessible. Classifying parcels from the surface to the bottom gives a different reference density profile than classifying in the opposite direction. However, this difference is negligible. We show that the reference state obtained by standard sorting methods is equivalent, though computationally more expensive, to the volume frequency distribution approach. The approach we present can be applied systematically and in a computationally efficient manner to investigate the APE budget of the ocean circulation using models or climatological data.

Application of complex extreme learning machine to multiclass classification problems with high dimensionality: a THz spectra classification problem

We extend extreme learning machine (ELM) classifiers to complex Reproducing Kernel Hilbert Spaces (RKHS) where the input/output variables as well as the optimization variables are complex-valued. A new family of classifiers, called complex-valued ELM (CELM) suitable for complex-valued multiple-input–multiple-output processing is introduced. In the proposed method, the associated Lagrangian is computed using induced RKHS kernels, adopting a Wirtinger calculus approach formulated as a constrained optimization problem similarly to the conventional ELM classifier formulation. When training the CELM, the Karush–Khun–Tuker (KKT) theorem is used to solve the dual optimization problem that consists of satisfying simultaneously smallest training error as well as smallest norm of output weights criteria. The proposed formulation also addresses aspects of quaternary classification within a Clifford algebra context. For 2D complex-valued inputs, user-defined complex-coupled hyper-planes divide the classifier input space into four partitions. For 3D complex-valued inputs, the formulation generates three pairs of complex-coupled hyper-planes through orthogonal projections. The six hyper-planes then divide the 3D space into eight partitions. It is shown that the CELM problem formulation is equivalent to solving six real-valued ELM tasks, which are induced by projecting the chosen complex kernel across the different user-defined coordinate planes. A classification example of powdered samples on the basis of their terahertz spectral signatures is used to demonstrate the advantages of the CELM classifiers compared to their SVM counterparts. The proposed classifiers retain the advantages of their ELM counterparts, in that they can perform multiclass classification with lower computational complexity than SVM classifiers. Furthermore, because of their ability to perform classification tasks fast, the proposed formulations are of interest to real-time applications.

Inverse modeling of the 14C bomb pulse in stalagmites to constrain the dynamics of soil carbon cycling at selected European cave sites

The decomposition of soil organic matter (SOM) is temperature dependent, but its response to a future warmer climate remains equivocal. Enhanced rates of decomposition of SOM under increased global temperatures might cause higher CO2 emissions to the atmosphere, and could therefore constitute a strong positive feedback. The magnitude of this feedback however remains poorly understood, primarily because of the difficulty in quantifying the temperature sensitivity of stored, recalcitrant carbon that comprises the bulk (>90%) of SOM in most soils. In this study we investigated the effects of climatic conditions on soil carbon dynamics using the attenuation of the 14C ‘bomb’ pulse as recorded in selected modern European speleothems. These new data were combined with published results to further examine soil carbon dynamics, and to explore the sensitivity of labile and recalcitrant organic matter decomposition to different climatic conditions. Temporal changes in 14C activity inferred from each speleothem was modelled using a three pool soil carbon inverse model (applying a Monte Carlo method) to constrain soil carbon turnover rates at each site. Speleothems from sites that are characterised by semi-arid conditions, sparse vegetation, thin soil cover and high mean annual air temperatures (MAATs), exhibit weak attenuation of atmospheric 14C ‘bomb’ peak (a low damping effect, D in the range: 55–77%) and low modelled mean respired carbon ages (MRCA), indicating that decomposition is dominated by young, recently fixed soil carbon. By contrast, humid and high MAAT sites that are characterised by a thick soil cover and dense, well developed vegetation, display the highest damping effect (D = c. 90%), and the highest MRCA values (in the range from 350 ± 126 years to 571 ± 128 years). This suggests that carbon incorporated into these stalagmites originates predominantly from decomposition of old, recalcitrant organic matter. SOM turnover rates cannot be ascribed to a single climate variable, e.g. (MAAT) but instead reflect a complex interplay of climate (e.g. MAAT and moisture budget) and vegetation development.

