Robust Uncertainty Quantification and Scalable Computation for Computer Models with Massive Output

Uncertainty quantification (UQ) is both an old and new concept. The current novelty lies in the interactions and synthesis of mathematical models, computer experiments, statistics, field/real experiments, and probability theory, with a particular emphasize on the large-scale simulations by computer models. The challenges not only come from the complication of scientific questions, but also from the size of the information. It is the focus in this thesis to provide statistical models that are scalable to massive data produced in computer experiments and real experiments, through fast and robust statistical inference.

Chapter 2 provides a practical approach for simultaneously emulating/approximating massive number of functions, with the application on hazard quantification of Soufri\`{e}re Hills volcano in Montserrate island. Chapter 3 discusses another problem with massive data, in which the number of observations of a function is large. An exact algorithm that is linear in time is developed for the problem of interpolation of Methylation levels. Chapter 4 and Chapter 5 are both about the robust inference of the models. Chapter 4 provides a new criteria robustness parameter estimation criteria and several ways of inference have been shown to satisfy such criteria. Chapter 5 develops a new prior that satisfies some more criteria and is thus proposed to use in practice.

The Relationship of Fear of Intimacy, Body Image Avoidance and Body Mass Index

Issues of body image and ability to achieve intimacy are connected to body weight, yet remain largely unexplored and have not been evaluated by gender. The underlying purpose of this research was to determine if avoidant attitudes and perceptions of one’s body may hold implications toward its use in intimate interactions, and if an above average body weight would tend to increase this avoidance. The National Health and Nutrition Examination Survey (NHANES, 1999-2002) finds that 64.5% of US adults are overweight, with 61.9% of women and 67.2% of men. The increasing prevalence of overweight and obesity in men and women shows no reverse trend, nor have prevention and treatment proven effective in the long term. The researcher gathered self-reported age, gender, height and weight data from 55 male and 58 female subjects (determined by a prospective power analysis with a desired medium effect size (r =.30) to determine body mass index (BMI), determining a mean age of 21.6 years and mean BMI of 25.6. Survey instruments consisted of two scales that are germane to the variables being examined. They were (1) Descutner and Thelen of the University of Missouri’s (1991) Fear-of-Intimacy scale and (2) Rosen, Srebnik, Saltzberg, and Wendt’s (1991) Body Image Avoidance Questionnaire. Results indicated that as body mass index increases, fear of intimacy increases (p<0.05) and that as body mass index increases, body image avoidance increases (p<0.05). The relationship that as body image avoidance increases, fear of intimacy increases was not supported, but approached significance at (p<0.07). No differences in these relationships were determined between gender groups. For age, the only observed relationship was that of a difference between scores for age groups [18 to 22 (group 1) and ages 23 to 34 (group 2)] for the relationship of body image avoidance and fear of intimacy (p<0.02). The results suggest that the relationship of body image avoidance and fear of intimacy, as well as age, bear consideration toward the escalating prevalence of overweight and obesity. An integrative approach to body weight that addresses issues of body image and intimacy may prove effective in prevention and treatment.

Parallel nonconvex generalized Benders decomposition for natural gas production network planning under uncertainty

A scenario-based two-stage stochastic programming model for gas production network planning under uncertainty is usually a large-scale nonconvex mixed-integer nonlinear programme (MINLP), which can be efficiently solved to global optimality with nonconvex generalized Benders decomposition (NGBD). This paper is concerned with the parallelization of NGBD to exploit multiple available computing resources. Three parallelization strategies are proposed, namely, naive scenario parallelization, adaptive scenario parallelization, and adaptive scenario and bounding parallelization. Case study of two industrial natural gas production network planning problems shows that, while the NGBD without parallelization is already faster than a state-of-the-art global optimization solver by an order of magnitude, the parallelization can improve the efficiency by several times on computers with multicore processors. The adaptive scenario and bounding parallelization achieves the best overall performance among the three proposed parallelization strategies.

