Theory of strongly correlated electron systems. I. Intersite coulomb interaction and the approximation of renormalized fermions in total energy calculations

The diagrammatic strong-coupling perturbation theory (SCPT) for correlated electron systems is developed for intersite Coulomb interaction and for a nonorthogonal basis set. The construction is based on iterations of exact closed equations for many - electron Green functions (GFs) for Hubbard operators in terms of functional derivatives with respect to external sources. The graphs, which do not contain the contributions from the fluctuations of the local population numbers of the ion states, play a special role: a one-to-one correspondence is found between the subset of such graphs for the many - electron GFs and the complete set of Feynman graphs of weak-coupling perturbation theory (WCPT) for single-electron GFs. This fact is used for formulation of the approximation of renormalized Fermions (ARF) in which the many-electron quasi-particles behave analogously to normal Fermions. Then, by analyzing: (a) Sham's equation, which connects the self-energy and the exchange- correlation potential in density functional theory (DFT); and (b) the Galitskii and Migdal expressions for the total energy, written within WCPT and within ARF SCPT, a way we suggest a method to improve the description of the systems with correlated electrons within the local density approximation (LDA) to DFT. The formulation, in terms of renormalized Fermions LIDA (RF LDA), is obtained by introducing the spectral weights of the many electron GFs into the definitions of the charge density, the overlap matrices, effective mixing and hopping matrix elements, into existing electronic structure codes, whereas the weights themselves have to be found from an additional set of equations. Compared with LDA+U and self-interaction correction (SIC) methods, RF LDA has the advantage of taking into account the transfer of spectral weights, and, when formulated in terms of GFs, also allows for consideration of excitations and nonzero temperature. Going beyond the ARF SCPT, as well as RF LIDA, and taking into account the fluctuations of ion population numbers would require writing completely new codes for ab initio calculations. The application of RF LDA for ab initio band structure calculations for rare earth metals is presented in part 11 of this study (this issue). (c) 2005 Wiley Periodicals, Inc.

Accounting for uncertainty in marine reserve design

Ecosystems and the species and communities within them are highly complex systems that defy predictions with any degree of certainty. Managing and conserving these systems in the face of uncertainty remains a daunting challenge, particularly with respect to developing networks of marine reserves. Here we review several modelling frameworks that explicitly acknowledge and incorporate uncertainty, and then use these methods to evaluate reserve spacing rules given increasing levels of uncertainty about larval dispersal distances. Our approach finds similar spacing rules as have been proposed elsewhere - roughly 20-200 km - but highlights several advantages provided by uncertainty modelling over more traditional approaches to developing these estimates. In particular, we argue that uncertainty modelling can allow for (1) an evaluation of the risk associated with any decision based on the assumed uncertainty; (2) a method for quantifying the costs and benefits of reducing uncertainty; and (3) a useful tool for communicating to stakeholders the challenges in managing highly uncertain systems. We also argue that incorporating rather than avoiding uncertainty will increase the chances of successfully achieving conservation and management goals.

Are you sure? the role of uncertainty in career

Although uncertainty is a fundamental human experience, professionals in the career field have largely overlooked the role that it plays in people's careers. The changed nature of careers has resulted in people experiencing increased uncertainty in their career that is beyond the uncertainty experienced in their job. The author explores the role of uncertainty in people's experience of their careers and examines the implications for career counseling theory and practice. A review of the career theory and career counseling literature indicates that although contemporary approaches have been offered to respond to the changed nature of career, none of the approaches have identified uncertainty as a core part of individuals' experience of their career. The broader literature on uncertainty is then reviewed at the societal, organizational, and individual levels.

The role of uncertainty in the relationship between fairness evaluations and willingness to pay

Participants in contingent valuation studies may be uncertain about a number of aspects of the policy and survey context. The uncertainty management model of fairness judgments states that individuals will evaluate a policy in terms of its fairness when they do not know whether they can trust the relevant managing authority or experience uncertainty due to insufficient knowledge of the general issues surrounding the environmental policy. Similarly, some researchers have suggested that, not knowing how to answer WTP questions, participants convey their general attitudes toward the public good rather than report well-defined economic preferences. These contentions were investigated in a sample of 840 residents in four urban catchments across Australia who were interviewed about their WTP for stormwater pollution abatement. Four sources of uncertainty were measured: amount of prior issue-related thought, trustworthiness of the water authority, insufficient scenario information, and WTP response uncertainty. A logistic regression model was estimated in each subsample to test the main effects of the uncertainty sources on WTP as well as their interaction with fairness and proenvironmental attitudes. Results indicated support for the uncertainty management model in only one of the four samples. Similarly, proenvironmental attitudes interacted rarely with uncertainty to a significant level, and in ways that were more complex than hypothesised. It was concluded that uncertain individuals were generally not more likely than other participants to draw on either fairness evaluations or proenvironmental attitudes when making decisions about paying for stormwater pollution abatement.

