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Introduction to R
Published in Richard J. Roiger, Just Enough R!, 2020
The latest version of R can be downloaded for free by clicking the download link at the Web site www.r-project.org shown in Figure 2.1. In the upper-left window under CRAN (Comprehensive R Archive Network) click on download which takes you to the CRAN download site. Scroll to find an appropriate site to download and install the latest version of R. Once installed, click the Ricon on your screen and you will see R’s graphical user interface (GUI)as in Figure 2.2. We could certainly use the RGUI for our work but, unless speed is of the utmost importance, the RStudio IDE is a much better choice. Before installing RStudio, we must quit R either with the q function—type q( ) after the caret—or simply close the R GUI window.
Cable Modems
Published in Keshab K. Parhi, Takao Nishitani, Digital Signal Processing for Multimedia Systems, 2018
to get from SNR to symbol error probability into the R-S, where Q(x) is the Q function that gives the probability of a unit variance Gaussian random variable exceeding x. For convenience we ignore the slight error caused by assuming the 64QAM symbol probability is equal to both the 7bit symbol and 8bit symbol error probability going into the R-S decoders. We also plot for convenience the error probability of an uncoded QAM symbol and note that the results for Annex A and B are only accurate when the uncoded probability is small (less than 0.01) because of the approximations used in (9). Note that in the region that cable modems are most often required to operate, output error probabilities between 10−8 and 10−12, the Annex B code is overall about 2dB better than the Annex A code.
Modeling and Calibration
Published in Stephen Horan, Introduction to PCM Telemetering Systems, 2018
If the error function is the integral of the Gaussian PDF from 0 to the point x, then the Q function is related to the integral of the PDF from x to infinity as shown in Figure 3.11. The Q function is related to the erf and erfc by the following equations: () Q(x)=12erfc(x2) () Q(x)=12[1−erf(x2)]
Statistical Modeling of the Effectiveness of Preventive Maintenance for Repairable Systems
Published in Technometrics, 2023
Xin YE, Jiaxiang CAI, Loon Ching TANG, Zhi-Sheng YE
For each setting above, we run 1, 000 Monte Carlo replications. The EM algorithm is then used to estimate the model parameters. In each iteration of the EM algorithm, the Q-function is maximized by optim() in R (R Core Team 2020). The constraints on the range of parameters are specified in Supplement Section S6.1, and the numerical issues are discussed in Supplement Section S6.2. Based on the 1, 000 replications, we calculate the bias, root mean squared error (RMSE), and the coverage probability of the two-sided equal-tailed 95% asymptotic confidence interval and 95% parametric percentile bootstrap confidence interval (Efron and Tibshirani 1994). To complete our discussion, we also examine the performance of the Bayesian method in the parameter estimation. We run 1, 000 Monte Carlo replications for each setting. The Gibbs sampling algorithm is implemented to sample posterior samples. The mean values of posterior samples and the 95% highest posterior density intervals are computed as the point estimations and credible interval estimations of parameters, respectively. Based on the 1, 000 replications, we calculate the bias, RMSE, and the coverage probability of the 95% highest posterior density interval. The implementation details can be found in Supplement Section S1. All the above computations were conducted on an Intel(R) Xeon(R) CPU E5-2698 v4 (2.20 GHz).
Calculations of crack stress intensity factors based on FEM and XFEM models
Published in Australian Journal of Mechanical Engineering, 2023
Yashi Liao, Xuhui Zhang, Bisheng Wang, Miaolei He
The definition of q-function in the region is as follows: in the integral region, when the distance from the node to crack tip is greater than the radius R, q is equal to 1 (such as the square node); other node-q functions q is equal to 0 (for example, the round node). The q-function of integral point could be determined by interpolation. Because the integral radius affected the integral region, the calculation accuracy of XFEM for SIF was also affected. If the integral radius was smaller, the singularity of SIF was more obvious; if the integral radius was larger, the integral unit could be increased, affecting the calculation efficiency (Figure 9 is the flow chart for determining integral radius).
Reinforcement learning based optimal decision making towards product lifecycle sustainability
Published in International Journal of Computer Integrated Manufacturing, 2022
Yang Liu, Miying Yang, Zhengang Guo
Scenarios 2a-b use Q-learning, which is a model-free RL approach based on interaction with the environment. In scenario 2b, raw data is gained through interaction with the environment. This can be based on simulation or collecting sensor data interactively. In this case, one can directly collect data about Product-X in operation. This data is used to learn a Q function incrementally similar to a value function on the state but considers the specific actions used to reach states. The Q function is updated per interaction (st,at,rt+1, st+1). Given a Q function, one can then generate an optimal policy.