Robust scenario formulations for strategic supply chain optimization under uncertainty

Strategic supply chain optimization (SCO) problems are often modelled as a two-stage optimization problem, in which the first-stage variables represent decisions on the development of the supply chain and the second-stage variables represent decisions on the operations of the supply chain. When uncertainty is explicitly considered, the problem becomes an intractable infinite-dimensional optimization problem, which is usually solved approximately via a scenario or a robust approach. This paper proposes a novel synergy of the scenario and robust approaches for strategic SCO under uncertainty. Two formulations are developed, namely, naïve robust scenario formulation and affinely adjustable robust scenario formulation. It is shown that both formulations can be reformulated into tractable deterministic optimization problems if the uncertainty is bounded with the infinity-norm, and the uncertain equality constraints can be reformulated into deterministic constraints without assumption of the uncertainty region. Case studies of a classical farm planning problem and an energy and bioproduct SCO problem demonstrate the advantages of the proposed formulations over the classical scenario formulation. The proposed formulations not only can generate solutions with guaranteed feasibility or indicate infeasibility of a problem, but also can achieve optimal expected economic performance with smaller numbers of scenarios.

Novel Formulation and Efficient Solution Strategy for Strategic Optimization of an Industrial Chemical Supply Chain Under Demand Uncertainty

This paper is concerned with strategic optimization of a typical industrial chemical supply chain, which involves a material purchase and transportation network, several manufacturing plants with on-site material and product inventories, a product transportation network and several regional markets. In order to address large uncertainties in customer demands at the different regional markets, a novel robust scenario formulation, which has been developed by the authors recently, is tailored and applied for the strategic optimization. Case study results show that the robust scenario formulation works well for this real industrial supply chain system, and it outperforms the deterministic formulation and the classical scenario-based stochastic programming formulation by generating better expected economic performance and solutions that are guaranteed to be feasible for all uncertainty realizations. The robust scenario problem exhibits a decomposable structure that can be taken advantage of by Benders decomposition for efficient solution, so the application of Benders decomposition to the solution of the strategic optimization is also discussed. The case study results show that Benders decomposition can reduce the solution time by almost an order of magnitude when the number of scenarios in the problem is large.

Climate change adaptation planning under uncertainty in Ho Chi Minh City, Vietnam: a case study on institutional vulnerability, adaptive capacity and climate change governance

Climate change is expected to have wide-ranging impacts on urban areas and creates additional challenges for sustainable development. Urban areas are inextricably linked with climate change, as they are major contributors to it, while also being particularly vulnerable to its impacts. Climate change presents a new challenge to urban areas, not only because of the expected rises in temperature and sea-level, but also the current context of failure to fully address the institutional barriers preventing action to prepare for climate change, or feedbacks between urban systems and agents. Despite the importance of climate change, there are few cities in developing countries that are attempting to address these issues systematically as part of their governance and planning processes. While there is a growing literature on the risks and vulnerabilities related to climate change, as yet there is limited research on the development of institutional responses, the dissemination of relevant knowledge and evaluation of tools for practical planning responses by decision makers at the city level. This thesis questions the dominant assumptions about the capacity of institutions and potential of adaptive planning. It argues that achieving a balance between climate change impacts and local government decision-making capacity is a vital for successful adaptation to the impacts of climate change. Urban spatial planning and wider environmental planning not only play a major role in reducing/mitigating risks but also have a key role in adapting to uncertainty in over future risk. The research focuses on a single province - the biggest city in Vietnam - Ho Chi Minh City - as the principal case study to explore this argument, by examining the linkages between urban planning systems, the structures of governance, and climate change adaptation planning. In conclusion it proposes a specific framework to offer insights into some of the more practical considerations, and the approach emphasises the importance of vertical and horizontal coordination in governance and urban planning.

