Overview of mathematical approaches used to model bacterial chemotaxis II: bacterial populations

We review the application of mathematical modeling to understanding the behavior of populations of chemotactic bacteria. The application of continuum mathematical models, in particular generalized Keller-Segel models, is discussed along with attempts to incorporate the microscale (individual) behavior on the macroscale, modeling the interaction between different species of bacteria, the interaction of bacteria with their environment, and methods used to obtain experimentally verified parameter values. We allude briefly to the role of modeling pattern formation in understanding collective behavior within bacterial populations. Various aspects of each model are discussed and areas for possible future research are postulated.

Past, present and future mathematical models for buildings (i)

This is the first of two articles presenting a detailed review of the historical evolution of mathematical models applied in the development of building technology, including conventional buildings and intelligent buildings. After presenting the technical differences between conventional and intelligent buildings, this article reviews the existing mathematical models, the abstract levels of these models, and their links to the literature for intelligent buildings. The advantages and limitations of the applied mathematical models are identified and the models are classified in terms of their application range and goal. We then describe how the early mathematical models, mainly physical models applied to conventional buildings, have faced new challenges for the design and management of intelligent buildings and led to the use of models which offer more flexibility to better cope with various uncertainties. In contrast with the early modelling techniques, model approaches adopted in neural networks, expert systems, fuzzy logic and genetic models provide a promising method to accommodate these complications as intelligent buildings now need integrated technologies which involve solving complex, multi-objective and integrated decision problems.

Past, present and future mathematical models for buildings (ii)

This article is the second part of a review of the historical evolution of mathematical models applied in the development of building technology. The first part described the current state of the art and contrasted various models with regard to the applications to conventional buildings and intelligent buildings. It concluded that mathematical techniques adopted in neural networks, expert systems, fuzzy logic and genetic models, that can be used to address model uncertainty, are well suited for modelling intelligent buildings. Despite the progress, the possible future development of intelligent buildings based on the current trends implies some potential limitations of these models. This paper attempts to uncover the fundamental limitations inherent in these models and provides some insights into future modelling directions, with special focus on the techniques of semiotics and chaos. Finally, by demonstrating an example of an intelligent building system with the mathematical models that have been developed for such a system, this review addresses the influences of mathematical models as a potential aid in developing intelligent buildings and perhaps even more advanced buildings for the future.

Modelling oil absorption during post-frying cooling - II: solution of the mathematical model, model testing and simulations

The mathematical models that describe the immersion-frying period and the post-frying cooling period of an infinite slab or an infinite cylinder were solved and tested. Results were successfully compared with those found in the literature or obtained experimentally, and were discussed in terms of the hypotheses and simplifications made. The models were used as the basis of a sensitivity analysis. Simulations showed that a decrease in slab thickness and core heat capacity resulted in faster crust development. On the other hand, an increase in oil temperature and boiling heat transfer coefficient between the oil and the surface of the food accelerated crust formation. The model for oil absorption during cooling was analysed using the tested post-frying cooling equation to determine the moment in which a positive pressure driving force, allowing oil suction within the pore, originated. It was found that as crust layer thickness, pore radius and ambient temperature decreased so did the time needed to start the absorption. On the other hand, as the effective convective heat transfer coefficient between the air and the surface of the slab increased the required cooling time decreased. In addition, it was found that the time needed to allow oil absorption during cooling was extremely sensitive to pore radius, indicating the importance of an accurate pore size determination in future studies.

Eliciting consumer preferences for certified animal-friendly foods: can elements of the theory of planned behavior improve choice experiment analysis?

Models used in neoclassical economics assume human behaviour to be purely rational. On the other hand, models adopted in social and behavioural psychology are founded on the ‘black box’ of human cognition. In view of these observations, this paper aims at bridging this gap by introducing psychological constructs in the well established microeconomic framework of choice behaviour based on random utility theory. In particular, it combines constructs developed employing Ajzen’s theory of planned behaviour with Lancaster’s theory of consumer demand for product characteristics to explain stated preferences over certified animal-friendly foods. To reach this objective a web survey was administered in the largest five EU-25 countries: France, Germany, Italy, Spain and the UK. Findings identify some salient cross-cultural differences between northern and southern Europe and suggest that psychological constructs developed using the Ajzen model are useful in explaining heterogeneity of preferences. Implications for policy makers and marketers involved with certified animal-friendly foods are discussed.

An overview of domestic energy models and a new approach with agent based modelling

Government targets for CO2 reductions are being progressively tightened, the Climate Change Act set the UK target as an 80% reduction by 2050 on 1990 figures. The residential sector accounts for about 30% of emissions. This paper discusses current modelling techniques in the residential sector: principally top-down and bottom-up. Top-down models work on a macro-economic basis and can be used to consider large scale economic changes; bottom-up models are detail rich to model technological changes. Bottom-up models demonstrate what is technically possible. However, there are differences between the technical potential and what is likely given the limited economic rationality of the typical householder. This paper recommends research to better understand individuals’ behaviour. Such research needs to include actual choices, stated preferences and opinion research to allow a detailed understanding of the individual end user. This increased understanding can then be used in an agent based model (ABM). In an ABM, agents are used to model real world actors and can be given a rule set intended to emulate the actions and behaviours of real people. This can help in understanding how new technologies diffuse. In this way a degree of micro-economic realism can be added to domestic carbon modelling. Such a model should then be of use for both forward projections of CO2 and to analyse the cost effectiveness of various policy measures.

