Use and abuse of mathematical models: an illustration from the 2001 foot and mouth disease epidemic in the United Kingdom

Foot and mouth disease (FMD) is a major threat, not only to countries whose economies rely on agricultural exports, but also to industrialised countries that maintain a healthy domestic livestock industry by eliminating major infectious diseases from their livestock populations. Traditional methods of controlling diseases such as FMD require the rapid detection and slaughter of infected animals, and any susceptible animals with which they may have been in contact, either directly or indirectly. During the 2001 epidemic of FMD in the United Kingdom (UK), this approach was supplemented by a culling policy driven by unvalidated predictive models. The epidemic and its control resulted in the death of approximately ten million animals, public disgust with the magnitude of the slaughter, and political resolve to adopt alternative options, notably including vaccination, to control any future epidemics. The UK experience provides a salutary warning of how models can be abused in the interests of scientific opportunism.

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.

Integration of chaos theory and mathematical models in building simulation: Part I: Literature review

Current mathematical models in building research have been limited in most studies to linear dynamics systems. A literature review of past studies investigating chaos theory approaches in building simulation models suggests that as a basis chaos model is valid and can handle the increasingly complexity of building systems that have dynamic interactions among all the distributed and hierarchical systems on the one hand, and the environment and occupants on the other. The review also identifies the paucity of literature and the need for a suitable methodology of linking chaos theory to mathematical models in building design and management studies. This study is broadly divided into two parts and presented in two companion papers. Part (I) reviews the current state of the chaos theory models as a starting point for establishing theories that can be effectively applied to building simulation models. Part (II) develops conceptual frameworks that approach current model methodologies from the theoretical perspective provided by chaos theory, with a focus on the key concepts and their potential to help to better understand the nonlinear dynamic nature of built environment systems. Case studies are also presented which demonstrate the potential usefulness of chaos theory driven models in a wide variety of leading areas of building research. This study distills the fundamental properties and the most relevant characteristics of chaos theory essential to building simulation scientists, initiates a dialogue and builds bridges between scientists and engineers, and stimulates future research about a wide range of issues on building environmental systems.

Integration of chaos theory and mathematical models in building simulation: Part II: Conceptual frameworks

Current mathematical models in building research have been limited in most studies to linear dynamics systems. A literature review of past studies investigating chaos theory approaches in building simulation models suggests that as a basis chaos model is valid and can handle the increasing complexity of building systems that have dynamic interactions among all the distributed and hierarchical systems on the one hand, and the environment and occupants on the other. The review also identifies the paucity of literature and the need for a suitable methodology of linking chaos theory to mathematical models in building design and management studies. This study is broadly divided into two parts and presented in two companion papers. Part (I), published in the previous issue, reviews the current state of the chaos theory models as a starting point for establishing theories that can be effectively applied to building simulation models. Part (II) develop conceptual frameworks that approach current model methodologies from the theoretical perspective provided by chaos theory, with a focus on the key concepts and their potential to help to better understand the nonlinear dynamic nature of built environment systems. Case studies are also presented which demonstrate the potential usefulness of chaos theory driven models in a wide variety of leading areas of building research. This study distills the fundamental properties and the most relevant characteristics of chaos theory essential to (1) building simulation scientists and designers (2) initiating a dialogue between scientists and engineers, and (3) stimulating future research on a wide range of issues involved in designing and managing building environmental systems.

Survival analysis of cereal crop variety innovations in the UK

This paper explores the changing survival patterns of cereal crop variety innovations in the UK since the introduction of plant breeders’ rights in the mid-1960s. Using non-parametric, semi-parametric and parametric approaches, we examine the determinants of the survival of wheat variety innovations, focusing on the impacts of changes to Plant Variety Protection (PVP) regime over the last four decades. We find that the period since the introduction of the PVP regime has been characterised by the accelerated development of new varieties and increased private sector participation in the breeding of cereal crop varieties. However, the increased flow of varieties has been accompanied by a sharp decline in the longevity of innovations. These trends may have contributed to a reduction in the returns appropriated by plant breeders from protected variety innovations and may explain the decline of conventional plant breeding in the UK. It may also explain the persistent demand from the seed industry for stronger protection. The strengthening of the PVP regime in conformity with the UPOV Convention of 1991, the introduction of EU-wide protection through the Community Plant Variety Office and the introduction of royalties on farm-saved seed have had a positive effect on the longevity of protected variety innovations, but have not been adequate to offset the long term decline in survival durations.

Survival analysis statistics applied to threshold data obtained from the ascending forced-choice method of limits

Sensory thresholds are often collected through ascending forced-choice methods. Group thresholds are important for comparing stimuli or populations; yet, the method has two problems. An individual may correctly guess the correct answer at any concentration step and might detect correctly at low concentrations but become adapted or fatigued at higher concentrations. The survival analysis method deals with both issues. Individual sequences of incorrect and correct answers are adjusted, taking into account the group performance at each concentration. The technique reduces the chance probability where there are consecutive correct answers. Adjusted sequences are submitted to survival analysis to determine group thresholds. The technique was applied to an aroma threshold and a taste threshold study. It resulted in group thresholds similar to ASTM or logarithmic regression procedures. Significant differences in taste thresholds between younger and older adults were determined. The approach provides a more robust technique over previous estimation methods.