Discontinuous Galerkin methods for the p-biharmonic equation from a discrete variational perspective

We study discontinuous Galerkin approximations of the p-biharmonic equation for p∈(1,∞) from a variational perspective. We propose a discrete variational formulation of the problem based on an appropriate definition of a finite element Hessian and study convergence of the method (without rates) using a semicontinuity argument. We also present numerical experiments aimed at testing the robustness of the method.

Maternal antenatal anxiety, postnatal stroking and emotional problems in children: outcomes predicted from pre and postnatal programming hypotheses

Background Mothers' self-reported stroking of their infants over the first weeks of life modifies the association between prenatal depression and physiological and emotional reactivity at 7 months, consistent with animal studies of the effects of tactile stimulation. We now investigate whether the effects of maternal stroking persist to 2.5 years. Given animal and human evidence for sex differences in the effects of prenatal stress we compare associations in boys and girls. Method From a general population sample of 1233 first-time mothers recruited at 20 weeks gestation we drew a random sample of 316 for assessment at 32 weeks, stratified by reported inter-partner psychological abuse, a risk indicator for child development. Of these mothers, 243 reported at 5 and 9 weeks how often they stroked their infants, and completed the Child Behavior Checklist (CBCL) at 2.5 years post-delivery. Results There was a significant interaction between prenatal anxiety and maternal stroking in the prediction of CBCL internalizing (p = 0.001) and anxious/depressed scores (p < 0.001). The effects were stronger in females than males, and the three-way interaction prenatal anxiety × maternal stroking × sex of infant was significant for internalizing symptoms (p = 0.003). The interactions arose from an association between prenatal anxiety and internalizing symptoms only in the presence of low maternal stroking. Conclusions The findings are consistent with stable epigenetic effects, many sex specific, reported in animal studies. While epigenetic mechanisms may be underlying the associations, it remains to be established whether stroking affects gene expression in humans.

Enterprise Architecture adoption method for Higher Education Institutions

During the last few years Enterprise Architecture has received increasing attention among industry and academia. Enterprise Architecture (EA) can be defined as (i) a formal description of the current and future state(s) of an organisation, and (ii) a managed change between these states to meet organisation’s stakeholders’ goals and to create value to the organisation. By adopting EA, organisations may gain a number of benefits such as better decision making, increased revenues and cost reductions, and alignment of business and IT. To increase the performance of public sector operations, and to improve public services and their availability, the Finnish Parliament has ratified the Act on Information Management Governance in Public Administration in 2011. The Act mandates public sector organisations to start adopting EA by 2014, including Higher Education Institutions (HEIs). Despite the benefits of EA and the Act, EA adoption level and maturity in Finnish HEIs are low. This is partly caused by the fact that EA adoption has been found to be difficult. Thus there is a need for a solution to help organisations to adopt EA successfully. This thesis follows Design Science (DS) approach to improve traditional EA adoption method in order to increase the likelihood of successful adoption. First a model is developed to explain the change resistance during EA adoption. To find out problems associated with EA adoption, an EA-pilot conducted in 2010 among 12 Finnish HEIs was analysed using the model. It was found that most of the problems were caused by misunderstood EA concepts, attitudes, and lack of skills. The traditional EA adoption method does not pay attention to these. To overcome the limitations of the traditional EA adoption method, an improved EA Adoption Method (EAAM) is introduced. By following EAAM, organisations may increase the likelihood of successful EA adoption. EAAM helps in acquiring the mandate for EA adoption from top-management, which has been found to be crucial to success. It also helps in supporting individual and organisational learning, which has also found to be essential in successful adoption.

Factors that influence the detection of psychological problems in adolescents attending general practices