Limit operators, collective compactness, and the spectral theory of infinite matrices

In the first half of this memoir we explore the interrelationships between the abstract theory of limit operators (see e.g. the recent monographs of Rabinovich, Roch and Silbermann (2004) and Lindner (2006)) and the concepts and results of the generalised collectively compact operator theory introduced by Chandler-Wilde and Zhang (2002). We build up to results obtained by applying this generalised collectively compact operator theory to the set of limit operators of an operator (its operator spectrum). In the second half of this memoir we study bounded linear operators on the generalised sequence space , where and is some complex Banach space. We make what seems to be a more complete study than hitherto of the connections between Fredholmness, invertibility, invertibility at infinity, and invertibility or injectivity of the set of limit operators, with some emphasis on the case when the operator is a locally compact perturbation of the identity. Especially, we obtain stronger results than previously known for the subtle limiting cases of and . Our tools in this study are the results from the first half of the memoir and an exploitation of the partial duality between and and its implications for bounded linear operators which are also continuous with respect to the weaker topology (the strict topology) introduced in the first half of the memoir. Results in this second half of the memoir include a new proof that injectivity of all limit operators (the classic Favard condition) implies invertibility for a general class of almost periodic operators, and characterisations of invertibility at infinity and Fredholmness for operators in the so-called Wiener algebra. In two final chapters our results are illustrated by and applied to concrete examples. Firstly, we study the spectra and essential spectra of discrete Schrödinger operators (both self-adjoint and non-self-adjoint), including operators with almost periodic and random potentials. In the final chapter we apply our results to integral operators on .

A theory of rational spatial agglomerations

We model the behavior of rational forward-looking agents in a spatial economy. The economic geography structure is built on Fujita et al. (1999)'s racetrack economy. Workers choose optimally what to consume at each period, as well as which spatial itinerary to follow in the geographical space. The spatial extent of the resulting agglomerations increases with the taste for variety and the expenditure share on manufactured goods, and decreases with transport costs. Because forward-looking agents anticipate the future formation of agglomerations, they are more responsive to spatial utility differentials than myopic agents. As a consequence, the emerging agglomerations are larger under perfect foresight spatial adjustments than under myopic ones.

Commodity futures prices: more evidence on forecast power, risk premia and the theory of storage

In this paper, we examine the temporal stability of the evidence for two commodity futures pricing theories. We investigate whether the forecast power of commodity futures can be attributed to the extent to which they exhibit seasonality and we also consider whether there are time varying parameters or structural breaks in these pricing relationships. Compared to previous studies, we find stronger evidence of seasonality in the basis, which supports the theory of storage. The power of the basis to forecast subsequent price changes is also strengthened, while results on the presence of a risk premium are inconclusive. In addition, we show that the forecasting power of commodity futures cannot be attributed to the extent to which they exhibit seasonality. We find that in most cases where structural breaks occur, only changes in the intercepts and not the slopes are detected, illustrating that the forecast power of the basis is stable over different economic environments.

On the difficulties of present theoretical models to predict the oxidation state of atomic Au adsorbed on regular sites of CeO2(111)

The electronic structure and oxidation state of atomic Au adsorbed on a perfect CeO2(111) surface have been investigated in detail by means of periodic density functional theory-based calculations, using the LDA+U and GGA+U potentials for a broad range of U values, complemented with calculations employing the HSE06 hybrid functional. In addition, the effects of the lattice parameter a0 and of the starting point for the geometry optimization have also been analyzed. From the present results we suggest that the oxidation state of single Au atoms on CeO2(111) predicted by LDA+U, GGA+U, and HSE06 density functional calculations is not conclusive and that the final picture strongly depends on the method chosen and on the construction of the surface model. In some cases we have been able to locate two well-defined states which are close in energy but with very different electronic structure and local geometries, one with Au fully oxidized and one with neutral Au. The energy difference between the two states is typically within the limits of the accuracy of the present exchange-correlation potentials, and therefore, a clear lowest-energy state cannot be identified. These results suggest the possibility of a dynamic distribution of Au0 and Au+ atomic species at the regular sites of the CeO2(111) surface.

Workaround motivation model (WAMM): an adaptation of the Theory of Interpersonal Behaviour

The study of workarounds (WA) has increased in importance due to their impact on patient safety and efficiency. However, there are no adequate theories to explain the motivation to create and use a workaround in a healthcare sitting. Although theories of technology acceptance help to understand the reasons to accept or reject technology, they fail to explain drivers for alternatives. Also workarounds involve creators and performers that have different motivations. Models such as Theory of Planned Behaviour (TPB) or Theory of Reasoned Action (TRA) can help to explain the role of workaround users, but lack explanation of workaround creators’ dynamics. Our aim is to develop a theoretical foundation to explain workaround motivation behaviour models with norms that relate to sanctions to provide an integrated Workaround Motivation Model; WAMM. The development of WAMM model is explained in this paper based on workaround cases as part of further research to establish the model.

Application of the Lighthill-Ford theory of spontaneous imbalance to clear-air turbulence forecasting

A new method of clear-air turbulence (CAT) forecasting based on the Lighthill–Ford theory of spontaneous imbalance and emission of inertia–gravity waves has been derived and applied on episodic and seasonal time scales. A scale analysis of this shallow-water theory for midlatitude synoptic-scale flows identifies advection of relative vorticity as the leading-order source term. Examination of leading- and second-order terms elucidates previous, more empirically inspired CAT forecast diagnostics. Application of the Lighthill–Ford theory to the Upper Mississippi and Ohio Valleys CAT outbreak of 9 March 2006 results in good agreement with pilot reports of turbulence. Application of Lighthill–Ford theory to CAT forecasting for the 3 November 2005–26 March 2006 period using 1-h forecasts of the Rapid Update Cycle (RUC) 2 1500 UTC model run leads to superior forecasts compared to the current operational version of the Graphical Turbulence Guidance (GTG1) algorithm, the most skillful operational CAT forecasting method in existence. The results suggest that major improvements in CAT forecasting could result if the methods presented herein become operational.