Complex Structures for Klein-Gordon theory on globally hyperbolic spacetimes

We develop a rigorous method to parametrize complex structures for Klein-Gordon theory in globally hyperbolic spacetimes that satisfy a completeness condition. The complex structures are conserved under time-evolution and implement unitary quantizations. They can be interpreted as corresponding to global choices of vacuum. The main ingredient in our construction is a system of operator differential equations. We provide a number of theorems ensuring that all ingredients and steps in the construction are well-defined. We apply the method to exhibit natural quantizations for certain classes of globally hyperbolic spacetimes. In particular, we consider static, expanding and Friedmann-Robertson-Walker spacetimes. Moreover, for a huge class of spacetimes we prove that the differential equation for the complex structure is given by the Gelfand-Dikki equation.

Development of Educational Print Materials for Physical Activity in Cancer: Evaluation of Readability and Suitability

Educational health materials may be important tools to increase physical activity in cancer patients. Nevertheless, most of the available resources regarding physical activity for cancer patients were found not suitable, had a low grade of readability, and thus, represent a significant barrier to behavior change. To date, little data about development criteria and evaluation of physical activity resources for cancer before their spread exist. The purposes of this study were (i) to describe the development of a physical activity guidebook designed for cancer patients and (ii) to test its readability and suitability. The guidebook was developed through multi-step passages, including group discussions, a literature review, identification of a motivational theory, and using previous research on exercise preferences, barriers, and facilitators to target the information. Two validated formulae were used to assess the readability, whereas thirty-four judges completed the Suitability of Assessment Materials questionnaire to evaluate the suitability of the guidebook. The guidebook was found readable for patients having at least a primary education, and the judges scored it as “superior” material. Our guidebook, following a rigorous method in the development phase, was considered to be suitable and readable. Further evaluations through clinical trials could investigate its effectiveness for behavior change and its impact on cancer patients.

Internal and External Validity in Ethical Reasoning

A particular approach to ethical reasoning has come to dominate much Anglo-American philosophy, one which assumes that the most rigorous method is to proceed by analysis of thought experiments. In thought experiments, features such as context and history are stripped away, and all factors other than those of ethical interest are stipulated to be equal. This chapter argues that even if a thought experiment produces results that are internally valid—in that it provides a genuine ethical insight about the highly controlled and simplified experimental scenario under discussion—this does not imply external validity. Just as in empirical experiments, there is a yawning gap between succeeding in the relatively easy project of establishing internal validity in a controlled and simplified context, and the more difficult one of establishing external validity in the messier and more complex real world.

Rigorous Method of Weights Calculation in Adjustment of Measurement Data with Different Qualities

In the traditional measurement theory, precision is defined as the dispersion of measured value, and is used as the basis of weights calculation in the adjustment of measurement data with different qualities, which leads to the trouble that trueness is completely ignored in the weight allocation. In this paper, following the pure concepts of probability theory, the measured value (observed value) is regarded as a constant, the error as a random variable, and the variance is the dispersion of all possible values of an unknown error. Thus, a rigorous formula for weights calculation and variance propagation is derived, which solves the theoretical trouble of determining the weight values in the adjustment of multi-channel observation data with different qualities. The results show that the optimal weights are not only determined by the covariance array of observation errors, but also related to the model of adjustment.

A novel approach to quantify metrics of upwelling intensity, frequency, and duration

The importance of coastal upwelling systems is widely recognized. However, several aspects of the current and future behaviors of these systems remain uncertain. Fluctuations in temperature because of anthropogenic climate change are hypothesized to affect upwelling-favorable winds and coastal upwelling is expected to intensify across all Eastern Boundary Upwelling Systems. To better understand how upwelling may change in the future, it is necessary to develop a more rigorous method of quantifying this phenomenon. In this paper, we use SST data and wind data in a novel method of detecting upwelling signals and quantifying metrics of upwelling intensity, duration, and frequency at four sites within the Benguela Upwelling System. We found that indicators of upwelling are uniformly detected across five SST products for each of the four sites and that the duration of those signals is longer in SST products with higher spatial resolutions. Moreover, the high-resolution SST products are significantly more likely to display upwelling signals at 25 km away from the coast when signals were also detected at the coast. Our findings promote the viability of using SST and wind time series data to detect upwelling signals within coastal upwelling systems. We highlight the importance of high-resolution data products to improve the reliability of such estimates. This study represents an important step towards the development of an objective method for describing the behavior of coastal upwelling systems.