Acceptance of relapse fears in breast cancer patients: effects of an act-based abridged intervention

Objective: Relapse fear is a common psychological scar in cancer survivors. The aim of this study is to assess the effects of an abridged version of Acceptance and Commitment Therapy (ACT) in breast cancer patients.Method: An open trial was developed with 12 non-metastatic breast cancer patients assigned to 2 conditions, ACT and waiting list. Interventions were applied in just one session and focused on the acceptance of relapse fears through a ‘defusion’ exercise. Interference and intensity of fear measured through subjective scales were collected after each intervention and again 3 months later. Distress, hypochondria and ‘anxious preocupation’ were also evaluated through standardized questionnaires.Results: The analysis revealed that ‘defusion’ contributed to decrease the interference of the fear of recurrence, and these changes were maintained three months after intervention in most subjects. 87% of participants showed clinically significant decreases in interference at follow-up sessions whereas no patient in the waiting list showed such changes. Statistical analysis revealed that the changes in interference were significant when comparing pre, post and follow-up treatment, and also when comparing ACT and waiting list groups. Changes in intensity of fear, distress, anxious preoccupation and hypochondria were also observed.Conclusions: Exposure through ‘defusion’ techniques might be considered a useful option for treatment of persistent fears in cancer patients. This study provides evidence for therapies focusing on psychological acceptance in cancer patients through short, simple and feasible therapeutic methods.

Resolving taxonomic uncertainty in vulnerable elasmobranchs: are the Madeira skate (Raja maderensis) and the thornback ray (Raja clavata) distinct species?

Skates and rays constitute the most speciose group of chondrichthyan fishes, yet are characterised by remarkable levels of morphological and ecological conservatism. They can be challenging to identify, which makes monitoring species compositions for fisheries management purposes problematic. Owing to their slow growth and low fecundity, skates are vulnerable to exploitation and species exhibiting endemism or limited ranges are considered to be the most at risk. The Madeira skate Raja maderensis is endemic and classified as ‘Data Deficient’ by the IUCN, yet its taxonomic distinctiveness from the morphologically similar and more wide-ranging thornback ray Raja clavata is unresolved. This study evaluated the sequence divergence of both the variable control region and cytochrome oxidase I ‘DNA barcode’ gene of the mitochondrial genome to elucidate the genetic differentiation of specimens identified as R. maderensis and R. clavata collected across much of their geographic ranges. Genetic evidence was insufficient to support the different species designations. However regardless of putative species identification, individuals occupying waters around the Azores and North African Seamounts represent an evolutionarily significant unit worthy of special consideration for conservation management.

Resolving taxonomic uncertainty in vulnerable elasmobranchs: are the Madeira skate (Raja maderensis) and the thornback ray (Raja clavata) distinct species?

Skates and rays constitute the most speciose group of chondrichthyan fishes, yet are characterised by remarkable levels of morphological and ecological conservatism. They can be challenging to identify, which makes monitoring species compositions for fisheries management purposes problematic. Owing to their slow growth and low fecundity, skates are vulnerable to exploitation and species exhibiting endemism or limited ranges are considered to be the most at risk. The Madeira skate Raja maderensis is endemic and classified as ‘Data Deficient’ by the IUCN, yet its taxonomic distinctiveness from the morphologically similar and more wide-ranging thornback ray Raja clavata is unresolved. This study evaluated the sequence divergence of both the variable control region and cytochrome oxidase I ‘DNA barcode’ gene of the mitochondrial genome to elucidate the genetic differentiation of specimens identified as R. maderensis and R. clavata collected across much of their geographic ranges. Genetic evidence was insufficient to support the different species designations. However regardless of putative species identification, individuals occupying waters around the Azores and North African Seamounts represent an evolutionarily significant unit worthy of special consideration for conservation management.