Background Epidemiological studies indicate that the prevalence of psychological problems in patients attending primary care services may be as high as 25%. Aim To identify factors that influence the detection of psychological difficulties in adolescent patients receiving primary care in the UK. Design of study A prospective study of 13-16 year olds consecutively attending general practices. Setting General practices, Norfolk, UK. Method Information was obtained from adolescents and parents using the validated Strengths and Difficulties Questionnaire (SDQ) and from GF`s using the consultation assessment form. Results Ninety-eight adolescents were recruited by 13 GPs in Norfolk (mean age = 14.4 years, SD = 1.08; 38 males, 60 females). The study identified psychological difficulties in almost one-third of adolescents (31/98, 31.6%). Three factors significant to the detection of psychological disorders in adolescents were identified: adolescents' perceptions of difficulties according to the self-report SDQ, the severity of their problems as indicated by the self-report SDQ, and whether psychological issues were discussed in the consultation. GPs did not always explore psychological problems with adolescents, even if GPs perceived these to be present. Nineteen of 31 adolescents with psychological difficulties were identified by GPs (sensitivity = 61.2%, specificity = 85.1%). A management plan or follow-up was made for only seven of 19 adolescents identified, suggesting that ongoing psychological difficulties in many patients are not being addressed. Conclusions GPs are in a good position to identify psychological issues in adolescents, but GPs and adolescents seem reluctant to explore these openly. Open discussion of psychological issues in GP consultations was found to be the most important factor in determining whether psychological difficulties in adolescents are detected by GPs.

Reduced relative entropy techniques for a posteriori analysis of multiphase problems in elastodynamics

We give an a posteriori analysis of a semidiscrete discontinuous Galerkin scheme approximating solutions to a model of multiphase elastodynamics, which involves an energy density depending not only on the strain but also the strain gradient. A key component in the analysis is the reduced relative entropy stability framework developed in Giesselmann (2014, SIAM J. Math. Anal., 46, 3518–3539). This framework allows energy-type arguments to be applied to continuous functions. Since we advocate the use of discontinuous Galerkin methods we make use of two families of reconstructions, one set of discrete reconstructions and a set of elliptic reconstructions to apply the reduced relative entropy framework in this setting.

Probabilistic wind power forecasts with an inverse power curve transformation and censored regression

Forecasting wind power is an important part of a successful integration of wind power into the power grid. Forecasts with lead times longer than 6 h are generally made by using statistical methods to post-process forecasts from numerical weather prediction systems. Two major problems that complicate this approach are the non-linear relationship between wind speed and power production and the limited range of power production between zero and nominal power of the turbine. In practice, these problems are often tackled by using non-linear non-parametric regression models. However, such an approach ignores valuable and readily available information: the power curve of the turbine's manufacturer. Much of the non-linearity can be directly accounted for by transforming the observed power production into wind speed via the inverse power curve so that simpler linear regression models can be used. Furthermore, the fact that the transformed power production has a limited range can be taken care of by employing censored regression models. In this study, we evaluate quantile forecasts from a range of methods: (i) using parametric and non-parametric models, (ii) with and without the proposed inverse power curve transformation and (iii) with and without censoring. The results show that with our inverse (power-to-wind) transformation, simpler linear regression models with censoring perform equally or better than non-linear models with or without the frequently used wind-to-power transformation.

Mesh adaptation on the sphere using optimal transport and the numerical solution of a Monge-Ampère type equation

An equation of Monge-Ampère type has, for the first time, been solved numerically on the surface of the sphere in order to generate optimally transported (OT) meshes, equidistributed with respect to a monitor function. Optimal transport generates meshes that keep the same connectivity as the original mesh, making them suitable for r-adaptive simulations, in which the equations of motion can be solved in a moving frame of reference in order to avoid mapping the solution between old and new meshes and to avoid load balancing problems on parallel computers. The semi-implicit solution of the Monge-Ampère type equation involves a new linearisation of the Hessian term, and exponential maps are used to map from old to new meshes on the sphere. The determinant of the Hessian is evaluated as the change in volume between old and new mesh cells, rather than using numerical approximations to the gradients. OT meshes are generated to compare with centroidal Voronoi tesselations on the sphere and are found to have advantages and disadvantages; OT equidistribution is more accurate, the number of iterations to convergence is independent of the mesh size, face skewness is reduced and the connectivity does not change. However anisotropy is higher and the OT meshes are non-orthogonal. It is shown that optimal transport on the sphere leads to meshes that do not tangle. However, tangling can be introduced by numerical errors in calculating the gradient of the mesh potential. Methods for alleviating this problem are explored. Finally, OT meshes are generated using observed precipitation as a monitor function, in order to demonstrate the potential power of the technique.