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.

Comparison of survival rates of captive-reared and wild-bred Mauritius kestrels (Falco punctatus) in a re-introduced population

Re-introduction is a technique widely used in the conservation of threatened bird species. With advances in aviculture the use of captive-produced individuals as the release stock is becoming more commonplace, and ideally, survival of captive-produced, released individuals should be no different from their wild-bred counterparts. During the late 1980s the Critically Endangered Mauritius kestrel (Falco punctatus) was successfully re-introduced into the Bambous mountain range, Mauritius, some 30 years after its local extinction. Between 1987 and 2001 the developing population was closely monitored enabling us to construct re-sighting histories for 88 released and 284 wild-bred kestrels. We used age-structured models in the survival analysis software program MARK to determine if an individual's origin influenced its subsequent survival. Our analysis indicated no compelling evidence for reduced survival among juvenile captive-reared and released individuals, relative to their wild-bred counterparts, across the majority of cohorts and only limited evidence of a cohort-specific effect. This study illustrates that despite the lack of a formal experimental approach it is still feasible to conduct an assessment of re-introduction outcomes and techniques.

Bayesian analysis of an inverse Gaussian correlated frailty model

In survival analysis frailty is often used to model heterogeneity between individuals or correlation within clusters. Typically frailty is taken to be a continuous random effect, yielding a continuous mixture distribution for survival times. A Bayesian analysis of a correlated frailty model is discussed in the context of inverse Gaussian frailty. An MCMC approach is adopted and the deviance information criterion is used to compare models. As an illustration of the approach a bivariate data set of corneal graft survival times is analysed. (C) 2006 Elsevier B.V. All rights reserved.

Comparison of survival rates of captive-reared and wild-bred Mauritius kestrels (falco punctatus) in a re-introduced population

Re-introduction is a technique widely used in the conservation of threatened bird species. With advances in aviculture the use of captive-produced individuals as the release stock is becoming more commonplace, and ideally, survival of captive-produced, released individuals should be no different from their wild-bred counterparts. During the late 1980s the Critically Endangered Mauritius kestrel (Falco punctatus) was successfully re-introduced into the Bambous mountain range, Mauritius, some 30 years after its local extinction. Between 1987 and 2001 the developing population was closely monitored enabling us to construct re-sighting histories for 88 released and 284 wild-bred kestrels. We used age-structured models in the survival analysis software program MARK to determine if an individual's origin influenced its subsequent survival. Our analysis indicated no compelling evidence for reduced survival among juvenile captive-reared and released individuals, relative to their wild-bred counterparts, across the majority of cohorts and only limited evidence of a cohort-specific effect. This study illustrates that despite the lack of a formal experimental approach it is still feasible to conduct an assessment of re-introduction outcomes and techniques. (C) 2003 Elsevier Ltd. All rights reserved.

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.

Effects of soil conditions and drought on egg hatching and larval survival of the clover root weevil (Sitona lepidus)

Soil-dwelling insect herbivores are significant pests in many managed ecosystems. Because eggs and larvae are difficult to observe, mathematical models have been developed to predict life-cycle events occurring in the soil. To date, these models have incorporated very little empirical information about how soil and drought conditions interact to shape these processes. This study investigated how soil temperature (10, 15, 20 and 25 °C), water content (0.02 (air dried), 0.10 and 0.25 g g−1) and pH (5, 7 and 9) interactively affected egg hatching and early larval lifespan of the clover root weevil (Sitona lepidus Gyllenhal, Coleoptera: Curculionidae). Eggs developed over 3.5 times faster at 25 °C compared with 10 °C (hatching after 40.1 and 11.5 days, respectively). The effect of drought on S. lepidus eggs was investigated by exposing eggs to drought conditions before wetting the soil (2–12 days later) at four temperatures. No eggs hatched in dry soil, suggesting that S. lepidus eggs require water to remain viable. Eggs hatched significantly sooner in slightly acidic soil (pH 5) compared with soils with higher pH values. There was also a significant interaction between soil temperature, pH and soil water content. Egg viability was significantly reduced by exposure to drought. When exposed to 2–6 days of drought, egg viability was 80–100% at all temperatures but fell to 50% after 12 days exposure at 10 °C and did not hatch at all at 20 °C and above. Drought exposure also increased hatching time of viable eggs. The effects of soil conditions on unfed larvae were less influential, except for soil temperature which significantly reduced larval longevity by 57% when reared at 25 °C compared with 10 °C (4.1 and 9.7 days, respectively). The effects of soil conditions on S. lepidus eggs and larvae are discussed in the context of global climate change and how such empirically based information could be useful for refining existing mathematical models of these processes.

A review and classification of the existing models of cyanobacteria

Bloom-forming and toxin-producing cyanobacteria remain a persistent nuisance across the world. Modelling of cyanobacteria in freshwaters is an important tool for understanding their population dynamics and predicting bloom occurrence in lakes and rivers. In this paper existing key models of cyanobacteria are reviewed, evaluated and classified. Two major groups emerge: deterministic mathematical and artificial neural network models. Mathematical models can be further subcategorized into those models concerned with impounded water bodies and those concerned with rivers. Most existing models focus on a single aspect such as the growth of transport mechanisms, but there are a few models which couple both.