Detecting wildlife poaching: a rigorous method for comparing patrol strategies using an experimental design

Many studies of wildlife poaching acknowledge the challenges of detecting poaching activities, but few address the issue. Data on poaching may be an inaccurate reflection of the true spatial distribution of events because of low detection rates. The deployment of conservation and law enforcement resources based on biased data could be ineffective or lead to unintended outcomes. Here, we present a rigorous method for estimating the probabilities of detecting poaching and for evaluating different patrol strategies. We illustrate the method with a case study in which imitation snares were set in a private nature reserve in South Africa. By using an experimental design with a known spatial distribution of imitation snares, we estimated the detection probability of the current patrol strategy used in the reserve and compared it to three alternative patrol strategies: spatially focused patrols, patrols with independent observers, and systematic search patterns. Although detection probabilities were generally low, the highest proportion of imitation snares was detected with systematic search strategies. Our study provides baseline data on the probability of detecting snares used for poaching, and presents a method that can be modified for use in other regions and for other types of wildlife poaching.

A revised Coastal Sensitivity Index for Canada’s marine coasts calculated using nonparametric statistics

A Coastal Sensitivity Index (CSI) quantifies a coastline's sensitivity to its physical environment in a useful way for coastal management. Traditionally a CSI is calculated as the mathematical aggregation of coastal sensitivity indicators, which may include factors such as coastal material, relief, and wave energy. The indicators differ depending on study area, but generally are assigned a score ranging from one to five in order of increasing sensitivity. These scores are then aggregated using either the square root of the product mean (the “classic” method), or the geometric mean. Both of these methods are limited by mathematical assumptions, lack of comparability, and the need for empirical validation. In this study, we applied an alternative nonparametric method of calculation, known as μ-statistics, to Canada's marine coasts to investigate a novel approach. μ-statistics, which offer a mathematically sound method of aggregating ordinal indicators, have a number of theoretical advantages over the classic and geometric mean methods. In practice, when applied to Canada’s marine coast, we find that the μ-statistics method (1) compresses the mid-range variability in the resulting sensitivity index, (2) accentuates positive and negative distribution tails, and (3) minimizes propagated errors by 190% and 50% respectively, compared to the classic and geometric mean methods. Additionally, the μ-statistics method has a theoretical foundation that relieves the necessity to empirically validate the aggregating assumptions and relies only on the assumptions inherent in the scoring method. μ-statistics thus provide a new, rigorous method for the calculation of coastal sensitivity indices.

Rigorous Method of Weights Calculation in Adjustment of Measurement Data with Different Qualities

In the traditional measurement theory, precision is defined as the dispersion of measured value, and is used as the basis of weights calculation in the adjustment of measurement data with different qualities, which leads to the trouble that trueness is completely ignored in the weight allocation. In this paper, following the pure concepts of probability theory, the measured value (observed value) is regarded as a constant, the error as a random variable, and the variance is the dispersion of all possible values of an unknown error. Thus, a rigorous formula for weights calculation and variance propagation is derived, which solves the theoretical problem of determining the weight values in the adjustment of multi-channel observation data with different qualities. The results show that the optimal weights are not only determined by the covariance array of observation errors, but also related to the model of adjustment.

Rigorous Method of Weights Calculation in Adjustment of Measurement Data with Different Qualities

In the traditional measurement theory, precision is defined as the dispersion of measured value, and is used as the basis of weights calculation in the adjustment of measurement data with different qualities, which leads to the trouble that trueness is completely ignored in the weight allocation. In this paper, following the pure concepts of probability theory, the measured value (observed value) is regarded as a constant, the error as a random variable, and the variance is the dispersion of all possible values of an unknown error. Thus, a rigorous formula for weights calculation and variance propagation is derived, which solves the theoretical problem of determining the weight values in the adjustment of multi-channel observation data with different qualities. The results show that the optimal weights are not only determined by the covariance array of observation errors, but also related to the model of adjustment.

Rigorous Method of Weights Calculation in Adjustment of Measurement Data with Different Qualities

In the traditional measurement theory, precision is defined as the dispersion of measured value, and is used as the basis of weights calculation in the adjustment of measurement data with different qualities, which leads to the trouble that trueness is completely ignored in the weight allocation. In this paper, following the concepts of pure probability theory, the measured value (observed value) is regarded as a constant, the error as a random variable, and the variance is interpreted as the dispersion of all possible values of the error. Thus, a rigorous formula for weights calculation and variance propagation is derived, which solves the theoretical problem of determining the weight values in the adjustment of multi-channel observation data with different qualities.