A Variance-Minimizing Filter for Large-Scale Applications

A truly variance-minimizing filter is introduced and its per for mance is demonstrated with the Korteweg– DeV ries (KdV) equation and with a multilayer quasigeostrophic model of the ocean area around South Africa. It is recalled that Kalman-like filters are not variance minimizing for nonlinear model dynamics and that four - dimensional variational data assimilation (4DV AR)-like methods relying on per fect model dynamics have dif- ficulty with providing error estimates. The new method does not have these drawbacks. In fact, it combines advantages from both methods in that it does provide error estimates while automatically having balanced states after analysis, without extra computations. It is based on ensemble or Monte Carlo integrations to simulate the probability density of the model evolution. When obser vations are available, the so-called importance resampling algorithm is applied. From Bayes’ s theorem it follows that each ensemble member receives a new weight dependent on its ‘ ‘distance’ ’ t o the obser vations. Because the weights are strongly var ying, a resampling of the ensemble is necessar y. This resampling is done such that members with high weights are duplicated according to their weights, while low-weight members are largely ignored. In passing, it is noted that data assimilation is not an inverse problem by nature, although it can be for mulated that way . Also, it is shown that the posterior variance can be larger than the prior if the usual Gaussian framework is set aside. However , i n the examples presented here, the entropy of the probability densities is decreasing. The application to the ocean area around South Africa, gover ned by strongly nonlinear dynamics, shows that the method is working satisfactorily . The strong and weak points of the method are discussed and possible improvements are proposed.

A systematic method of parameterisation estimation using data assimilation

In numerical weather prediction, parameterisations are used to simulate missing physics in the model. These can be due to a lack of scientific understanding or a lack of computing power available to address all the known physical processes. Parameterisations are sources of large uncertainty in a model as parameter values used in these parameterisations cannot be measured directly and hence are often not well known; and the parameterisations themselves are also approximations of the processes present in the true atmosphere. Whilst there are many efficient and effective methods for combined state/parameter estimation in data assimilation (DA), such as state augmentation, these are not effective at estimating the structure of parameterisations. A new method of parameterisation estimation is proposed that uses sequential DA methods to estimate errors in the numerical models at each space-time point for each model equation. These errors are then fitted to pre-determined functional forms of missing physics or parameterisations that are based upon prior information. We applied the method to a one-dimensional advection model with additive model error, and it is shown that the method can accurately estimate parameterisations, with consistent error estimates. Furthermore, it is shown how the method depends on the quality of the DA results. The results indicate that this new method is a powerful tool in systematic model improvement.

Computing the Cassels–Tate pairing on the 3-Selmer group of an elliptic curve

We extend the method of Cassels for computing the Cassels-Tate pairing on the 2-Selmer group of an elliptic curve, to the case of 3-Selmer groups. This requires significant modifications to both the local and global parts of the calculation. Our method is practical in sufficiently small examples, and can be used to improve the upper bound for the rank of an elliptic curve obtained by 3-descent.

A device to improve the Schleger and Turner method for sweating rate measurements

The objective of this study was to test a device developed to improve the functionality, accuracy and precision of the original technique for sweating rate measurements proposed by Schleger and Turner [Schleger AV, Turner HG (1965) Aust J Agric Res 16:92-106]. A device was built for this purpose and tested against the original Schleger and Turner technique. Testing was performed by measuring sweating rates in an experiment involving six Mertolenga heifers subjected to four different thermal levels in a climatic chamber. The device exhibited no functional problems and the results obtained with its use were more consistent than with the Schleger and Turner technique. There was no difference in the reproducibility of the two techniques (same accuracy), but measurements performed with the new device had lower repeatability, corresponding to lower variability and, consequently, to higher precision. When utilizing this device, there is no need for physical contact between the operator and the animal to maintain the filter paper discs in position. This has important advantages: the animals stay quieter, and several animals can be evaluated simultaneously. This is a major advantage because it allows more measurements to be taken in a given period of time, increasing the precision of the observations and diminishing the error associated with temporal hiatus (e.g., the solar angle during field studies). The new device has higher functional versatility when taking measurements in large-scale studies (many animals) under field conditions. The results obtained in this study suggest that the technique using the device presented here could represent an advantageous alternative to the original technique described by Schleger and Turner.