Reflection using the derivability conditions

Reflection principles are a way to build non-conservative true extensions of a theory. However the application of a reflection principle needs a proof predicate, and the effort needed to provide this is so great as to be not really practical. We look at a possible way to avoid this effort by using, instead of a proof predicate, a predicate defined using only necessary `modal' properties. Surprisingly, we can produce powerful non-conservative extensions this way. But a reflection principle based on such a predicate is essentially weaker, and we also consider its limitations

Measurement of conduction, radiation, and convection thermal energy to assess baking performance in residential ovens.

Residential ovens are complicated thermal environments capable of delivering convection, conduction, and radiation heat transfer to food. The amount and mode of heat transfer can change based on the design of the oven cavity, cooling systems, and oven cycle algorithms. Studies have shown that the changes in one heat transfer mode can have an impact on the quality of baked goods. The many variables involved make designing residential ovens a time consuming and costly process. The goal of this study is to adapt thermal energy sensing technology to collect energy data from a residential oven and develop correlations to quality characteristics of baked cakes. The quality characteristics measured in this study are browning, porosity, rise height, and mass loss. Testing was limited to white cakes baked in a traditional bake mode with no convection fan. The correlation models developed should reliably predict the final quality measurements of baked cakes using thermal energy data collected in an oven cycle of matching parameters. The sensors used in this study can detect incoming thermal energy and break it up into component heat transfer modes of conduction, convection, and radiation. The sensors were placed in small cake tins to match the conditions of baking cakes. A test plan was performed to collect thermal energy data at a variety of oven temperature setpoints, rack positions, and bake times. Each test run was repeated, replacing the sensors with cakes, and the quality characteristics of the baked cakes were recorded. The thermal energy sensors performed well, splitting energy absorbed into conduction, convection, and radiation components. The thermal data was repeatable, showing less than two percent variation after ten minutes of testing on the middle rack at any given temperature setpoint. It was confirmed from previous studies that conduction dominates a traditional bake mode, contributing about 59% of the total energy absorbed. Second is radiation and finally convection, due to the lack of an active convection fan during a traditional bake mode. It was found that top and bottom browning L* color values correlated linearly with radiation and conduction energy absorbed, respectively. The coefficient of determination (R2) for these models was 0.97 for bottom browning and 0.95 for top browning. Validation data was limited, so further testing would improve the confidence of these models. The porosity and rise height metrics were not able to be correlated with the data collected. It is possible that the measurement methods of these cake quality metrics were not robust enough for reliable data, or the thermal energy data collected was not relevant to changes in porosity or rise. Future testing could investigate alternate thermal data to determine what correlative factors can be used to predict porosity and rise. Finally, mass loss was well correlated to a polynomial regression of total energy with a 0.98 R2 value

Analysis of 24-Hour Ambulatory Blood Pressure Monitoring Data using Orthonormal Polynomials in the Linear Mixed Model

The use of 24-hour ambulatory blood pressure monitoring (ABPM) in clinical practice and observational epidemiological studies has grown considerably in the past 25 years. ABPM is a very effective technique for assessing biological, environmental, and drug effects on blood pressure. In order to enhance the effectiveness of ABPM for clinical and observational research studies via analytical and graphical results, developing alternative data analysis approaches are important. The linear mixed model for the analysis of longitudinal data is particularly well-suited for the estimation of, inference about, and interpretation of both population and subject-specific trajectories for ABPM data. Subject-specific trajectories are of great importance in ABPM studies, especially in clinical research, but little emphasis has been placed on this dimension of the problem in the statistical analyses of the data. We propose using a linear mixed model with orthonormal polynomials across time in both the fixed and random effects to analyze ABPM data. Orthonormal polynomials in the linear mixed model may be used to develop model-based, subject-specific 24-hour ABPM correlates of cardiovascular disease outcomes. We demonstrate the proposed analysis technique using data from the Dietary Approaches to Stop Hypertension (DASH) study, a multicenter, randomized, parallel arm feeding study that tested the effects of dietary patterns on blood pressure