Background Brachial artery ultrasound has been proposed as an inexpensive, accurate way to assess cardiovascular risk in populations. However, analysis and interpretation of these data are not uniform.
Methods We analysed the relationship between relative and absolute changes in brachial artery diameter in response to flow-mediated dilation and age, gender and baseline diameter among 4040 ultrasound examinations from subjects aged 14 to 98 years.
Results Reproducibility studies demonstrated intra- and interreader and intrasubject correlations from 0.67 to 0.84 for repeated measures of per cent change in diameter. Per cent change in diameter after flow stimulus was 3.58 ± 0.10% (mean ± standard deviation). Corresponding values for baseline diameter and absolute change in diameter were 4.43 ± 0.87 mm and 0.15 ± 0.01 mm, respectively. Baseline diameter and its variance were inversely related to per cent change in diameter (P < 0.001). In contrast, absolute change in diameter was more uniform throughout the range of baseline diameters. Baseline diameter was directly related, and per cent change in diameter inversely related, to age (P < 0.001 for all three measures). Time to maximum vasodilator response increased with age (P < 0.001). Women (n=2315) had significantly larger per cent change in diameter than men (n=1725) (P < 0.001). However, after adjustment for age and baseline diameter, per cent and absolute change were 5% smaller in women than men (P < 0.05 for both). In multivariate analysis, age was overwhelmingly the most important determinant of absolute change in diameter (P < 0.001).
Conclusions Automated analysis of brachial flow-mediated vasodilator responses is both feasible and reproducible in large-scale clinical and population-based research.
The electricity price volatility brings challenges to bidding strategies in the electricity markets. In this paper, we propose a minimax regret approach for a market participant to obtain an optimal bidding strategy and the corresponding self-scheduled generation plans. Motivated by recently proposed robust optimization approaches, our approach relies on the confidence intervals of price forecasts rather than point estimators. We reformulate the minimax regret model as a mixed-integer linear program (MILP), and solve it by the Benders' decomposition algorithm. Moreover, we design a bidding strategy based on the price forecast confidence intervals to generate the offer curve. Finally, we numerically test the minimax regret approach, in comparison with the robust optimization approach, on three types of thermal generators by using real electricity price data from PJM to verify the effectiveness of our proposed approach.Index Terms-Benders' decomposition, bidding strategy, electricity markets, min-max regret, self-scheduling, uncertainty.
NOMENCLATURE
A. Parameters
Set of operation time span.End time of operation time span.Thermal generator start-up cost in period .Thermal generator shut-down cost in period .Minimum time for a thermal generator keeping on.Minimum time for a thermal generator keeping off.Maximum ramp-up rate of a thermal generator.Maximum ramp-down rate of a thermal generator.Maximum ramp-up rate of a thermal generator at start-up stage.Maximum ramp-down rate of a thermal generator at shut-down stage.Maximal output of an online thermal generator.Electricity price at period .Upper bound of the electricity price at period .Lower bound of the electricity price at period .Lower bound of the sum of weighted prices in all operational time periods.
B. Decision VariablesBinary variable to indicate the start-up status of a thermal generator at period .Binary variable to indicate the shut-down status of a thermal generator at period .Binary variable to indicate the on/off status of a thermal generator at time period .Output of a thermal generator at period .Binary variable to indicate the start-up status of a thermal generator under perfect electricity price information.Binary variable to indicate the shut-down status of a thermal generator under perfect electricity price information.Binary variable to indicate the on/off status of a thermal generator under perfect electricity price information.Output of a thermal generator under perfect electricity price information.Auxiliary binary decision variables.Auxiliary continuous decision variables.
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