Modelling frontal discontinuities in wind fields

A Bayesian procedure for the retrieval of wind vectors over the ocean using satellite borne scatterometers requires realistic prior near-surface wind field models over the oceans. We have implemented carefully chosen vector Gaussian Process models; however in some cases these models are too smooth to reproduce real atmospheric features, such as fronts. At the scale of the scatterometer observations, fronts appear as discontinuities in wind direction. Due to the nature of the retrieval problem a simple discontinuity model is not feasible, and hence we have developed a constrained discontinuity vector Gaussian Process model which ensures realistic fronts. We describe the generative model and show how to compute the data likelihood given the model. We show the results of inference using the model with Markov Chain Monte Carlo methods on both synthetic and real data.

A novel approach to modelling and exploiting uncertainty in stochastic control systems

We consider an inversion-based neurocontroller for solving control problems of uncertain nonlinear systems. Classical approaches do not use uncertainty information in the neural network models. In this paper we show how we can exploit knowledge of this uncertainty to our advantage by developing a novel robust inverse control method. Simulations on a nonlinear uncertain second order system illustrate the approach.

Conditional distribution modeling for estimating and exploiting uncertainty in control systems

This paper presents a general methodology for estimating and incorporating uncertainty in the controller and forward models for noisy nonlinear control problems. Conditional distribution modeling in a neural network context is used to estimate uncertainty around the prediction of neural network outputs. The developed methodology circumvents the dynamic programming problem by using the predicted neural network uncertainty to localize the possible control solutions to consider. A nonlinear multivariable system with different delays between the input-output pairs is used to demonstrate the successful application of the developed control algorithm. The proposed method is suitable for redundant control systems and allows us to model strongly non Gaussian distributions of control signal as well as processes with hysteresis.

Handling and communicating uncertainty in chained geospatial web services

Recent developments in service-oriented and distributed computing have created exciting opportunities for the integration of models in service chains to create the Model Web. This offers the potential for orchestrating web data and processing services, in complex chains; a flexible approach which exploits the increased access to products and tools, and the scalability offered by the Web. However, the uncertainty inherent in data and models must be quantified and communicated in an interoperable way, in order for its effects to be effectively assessed as errors propagate through complex automated model chains. We describe a proposed set of tools for handling, characterizing and communicating uncertainty in this context, and show how they can be used to 'uncertainty- enable' Web Services in a model chain. An example implementation is presented, which combines environmental and publicly-contributed data to produce estimates of sea-level air pressure, with estimates of uncertainty which incorporate the effects of model approximation as well as the uncertainty inherent in the observational and derived data.

Knowledge management in the energy sector:review and future directions

Purpose – The purpose of this paper is to examine the state of knowledge management (KM) in the energy sector and more broadly, and consider future directions for research and practice. Design/methodology/approach – The paper reviews the literature on KM and the practice of KM as relevant to the energy sector. Findings – There are many examples of good practice in KM in the sector, and some organisations, especially in the oil industry, are seen as leaders in KM practice. However, other organisations have yet to embark on explicit KM initiatives or projects at all. In addition, some parts of the energy sector discuss KM without any reference to the more general KM literature. Originality/value – Although some parts of the energy sector have justifiably earned a good reputation for KM, other parts are completely unaware of the field, as is apparent from the literature. This review helps to raise awareness and guide future work.

Probabilistic uncertainty in an interoperable framework

This thesis provides an interoperable language for quantifying uncertainty using probability theory. A general introduction to interoperability and uncertainty is given, with particular emphasis on the geospatial domain. Existing interoperable standards used within the geospatial sciences are reviewed, including Geography Markup Language (GML), Observations and Measurements (O&M) and the Web Processing Service (WPS) specifications. The importance of uncertainty in geospatial data is identified and probability theory is examined as a mechanism for quantifying these uncertainties. The Uncertainty Markup Language (UncertML) is presented as a solution to the lack of an interoperable standard for quantifying uncertainty. UncertML is capable of describing uncertainty using statistics, probability distributions or a series of realisations. The capabilities of UncertML are demonstrated through a series of XML examples. This thesis then provides a series of example use cases where UncertML is integrated with existing standards in a variety of applications. The Sensor Observation Service - a service for querying and retrieving sensor-observed data - is extended to provide a standardised method for quantifying the inherent uncertainties in sensor observations. The INTAMAP project demonstrates how UncertML can be used to aid uncertainty propagation using a WPS by allowing UncertML as input and output data. The flexibility of UncertML is demonstrated with an extension to the GML geometry schemas to allow positional uncertainty to be quantified. Further applications and developments of UncertML are discussed.

Managing uncertainty in complex stochastic models: design and emulation of a Rabies model

In this paper we present a novel method for emulating a stochastic, or random output, computer model and show its application to a complex rabies model. The method is evaluated both in terms of accuracy and computational efficiency on synthetic data and the rabies model. We address the issue of experimental design and provide empirical evidence on the effectiveness of utilizing replicate model evaluations compared to a space-filling design. We employ the Mahalanobis error measure to validate the heteroscedastic Gaussian process based emulator predictions for both the mean and (co)variance. The emulator allows efficient screening to identify important model inputs and better understanding of the complex behaviour of the rabies model.