A new method for resolving uncertainty of energy requirements in large water breathers: the ‘mega-flume’ seagoing swim-tunnel respirometer

Body size is a key determinant of metabolic rate, but logistical constraints have led to a paucity of energetics measurements from large water-breathing animals. As a result, estimating energy requirements of large fish generally relies on extrapolation of metabolic rate from individuals of lower body mass using allometric relationships that are notoriously variable. Swim-tunnel respirometry is the ‘gold standard’ for measuring active metabolic rates in water-breathing animals, yet previous data are entirely derived from body masses <10 kg – at least one order of magnitude lower than the body masses of many top-order marine predators. Here, we describe the design and testing of a new method for measuring metabolic rates of large water-breathing animals: a c. 26 000 L seagoing ‘mega-flume’ swim-tunnel respirometer. We measured the swimming metabolic rate of a 2·1-m, 36-kg zebra shark Stegostoma fasciatum within this new mega-flume and compared the results to data we collected from other S. fasciatum (3·8–47·7 kg body mass) swimming in static respirometers and previously published measurements of active metabolic rate measurements from other shark species. The mega-flume performed well during initial tests, with intra- and interspecific comparisons suggesting accurate metabolic rate measurements can be obtained with this new tool. Inclusion of our data showed that the scaling exponent of active metabolic rate with mass for sharks ranging from 0·13 to 47·7 kg was 0·79; a similar value to previous estimates for resting metabolic rates in smaller fishes. We describe the operation and usefulness of this new method in the context of our current uncertainties surrounding energy requirements of large water-breathing animals. We also highlight the sensitivity of mass-extrapolated energetic estimates in large aquatic animals and discuss the consequences for predicting ecosystem impacts such as trophic cascades.

A new method for resolving uncertainty of energy requirements in large water breathers: the ‘mega-flume’ seagoing swim-tunnel respirometer

Body size is a key determinant of metabolic rate, but logistical constraints have led to a paucity of energetics measurements from large water-breathing animals. As a result, estimating energy requirements of large fish generally relies on extrapolation of metabolic rate from individuals of lower body mass using allometric relationships that are notoriously variable. Swim-tunnel respirometry is the ‘gold standard’ for measuring active metabolic rates in water-breathing animals, yet previous data are entirely derived from body masses <10 kg – at least one order of magnitude lower than the body masses of many top-order marine predators. Here, we describe the design and testing of a new method for measuring metabolic rates of large water-breathing animals: a c. 26 000 L seagoing ‘mega-flume’ swim-tunnel respirometer. We measured the swimming metabolic rate of a 2·1-m, 36-kg zebra shark Stegostoma fasciatum within this new mega-flume and compared the results to data we collected from other S. fasciatum (3·8–47·7 kg body mass) swimming in static respirometers and previously published measurements of active metabolic rate measurements from other shark species. The mega-flume performed well during initial tests, with intra- and interspecific comparisons suggesting accurate metabolic rate measurements can be obtained with this new tool. Inclusion of our data showed that the scaling exponent of active metabolic rate with mass for sharks ranging from 0·13 to 47·7 kg was 0·79; a similar value to previous estimates for resting metabolic rates in smaller fishes. We describe the operation and usefulness of this new method in the context of our current uncertainties surrounding energy requirements of large water-breathing animals. We also highlight the sensitivity of mass-extrapolated energetic estimates in large aquatic animals and discuss the consequences for predicting ecosystem impacts such as trophic cascades.

Multiple robots formation manoeuvring and collision avoidance strategy

This paper presents a multiple robots formation manoeuvring and its collision avoidance strategy. The direction priority sequential selection algorithm is employed to achieve the raw path, and a new algorithm is then proposed to calculate the turning compliant waypoints supporting the multi-robot formation manoeuvre. The collision avoidance strategy based on the formation control is presented to translate the collision avoidance problem into the stability problem of the formation. The extension-decomposition-aggregation scheme is next applied to solve the formation control problem and subsequently achieve the collision avoidance during the formation manoeuvre. Simulation study finally shows that the collision avoidance problem can be conveniently solved if the stability of the constructed formation including unidentified objects can be satisfied.